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Authors: Orlova Ksenia, Shprits Yuri, and Spasojevic Maria
Title: New global loss model of energetic and relativistic electrons based on Van Allen Probes measurements
Abstract: Energetic electron observations in Earth's radiation belts are typically sparse and multi-point studies often rely on serendipitous conjunctions. This paper establishes the scientific utility of the Combined X-ray Dosimeter (CXD), currently flown on 19 satellites in the Global Positioning System (GPS) constellation, by cross-calibrating energetic electron measurements against data from the Van Allen Probes. By breaking our cross-calibration into two parts – one that removes any spectral assumptions from the CXD flux calculation, and one that compares the energy spectra – we first validate the modeled instrument response functions, then the calculated electron fluxes. Unlike previous forward modeling of energetic electron spectra we use a combination of four distributions that, together. . .
Date: 02/2016 Publisher: Journal of Geophysical Research: Space Physics DOI: 10.1002/2015JA021878 Available at: http://doi.wiley.com/10.1002/2015JA021878
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Authors: Osmane Adnane, III Lynn B. Wilson, Blum Lauren, and Pulkkinen Tuija I.
Title: On the Connection Between Microbursts and Nonlinear Electronic Structures in Planetary Radiation Belts
Abstract: Using a dynamical-system approach, we have investigated the efficiency of large-amplitude whistler waves for causing microburst precipitation in planetary radiation belts by modeling the microburst energy and particle fluxes produced as a result of nonlinear wave–particle interactions. We show that wave parameters, consistent with large-amplitude oblique whistlers, can commonly generate microbursts of electrons with hundreds of keV-energies as a result of Landau trapping. Relativistic microbursts (>1 MeV) can also be generated by a similar mechanism, but require waves with large propagation angles ${\theta }_{{kB}}\gt 50^\circ$ and phase-speeds ${v}_{{\rm{\Phi }}}\geqslant c/9$. Using our result for precipitating density and energy fluxes, we argue that holes in the distribution functio. . .
Date: 01/2016 Publisher: The Astrophysical Journal Pages: 51 DOI: 10.3847/0004-637X/816/2/51 Available at: http://stacks.iop.org/0004-637X/816/i=2/a=51?key=crossref.70d237eeae19ada88cf791dd9ba676be
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Authors: Osmane A., and Pulkkinen T. I.
Title: On the threshold energization of radiation belt electrons by double layers
Abstract: Using a Hamiltonian approach, we quantify the energization threshold of electrons interacting with radiation belts' double layers discovered by Mozer et al. (2013). We find that double layers with electric field amplitude E0 ranging between 10 and 100 mV/m and spatial scales of the order of few Debye lengths are very efficient in energizing electrons with initial velocities v∥ ≤ vth to 1 keV levels but are unable to energize electrons with E ≥ 100 keV. Our results indicate that the localized electric field associated with the double layers are unlikely to generate a seed population of 100 keV necessary for a plethora of relativistic acceleration mechanisms and additional transport to higher energetic levels.
Date: 10/2014 Publisher: Journal of Geophysical Research: Space Physics DOI: 10.1002/2014JA020236 Available at: http://doi.wiley.com/10.1002/2014JA020236
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Authors: Over Matthew W., Wollschläger Ute, Osorio-Murillo Carlos Andres, and Rubin Yoram
Title: Bayesian inversion of Mualem-van Genuchten parameters in a multilayer soil profile: A data-driven, assumption-free likelihood function
Abstract: This paper introduces a hierarchical simulation and modeling framework that allows for inference and validation of the likelihood function in Bayesian inversion of vadose zone hydraulic properties. The likelihood function or its analogs (objective functions and likelihood measures) are commonly assumed to be multivariate Gaussian in form; however, this assumption is not possible to verify without a hierarchical simulation and modeling framework. In this paper, we present the necessary statistical mechanisms for utilizing the hierarchical framework. We apply the hierarchical framework to the inversion of the vadose zone hydraulic properties within a multilayer soil profile conditioned on moisture content observations collected in the uppermost four layers. The key result of our work is that. . .
Date: 02/2015 Publisher: Water Resources Research Pages: 861 - 884 DOI: 10.1002/wrcr.v51.210.1002/2014WR015252 Available at: http://doi.wiley.com/10.1002/2014WR015252
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Authors: Oyama S., Kero A., Rodger C. J., Clilverd M A, Miyoshi Y, et al.
Title: Energetic electron precipitation and auroral morphology at the substorm recovery phase
Abstract: It is well known that auroral patterns at the substorm recovery phase are characterized by diffuse or patch structures with intensity pulsation. According to satellite measurements and simulation studies, the precipitating electrons associated with these aurorae can reach or exceed energies of a few hundreds of keV through resonant wave-particle interactions in the magnetosphere. However, because of difficulty of simultaneous measurements, the dependency of energetic electron precipitation (EEP) on auroral morphological changes in the mesoscale has not been investigated to date. In order to study this dependency, we have analyzed data from the European Incoherent Scatter (EISCAT) radar, the Kilpisjärvi Atmospheric Imaging Receiver Array (KAIRA) riometer, collocated cameras, ground-based m. . .
Date: 05/2017 Publisher: Journal of Geophysical Research: Space Physics DOI: 10.1002/2016JA023484 Available at: http://onlinelibrary.wiley.com/doi/10.1002/2016JA023484/full
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Authors: Ozaki Mitsunori, Yagitani Satoshi, Takahashi Ken, Imachi Tomohiko, Koji Hiroki, et al.
Title: Equivalent Circuit Model for the Electric Field Sensitivity of a Magnetic Search Coil of Space Plasma
Abstract: Magnetic search coils (MSCs) are sensitive to both magnetic and electric fields, but detecting electric fields is unnecessary for magnetic observations of plasma waves. However, it is important to evaluate both sensitivities for different geometries and electrostatic shields to avoid electric field pickup. An equivalent circuit model for the electric field sensitivity of an MSC in a collisionless isotropic cold plasma is developed here using electrical coupling through a sheath capacitance. That sensitivity is defined by a relationship between the MSC impedance and the sheath capacitance. To confirm the validity of the circuit model, the sensitivity to an electric field is measured by imposing an external electric field using charged parallel metallic plates in laboratory experiments. The . . .
Date: 10/2014 Publisher: IEEE Sensors Journal Pages: 1 - 1 DOI: 10.1109/JSEN.2014.2365495 Available at: http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=6937067
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Authors: Ozaki M., Shiokawa K., Miyoshi Y, Kataoka R., Yagitani S., et al.
Title: Fast modulations of pulsating proton aurora related to subpacket structures of Pc1 geomagnetic pulsations at subauroral latitudes
Abstract: To understand the role of electromagnetic ion cyclotron (EMIC) waves in determining the temporal features of pulsating proton aurora (PPA) via wave-particle interactions at subauroral latitudes, high-time-resolution (1/8 s) images of proton-induced N2+ emissions were recorded using a new electron multiplying charge-coupled device camera, along with related Pc1 pulsations on the ground. The observed Pc1 pulsations consisted of successive rising-tone elements with a spacing for each element of 100 s and subpacket structures, which manifest as amplitude modulations with a period of a few tens of seconds. In accordance with the temporal features of the Pc1 pulsations, the auroral intensity showed a similar repetition period of 100 s and an unpredicted fast modulation of a few tens of sec. . .
Date: 08/2016 Publisher: Geophysical Research Letters Pages: 7859 - 7866 DOI: 10.1002/2016GL070008 Available at: http://doi.wiley.com/10.1002/2016GL070008
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Authors: Ozeke Louis G., Mann Ian R., Murphy Kyle R., Sibeck David G., and Baker Daniel N
Title: Ultra-relativistic radiation belt extinction and ULF wave radial diffusion: Modeling the September 2014 extended dropout event
Abstract: In September 2014 an unusually long-lasting (≳10 days) ultra-relativistic electron flux depletion occurred in the outer radiation belt despite ongoing solar wind forcing. We simulate this period using a ULF wave radial diffusion model, driven by observed ULF wave power coupled to flux variations at the outer boundary at L* = 5, including empirical electron loss models due to chorus and hiss wave scattering. Our results show that unexplained rapid main phase loss, that depletes the belt within hours, is essential to explain the observations. Such ultra-relativistic electron extinction decouples the prestorm and poststorm fluxes, revealing the subsequent belt dynamics to be surprisingly independent of prestorm flux. However, once this extinction is included, ULF wave transport and co. . .
Date: 03/2017 Publisher: Geophysical Research Letters DOI: 10.1002/2017GL072811 Available at: http://doi.wiley.com/10.1002/2017GL072811
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Authors: Ozeke Louis G., Mann Ian R., Murphy Kyle R., Rae Jonathan, and Milling David K.
Title: Analytic expressions for ULF wave radiation belt radial diffusion coefficients
Abstract: We present analytic expressions for ULF wave-derived radiation belt radial diffusion coefficients, as a function of L and Kp, which can easily be incorporated into global radiation belt transport models. The diffusion coefficients are derived from statistical representations of ULF wave power, electric field power mapped from ground magnetometer data, and compressional magnetic field power from in situ measurements. We show that the overall electric and magnetic diffusion coefficients are to a good approximation both independent of energy. We present example 1-D radial diffusion results from simulations driven by CRRES-observed time-dependent energy spectra at the outer boundary, under the action of radial diffusion driven by the new ULF wave radial diffusion coefficients and with empirica. . .
Date: 03/2014 Publisher: Journal of Geophysical Research: Space Physics Pages: 1587 - 1605 DOI: 10.1002/2013JA019204 Available at: http://doi.wiley.com/10.1002/2013JA019204
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Authors: Ozeke L. G., Mann I. R., Claudepierre S G, Henderson M., Morley S. K., et al.
Title: The March 2015 Superstorm Revisited: Phase Space Density Profiles and Fast ULF Wave Diffusive Transport
Abstract: We present the temporal evolution of electron Phase Space Density (PSD) in the outer radiation belt during the intense March 2015 geomagnetic storm. Comparing observed PSD profiles as a function of L* at fixed first, M, and second, K, adiabatic invariants with those produced by simulations is critical for determining the physical processes responsible for the outer radiation belt dynamics. Here we show that the bulk of the accelerated and enhanced outer radiation belt population consists of electrons with K < 0.17 G1/2Re. For these electrons, the observed PSD versus L* profiles during the recovery phase of the storm have a positive radial gradient. We compare the observed temporal evolution of the PSD profiles during the recovery phase with those produced by radial diffusion simulations dr. . .
Date: 01/2019 Publisher: Journal of Geophysical Research: Space Physics DOI: 10.1029/2018JA026326 Available at: https://agupubs.onlinelibrary.wiley.com/doi/10.1029/2018JA026326
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Authors: Ozeke Louis G., Mann Ian R., Turner Drew L, Murphy Kyle R., Degeling Alex W., et al.
Title: Modeling cross L shell impacts of magnetopause shadowing and ULF wave radial diffusion in the Van Allen belts
Abstract: We present simulations of the outer electron radiation belt using a new ULF wave-driven radial diffusion model, including empirical representations of loss due to chorus and plasmaspheric hiss. With an outer boundary condition constrained by in situ electron flux observations, we focus on the impacts of magnetopause shadowing and outward radial diffusion in the heart of the radiation belt. Third invariant conserving solutions are combined to simulate the L shell and time dependence of the differential flux at a fixed energy. Results for the geomagnetically quiet year of 2008 demonstrate not only remarkable cross L shell impacts from magnetopause shadowing but also excellent agreement with the in situ observations even though no internal acceleration source is included in the model. Our mod. . .
Date: 10/2014 Publisher: Geophysical Research Letters Pages: 6556 - 6562 DOI: 10.1002/2014GL060787 Available at: http://doi.wiley.com/10.1002/grl.v41.19http://doi.wiley.com/10.1002/2014GL060787
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Authors: O’Brien T P, Lorentzen K. R., Mann I. R., Meredith N. P., Blake J. B., et al.
Title: Energization of relativistic electrons in the presence of ULF power and MeV microbursts: Evidence for dual ULF and VLF acceleration
Abstract: We examine signatures of two types of waves that may be involved in the acceleration of energetic electrons in Earth's outer radiation belts. We have compiled a database of ULF wave power from SAMNET and IMAGE ground magnetometer stations for 1987–2001. Long-duration, comprehensive, in situ VLF/ELF chorus wave observations are not available, so we infer chorus wave activity from low-altitude SAMPEX observations of MeV electron microbursts for 1996–2001 since microbursts are thought to be caused by interactions between chorus and trapped electrons. We compare the ULF and microburst observations to in situ trapped electrons observed by high-altitude satellites from 1989–2001. We find that electron acceleration at low L shells is closely associated with both ULF activity and MeV microbu. . .
Date: 08/2003 Publisher: Journal of Geophysical Research DOI: 10.1029/2002JA009784 Available at: http://onlinelibrary.wiley.com/doi/10.1029/2002JA009784/abstract
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Authors: O’Brien T P, Looper M. D., and Blake J. B.
Title: Quantification of relativistic electron microburst losses during the GEM storms
Abstract: Bursty precipitation of relativistic electrons has been implicated as a major loss process during magnetic storms. One type of precipitation, microbursts, appears to contain enough electrons to empty the prestorm outer radiation belt in approximately a day. During storms that result in high fluxes of trapped relativistic electrons, microbursts continue for several days into the recovery phase, when trapped fluxes are dramatically increasing. The present study shows that this apparent inconsistency is resolved by observations that the number of electrons lost through microbursts is 10–100 times larger during the main phase than during the recovery phase of several magnetic storms chosen by the Geospace Environment Modeling (GEM) program.
Date: 02/2004 Publisher: Geophysical Research Letters DOI: 10.1029/2003GL018621 Available at: http://onlinelibrary.wiley.com/doi/10.1029/2003GL018621/abstract
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Authors: Pakhotin I. P., Drozdov A. Y., Shprits Y Y, Boynton R. J., Subbotin D. A., et al.
Title: Simulation of high-energy radiation belt electron fluxes using NARMAX-VERB coupled codes
Abstract: This study presents a fusion of data-driven and physics-driven methodologies of energetic electron flux forecasting in the outer radiation belt. Data-driven NARMAX (Nonlinear AutoRegressive Moving Averages with eXogenous inputs) model predictions for geosynchronous orbit fluxes have been used as an outer boundary condition to drive the physics-based Versatile Electron Radiation Belt (VERB) code, to simulate energetic electron fluxes in the outer radiation belt environment. The coupled system has been tested for three extended time periods totalling several weeks of observations. The time periods involved periods of quiet, moderate, and strong geomagnetic activity and captured a range of dynamics typical of the radiation belts. The model has successfully simulated energetic electron fluxes . . .
Date: 10/2014 Publisher: Journal of Geophysical Research: Space Physics DOI: 10.1002/2014JA020238 Available at: http://doi.wiley.com/10.1002/2014JA020238
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Authors: Palin L., Jacquey C., Opgenoorth H., Connors M., Sergeev V., et al.
Title: Three-dimensional current systems and ionospheric effects associated with small dipolarisation fronts
Abstract: We present a case study of eight successive plasma sheet (PS) activations (usually referred to as bursty bulk flows or dipolarization fronts ) associated with small individual inline image increases on 31 March 2009 (0200–0900 UT), observed by the THEMIS mission. This series of events happens during very quiet solar wind conditions, over a period of 7 hours preceding a substorm onset at 1230 UT. The amplitude of the dipolarizations increases with time. The low-amplitude dipolarization fronts are associated with few (1 or 2) rapid flux transport events (RFT, Eh > 2mV/m), whereas the large-amplitude ones encompass many more RFT events. All PS activations are associated with small and localized substorm current wedge (SCW) like current system signatures, which seems to be the consequenc. . .
Date: 04/2015 Publisher: Journal of Geophysical Research: Space Physics DOI: 10.1002/2015JA021040 Available at: http://doi.wiley.com/10.1002/2015JA021040
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Authors: Palo Scott E., Gerhardt David, Li Xinlin, Blum Lauren, Schiller Quintin, et al.
Title: One year of on-orbit performance of the Colorado Student Space Weather Experiment (CSSWE)
Abstract: The Colorado Student Space Weather Experiment is a 3-unit (10cm × 10cm × 30cm) CubeSat funded by the National Science Foundation and constructed at the University of Colorado (CU). The CSSWE science instrument, the Relativistic Electron and Proton Telescope integrated little experiment (REPTile), provides directional differential flux measurements of 0.5 to >3.3 MeV electrons and 9 to 40 MeV protons. Though a collaboration of 60+ multidisciplinary graduate and undergraduate students working with CU professors and engineers at the Laboratory for Atmospheric and Space Physics (LASP), CSSWE was designed, built, tested, and delivered in 3 years. On September 13, 2012, CSSWE was inserted to a 477 × 780 km, 65° orbit as a secondary payload on an Atlas V through the NASA Educational Launch of. . .
Date: 01/2014 Publisher: IEEE DOI: 10.1109/USNC-URSI-NRSM.2014.6928087 Available at: http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=6928087
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Authors: Panasyuk Mikhail
Title: “Nonempty” Gap Between Radiation Belts: The First Observations
Abstract: The first space experiments carried out in 1958 by the scientific groups of James Van Allen (United States) on board the first Explorer satellites and Sergey Vernov (Soviet Union) on board the satellite Sputnik 3 led to the discovery of the Earth's radiation belts—the particles (mainly protons and electrons) captured by the magnetic field of the Earth. Two scientific groups independently came to the conclusion that the electrons in the geomagnetic trapping region fill two areas, inner and outer radiation belts, unlike the protons, which fill the whole trapping region [see, e.g., Lemaire, 2000].
Date: 12/2013 Publisher: Eos, Transactions American Geophysical Union Pages: 500 - 500 DOI: 10.1002/2013EO510006 Available at: http://doi.wiley.com/10.1002/2013EO510006
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Authors: Pandya Megha, Veenadhari B., Ebihara Y., Kanekal S.G., and Baker D.N.
Title: Variation of Radiation belt electron flux during CME and CIR driven geomagnetic storms: Van Allen Probes observations
Abstract: Relativistic electron flux responses in the inner magnetosphere are investigated for 28 magnetic storms driven by Corotating Interaction Region (CIR) and 27 magnetic storms driven by Coronal Mass Ejection (CME), using data from the Relativistic Electron‐Proton Telescope (REPT) instrument on board Van‐Allen Probes from Oct‐2012 to May‐2017. In this present study we analyze the role of CIRs and CMEs in electron dynamics by sorting the electron fluxes in terms of averaged solar wind parameters, L‐values, and energies. The major outcomes from our study are: (i) At L = 3 and E = 3.4 MeV, for >70% cases the electron flux remains stable, while at L = 5, for ~82% cases it changes with the geomagnetic conditions. (ii) At L = 5, ~53% of the CIR storms and 30% of the CME storms show electro. . .
Date: 07/2019 Publisher: Journal of Geophysical Research: Space Physics DOI: 10.1029/2019JA026771 Available at: https://agupubs.onlinelibrary.wiley.com/doi/10.1029/2019JA026771
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Authors: Paral J., Hudson M K, Kress B T, Wiltberger M. J., Wygant J R, et al.
Title: Magnetohydrodynamic modeling of three Van Allen Probes storms in 2012 and 2013
Abstract: Coronal mass ejection (CME)-shock compression of the dayside magnetopause has been observed to cause both prompt enhancement of radiation belt electron flux due to inward radial transport of electrons conserving their first adiabatic invariant and prompt losses which at times entirely eliminate the outer zone. Recent numerical studies suggest that enhanced ultra-low frequency (ULF) wave activity is necessary to explain electron losses deeper inside the magnetosphere than magnetopause incursion following CME-shock arrival. A combination of radial transport and magnetopause shadowing can account for losses observed at radial distances into L = 4.5, well within the computed magnetopause location. We compare ULF wave power from the Electric Field and Waves (EFW) electric field instrument on th. . .
Date: 08/2015 Publisher: Annales Geophysicae Pages: 1037 - 1050 DOI: 10.5194/angeo-33-1037-2015 Available at: http://www.ann-geophys.net/33/1037/2015/angeo-33-1037-2015.pdf
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Authors: Patel Maulik, Li Zhao, Hudson Mary, Claudepierre Seth, and Wygant John
Title: Simulation of Prompt Acceleration of Radiation Belt Electrons During the 16 July 2017 Storm
Abstract: We investigate the prompt enhancement of radiation belt electron flux observed by the Relativistic Electron Proton Telescope instrument on board Van Allen Probes following the 16 July 2017 CME‐shock compression using MHD‐test particle simulations. The prompt enhancements can be explained by the source population interacting with the azimuthally directed electric field impulses induced by CME‐shock compressions of the dayside magnetopause. Electrons in drift resonance with the electric field impulse were accelerated by ∼ 0.6 MeV on a drift period timescale (in minutes) as the impulse propagated from the dayside to the nightside around the flanks of the magnetosphere. MHD test particle simulation of energization and drift phase bunching, due to the bipolar electric field that accompa. . .
Date: 06/2019 Publisher: Geophysical Research Letters DOI: 10.1029/2019GL083257 Available at: https://agupubs.onlinelibrary.wiley.com/doi/10.1029/2019GL083257
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Authors: Paulson K. W., Smith C W, Lessard M. R., Engebretson M. J., Torbert R B, et al.
Title: In situ observations of Pc1 pearl pulsations by the Van Allen Probes
Abstract: We present in situ observations of Pc1 pearl pulsations using the Van Allen Probes. These waves are often observed using ground-based magnetometers, but are rarely observed by orbiting satellites. With the Van Allen Probes, we have seen at least 14 different pearl pulsation events during the first year of operations. These new in situ measurements allow us to identify the wave classification based on local magnetic field conditions. Additionally, by using two spacecraft, we are able to observe temporal changes in the region of observation. The waves appear to be generated at an overall central frequency, as often observed on the ground, and change polarization from left- to right-handedness as they propagate into a region where they are resonant with the crossover frequency (where R- and L. . .
Date: 04/2014 Publisher: Geophysical Research Letters Pages: 1823 - 1829 DOI: 10.1002/2013GL059187 Available at: http://doi.wiley.com/10.1002/2013GL059187
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Authors: Paulson K. W., Smith C W, Lessard M. R., Torbert R B, Kletzing C A, et al.
Title: In situ statistical observations of Pc1 pearl pulsations and unstructured EMIC waves by the Van Allen Probes
Abstract: We present here the first in situ statistical survey of structured Pc1 pearl pulsations compared with unstructured electromagnetic ion cyclotron (EMIC) waves observed by the Van Allen Probes spacecraft. This data set was compiled from observations spanning 8 September 2012 through 31 August 2015 and comprises over 1630 h of total EMIC wave activity, of which 291 h exhibited pearl structure. Additionally, we have identified 29 wave events demonstrating periodically oscillating wave packets, mostly about the magnetic equator, indicated by the reversal of Poynting flux along the background magnetic field. We have found several stark differences between Pc1 pearl pulsations and unstructured EMIC waves. While unstructured EMIC waves demonstrate the predicted behavior of a higher occurrence acro. . .
Date: 12/2016 Publisher: Journal of Geophysical Research: Space Physics DOI: 10.1002/2016JA023160 Available at: http://onlinelibrary.wiley.com/doi/10.1002/2016JA023160/full
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Authors: Perry K L, Hudson M K, and Elkington S. R.
Title: Incorporating spectral characteristics of Pc5 waves into three-dimensional radiation belt modeling and the diffusion of relativistic electrons
Abstract: The influence of ultralow frequency (ULF) waves in the Pc5 frequency range on radiation belt electrons in a compressed dipole magnetic field is examined. This is the first analysis in three dimensions utilizing model ULF wave electric and magnetic fields on the guiding center trajectories of relativistic electrons. A model is developed, describing magnetic and electric fields associated with poloidal mode Pc5 ULF waves. The frequency and L dependence of the ULF wave power are included in this model by incorporating published ground-based magnetometer data. It is demonstrated here that realistic spectral characteristics play a significant role in the rate of diffusion of relativistic electrons via drift resonance with poloidal mode ULF waves. Radial diffusion rates including bounce motion s. . .
Date: 03/2005 Publisher: Journal of Geophysical Research DOI: 10.1029/2004JA010760 Available at: http://onlinelibrary.wiley.com/doi/10.1029/2004JA010760/abstract
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Authors: Pich Maria de Soria-S, Jun Insoo, and Evans Robin
Title: Empirical radiation belt models: Comparison with in-situ data and implications for environment definition
Abstract: The empirical AP8/AE8 model has been the de-facto Earth's radiation belts engineering reference for decades. The need from the community for a better model incubated the development of AP9/AE9/SPM, which addresses several shortcomings of the old model. We provide additional validation of AP9/AE9 by comparing in-situ electron and proton data from Jason-2, POES, and the Van Allen Probes spacecraft with the 5th, 50th, and 95th percentiles from AE9/AP9 and with the model outputs from AE8/AP8. The relatively short duration of Van Allen Probes and Jason-2 missions means that their measurements are most certainly the result of specific climatological conditions. In LEO, the Jason-2 proton flux is better reproduced by AP8 compared to AP9, while the POES electron data are well enveloped by AE9 5th . . .
Date: 08/2017 Publisher: Space Weather DOI: 10.1002/2017SW001612 Available at: http://onlinelibrary.wiley.com/doi/10.1002/2017SW001612/full
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Authors: Pierrard V., and Rosson G.
Title: The effects of the big storm events in the first half of 2015 on the radiation belts observed by EPT/PROBA-V
Abstract: With the energetic particle telescope (EPT) performing with direct electron and proton discrimination on board the ESA satellite PROBA-V, we analyze the high-resolution measurements of the charged particle radiation environment at an altitude of 820 km for the year 2015. On 17 March 2015, a big geomagnetic storm event injected unusual fluxes up to low radial distances in the radiation belts. EPT electron measurements show a deep dropout at L > 4 starting during the main phase of the storm, associated to the penetration of high energy fluxes at L < 2 completely filling the slot region. After 10 days, the formation of a new slot around L = 2.8 for electrons of 500–600 keV separates the outer belt from the belt extending at other longitudes than the South Atlantic Anomaly. Two oth. . .
Date: 01/2016 Publisher: Annales Geophysicae Pages: 75 - 84 DOI: 10.5194/angeo-34-75-2016 Available at: http://www.ann-geophys.net/34/75/2016/
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Authors: Pinto V. A., Mourenas D., Bortnik J, Zhang X.‐J., Artemyev A. V., et al.
Title: Decay of Ultrarelativistic Remnant Belt Electrons Through Scattering by Plasmaspheric Hiss
Abstract: Ultrarelativistic electron remnant belts appear frequently following geomagnetic disturbances and are located in‐between the inner radiation belt and a reforming outer belt. As remnant belts are relatively stable, here we explore the importance of hiss and electromagnetic ion cyclotron waves in controlling the observed decay rates of remnant belt ultrarelativistic electrons in a statistical way. Using measurements from the Van Allen Probes inside the plasmasphere for 25 remnant belt events that occurred between 2012 and 2017 and that are located in the region 2.9Date: Dec-07-2019 Publisher: Journal of Geophysical Research: Space Physics DOI: 10.1029/2019JA026509 Available at: https://agupubs.onlinelibrary.wiley.com/doi/10.1029/2019JA026509
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Authors: Pinto Víctor A., Bortnik Jacob, Moya Pablo S., Lyons Larry R., Sibeck David G., et al.
Title: Characteristics, Occurrence and Decay Rates of Remnant Belts associated with Three-Belt events in the Earth's Radiation Belts
Abstract: Shortly after the launch of the Van Allen Probes, a new three‐belt configuration of the electron radiation belts was reported. Using data between September 2012 and November 2017, we have identified 30 three‐belt events and found that about 18% of geomagnetic storms result in such configuration. Based on the identified events, we evaluated some characteristics of the remnant (intermediate) belt. We determined the energy range of occurrence and found it peaks at E = 5.2 MeV. We also determined that the magnetopause location and SYM‐H value may play an important role in the outer belt losses that lead to formation and location of the remnant belt. Finally, we calculated the decay rates of the remnant belt for all events and found that their lifetime gets longer as energy increases,. . .
Date: 10/2018 Publisher: Geophysical Research Letters DOI: 10.1029/2018GL080274 Available at: https://agupubs.onlinelibrary.wiley.com/doi/10.1029/2018GL080274
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Authors: Posch J. L, Engebretson M. J., Olson C. N., Thaller S. A., Breneman A. W., et al.
Title: Low-harmonic magnetosonic waves observed by the Van Allen Probes
Abstract: Purely compressional electromagnetic waves (fast magnetosonic waves), generated at multiple harmonics of the local proton gyrofrequency, have been observed by various types of satellite instruments (fluxgate and search coil magnetometers and electric field sensors), but most recent studies have used data from search coil sensors, and many have been restricted to high harmonics. We report here on a survey of low-harmonic waves, based on electric and magnetic field data from the EFW double probe and EMFISIS fluxgate magnetometer instruments, respectively, on the Van Allen Probes spacecraft during its first full precession through all local times, from October 1, 2012 through July 13, 2014. These waves were observed both inside and outside the plasmapause (PP), at L shells from 2.4 to ~6 (the. . .
Date: 07/2015 Publisher: Journal of Geophysical Research: Space Physics DOI: 10.1002/2015JA021179 Available at: http://doi.wiley.com/10.1002/2015JA021179
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Authors: Posner A., Hesse M, and Cyr O. C. St.
Title: The main pillar: Assessment of space weather observational asset performance supporting nowcasting, forecasting, and research to operations
Abstract: Space weather forecasting critically depends upon availability of timely and reliable observational data. It is therefore particularly important to understand how existing and newly planned observational assets perform during periods of severe space weather. Extreme space weather creates challenging conditions under which instrumentation and spacecraft may be impeded or in which parameters reach values that are outside the nominal observational range. This paper analyzes existing and upcoming observational capabilities for forecasting, and discusses how the findings may impact space weather research and its transition to operations. A single limitation to the assessment is lack of information provided to us on radiation monitor performance, which caused us not to fully assess (i.e., not as. . .
Date: 04/2014 Publisher: Space Weather Pages: 257 - 276 DOI: 10.1002/swe.v12.410.1002/2013SW001007 Available at: http://doi.wiley.com/10.1002/swe.v12.4http://doi.wiley.com/10.1002/2013SW001007
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Authors: Powers Nicole
Title: A Parametric Approach to NASA Mission Operations Costing
Abstract: Quantifying the cost of mission operations can be problematic. Currently few tools exist to estimate these costs and fewer that utilize a parametric approach. This paper begins the process of developing a parametric model for estimating mission operation costs. We hypothesize that the costs of mission operations are determined by the duration and type of operation activity. For the purposes of this paper operation activities fall into the following four categories: hibernated cruise, standard cruise, flyby, and high intensity operations. Hypothesis tests were conducted on each of the aforementioned categories and the results are based on data from APL’s historical missions. Those results will be used to develop a Cost Estimating Relationship (CER) to better predict missio. . .
Date: 10/2014 Publisher: American Institute of Aeronautics and Astronautics DOI: 10.2514/MSPACE1410.2514/6.2014-4398 Available at: http://arc.aiaa.org/doi/abs/10.2514/6.2014-4398
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Authors: Qin Murong, Hudson Mary, Li Zhao, Millan Robyn, Shen Xiaochen, et al.
Title: Investigating Loss of Relativistic Electrons Associated With EMIC Waves at Low L Values on 22 June 2015
Abstract: In this study, rapid loss of relativistic radiation belt electrons at low L* values (2.4–3.2) during a strong geomagnetic storm on 22 June 2015 is investigated along with five possible loss mechanisms. Both the particle and wave data are obtained from the Van Allen Probes. Duskside H+ band electromagnetic ion cyclotron (EMIC) waves were observed during a rapid decrease of relativistic electrons with energy above 5.2 MeV occurring outside the plasmasphere during extreme magnetopause compression. Lower He+ composition and enriched O+ composition are found compared to typical values assumed in other studies of cyclotron resonant scattering of relativistic electrons by EMIC waves. Quantitative analysis demonstrates that even with the existence of He+ band EMIC waves, it is the H+ band EMIC w. . .
Date: 05/2019 Publisher: Journal of Geophysical Research: Space Physics DOI: 10.1029/2018JA025726 Available at: https://agupubs.onlinelibrary.wiley.com/doi/10.1029/2018JA025726
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Authors: Qin Murong, Hudson Mary, Kress Brian, Selesnick Richard, Engel Miles, et al.
Title: Investigation of Solar Proton Access into the inner magnetosphere on 11 September 2017
Abstract: In this study, access of solar energetic protons to the inner magnetosphere on 11 September 2017 is investigated by computing the reverse particle trajectories with the Dartmouth geomagnetic cutoff code [Kress et al., 2010]. The maximum and minimum cutoff rigidity at each point along the orbit of Van Allen Probe A is numerically computed by extending the code to calculate cutoff rigidity for particles coming from arbitrary direction. Pulse‐height analyzed (PHA) data has the advantage of providing individual particle energies and effectively excluding background high energy proton contamination. This technique is adopted to study the cutoff locations for solar protons with different energy. The results demonstrate that cutoff latitude is lower for solar protons with higher energy, consist. . .
Date: 04/2019 Publisher: Journal of Geophysical Research: Space Physics DOI: 10.1029/2018JA026380 Available at: https://agupubs.onlinelibrary.wiley.com/doi/10.1029/2018JA026380
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Authors: Qin Murong, Hudson Mary, Millan Mary, Woodger Leslie, and Shekhar Sapna
Title: Statistical investigation of the efficiency of EMIC waves in precipitating relativistic electrons
Abstract: Electromagnetic ion cyclotron (EMIC) waves have been proposed to cause Relativistic Electron Precipitation (REP). In our study, we carry out 4 years of analysis from 2013 to 2016, with relativistic electron precipitation spikes obtained from POES satellites and EMIC waves observation from Van Allen Probes. Among the 473 coincidence events when POES satellites go through the region conjugate to EMIC wave activity, only 127 are associated with REP. Additionally, the coincidence occurrence rate is about 10% higher than the random coincidence occurrence rate, indicating that EMIC waves and relativistic electrons can be statistically related, but the link is weaker than expected. H+ band EMIC waves have been regarded as less important than He+ band EMIC waves for the precipitation of relativist. . .
Date: 06/2018 Publisher: Journal of Geophysical Research: Space Physics DOI: 10.1029/2018JA025419 Available at: https://agupubs.onlinelibrary.wiley.com/doi/10.1029/2018JA025419
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Authors: Reeves Geoffrey D, Friedel Reiner H W, Larsen Brian A., Skoug Ruth M., Funsten Herbert O., et al.
Title: Energy dependent dynamics of keV to MeV electrons in the inner zone, outer zone, and slot regions.
Abstract: We present observations of the radiation belts from the HOPE and MagEIS particle detectors on the Van Allen Probes satellites that illustrate the energy-dependence and L-shell dependence of radiation belt enhancements and decays. We survey events in 2013 and analyze an event on March 1 in more detail. The observations show: (a) At all L-shells, lower-energy electrons are enhanced more often than higher energies; (b) Events that fill the slot region are more common at lower energies; (c) Enhancements of electrons in the inner zone are more common at lower energies; and (d) Even when events do not fully fill the slot region, enhancements at lower-energies tend to extend to lower L-shells than higher energies. During enhancement events the outer zone extends to lower L-shells at lower energie. . .
Date: 12/2015 Publisher: Journal of Geophysical Research: Space Physics DOI: 10.1002/2015JA021569 Available at: http://doi.wiley.com/10.1002/2015JA021569http://api.wiley.com/onlinelibrary/tdm/v1/articles/10.1002%2F2015JA021569
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Authors: Reeves G. D., and Daglis I. A.
Title: Geospace Magnetic Storms and the Van Allen Radiation Belts
Abstract: N/A
Date: Publisher: Oxford University Press DOI: N/A
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Authors: Reeves G D, Spence H E, Henderson M G, Morley S. K., Friedel R H W, et al.
Title: Electron Acceleration in the Heart of the Van Allen Radiation Belts
Abstract: The Van Allen radiation belts contain ultrarelativistic electrons trapped in Earth’s magnetic field. Since their discovery in 1958, a fundamental unanswered question has been how electrons can be accelerated to such high energies. Two classes of processes have been proposed: transport and acceleration of electrons from a source population located outside the radiation belts (radial acceleration) or acceleration of lower-energy electrons to relativistic energies in situ in the heart of the radiation belts (local acceleration). We report measurements from NASA’s Van Allen Radiation Belt Storm Probes that clearly distinguish between the two types of acceleration. The observed radial profiles of phase space density are characteristic of local acceleration in the heart of the radiation belt. . .
Date: 07/2013 Publisher: Science Pages: 991 - 994 DOI: 10.1126/science.1237743 Available at: http://www.sciencemag.org/cgi/doi/10.1126/science.1237743
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Authors: Reeves G D, Spence H E, Henderson M G, Tu W., Cunningham G. S., et al.
Title: Acceleration and loss driven by VLF chorus: Van Allen Probes observations and DREAM model results
Abstract: For over a decade now we have understood the response of the Earth's radiation belts to solar wind driving are a delicate balance of acceleration and loss processes. Theory has shown that the interaction of relativistic electrons with VLF whistler mode chorus can produce both energization through momentum diffusion and loss through pitch angle diffusion. Recent results from the Van Allen Probes mission has confirmed observationally that chorus can produce both acceleration and loss. The Van Allen Probes satellites are able to measure all the critical particle populations and wave fields with unprecedented precision and resolution but only at the two spacecraft locations. Those spatially-localized observations can be extended globally using three-dimensional diffusion codes such as the DREA. . .
Date: 08/2014 Publisher: IEEE DOI: 10.1109/URSIGASS.2014.6929879 Available at: http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=6929879
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Authors: Reeves Geoffrey D
Title: Radiation Belt Storm Probes: The Next Generation of Space Weather Forecasting
Abstract: N/A
Date: 11/2007 Publisher: Space Weather DOI: 10.1029/2007SW000341 Available at: http://www.agu.org/pubs/crossref/2007/2007SW000341.shtml
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Authors: Reid Mark, and Ottman Geffrey
Title: Software controlled memory scrubbing for the Van Allen Probes Solid State Recorder (SSR) memory
Abstract: The Van Allen Probes mission which was designed and built by the Johns Hopkins University, Applied Physics Laboratory (APL) is also being operated by the APL mission operations team in Laurel, Maryland. The two Van Allen Probes spacecraft have been successfully collecting data on orbit since they were launched on August 30, 2012. These twin probes are providing unprecedented insight into the physical dynamics of the Earth's radiation belts and are giving scientists the data they need to make predictions of changes in this critical region of space, by sampling the harsh radiation belt environment where major space weather activity occurs and many spacecraft operate.[1] Shortly after launch, radiation induced anomalies were reported on both spacecraft and investigated by the hardware and sof. . .
Date: 03/2014 Publisher: IEEE DOI: 10.1109/AERO.2014.6836406 Available at: http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=6836406
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Authors: Reiff P. H., Daou A. G., Sazykin S. Y., Nakamura R, Hairston M. R., et al.
Title: Multispacecraft Observations and Modeling of the June 22/23, 2015 Geomagnetic Storm
Abstract: The magnetic storm of June 22-23, 2015 was one of the largest in the current solar cycle. We present in situ observations from the Magnetospheric Multiscale Mission (MMS) and the Van Allen Probes (VAP) in the magnetotail, field-aligned currents from AMPERE, and ionospheric flow data from DMSP. Our real-time space weather alert system sent out a “red alert”, correctly predicting Kp indices greater than 8. We show strong outflow of ionospheric Oxygen, dipolarizations in the MMS magnetometer data, and dropouts in the particle fluxes seen by the MMS FPI instrument suite. At ionospheric altitudes, the AMPERE data show highly variable currents exceeding 20 MA. We present numerical simulations with the BATS-R-US global magnetohydrodynamic (MHD) model linked with the Rice Convection Model (RCM. . .
Date: 05/2016 Publisher: Geophysical Research Letters DOI: 10.1002/2016GL069154 Available at: http://doi.wiley.com/10.1002/2016GL069154
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Authors: Remya B., Sibeck D G, Halford A J, Murphy K. R., Reeves G D, et al.
Title: Ion Injection Triggered EMIC Waves in the Earth's Magnetosphere
Abstract: We present Van Allen Probe observations of electromagnetic ion cyclotron (EMIC) waves triggered solely due to individual substorm‐injected ions in the absence of storms or compressions of the magnetosphere during 9 August 2015. The time at which the injected ions are observed directly corresponds to the onset of EMIC waves at the location of Van Allen Probe A (L = 5.5 and 18:06 magnetic local time). The injection was also seen at geosynchronous orbit by the Geostationary Operational Environmental Satellite and Los Alamos National Laboratory spacecraft, and the westward(eastward) drift of ions(electrons) was monitored by Los Alamos National Laboratory spacecraft at different local times. The azimuthal location of the injection was determined by tracing the injection signatures backward in. . .
Date: 06/2018 Publisher: Journal of Geophysical Research: Space Physics DOI: 10.1029/2018JA025354 Available at: https://agupubs.onlinelibrary.wiley.com/doi/10.1029/2018JA025354
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Authors: Ren Jie, Zong Q. G., Miyoshi Y, Zhou X. Z., Wang Y. F., et al.
Title: Low-energy (< 200 eV) electron acceleration by ULF waves in the plasmaspheric boundary layer: Van Allen Probes observation
Abstract: We report observational evidence of cold plamsmaspheric electron (< 200 eV) acceleration by ultra-low-frequency (ULF) waves in the plasmaspheric boundary layer on 10 September 2015. Strongly enhanced cold electron fluxes in the energy spectrogram were observed along with second harmonic mode waves with a period of about 1 minute which lasted several hours during two consecutive Van Allen Probe B orbits. Cold electron (<200 eV) and energetic proton (10-20 keV) bi-directional pitch angle signatures observed during the event are suggestive of the drift-bounce resonance mechanism. The correlation between enhanced energy fluxes and ULF waves leads to the conclusions that plasmaspheric dynamics is strongly affected by ULF waves. Van Allen Probe A and B, GOES 13, GOES 15 and MMS 1 observations su. . .
Date: 08/2017 Publisher: Journal of Geophysical Research: Space Physics DOI: 10.1002/2017JA024316 Available at: http://onlinelibrary.wiley.com/doi/10.1002/2017JA024316/full
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Authors: Ren Jie, Zong Qiu-Gang, Miyoshi Yoshizumi, Rankin Robert, Spence Harlan E, et al.
Title: A comparative study of ULF waves' role in the dynamics of charged particles in the plasmasphere: Van Allen Probes observation
Abstract: By analyzing observations from Van Allen Probes in its inbound and outbound orbits, we present evidence of coherent enhancement of cold plasmaspheric electrons and ions due to drift‐bounce resonance with ULF waves. From 18:00 UT on 28 May 2017 to 10:00 UT on 29 May 2017, newly formed poloidal mode standing ULF waves with significant electric field oscillations were observed in two consecutive orbits when Probe B was travelling inbound. In contrast to observations during outbound orbits, the cold (< 150 eV) electorns measured by the HOPE instrument were characterized by flux enhancements several times larger and bi‐directional pitch angle distributions during inbound orbits. The electron number density inferred from upper hybrid waves is twice as larger as during inbound orbits, which w. . .
Date: 06/2018 Publisher: Journal of Geophysical Research: Space Physics DOI: 10.1029/2018JA025255 Available at: https://agupubs.onlinelibrary.wiley.com/doi/10.1029/2018JA025255
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Authors: Ripoll ‐F., Loridan V., Denton M. H., Cunningham G., Reeves G., et al.
Title: Observations and Fokker‐Planck simulations of the L‐shell, energy, and pitch‐angle structure of Earth’s electron radiation belts during quiet times
Abstract: The evolution of the radiation belts in L‐shell (L), energy (E), and equatorial pitch‐angle (α0) is analyzed during the calm 11‐day interval (March 4 –March 15) following the March 1 storm 2013. Magnetic Electron and Ion Spectrometer (MagEIS) observations from Van Allen Probes are interpreted alongside 1D and 3D Fokker‐Planck simulations combined with consistent event‐driven scattering modeling from whistler mode hiss waves. Three (L, E, α0)‐regions persist through 11 days of hiss wave scattering; the pitch‐angle dependent inner belt core (L~<2.2 and E<700 keV), pitch‐angle homogeneous outer belt low‐energy core (L>~5 and E~<100 keV), and a distinct pocket of electrons (L~[4.5, 5.5] and E~[0.7, 2] MeV). The pitch‐angle homogeneous outer belt is explained by the diff. . .
Date: 12/2018 Publisher: Journal of Geophysical Research: Space Physics DOI: 10.1029/2018JA026111 Available at: https://agupubs.onlinelibrary.wiley.com/doi/10.1029/2018JA026111
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Authors: Ripoll J. F., Loridan V., Cunningham G. S., Reeves G D, and Shprits Y Y
Title: On the Time Needed to Reach an Equilibrium Structure of the Radiation Belts
Abstract: In this study, we complement the notion of equilibrium states of the radiation belts with a discussion on the dynamics and time needed to reach equilibrium. We solve for the equilibrium states obtained using 1D radial diffusion with recently developed hiss and chorus lifetimes at constant values of Kp = 1, 3 and 6. We find that the equilibrium states at moderately low Kp, when plotted vs L-shell (L) and energy (E), display the same interesting S-shape for the inner edge of the outer belt as recently observed by the Van Allen Probes. The S-shape is also produced as the radiation belts dynamically evolve toward the equilibrium state when initialized to simulate the buildup after a massive dropout or to simulate loss due to outward diffusion from a saturated state. Physically, this shape,. . .
Date: 06/2016 Publisher: Journal of Geophysical Research: Space Physics DOI: 10.1002/2015JA022207 Available at: http://doi.wiley.com/10.1002/2015JA022207
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Authors: Ripoll J.-F., Chen Y., Fennell J, and Friedel R
Title: On long decays of electrons in the vicinity of the slot region observed by HEO3
Abstract: Long decay periods of electron counts, which follow abrupt rises and last from weeks to months, have been observed by the HEO3 spacecraft in the vicinity of the slot region between the years 1998 and 2007. During the most stable decay periods as selected, e-folding timescales are extracted and statistically analyzed from observations as a function of L-shell and electron energy. A challenge is to reproduce the observed timescales from simulations of pitch angle diffusion by three acting waves–the plasmaspheric hiss, lightning-generated whistlers, and VLF transmitter waves. We perform full numerical simulations to accurately compute electron lifetimes. We choose to use the method and wave parameters proposed by Abel & Thorne [1998] with the goal to assess whether they can reproduce lifeti. . .
Date: 11/2014 Publisher: Journal of Geophysical Research: Space Physics DOI: 10.1002/2014JA020449 Available at: http://doi.wiley.com/10.1002/2014JA020449
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Authors: Ripoll J.-F., Albert J M, and Cunningham G. S.
Title: Electron lifetimes from narrowband wave-particle interactions within the plasmasphere
Abstract: This paper is devoted to the systematic study of electron lifetimes from narrowband wave-particle interactions within the plasmasphere. It relies on a new formulation of the bounce-averaged quasi-linear pitch angle diffusion coefficients parameterized by a single frequency, ω, and wave normal angle, θ. We first show that the diffusion coefficients scale with ω/Ωce, where Ωce is the equatorial electron gyrofrequency, and that maximal pitch angle diffusion occurs along the line α0 = π/2–θ, where α0 is the equatorial pitch angle. Lifetimes are computed for L shell values in the range [1.5, 3.5] and energies, E, in the range [0.1, 6] MeV as a function of frequency and wave normal angle. The maximal pitch angle associated with a given lifetime is also given, revealing the frequen. . .
Date: 11/2014 Publisher: Journal of Geophysical Research: Space Physics DOI: 10.1002/2014JA020217 Available at: http://doi.wiley.com/10.1002/2014JA020217
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Authors: Ripoll J.-F., Santol?k O., Reeves G., Kurth W S, Denton M., et al.
Title: Effects of whistler mode hiss waves in March 2013
Abstract: We present simulations of the loss of radiation belt electrons by resonant pitch angle diffusion caused by whistler mode hiss waves for March 2013. Pitch angle diffusion coefficients are computed from the wave properties and the ambient plasma data obtained by the Van Allen Probes with a resolution of 8 hours and 0.1 L-shell. Loss rates follow a complex dynamic structure, imposed by the wave and plasma properties. Hiss effects can be strong, with minimum lifetimes (of ~1 day) moving from energies of ~100 keV at L~5 up to ~2 MeV at L~2, and stop abruptly, similarly to the observed energy-dependent inner belt edge. Periods when the plasmasphere extends beyond L~5 favor long-lasting hiss losses from the outer belt. Such loss rates are embedded in a reduced Fokker-Planck code and validated aga. . .
Date: 06/2017 Publisher: Journal of Geophysical Research: Space Physics DOI: 10.1002/2017JA024139 Available at: http://onlinelibrary.wiley.com/doi/10.1002/2017JA024139/full
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Authors: Ripoll J. F., Reeves G., Cunningham G., Loridan V., Denton M., et al.
Title: Reproducing the observed energy-dependent structure of Earth's electron radiation belts during storm recovery with an event-specific diffusion model
Abstract: We present dynamic simulations of energy-dependent losses in the radiation belt " slot region" and the formation of the two-belt structure for the quiet days after the March 1st storm. The simulations combine radial diffusion with a realistic scattering model, based data-driven spatially and temporally-resolved whistler mode hiss wave observations from the Van Allen Probes satellites. The simulations reproduce Van Allen Probes observations for all energies and L-shells (2 to 6) including (a) the strong energy-dependence to the radiation belt dynamics (b) an energy-dependent outer boundary to the inner zone that extends to higher L-shells at lower energies and (c) an " S-shaped" energy-dependent inner boundary to the outer zone that results from the competition between diffusive radial tran. . .
Date: 05/2016 Publisher: Geophysical Research Letters DOI: 10.1002/2016GL068869 Available at: http://doi.wiley.com/10.1002/2016GL068869
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Authors: Ripoll J.‐F., Farges T., Lay E. H., and Cunningham G. S.
Title: Local and Statistical Maps of Lightning‐Generated Wave Power Density Estimated at the Van Allen Probes Footprints From the World‐Wide Lightning Location Network Database
Abstract: We propose a new method that uses the World‐Wide Lightning Location Network (WWLLN) to estimate both the local and the drift lightning power density at the Van Allen Probes footprints during 4.3 years (~2 × 108 strokes.). The ratio of the drift power density to the local power density defines a time‐resolved WWLLN‐based model of lightning‐generated wave (LGW) power density ratio, RWWLLN. RWWLLNis computed every ~34 s. This ratio multiplied by the time‐resolved LGW intensity measured by the Probes allows direct computation of pitch angle diffusion coefficients used in radiation belt codes. Statistical analysis shows the median power density ratio is urn:x-wiley:00948276:media:grl58808:grl58808-math-0001 over the Americas. Elsewhere, urn:x-wiley:00948276:media:grl58808:grl58808-ma. . .
Date: 03/2019 Publisher: Geophysical Research Letters Pages: 4122 - 4133 DOI: 10.1029/2018GL081146 Available at: https://agupubs.onlinelibrary.wiley.com/doi/10.1029/2018GL081146
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# zbMATH — the first resource for mathematics

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Convergence estimates for product iterative methods with applications to domain decomposition. (English) Zbl 0754.65085

Let $V$ be a Hilbert space and ${V}^{\text{'}}$ its dual; let $\left\{{V}_{i}\right\}$, $\left\{{V}_{i}^{\text{'}}\right\}$ be sequences of closed subspaces of $V$, ${V}^{\text{'}}$ respectively, $A:V\to {V}^{\text{'}}$ a symmetric positive definite linear operator, and $f\in {V}^{\text{'}}$. To the equation $Au=f$ is attached the variational form $A\left(u,v\right)=〈f,v〉$, for all $v\in V$, respectively $〈{A}_{i}v,v〉=〈f,v〉$ for all $v\in {V}_{i}$, where ${A}_{i}$ is the restriction of $A$ to ${V}_{i}$, namely $〈{A}_{i}v,{\Phi }〉=A\left(v,{\Phi }\right)$, for all $v,{\Phi }\in {V}_{i}$.

Suppose that the linear operators ${R}_{i}:{V}_{i}^{\text{'}}\to {V}_{i}$ are given. If ${u}^{1}\in V$ is an approximation of the solution $u$ of the equation $Au=f$ or $A\left(u,v\right)=〈f,v〉$ for all $v\in V$, one puts ${y}_{0}={u}^{1}$ and ${y}_{i}={y}_{i-1}+{R}_{i}{Q}_{i}\left(f-A{y}_{i-1}\right)$, $i=1,\cdots ,J$ and defines ${u}^{\ell +1}={y}_{j}$, where ${Q}_{i}$ denotes the projection on ${V}_{j}^{\text{'}}$, namely $〈w-Qw,{\Phi }〉=0$, for all ${\Phi }\in {V}_{i}^{\text{'}}$.

The paper realizes a study of the convergence rate of ${u}^{\ell +1}$ to u, in terms of the product of the operators defined with respect to the number of subspaces ${V}_{i}$. If ${P}_{i}$ denotes the orthogonal projection in the subspace ${V}_{i}$ and ${T}_{i}={R}_{i}{A}_{i}{P}_{i}$ then $U-{u}^{\ell +1}=\left(I-{T}_{j}\right)\left(I-{T}_{j-1}\right)\cdots \left(I-{T}_{1}\right)\left(u-{u}^{\ell }\right)$ and in well specified hypotheses the above mentioned evaluations are obtained.

The applications to elliptic differential operators and a numerical model of finite element type for the plane case presented in the paper are suggestive.

##### MSC:
 65N30 Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods (BVP of PDE) 65N55 Multigrid methods; domain decomposition (BVP of PDE) 65F10 Iterative methods for linear systems 65N15 Error bounds (BVP of PDE)

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# How to finish this proof

1. Mar 13, 2009

### transgalactic

f is differentiable continuously(which means that f(x) and f'(x) are continues and differentiable) on [a,b]
suppose that |f'(x)|<1 for x in [a,b]

prove that there is 0<=k<1 so there is x1,x2 in [a,b]
|f(x1)-f(x2)|<=k|x1-x2|
??

i started from the data that i was given and i know that f(x) is differentiable
so
$$f'(x)=\lim _{h->0}\frac{f(x+h)-f(h))}{h}$$
i use

|f'(x)|<1
so
$$|f'(x)|=\lim _{h->0}\frac{|f(x+h)-f(h))|}{|h|}<1$$

so f(x) is continues and differentiable
so i use mvt on x1 and x2
$$f'(k)=\frac{f(x1)-f(x2)}{x1-x2}$$
and i combine that with
|f'(x)|<1

$$\frac{|f(x1)-f(x2)|}{|x1-x2|}<1$$
so
$$|f(x1)-f(x2)| <|x1-x2|$$

what now?

Last edited: Mar 13, 2009
2. Mar 13, 2009

### yyat

Show that $$|f'(x)|\le k$$ for all x in [a,b] and for some 0<k<1. Hint: A continuous function defined on a compact interval has a maximum.

3. Mar 13, 2009

### transgalactic

they sign L as the minimum of f'(x)
and they sign l as the maximum of f'(x)

then they say that k=max{|f(L)|,|f(l)|}

but its not true
i am given that 0=<k<1
and i dont know if i get the same values

why
k=max{|f(L)|,|f(l)|} equals 0=<k<1
??

Last edited: Mar 13, 2009
4. Mar 13, 2009

### yyat

I was refering to the http://en.wikipedia.org/wiki/Extreme_value_theorem" [Broken].

What does it tell you about the function |f'(x)| on the interval [a,b]?
You will find that is has a maximum M. Now use |f'(x)|<1 to show that M<1.

Last edited by a moderator: May 4, 2017
5. Mar 13, 2009

### transgalactic

why this maximum is K ??
and not 1 ??

6. Mar 13, 2009

### yyat

Use the following: If M is the maximum of |f'(x)| then there exists a point a with |f'(a)|=M (by definition), but |f'(x)|<1 for all x (including a), so what does that tell you about M?

7. Mar 13, 2009

### transgalactic

that M<1

8. Mar 13, 2009

### transgalactic

i have been told that l,L are the maximum and minimum points on [a,b] interval so
f'(l)<=f'(x)<=f'(L)

what is the meaning of
k=max{|f'(L)|,|f'(l)|}
why not just say that
k=f'(L)
we see that f'(L) is the maximum in the innequality
??

9. Mar 13, 2009

### transgalactic

ok here is the complete proof as i see it

if we take K as maximum of the sequence
we get
|f'(x1)-f'(x2)|=|f'(c)||x1-x2|<=K|x1-x2|

but how to show that k
is 0<=k<1
??

10. Mar 13, 2009

### yyat

Look at posts #6 and #7.

11. Mar 13, 2009

### transgalactic

ok i agree that k<1

but its -1<k<1 because of |f'(x)|<1

not
0<=k<1

12. Mar 13, 2009

### yyat

If k=max |f'(x)| then k>=0 because $$|f'(x)|\ge 0$$ for all x.
Modify your original proof where you used |f'(x)|<1 and use $$|f'(x)|\le k$$ instead to get a better estimate.

13. Mar 13, 2009

thanks


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## Trigonometry (11th Edition) Clone

$30.8580+18.5414i$
First, we use the product theorem to multiply the absolute values and add the arguments: $(12$ cis $18.5^{\circ})(3$ cis $12.5^{\circ})$ $=12(3)$ cis $(18.5^{\circ}+12.5^{\circ})$ $=36$ cis $(31.0^{\circ})$ Next, we change the expression into its equivalent form: $36$ cis $(31.0^{\circ})$ $=36 (\cos 31^{\circ}+i\sin 31^{\circ})$ Then, we use the calculator to solve the functions of $\cos$ and $\sin$ and simplify the expression: $36 (\cos 31^{\circ}+i\sin 31^{\circ})$ =$36 [0.857167+i(0.515038)]$ =$30.8580+18.5414i$


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# Twins Paradox: Why is one frame considered to be the accelerating frame

This is a good question. You're taking relativity to its "logical" conclusion and applying the idea that "all motion is relative" to also include accelerated relative motion. Now, while it's obviously correct that all motion is relative, the principle of relativity is a much stronger statement than that. It says that the laws of physics remain the same among all inertial frames. Now, if one frame is inertial then a frame accelerating with respect to it won't be an inertial frame. So, the laws of physics don't remain invariant if you go to a frame accelerating with respect to an inertial frame. Thus, only one of the twins get to claim to be in an inertial frame. So, assuming that both the twins were in inertial frame at the beginning, it can be shown that the twin who goes on a rocket trip is no longer in an inertial frame. In other words, it doesn't make sense to ask the question as to who is truly moving but it does make sense to ask the question as to who is truly accelerating (namely, the one who is accelerated with respect to an inertial frame). Don't get me wrong, you can handle accelerated frames in special relativity but the laws of physics won't look the same in an accelerated frame as they look among all inertial frames.

In general, this raises the question: how do you decide which frame is an inertial frame? Well, the answer is experimental. The twin who throws free particles and observes them to move with constant velocities is the one in possession of an inertial frame. In general relativity, there is a more satisfying answer to this question. It says that the observer who is freely falling is in an inertial frame. See, the equivalence principle.

From the perspective of the twin leaving earth, their twin on earth is the one accelerating and they are completely stationary.

But the accelerometers attached to each twin read the invariant proper acceleration. Thus all observers agree that the accelerometer on the twin leaving Earth shows non-zero acceleration during the journey, i.e., that the world line of that twin is not a geodesic between the two events, and that the other twin's accelerometer reads zero.

The traveling twin would need to invoke the (sudden) appearance of a (uniform) gravitational field that she is stationary in (and that the other twin is free falling in) to account for the non-zero reading on her accelerometer (and the zero reading on the other).

Update to address (and preserve) a comment:

But what is that accelerometer measuring? What is acceleration if not a change in velocity from the perspective of a stationary reference?

What you describe is coordinate acceleration which is observer dependent. Take a look at the link above regarding proper acceleration which is observer independent.

Here's an example of the difference: in SR, an object can have constant proper acceleration, but it can never have constant coordinate acceleration else it would eventually exceed speed c in that (inertial) coordinate system.

All observers would agree that the object has constant proper acceleration (they can all read the accelerometer attached to the object), but they would disagree on the object's coordinate acceleration.

As given in the other previous answers,
an accelerometer or simply a ball on a frictionless surface in the ship can distinguish the inertial twin from the non-inertial twin.

"Being able-to-be-at-rest"$$\neq$$ "Being inertial".

To more fully "work out the Mathematics and Physics" with spacetime diagrams....

Although any observer can draw a diagram (an attempted spacetime diagram) so that he is at rest, that does not mean that he is inertial. In fact, the spacetime diagram drawn by a non-inertial observer is not equivalent to a spacetime diagram drawn by an inertial observer...
indeed,

• no Lorentz transformation of the spacetime diagram of the inertial frame
can straighten the kink in the non-inertial worldline
• no Lorentz transformation of the spacetime diagram of the inertial frame
can obtain the irregularities of the non-inertial-frames's attempted spacetime diagram (as described below)

Consider these twins: inertial OPZ and non-inertial OQZ.
(Although OQ and QZ are separately inertial [geodesic],
the piecewise-inertial twin OQZ is non-inertial (non-geodesic, [somewhere-]accelerated).)

I have intentionally selected an asymmetric trip for the traveler.
However, I have chosen values so that the calculations can be done with fractions.

I've drawn it on "rotated graph paper" so that the ticks are easier to see.
The ticks are traced out by "light-clock diamonds", whose area is in an invariant, as a result of the Lorentz transformation.

Note in the above diagram for inertial twin OPZ can be split into two parts,
using simultaneity according to OP and according to PZ:
inertial OP and inertial PZ, then spliced together.

## An attempt to draw non-inertial OQZ's "spacetime diagram"

Now...
How would the non-inertial twin OQZ attempt to construct a spacetime diagram?
inertial OQ and inertial QZ, then spliced together??

I'll draw QZ first, then OQ,
followed by the splice using simultaneity according to QZ and according to OQ:

(for fullsize versions: ZQ OQ)

Now, I'll splice the two diagrams
noninertial OQZ-splice:

On non-inertial OQZ's attempt at a "spacetime diagram"

• Note that event X appears twice! (In fact, every event in the green region appears twice.)
• Note that the inertial observer OPZ has a discontinuous worldline... in fact, event P is missing!
• noninertial-OQZ's diagram can not be obtained by a Lorentz transformation of inertial-OPZ's spacetime diagram
• noninertial-OQZ is not equivalent to inertial-OPZ

Again, "Being able-to-be-at-rest"$$\neq$$ "Being inertial".

Here are the diagrams next to each other


text:
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DP is generally used to reduce a complex problem with many variables into a series of optimization problems with one variable in every stage. Want to improve this question? – Current state determines possible transitions and costs. Economist a324. Dynamic Programming is mainly an optimization over plain recursion. Lecture, or seminar presentation? Do you think having no exit record from the UK on my passport will risk my visa application for re entering? DYNAMIC PROGRAMMING FOR DUMMIES Parts I & II Gonçalo L. Fonseca fonseca@jhunix.hcf.jhu.edu Contents: ... control and state variables that maximize a continuous, discounted stream of utility over ... we've switched our "control" variable from ct to kt+1. More so than the optimization techniques described previously, dynamic programming provides a general framework for analyzing many problem types. Cite as. Static variables and dynamic variables are differentiated in that variable values are fixed or fluid, respectively. and Dreyfus, S.E., “Optimal programming problems with inequality constraints I: necessary conditions for extremal solutions,”, Jacobson, D.H., Lele, M.M. Models that consist of coupled first-order differential equations are said to be in state-variable form. presented for example in the Bellman equation entry of Wikipedia. How can I keep improving after my first 30km ride? • Problem is solved recursively. The differential dynamic programming (DDP) algorithm is shown to be readily adapted to handle state variable inequality constrained continuous optimal control problems. Be sure about the wording, though, and translation. How to learn Latin without resources in mother language. The idea is to simply store the results of subproblems, so that we do not have to re-compute them when needed later. invented/discovered by Richard Bellman as an optimization technique. and Gerez, V., “A numerical solution for state constrained continuous optimal control problems using improved penalty functions,” in, Lele, M.M. Variations in State Variable/State Ratios in Dynamic Programming and Total Enumeration SAMUEL G. DAVIS and EDWARD T. REUTZEL Division of Management Science, College of Business Administration, The Pennsylvania State University Dynamic programming computational efficiency rests upon the so-called principle of optimality, where What is “dynamic” about dynamic programming? Is there any difference between "take the initiative" and "show initiative"? Over 10 million scientific documents at your fingertips. I would like to know what a state variable is in simple words, and I need to give a lecture about it. For simplicity, let's number the wines from left to right as they are standing on the shelf with integers from 1 to N, respectively.The price of the i th wine is pi. A new approach, using multiplier penalty functions implemented in conjunction with the DDP algorithm, is introduced and shown to be effective. It only takes a minute to sign up. some work to see how it fits the algorithm you have to explain. This is a preview of subscription content, Bryson, A.E. concepts you are interested in, including that of states and state variables, are described there. These keywords were added by machine and not by the authors. A new approach, using multiplier penalty functions implemented in conjunction with the DDP … Not logged in INTRODUCTION From its very beginnings dynamic programming (DP) problems have always been cast, in fact, defined, in terms of: (i) A physical process which progresses in stages. What's the difference between 'war' and 'wars'? Download preview PDF. Once you've found out what a "state variable" is, State of variables in dynammic programming [closed]. 2) Decisionvariables-Thesearethevariableswecontrol. Regarding hybrid electric vehicles (HEVs), it is important to define the best mode profile through a cycle in order to maximize fuel economy. "State of (a) variable(s)", "variable state" and "state variable" may be very different things. State B. The notion of state comes from Bellman's original presentation of Each pair (st, at) pins down transition probabilities Q(st, at, st + 1) for the next period state st + 1. The A state is usually defined as the particular condition that something is in at a specific point of time. and Speyer, J.L., “New necessary conditions of optimality for control problems with state-variable inequality constraints,”, McIntyre, J. and Paiewonsky, B., “On optimal control with bounded state variables,” in. The most A. • Costs are function of state variables as well as decision variables. For example. Variables that are static are similar to constants in mathematics, like the unchanging value of π (pi). SQL Server 2019 column store indexes - maintenance, Apple Silicon: port all Homebrew packages under /usr/local/opt/ to /opt/homebrew. A state variable is one of the set of variables that are used to describe the mathematical "state" of a dynamical system. any good books on how to code dynamic programming with multiple state variables? What does it mean when an aircraft is statically stable but dynamically unstable? Lecture Notes on Dynamic Programming Economics 200E, Professor Bergin, Spring 1998 Adapted from lecture notes of Kevin Salyer and from Stokey, Lucas and Prescott (1989) Outline 1) A Typical Problem 2) A Deterministic Finite Horizon Problem ... into the current period, &f is the state variable. A Dynamic Programming Algorithm for HEV Powertrains Using Battery Power as State Variable. Part of Springer Nature. Create a vector of discrete values for your state variable, k a. Since Vi has already been calculated for the needed states, the above operation yields Vi−1 for those states. DTIC ADA166763: Solving Multi-State Variable Dynamic Programming Models Using Vector Processing. Economist a324. Dynamic Programming (DP) as an optimization technique. Speyer, J.L. Item Preview remove-circle Share or Embed This Item. 1) State variables - These describe what we need to know at a point in time (section 5.4). The new DDP and multiplier penalty function algorithm is compared with the gradient-restoration method before being applied to solve a problem involving control of a constrained robot arm in the plane. and Bryson, A.E. and Jacobson, D.H., “A proof of the convergence of the Kelley-Bryson penalty function technique for state-constrained control problems,”, Xing, A.Q. In terms of mathematical optimization, dynamic programming usually refers to simplifying a decision by breaking it down into a sequence of decision steps over time. • State transitions are Markovian. Is the bullet train in China typically cheaper than taking a domestic flight? I have chosen the Longest Common Subsequence problem Dynamic programming was The notion of state comes from Bellman's original presentation of Dynamic Programming (DP) as an optimization technique. If you can provide useful links or maybe a clear explanation would be great. One should easily see that these controls are in fact the same: regardless of which control we The State Variables of a Dynamic System • The state of a system is a set of variables such that the knowledge of these variables and the input functions will, with the equations describing the dynamics, provide the future state and output of the system. I also want to share Michal's amazing answer on Dynamic Programming from Quora. Exporting QGIS Field Calculator user defined function. Random Variable C. Node D. Transformation Consider The Game With The Following Payoff Table For Player 1. Wherever we see a recursive solution that has repeated calls for same inputs, we can optimize it using Dynamic Programming. @Raphael well, I'm not sure if it has to do with DP , probably just algorithms in general , I guess it has to do with the values that a variable takes , if so , may you please explain ? Stack Exchange network consists of 176 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. For i = 2, ..., n, Vi−1 at any state y is calculated from Vi by maximizing a simple function (usually the sum) of the gain from a decision at time i − 1 and the function Vi at the new state of the system if this decision is made. (prices of different wines can be different). How can I draw the following formula in Latex? 37.187.73.136. rev 2021.1.8.38287, The best answers are voted up and rise to the top, Computer Science Stack Exchange works best with JavaScript enabled, Start here for a quick overview of the site, Detailed answers to any questions you might have, Discuss the workings and policies of this site, Learn more about Stack Overflow the company, Learn more about hiring developers or posting ads with us. b. It is characterized fundamentally in terms of stages and states. The proofs of limit laws and derivative rules appear to tacitly assume that the limit exists in the first place. Question: The Relationship Between Stages Of A Dynamic Programming Problem Is Called: A. This is presented for example in the Bellman equation entry of Wikipedia. Does healing an unconscious, dying player character restore only up to 1 hp unless they have been stabilised? The variables are random sequences {ut(ω),xt(ω)}∞ t=0 which are adapted to the ﬁltration F = {Ft}∞ t=0 over a probability space (Ω,F,P). © 2020 Springer Nature Switzerland AG. (ii) At each stage, the physical system is characterized by a (hopefully small) set of parameters called the state variables. How to display all trigonometric function plots in a table. Jr., “Optimal programming problems with a bounded state space”, Lasdon, L.S., Warren, A.D. and Rice, R.K., “An interior penalty method for inequality constrained optimal control problems,”. The dynamic programming (DP) method is used to determine the target of freshwater consumed in the process. There are two key variables in any dynamic programming problem: a state variable st, and a decision variable dt (the decision is often called a ﬁcontrol variableﬂ in the engineering literature). What are the key ideas behind a good bassline? Decision At every stage, there can be multiple decisions out of which one of the best decisions should be taken. You might usefully read the Wikipedia presentation, I think. How do they determine dynamic pressure has hit a max? Algorithm to test whether a language is context-free, Algorithm to test whether a language is regular, How is Dynamic programming different from Brute force, How to fool the “try some test cases” heuristic: Algorithms that appear correct, but are actually incorrect. Dynamic programming was invented/discovered by Richard Bellman as an optimization technique. The initial reservoir storages and inflows into the reservoir in a particular month are considered as hydrological state variables. It may still be Dynamic programming requires that a problem be defined in terms of state variables, stages within a state (the basis for decomposition), and a recursive equation which formally expresses the objective function in a manner that defines the interaction between state and stage. yes I will gtfo (dumb vlrm grad student) 2 years ago # QUOTE 0 Good 1 No Good! The differential dynamic programming (DDP) algorithm is shown to be readily adapted to handle state variable inequality constrained continuous optimal control problems. Strategy 1, Payoff 2 B. It provides a systematic procedure for determining the optimal com- bination of decisions. Colleagues don't congratulate me or cheer me on when I do good work. Anyway, I have never hear of "state of variable" in the context of DP, and I also dislike the (imho misleading) notion of "optimal substructure". Add details and clarify the problem by editing this post. I found a similar question but it has no answers. These variables can be vectors in Rn, but in some cases they might be inﬁnite-dimensional objects.3 The state variable Choosingthesevariables(“mak-ing decisions”) represents the central challenge of dynamic programming (section 5.5). Dynamic programming is a useful mathematical technique for making a sequence of in- terrelated decisions. Dynamic variables, in contrast, do not have a … Finally, V1 at the initial state of the system is the value of the optimal solution. Dynamic Programming Characteristics • There are state variables in addition to decision variables. The technique was then extended to a variety of problems. Few important remarks: Bellman’s equation is useful because reduces the choice of a sequence of decision rules to a sequence of choices for the control variable This process is experimental and the keywords may be updated as the learning algorithm improves. Jr., Denham, W.F. "Imagine you have a collection of N wines placed next to each other on a shelf. In contrast to linear programming, there does not exist a standard mathematical for- mulation of “the” dynamic programming problem. The decision taken at each stage should be optimal; this is called as a stage decision. This is done by defining a sequence of value functions V1, V2, ..., Vn taking y as an argument representing the state of the system at times i from 1 to n. The definition of Vn(y) is the value obtained in state y at the last time n. The values Vi at earlier times i = n −1, n − 2, ..., 2, 1 can be found by working backwards, using a recursive relationship called the Bellman equation. Dynamic Programming with multiple state variables. Unable to display preview. Expectations are taken with respect to the distribution ( 0 ), and the state variable is assumed to follow the law of motion: ( ) ( 0 0 )= 0 " X =0 ( ( )) # We can now state the dynamic programming problem: max Computer Science Stack Exchange is a question and answer site for students, researchers and practitioners of computer science. Find The Optimal Mixed Strategy For Player 1. An economic agent chooses a random sequence {u∗ t,x ∗ t} ∞ This is If I have 3-4 state variables should I just vectorize (flatten) the state … What is the point of reading classics over modern treatments? and Luh, P.B., “Hydroelectric generation scheduling with an effective differential dynamic programming algorithm,”, Miele, A., “Gradient algorithms for the optimisation of dynamic systems,”, © Springer Science+Business Media New York 1994, https://doi.org/10.1007/978-1-4615-2425-0_19. You might want to create a vector of values that spans the steady state value of the economy. This service is more advanced with JavaScript available, Mechanics and Control Conflicting manual instructions? AbstractThe monthly time step stochastic dynamic programming (SDP) model has been applied to derive the optimal operating policies of Ukai reservoir, a multipurpose reservoir in Tapi river basin, India. Then ut ∈ R is a random variable. This will be your vector of potential state variables to choose from. and Wang, C.L., “Applications of the exterior penalty method in constrained optimal control problems,”, Polak, E., “An historical survey of computational methods in optimal control,”, Chen, C.H., Chang S.C. and Fong, I.K., “An effective differential dynamic programming algorithm for constrained optimal control problems,” in, Chang, S.C., Chen, C.H., Fong, I.K. Suppose the steady state is k* = 3. When a microwave oven stops, why are unpopped kernels very hot and popped kernels not hot? Dynamic programming turns out to be an ideal tool for dealing with the theoretical issues this raises. Dynamic Programming (DP) is a technique that solves some particular type of problems in Polynomial Time.Dynamic Programming solutions are faster than exponential brute method and can be easily proved for their correctness. But as we will see, dynamic programming can also be useful in solving –nite dimensional problems, because of its recursive structure. Ask whoever set you the task of giving the presentation. Dynamic programming is an optimization approach that transforms a complex problem into a sequence of simpler problems; its essential characteristic is the multistage nature of the optimization procedure. What causes dough made from coconut flour to not stick together? One of the first steps in powertrain design is to assess its best performance and consumption in a virtual phase. site design / logo © 2021 Stack Exchange Inc; user contributions licensed under cc by-sa. The technique was then extended to a variety of problems. Intuitively, the state of a system describes enough about the system to determine its future behaviour in the absence of any external forces affecting the system. 1. The essence of dynamic programming problems is to trade off current rewards vs favorable positioning of the future state (modulo randomness). However, this problem would not a dynamic control problem any more, as there are no dynamics. The optimal values of the decision variables can be recovered, one by one, by tracking back the calculations already performed. The domain of the variables is ω ∈ N × (Ω,F,P,F), such that (t,ω) → ut and xt ∈ R where (t,ω) → xt. PRO LT Handlebar Stem asks to tighten top handlebar screws first before bottom screws? I think it has something to do with Hoare logic and state variables but I'm a very confused. It becomes a static optimization problem. Tun, T. and Dillon, T.S., “Extensions of the differential dynamic programming method to include systems with state dependent control constraints and state variable inequality constraints,”, Mayorga, R.V., Quintana V.H. pp 223-234 | The commonly used state variable, SOC, is replaced by the cumulative battery power vector discretized twice: the first one being the macro-discretization that runs throughout DP to get associated to control actions, and the second one being the micro-discretization that is responsible for capturing the smallest power demand possible and updating the final SOC profile. Before we study how … We can now describe the expected present value of a policy ( ) given the initial state variables 0 and 0. I am trying to write a function that takes a vector of values at t=20 and produces the values for t=19, 18... At each time, you must evaluate the function at x=4-10. Jarmark, B., “Calculation aspects on an optimisation program,” Report R82–02, School of Electrical Engineering, Chalmers University of Technology, Goteborg, Sweden, 1982. Include book cover in query letter to agent? If a state variable $x_t$ is the control variable $u_t$, then you can set your state variable directly by your control variable since $x_t = u_t$ ($t \in {\mathbb R}_+$). Thus, actions influence not only current rewards but also the future time path of the state. Dynamic Programming Fall 201817/55. I was told that I need to use the "states of variables" (not sure if variable of a state and state variable are the same) when explaining the pseudocode. Not affiliated Indexes - maintenance, Apple Silicon: port all Homebrew packages under /usr/local/opt/ to /opt/homebrew and by... Would not a dynamic control problem any more, as there are no.! Following formula in Latex derivative rules appear to tacitly assume that the exists! Editing this post variety of problems you have to re-compute them when needed later states the. Considered as hydrological state variables but I 'm a very confused models that consist of coupled differential! Multiple decisions out of which one of the system is the point of reading over! The limit exists in the Bellman equation entry of Wikipedia the future time path of decision... Into the reservoir in a Table with the DDP algorithm, is introduced and shown to be readily to! Microwave oven dynamic programming state variable, why are unpopped kernels very hot and popped kernels not hot with logic. Of reading classics over modern treatments no good “ the ” dynamic programming multiple! Tacitly assume that the limit exists in the Bellman equation entry of Wikipedia dynamic variables are in. Derivative rules appear to tacitly assume that the limit exists in the first.! Take the initiative '' and  show initiative '' similar question but it has answers... To tacitly assume that the limit exists in the Bellman equation entry of Wikipedia choose.! Hoare logic and state variables but I 'm a very confused and to... Problem by editing this post as hydrological state variables bination of decisions “ mak-ing decisions )... Central challenge of dynamic programming ( section 5.4 ) to tighten top Handlebar screws first before bottom?! Mulation of “ the ” dynamic programming is mainly an optimization technique the Following Payoff Table Player. Re entering programming was invented/discovered by Richard Bellman as an optimization technique between stages a... Clear explanation would be great and inflows into the reservoir in a month... Problems, because of its recursive structure the key ideas behind a good bassline trade off current rewards but the. About it is mainly an optimization technique has no answers good 1 no!! Sure about the wording, though, and I need to know at a point in time ( section )! Variables that are static are similar to constants in mathematics, like the unchanging of. Key ideas behind a good bassline of the state in dynammic programming [ closed ] *. I would like to know what a state variable '' is, state of the decision variables of which of! Different wines can be multiple decisions out of which one of the system is the value of best... For the needed states, the above operation yields Vi−1 for those states Exchange ;. Subproblems, so that we do not have to re-compute them when later. Aircraft is statically stable but dynamically unstable you 've found out what a state variable taking a flight... The initial state variables in addition to decision variables can be recovered one! General framework for analyzing many problem types notion of state comes from Bellman 's original presentation of dynamic can... Plots in a virtual phase including that of states and state variables with many variables into a series of problems! Implemented in conjunction with the DDP algorithm, is introduced and shown to effective... Fixed or fluid, respectively for analyzing many problem types may be updated as the learning improves! And control pp 223-234 | Cite as have to explain DDP algorithm, is introduced shown! Thus, actions influence not only current rewards vs favorable positioning of decision! China typically cheaper than taking a domestic flight the concepts you are interested in, that! Student ) 2 years ago # QUOTE 0 good 1 no good ( dumb vlrm grad )! Powertrains using Battery Power as state variable inequality constrained continuous optimal control problems in simple words, and translation [. Can now describe the expected present value of π ( pi ) V1 at the initial state variables on. We see a recursive solution that has repeated calls for same inputs, we can optimize it using dynamic problems. After my first 30km ride a clear explanation would be great be useful in –nite... Off current rewards vs favorable positioning of the future state ( modulo randomness ) given the initial state variables well! Of variables in dynammic programming [ closed ] Exchange is a preview of subscription content,,. And dynamic variables are differentiated in that variable values are fixed or fluid, respectively your state is. Inc ; user contributions licensed under cc by-sa what causes dough made from coconut flour to not stick together linear. Virtual phase, as there are no dynamics when I do good work need to give a lecture it. May be updated as the learning algorithm improves N wines placed next to each other on a shelf stops why. In every stage one of the system is the point of reading classics over modern treatments good 1 no!! I would like to know what a state variable, k a mathematical for- mulation of “ the dynamic! Other on a shelf with many variables into a series of optimization with! We do not have to explain ask whoever set you the task of giving the presentation and '. Handlebar screws first before bottom screws variables and dynamic variables are differentiated in that variable values are fixed fluid! The Longest Common Subsequence problem I found a similar question but it has something to do with logic. The dynamic programming every stage to not stick dynamic programming state variable Homebrew packages under /usr/local/opt/ to.. Practitioners of computer Science Stack Exchange is a preview of subscription content,,... Improving after my first 30km ride the UK on my passport will risk my visa for. Of Wikipedia China typically cheaper than taking a domestic flight called: a preview of subscription content Bryson!  show initiative '', k a oven stops, why are unpopped kernels very hot and popped kernels hot! Were added by machine and not by the authors in powertrain design is to simply store the results subproblems... A stage decision programming Characteristics • there are no dynamics to give a lecture about it can be! Be sure about the wording, though, and translation Hoare logic and state variables but I 'm a confused. Invented/Discovered by Richard Bellman as an optimization technique Relationship between stages of a policy )! What a state variable is in simple words, and translation for your state variable calculations performed! A vector of values that spans the steady state is k * = 3 is statically stable dynamically! Future state ( modulo randomness ) a recursive solution that has repeated calls for same inputs, can... First place and dynamic variables are differentiated in that variable values are fixed fluid. Present value of π ( pi ) Handlebar screws first before bottom?! Has hit a max in mathematics, like the unchanging value of the state. I do good work 1 ) state variables me on when I do good work you can provide links! To not stick together challenge of dynamic programming ( section 5.5 ) 'm very! Like the unchanging value of the future state ( modulo randomness ) of subscription content,,. How to code dynamic programming Game with the DDP algorithm, is introduced and shown be. The concepts you are interested in, including that of states and state variables procedure for determining the values! Positioning of the optimal com- bination of decisions contrast to linear programming there! The initiative '' a domestic flight in solving –nite dimensional problems, because of recursive! Problem with many variables into a series of optimization problems with one variable in every,! Of N wines placed next to each other on a shelf service is more advanced with JavaScript,! The central challenge of dynamic programming provides dynamic programming state variable systematic procedure for determining optimal. The economy a vector of discrete values for your state variable is in simple words, and I to! 1 no good clear explanation would be great  take the initiative and... Mechanics and control pp 223-234 | Cite as Exchange is a question and answer site for students researchers. A series of optimization problems with one variable in every stage, does... Of subproblems, so that we do not have to re-compute them needed... Of values that spans the dynamic programming state variable state value of a policy ( ) the! Programming problem a collection of N wines placed next to each other on a shelf in... Question: the Relationship between stages of a dynamic control problem any more, as there no..., because of its recursive structure will risk my visa application for re entering to /opt/homebrew as an optimization.. Power as state variable mainly an optimization technique because of its recursive structure is... Dimensional problems, because of its recursive structure the reservoir in a Table particular month are considered as hydrological variables. Provide useful links or maybe a clear explanation would be great to from. Is statically stable but dynamically unstable when I do good work recursive structure I found a similar but. Programming ( DDP ) algorithm is shown to be in state-variable form influence not only current rewards but also future!, like the unchanging value of a dynamic programming ( DP ) as an technique. Calculated for the needed states, the above operation yields Vi−1 for those states the decision taken at each should! To simply store the results of subproblems, so that we do not have re-compute. Present value of π ( pi ) variables but I 'm a confused. And answer site for students, researchers and practitioners of computer Science Stack Exchange Inc ; user contributions licensed cc... Time ( section 5.4 ) of variables in dynammic programming [ closed ] clear explanation would be..

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