text:
# Modeling the Response of a Fast Ion Loss Detector Using Orbit Tracing Techniques in a Neutral Beam Prompt Loss Study on the DIII-D Tokamak

This paper details a method for correlating measurements of beam ion losses with the injection of individual beams in the DIII-D tokamak. This turns out to be a great tool for making sense of the measurements. The probe measures ion impacts, and then we use particle orbit calculations to backtrack the ions to specific beams. This allows us to calibrate the energy and pitch angle range of the probe. This turned out to be a great idea as it expanded into other areas of energetic particle research at DIII-D, including the concept of using the beams as a “light ion beam probe.”

This was also the first paper that I published as a postdoctoral researcher with Plasma Physics Group at UC Irvine. My Ph.D. thesis was in the area of basic plasma physics, so it was an intimidating step to move to magnetic fusion. I was assigned to the loss detector probe and the idea for mapping injected beam ions to the probe came from the combination of my need to figure out how the diagnostic worked (so that I could actually be productive!) and R. Nazikian’s brilliant suggestion.

The following article appears in Review of Scientific Instruments as,
D.C. Pace, R.K. Fisher, M. García-Muñoz, D. S. Darrow, W. W. Heidbrink, C. M. Muscatello, R. Nazikian, M. A. Van Zeeland, and Y. B. Zhu, Rev. Sci. Instrum. 81, 10D305 (2010).

## Modeling the Response of a Fast Ion Loss Detector Using Orbit Tracing Techniques in a Neutral Beam Prompt Loss Study on the DIII-D Tokamak

### Abstract

A numerical model describing the expected measurements of neutral beam prompt-losses by a newly commissioned fast ion loss detector (FILD) in DIII-D is presented. This model incorporates the well understood neutral beam deposition profiles from all eight DIII-D beamlines to construct a prompt-loss source distribution. The full range of detectable ion orbit phase space available to the FILD is used to calculate ion trajectories that overlap with neutral beam injection footprints. Weight functions are applied to account for the level of overlap between these detectable orbits and the spatial and velocity (pitch) properties of ionized beam neutrals. An experimental comparison is performed by firing each neutral beam individually in the presence of a ramping plasma current. Fast ion losses determined from the model are in agreement with measured losses. It is suggested that this technique can be applied to an ion loss source distribution caused by Alfvén eigenmode-induced transport, allowing for quantitative comparisons between theoretical and experimentally observed fast ion losses in the presence of such modes.

### I. INTRODUCTION

The ultimate success of the tokamak as a fusion energy device depends on the ability to confine fusion products that are of considerably greater energy than the thermal background plasma. Energetic ion losses due to high-frequency (f > 50 kHz) MHD modes have been inferred from bolometer arrays [1] and directly observed by scintillator-based detectors [2]. Losses caused by sawtooth oscillations have also been directly observed [3]. The reverse-orbit technique discussed here is intended to demonstrate a method by which loss measurements from a device wall can be used to infer regions of interaction (in both absolute position and wave-particle phase space) between instabilities and energetic ions. Beginning with measurements of the orbit properties of ions that strike the detector, it is possible to trace the earlier path of the ion to determine locations of overlap between it and any instability. The validity of this method rests on the assumption that the ions of interest very nearly follow trajectories prescribed by the equilibrium field during the time that elapses between the event of interest and detection at the wall. This transit time is on the order of tens of microseconds, which is much less than the slowing-down time of injected beam neutrals (tens of milliseconds).

Here, neutral beam prompt-losses are studied through a carefully designed DIII-D discharge that fires each of the eight available sources individually. Ions that are observed by the Fast Ion Loss Detector (FILD) are traced in reverse time to quantify their overlap with the injection footprint of the relevant beam source. The same framework is suggested for use with any particular source of fast-ion emissivity. A similar approach has been previously employed [4] using the trajectories of fusion products to measure the poloidal magnetic field in a tokamak. Future work will apply this procedure to the fast-ion source that is generated from instabilities that drive ions onto loss orbits.

Scintillator-based energetic ion loss detectors have been used on many fusion devices since first being developed on TFTR [5]. A new FILD [6] has recently been installed for use at DIII-D. The FILD design is based on a diagnostic in use at ASDEX-U [7]. These detectors use fast-response scintillators to detect light from ion impacts. A collimating aperture is placed in the heat shield surrounding the scintillator, which results in a particular mapping between the pitch angles and gyroradii of impacting ions onto the two-dimensional detector. Imaging the scintillator with a camera provides time resolved measurements of the particular ion orbits that are lost at the wall position of the detector. This information is used to trace the ion along the trajectory it followed en route to the detector.

The setup of the experimental discharge is described in Sec. II. The analysis method used to interpret FILD data and place it in context with measurements in the plasma core is discussed by way of a neutral beam prompt-loss study presented in Sec. III. A summary of the results for the example discharge is given in Sec. IV. Finally, a discussion of future applications is presented in Sec. V.

### II. NEUTRAL BEAM PROMPT-LOSS SETUP

In order to verify the technique of reverse-orbit tracing, prompt-losses from neutral beam injection is studied in the DIII-D tokamak. Given the thorough understanding of neutral beam injection (NBI) in tokamaks (see Sec. 2.2 of [8] for an extensive reference list, and [9] for more recent experimental verification of NBI theory), a DIII-D discharge was designed to inject each of its eight sources individually. With each beam pulse a collection of prompt-losses occur. These are due to ionization events that place the energetic ion on an orbit that terminates on the vessel wall. Each neutral beam source is injected for a 10 ms pulse during a plasma current ramp as shown in Fig. 1 from Shot 141223 with Bo = 2.05 T. The purpose of ramping the plasma current is that it increases the amplitude of the poloidal magnetic field, causing variation in both the pitch angles of the energetic ions and the location at which they strike the wall. The FILD is located at the 225◦ toroidal position in a port that is approximately 45◦ below the midplane.

Fig. 1: Plasma current and neutral beam injection for Shot 141223. The line labeled “Camera Exposure” highlights the trigger of the camera frame shown in Fig. 2. The width of this line indicates the 1 ms exposure time of that frame.

### III. FILD MODEL OF PROMPT-LOSS DETECTION

Fig. 2: Negative image of FILD camera frame showing prompt-losses as the dark region between 60◦ ≤ α ≤ 75◦. (Shot 141223, t = 380 ms)

The concept of modeling FILD measurements centers on comparing the ion orbits for which the detector is sensitive to a specific source that drives ion losses. In the case of the neutral beam prompt-loss study presented here, the source of lost ions is determined according to the injection of any particular DIII-D beamline. In the description of the method presented in this Section, the specific example from a single pulse will be shown. This example is a pulse of the 210L neutral beam source that occurs over 380 ≤ t ≤ 390 ms. Figure 2 shows a camera image from the FILD during injection of the 210L source. The camera is exposed for 1 ms beginning at t = 380 ms. The frame is displayed as a negative image for clarity, meaning that the dark region appearing over pitch angles 60◦ ≤ α ≤ 75◦ corresponds to a large flux of impacting ions. The FILD measures pitch angle, α, which is related to the commonly cited orbit pitch as, cos(α) = v∥/v, where v∥ is the particle’s velocity parallel to the total magnetic field and v is the particle’s total velocity.

#### A. Weight Functions Applied to Neutral Beam Injection

The objective of modeling the FILD is to accurately account for an observed signal, in both amplitude and orbit phase space, given the well known source of prompt-loss ions due to neutral beam injection. The number of ions that are expected to reach the FILD, NFILD, is a function of energy, Eo, and pitch, $v_\parallel/v$. If the total number of ions seeded by the beam onto prompt-loss orbits is given by, Nnbi = Nnbi(R, φ, z, Eo, $v_\parallel/v$), then this must represent the largest possible signal any loss detector could observe. Any given detector is located at a fixed spatial position, however, which limits the ion orbits that can be detected to those that feature a trajectory leading to intersection with the diagnostic. These detectable orbits are accumulated, or extracted, through reducing Nnbi by applying weight functions, W. Each weight function in this model features a value between zero and one. The number of ions expected to reach the FILD is,

$N_{\text{FILD}}(E_o, v_\parallel/v) = \sum_L W_{\text{pitch}} W_{R,\phi,z} N_{\text{nbi}}$

where $W_{R,\phi,z}$ is the spatial weight function, $W_{\text{pitch}}$ is the pitch (or velocity) weight function, and the sum is taken over the trajectory of the ion, $L$.

#### B. Reverse-Orbit Trajectories

Any measurement by the FILD provides simultaneous observations of an ion’s energy, pitch, and location (knowing that the ion must have passed through the entrance aperture to reach the scintillator). Detectors of this design are restricted in the gyroradii and pitches that can be detected due to the geometry of the probe head and the collimating aperture. The range of detectable ion orbits is determined by calculating ion trajectories using the plasma’s magnetic equilibrium and collecting statistics on the parameters that both reach the scintillator and avoid the probe head. The FILD at DIII-D is capable of detecting ions of gyroradius, $r_L$, in the range $1.5 \leq r_L \leq 5.0$ cm and pitch angles, $\alpha$, in the range $30^\circ \leq \alpha \leq 75^\circ$. The strike map overlaid on the camera frame of Fig. 2 indicates these limits. While there are at least two well established codes for calculating these maps, neither is the subject of a detailed published treatment. The mapping shown here is calculated using EfipDesign (described, but not named, in Sec. II of [10]). Secondary calculations with NLSDETSIM (described, but not named, in [11]) are ongoing and presently consistent with the EfipDesign results.

From the total measurable orbit parameter space, a collection of ion trajectories are calculated in reverse time. These ions begin at the spatial position of the collimating FILD aperture and are traced backwards in time. Orbits are calculated using the measured mag- netic equilibrium and a code that solves the Lorentz force equation (a descendent of [12]). Fast ion orbits are often calculated in this manner to contribute to the understanding of various diagnostic observations (e.g., see Fig. 4 of [13] for an application with respect to fast-ion Dα imaging). For the model FILD, the orbits must be calculated over a long enough time period to reproduce any overlap between the orbit and the beam footprint. The elapsed time, however, must also be short enough that the magnetic equilibrium is static and only prompt-losses are captured. An optimum value is determined empirically and nearly all or- bit calculations are performed within a 60 μs time window. This time period is much shorter than the tens of milliseconds that represent the slowing-down time of injected neutrals.

The FILD strike map is a function of gyroradius, which can be expressed as an energy value once the total magnetic field amplitude is known. For the model FILD that focuses on neutral beam prompt-losses, full energy surveys are not necessary. A prompt-loss ion does not thermalize because it escapes to the vessel wall too quickly. That leads to the requirement that the energy of such a detected ion must be a value that is directly seeded by the neutral beam. Due to the presence of molecular deuterium, neutral beams with a set injection energy (voltage) produce neutrals with full, one-half, and one-third energies. Only orbit trajectories with these three energy values are calculated. For each energy value, orbits are calculated for 40 different pitch angles spaced evenly between 20◦ ≤ α ≤ 83◦. The pitch angle range is purposely set to extend slightly beyond the FILD’s detection range to ensure that any nearly detectable losses are tabulated.

#### C. Spatial Weighting

The spatial weighting consists of quantifying how well a prompt-loss orbit overlaps with neutral beam injection throughout the three-dimensional space of the tokamak. With all $W_{R,\phi,z}$ initially set to zero, a value of $W_{R,\phi,z} = 1$ is assigned at positions along $L$ for which the following three conditions are met.

1. The vertical position of the ion is within $-0.5 \leq z \leq 0.5$ m.
2. The toroidal position of the ion is within the boundaries for the relevant neutral beam source.
3. The parallel velocity of the ion is in the same direction as the injection from the neutral beam source.

Condition 1 is empirically known to encompass the entire vertical extent of any beamline. It is possible for this condition to be satisfied at a position for which there are no injected neutrals. In that situation, the injected neutral density and ionization profiles will be equal to zero and remove any expectation of signal. Condition 2 accounts for the position of the FILD. Placing the detector at a different toroidal (or poloidal) location will affect which prompt-loss orbits are detected. While condition 3 is technically part of the pitch weighting, it is checked at this stage because it follows the same binary description as the spatial considerations (i.e., if the ion exhibits a parallel velocity that is opposite the injected value, then that orbit must be weighted to zero because it is not a valid prompt-loss candidate). The pitch weighting calculated in Sec. III E displays a more complex variation. There is no check on the major radius overlap because all injected neutral beams cover the entire major radius across their sightline.

The injection geometry of a neutral beam is described in terms of its full three-dimensional spatial extent. The toroidal extent of an injected beam is calculated from the geometry of the sightline along the beam on the vertical midplane. This is equivalent to following the toroidal coverage of the beamlines as shown in Fig. 1 of [9]. The vertical extent of the neutral beams is most recently calculated and experimentally verified in [14]. Accounting for both the toroidal and poloidal geometry of the FILD relative to the lost ion source provides for a rigorous model of the observations and allows for a systematic calculation of expected signals for a second FILD to be deployed on DIII-D in the future [15].

#### D. Prompt-loss Ions Seeded by Neutral Beams

Determination of the number density of prompt-loss ions from neutral beam injection, Nnbi, is achieved by calculating ionization profiles based on modeled neutral density profiles. These densities are determined according to the procedure developed in [14], which applies a standard “pencil beam” treatment repeatedly to construct a density profile across the Rz-plane. From the injected neutral density profiles, the ionization profile is calculated by taking the gradient along the major radius for each value of constant z because ionization is due to electron impacts and charge exchange events. This sets the value of Nnbi as a function of position. Beam injection paths and energies are known, along with the magnetic equilibrium, and since each position corresponds to a primary injected pitch angle as well, we have $N_{\text{nbi}} = N_{\text{nbi}}(R, \phi, z, E_o, v_\parallel/v)$.

The numerical value of $N_{\text{nbi}}$ is meaningful, though it is treated as arbitrary in this study and only relative differences as a function of ion energy and pitch are considered. Prompt-loss signals in DIII-D are typically large enough to saturate the CCD camera of the FILD, making calibrated lost ion fluxes impossible to determine. Improving this technique and the measurements (partially through an array of photomultiplier tubes that record the signal from narrow regions of the scintillator with high time resolution and no saturation) to quantitatively verify detected lost ion flux levels is a future objective.

#### E. Pitch Weighting

For every ion path, at every position for which $W_{R,\phi,z} \neq 0$, the pitch weight factor, $W_{\text{pitch}}$, is calculated. The spatial weight is calculated first for the computational benefit of reducing the number of pitch operations that need to be performed (i.e., there is no reason to attempt a pitch weight calculation at a position where there are no injected neutrals). Pitch angles seeded by a neutral beam along the major radius are calculated as the angle between this sightline of the neutral beam and the toroidal magnetic field using $v_\parallel = v_\phi$. This is considered the ideal injected pitch angle.

It is necessary to describe the entire range of injected pitch angles in order to determine whether a prompt-loss ion trajectory is capable of originating from any given beam source. The modeled variation about this ideal value is treated by way of a Gaussian spread defined according to horizontal ($R\phi$-plane) divergence of the beam. Horizontal divergence is used because the ideal pitch is defined using only the toroidal field, making only the horizontal divergence relevant. The horizontal divergence, $\theta_h = 8.73 \times 10^{-3}$ [rad], is smaller than the vertical ($Rz$-plane) divergence, $\theta_v = 2.27 \times 10^{-2}$ [rad], resulting in a stronger constraint (Fig. 3 provides an example of the narrow region that defines an overlap in pitch). These divergences have been measured or tested in experimental work [14] and are used in both TRANSP [16] modeling and fast-ion D$_\alpha$ spectroscopy simulations [17] for each of DIII-D’s neutral beams. At every position where a pitch weight is calculated, this value is described as a Guassian of unity amplitude centered on the ideal value with a width (standard deviation, $\sigma_p$) equal to the horizontal divergence of the neutral beam. The pitch weight term is described in functional form according to,

Fig. 3: Pitch weight function for pnbi = 0.6. The red diamonds indicate the discrete points as encountered in the model.

$p_{\text{ion}} = v_\parallel / v \\ \sigma_p = p_{\text{nbi}} - \cos\left(\cos^{-1}(p_{\text{nbi}}) + \theta_h \right) \\ W_{\text{pitch}} = \exp\left[-\frac{1}{2} \left( \frac{p_{\text{ion}} - p_{\text{nbi}}}{\sigma_p}\right)^2 \right] \; ,$

where $p_{\text{nbi}} = p_{\text{nbi}}(R,\phi,z)$ is the ideal injected pitch angle of the neutral beam.

An example of $W_{\text{pitch}}$ is shown in Fig. [3], which sets $p_{\text{nbi}} = 0.6$ (resulting in $\sigma_p = 0.007$). In the model, as in the figure, the pitch axis is divided into $1000$ elements covering $-1.0 \leq v_\parallel/v \leq 1.0$. Figure 3 demonstrates the narrow range of pitches expected from neutral beam injection. The value of $W_{\text{pitch}}$ is determined from this type of profile using an interpolation, therefore, the resolution as shown in the inset of Fig. [3] is sufficient.

#### F. Expected FILD Observations

Fig. 4: Expected FILD observation density for the 210L example case presented throughout this description.

At this point, it should be clarified that the technique described here focuses on proof-of-principle demonstration and is not capable of estimating absolute flux levels. The units of $N_{\text{nbi}}$ are not those of emissivity (number/volume/time) because it is difficult to define the proper path length given the three-dimensional geometry of neutral beams. The next iteration of this model will treat the production of prompt-loss ions as a true emissivity, with the proper units, thereby allowing for absolute flux level calculations. The present results are in arbitrary units and are useful to study the observed pitch angle ranges of prompt-losses. The results from the 210L case are presented in Fig. 4. With a magnetic field at the FILD of $B_{\text{FILD}} = 1.51$ T, the corresponding gyroradii for the full, one-half, and one-third energies are approximately $3.8$ cm, $2.7$ cm, and $2.2$ cm, respectively. Figure 4 contains the same information as the FILD camera data in Fig. 2. Qualitative comparisons are excellent as they both indicate losses featuring a $60^\circ \leq \alpha \leq 75^\circ$ pitch angle range and all injection energies. The upper limit at $75^\circ$ must be tempered by the fact that it is also the edge of the detectable range for the FILD. This upper limit of detectable pitch angle also makes it difficult to confirm the narrower pitch angle ranges at lower energy that are shown in the model result of Fig. 4.

The model results support the continuous band seen in the camera data because the gyroradius resolution of the FILD is on the order of 1 cm. Resolution is a function of gyroradius and pitch angle, however, and it must be calculated using a code like EfipDesign or NLSDETSIM for each gyroradius/pitch angle pair. This fully determined resolution will be convolved with the model results to generate expected FILD camera frames.

### IV. SURVEY OF SHOT 141223

A comparison between the model, or expected, pitch angle observations and the FILD camera data is presented in Fig. 5. Each neutral beam source is depicted by a unique symbol with black representing experimental observations and red illustrating the model results. The plasma current is evolving during each 10 ms neutral beam pulse; the range covered is narrower than the width of the symbols used in the plot. Vertical error bars represent the entire range of pitch angles for which either the camera data or the model returned losses. Some error bars and plotting symbols in the range above the $75^\circ$ pitch angle have been omitted for clarity. For the FILD camera data, the pitch angle error bars also add $\pm5^\circ$ to represent the uncertainty in pitch angle measurement that is caused by vibration of the optics platform to which the camera is attached. The blue horizontal lines indicate the boundary of pitch angles that the FILD is capable of detecting. Model data well outside of this range should not be detected by the FILD, though values very close to the boundary may be observed due to FILD resolution. Cases for which there is no observed loss in the FILD camera data are not placed in the plot because they would obscure the zero result from the model (null results from the model are displayed as less than $5^\circ$ pitch angle).

Fig. 5: Pitch angle of ion losses at full beam energy as measured (black) and as calculated from the model (red) for the 210L (top panel), 210R (middle panel), and all other neutral beam sources (bottom panel). Each neutral beam source is represented by a unique plotting symbol. The pitch angle range that the FILD is capable of detecting is indicated by the horizontal bars, and model results outside of this range are not expected to be observed experimentally.

Figure 5 indicates that the model developed here to describe neutral beam prompt-loss detection by the DIII-D FILD is capable of accurately reproducing the experimentally observed results. The 210L neutral beam, denoted by the $\triangle$ symbol, is shown in the top panel of Fig. 5 and is well described at all values of plasma current. Model results for the 210L source occurring below $40^\circ$ pitch angles may be due to numerical error. The 210R beam ($\times$), shown in the middle panel of Fig. 5, is well described at the larger values of plasma current and further study is required to uncover the cause of discrepancies for $I_p < 800$ kA. Few prompt-loss results are observed in the FILD camera data for neutral beams located at other toroidal positions, however, the observations for the 30R, 150R, and 330R sources near $500$ kA are reproduced by the model and shown in the bottom panel of Fig. 5. All neutral beams produce prompt-loss populations, so the lack of an observed signal by the FILD is due to either its wall position (i.e., the prompt-losses strike at other toroidal and poloidal positions) or its detection range (i.e., the prompt-losses occur at pitch angles beyond the detection range shown in Fig. 5).

### V. FUTURE APPLICATIONS

The study presented here focuses on the well established physics of neutral beam injection into a tokamak for the purpose of validating this conceptual treatment. Future application of this technique is aimed at improving understanding of fast ion losses driven by Alfvén eigenmodes (AEs). For this more complicated study it will be necessary to calculate the lost ion source function using a code that accounts for interactions between fast ions and AEs. It is suggested that such a code, ORBIT [18], could provide the source for the model FILD by following perturbed ion orbits to the last closed flux surface. The distribution of these ions along the last closed flux surface is analogous to the prompt-loss ion density of the neutral beam case. Such an effort will lead to a quantitative comparison between expected and measured fast ion losses, thereby providing valuable constraining data from which to improve the relevant transport models.

### REFERENCES

1 H. H. Duong, W. W. Heidbrink, E. J. Strait, T. W. Petrie, R. Lee, R. A. Moyer, and J. G. Watkins, Nucl. Fusion, 33, 749 (1993).

2 M. García-Munñoz, H.-U. Fahrbach, S. Gu ̈nter, V. Igochine, M. J. Mantsinen, M. Maraschek, P. Martin, P. Piovesan, K. Sassenberg, and H. Zohm, Phys. Rev. Lett., 100, 055005 (2008).

3 Y. I. Kolesnichenko, V. V. Lutsenko, R. B. White, Y. V. Yakovenko, and S. J. Zweben, Phys. Plasmas, 6, 1117 (1999).

4 W. W. Heidbrink and J. D. Strachan, Rev. Sci. Instrum., 56, 501 (1985).

5 S. J. Zweben, Nucl. Fusion, 29, 825 (1989).

6 R. K. Fisher, D. C. Pace, M. Garc ́ıa-Mun ̃oz, W. W. Heidbrink, C. M. Muscatello, M. A.Van Zeeland, and Y. B. Zhu, Rev. Sci. Instrum., this issue (2010).

7 M. García-Munñoz, Fast Response Scintillator Based Detector for MHD Induced Energetic Ion Losses in ASDEX Upgrade, Ph.D. thesis, Ludwig-Maximillian-University of Munich (2006).

8 W. W. Heidbrink and G. J. Sadler, Nucl. Fusion, 34, 535 (1994).

9 W. W. Heidbrink, M. Murakami, J. M. Park, C. C. Petty, M. A. V. Zeeland, J. H. Yu, and G. R. McKee, Plasma Phys. Cont. Fusion, 51, 125001 (32pp) (2009).

10 A. Werner, A. Weller, and D. S. Darrow (W7-AS Team), Rev. Sci. Instrum., 72, 780 (2001).

11 S. J. Zweben, R. L. Boivin, M. Diesso, S. Hayes, H. W. Hendel, H. Park, and J. D. Strachan, Nucl. Fusion, 30, 1551 (1990).

12 J. Felt, C. W. Barnes, R. E. Chrien, S. A. Cohen, W. W. Heidbrink, D. Manos, and S. Zweben, Rev. Sci. Instrum., 61, 3262 (1990).

13 M. A. V. Zeeland, W. W. Heidbrink, and J. H. Yu, Plasma Phys. Cont. Fusion, 51, 055001 (2009).

14 M. A. V. Zeeland, J. H. Yu, N. H. Brooks, W. W. Heidbrink, K. H. Burrell, R. J. Groebner, A. W. Hyatt, T. C. Luce, N. Pablant, W. M. Solomon, and M. R. Wade, Plasma Phys. Cont. Fusion, 52, 045006 (2010).

15 R. K. Fisher and W. W. Heidbrink, private communication (2010).

16 http://w3.pppl.gov/transp/.

17 W. W. Heidbrink, K. H. Burrell, Y. Luo, N. A. Pablant, and E. Ruskov, Plasma Phys. Cont. Fusion, 46, 1855 (2004).

18 R. B. White and M. S. Chance, Phys. Fluids, 27, 2455 (1984).


text:
## Visualizing group structure, part 2: prime vs. composite, CRT

Some time ago I’ve generated colored addition/multiplication tables in order to visualize group structure. My idea was to compare extension fields of same order with different reduction polynomials, and to compare elliptic curve groups with groups of integers modulo a prime ($\mathbb{Z}_p$). However, as pointed out by an attentive reader, I’ve messed up claiming that the latter group is used by RSA. It is not, it’s used for e.g. DSA, while RSA uses a composite modulus: the product of two prime numbers.

So, how do $\mathbb{Z}_p^*$ and $\mathbb{Z}_n^*$ compare?

## Understanding the Montgomery reduction algorithm

The Montgomery reduction algorithm finds the remainder of a division. Many cryptographic schemes work with numbers modulo a prime. When you have to multiply two numbers with e.g. 128 bits each, first you multiply them the usual way (there are many techniques for this) to obtain a 256-bit (“double precision”) number. Then you need to reduce this result modulo the prime you’re working with, that is, compute the remainder of the division of this number over the prime.

You can compute the remainder of a division with the “schoolbook” technique everyone learns in school, but that is expensive and requires divisions, with are costly in many platforms (some microcontrollers don’t even have a division instruction). Montgomery reduction only needs a division by a powers of the integer size, which are cheap for computers.

Here I’ll try to explain how it works, in an informal approach. For detailed proofs of its correctness, check e.g. the chapter 14 of the Handbook of Applied Cryptography or the original paper.

## Understanding the extended Euclidean algorithm

The Euclidean algorithm finds the greatest common divisor of two numbers a and b. There is an extended version of it that also finds two numbers x and y such that ax + by = gcd(a,b). This is useful when searching for modular multiplicative inverses.

The algorithm is simple, but I’ve never bothered to study why and how it works (a shame, really, but sometimes you have to postpone the understanding of some basic things in order to go on…). Finally I’ve decide to put some thought on it and came up with this (this is not a proof; it’s just some intuitive thinking to grasp the inner workings of the algorithm).

## The Frobenius endomorphism with finite fields

The Frobenius endomorphism is defined as:

$\Phi(x)=x^p$

where p is the characteristic of the ring you’re working with. Simple, right?

If you’re working with a field with prime order, then Frobenius is actually the identity map. Since the order of the multiplicative subgroup is p, when you raise to the power of p you get back to x due to Fermat’s little theorem. Things get more interesting when you’re working with a extension field (i.e. a field which order is a prime power).

I’m studying pairings for my master’s degree and the Frobenius endomorphism appears all the time in their computation. For example, you need to do a “final exponentation” which can be split in multiple exponentiations, and some of them are to the power of p. This is good because powering to p is “easy” due to Frobenius, or at least all the papers I read said so. But for a while I couldn’t see why, and that’s the reason I’m posting this. It’s really easy; it’s just not that obvious to see why.

format: plain


text:
# Analyse et Estimations Spectrales des Processus alpha-Stables non-Stationnaires

Abstract : In this work a new spectral representation of a symmetric alpha-stable processes is introduced. It is based on a covariation pseudo-additivity and Morse-Transue's integral with respect to a bimesure built by using pseudo-additivity property. This representation, specific to S$\alpha$S processes, is analogous to the covariance of second order processes. On the other hand, it generalizes the representation established for stochastic integrals with respect to symmetric alpha-stable process of independent increments. We provide a classification of non-stationary harmonizable processes; this classification is based on the bimesure structure. In particular, we defined and investigated periodically covariated processes. To simulate and build this unusual class, a new decomposition in the Lepage's type series was derived. Finally, to apply this results in practical situations, a nonparametric estimation of spectral densities are discussed. In particular, in the case of periodically covariated processes, an almost sure convergent estimators was derived under the strong mixing condition.
Keywords :
Document type :
Theses
Domain :

Cited literature [93 references]

https://tel.archives-ouvertes.fr/tel-00138027
Contributor : Nourddine Azzaoui <>
Submitted on : Friday, March 23, 2007 - 9:58:20 AM
Last modification on : Friday, June 8, 2018 - 2:50:07 PM
Long-term archiving on : Wednesday, April 7, 2010 - 12:26:20 AM

### Identifiers

• HAL Id : tel-00138027, version 1

### Citation

Nourddine Azzaoui. Analyse et Estimations Spectrales des Processus alpha-Stables non-Stationnaires. Mathématiques [math]. Université de Bourgogne, 2006. Français. ⟨tel-00138027⟩

Record views


text:
# Talk:Law of Large Numbers

## The Law of Large Numbers is a Counterexample to the Theory of Evolution

You can't apply the Law of Large Numbers to a time series with a trend. That's just bad math, not a counterexample! AugustO 20:11, 14 March 2012 (EDT)

The Theory of Evolution, as it is commonly taught, does claim that some new species arose due to random fluctuations.
Man. This is so wrong I don't even know where to start. So I'm not going to because I'll get 90/10'ed out the door. It's like an infinite manifold of wrongness. Just know this, you are applying probability theory -a theory you only partially understand- to evolution, a theory you completely don't understand. --JoshuaB 20:48, 14 March 2012 (EDT)

I will explain why I believe that the law of large numbers is not a good (and probably, to be honest, misleading) counterexample to evolution: Evolutionists would argue that the hypotheses of the law of large numbers (that the random variables are independent and identically distributed) are not satisfied. I understand that the concept of i.i.d. is technical and difficult to explain, but it is nevertheless essential to the theorem. As an example, take the sample space {H,T} corresponding to flipping a fair coin once, and for each positive integer i, let Xi equal 1 if the outcome is H and 0 if the outcome is T. In other words, if the outcome is H, then $X_1 = X_2 = \cdots = 1$, and if the outcome is T, then $X_1 = X_2 = \cdots =0$. Note that $X_1, X_2, \ldots$ are all Bernoulli random variables with parameter $p=\frac{1}{2}$, so they are identically distributed. However, it is clear that the law of large numbers does not hold, as $\frac{X_1 + \cdots + X_n}{n}$ is always either 1 or 0. Therefore, independence is an essential hypothesis. In general, time series are not independent (imagine the Dow Jones index where the closing values are always independent and seeing the index go from 13000 one day to 175 the next!).

Random variables must be functions to the real numbers, so it is ambiguous what the statement "populations of species can randomly drift away from their 'mean'" is intended to mean without a quantification. Nevertheless, using height as a characteristic to measure for the sake of argument, it is clear why the law of large numbers does not hold. If we observe the height of a randomly selected member of a population each year, the observations are random variables. Nevertheless, evolutionists would provide two explanations for why the law of large numbers does not hold in this experiment. First, evolutionists would argue that factors like genetic drift allow for the events of one time period to affect the height distribution of a population in future time periods. Second, evolutionists would suggest that trends in random height suggest precisely the conclusion that the distribution of population heights is changing with each year, indicating that the random variables are not identically distributed. This suggests precisely the conclusion that the population is changing over time. By the way, looking at the statement of the weak law of large numbers, it is clear that if the random variables are not identically distributed (especially if they do not have the same mean), then the "mean" μ in the statement of the theorem is completely meaningless, mathematically. GregG 23:06, 14 March 2012 (EDT)

Folks, if it's so obvious that the Law of Large Numbers does not disprove the theory of random genetic drift -- which is central to the theory of evolution -- then it should be easy to explain in a few sentences free of jargon. Right?--Andy Schlafly 23:17, 14 March 2012 (EDT)
I'll give it a try. The law of large numbers requires the sample observations (such as heights) to come from the same distribution. Trends are seen in the heights over time. Evolutionists would argue that this may suggest that the distribution of heights in the population (and thus the population) is, in fact, changing over time (which would make the law of large numbers inapplicable to these observations). GregG 23:24, 14 March 2012 (EDT)
Andy, you ever hear of something called a "one-way hash function"? It's a cryptographic (or loosely mathematical) term for something that's easy to solve in one direction, but a real pain to solve in reverse. Sort of like cubing versus finding the cube route. Anyway, you're laying out a one-way hash argument. Your statement is simple, but the disproof would require more effort than I'm willing to expend. But in brief, the human race may have a mean height, weight, skin tone... or whatever. If you take measurements at random intervals you will find that the mean is gradually changing, not that populations are gravitating back towards the original mean. And what do we call a change over time? --JoshuaB 23:33, 14 March 2012
How about this for a short explanation. Microevolution (which has been observed to exist in the wild) relies on genetic drift. Since genetic drift it known to happen in microevolution the law of truly large numbers is either false, or it does not apply. --HHB 18:15, 15 March 2012 (EDT)

Hello. It is very easy. Law of large numbers requires that $X_1,X_2,\dots$ are independent (i.e. every finite subset of them is independent). Yet, a child has usually similar properties to an adult. Therefore Xi + 1 is not independent of Xi. It does not mean they are perfectly correlated - a child might sometimes be different from its parent. But they are definitely not independent, and therefore you cannot use the law. Using a mathematical theorem when assumptions are not fully satisfied will easily give you absurd conclusions - think what happens if you to use Pythagorean theorem in an acute triangle. --Cipe 15:54, 17 March 2012 (EDT)

The Law of Large Numbers establishes that populations revert to their averages over time. Children of extraordinarly bright or athletic parents are, on average, not so extraordinary. Nothing said above disproves this logical truth. Darwin and other founders of evolution were weak in mathematics and probability, and their reliance on random genetic drift is nonsensical as illustrated by the Law of Large Numbers.--Andy Schlafly 00:36, 18 March 2012 (EDT)
Genetic Drift wasn't described until the mid-1900s. How can Darwin have been reliant on it when proposing his theory? --RedGoliath 11:58, 18 March 2012 (GMT)
OK, fine: the other Darwinists who relied on random genetic drift (presumably to try to fit the evidence to Darwin's theory) "were weak in mathematics and probability, and their reliance on random genetic drift is nonsensical as illustrated by the Law of Large Numbers."--Andy Schlafly 10:58, 18 March 2012 (EDT)
Andy, please consider teaching a course on mathematics and probability (or science in general), explaining systematically and in detail where lame-stream science goes wrong. I admit that I am confused right now, having been indoctrinated by liberal science classes all my life, and would enroll immediately. We need the arguments to fight Darwinism effectively! Think about how we, your students, could act as multipliers! I am sure that you would do much better than the Question Evolution campaign, which I admit I am not a fan of. --FrederickT3 14:06, 18 March 2012 (EDT)
When I did teach (offline) a science class and pointed out the many flaws in the theory of evolution, one family asked me for additional copies of an inexpensive course book entitled "Evolution Cruncher." He then passed the book out to his fellow scientists at work, and it opened their eyes to all the lies they had been taught in school. There were astounded ... and grateful. My own experience in waking up to the lies taught to me in school was similar.--Andy Schlafly 15:03, 18 March 2012 (EDT)
"Children of extraordinarly bright or athletic parents are, on average, not so extraordinary." Yes. But I think that they are on average better than children of very weak people. And this is enough to show that properties of children and their parents are not independent. If they were independent, a child of two athletes would have the same distribution as child of two physically feeble people. As another example, genetic diseases exist, and a child of ill parents has larger chances to be ill as well.
Do you accept microevolution? I think your interpretation of law of large numbers disproves also microevolution. Regards, --Cipe 19:40, 18 March 2012 (EDT)
No, I don't think microevolution entails random genetic drift. Perhaps you could define the term - if it means "evolution" as that term is traditionally understood, then it is not true for the same reasons evolution is not.--Andy Schlafly 21:09, 18 March 2012 (EDT)
How does microevolution happen if not for genetic drift? --HHB 21:35, 19 March 2012 (EDT)


text:
Forum:A Database Of Signatures Of Selection In The 1000 Genomes Dataset
7
33
Entering edit mode
8.4 years ago

The 1000 Genomes Selection Browser is a database of Signatures of Selection in the Human Genome, based on the 1000 Genomes Phase I data. It is freely accessible at http://hsb.upf.edu/

The browser, based on a custom UCSC Genome Browser installment, allows to easily navigate the genome and visualize regions that are candidate for having been involved in an event of selection in any of the African, European, or Asian populations. The data can also be easily downloaded for further analysis here.

Our browser includes a total of 17 tests for selection. For each test of selection, we provide a raw score, plus a ranked score which compares each position to the rest of the genome.

1. Tajima’s D (Tajima, 1989): Comparison of estimates of the number of segregating sites and the mean pairwise difference between sequences.

2. CLR (Nielsen et al., 2005). Multilocus Composite Likelihood Ratio Test. Read more about the CLR

3. Fay and Wu’s H (Fay & Wu, 2000): Comparison of the number of derived segregating sites at low and high frequencies and the number of variants at intermediate frequencies.

4. Fu and Li’s F* (Fu, 1997): Comparison of the number of singleton mutations and the mean pairwise difference between sequences.

5. Fu and Li’s D* (Fu, 1997): Comparison of the number of singleton mutations and the total number of nucleotide variants.

6. R2 (Ramos-Onsins and Rozas. 2002) Comparison of the difference between the number of singletons per sequence and the average number of nucleotide differences.

7. XP-EHH (Sabeti et al., 2007): Cross-population extended haplotype homozygosity.

8. Delta iHH (Voight et al., 2006, Grossman et al., 2010): difference between two integrated haplotype homozygosity scores.

9. iHS (Voight et al., 2006): log ratio between two integrated haplotype homozygosity scores.

10. EHH average (Sabeti et al., 2002): Extended halotype homozygosity; weighted average for all core haplotypes of the position at which the haplotype homozygosity decays to <=0.5.

11. Wall’s B (Wall, 2000): Counts the number of pairs of adjacent segregating sites that are congruent (if the subset of the data consisting of the two sites contains only two different haplotypes)

12. Wall’s Q (Wall, 2000): Adds the number of partitions (two disjoint subsets whose union is the set of individuals in the sample) induced by congruent pairs to Wall’s B.

13. Fu’s Fs (Fu, 1997): Based on Ewens’ sampling distribution, taking into account the number of different haplotypes in the sample.

14. Dh (Nei, 1987): Summary statistic based on the number of different haplotypes in the sample

15. Fst (Weir and Cockerham, 1984) : global and pairwise

16. delta DAF: difference of Derived allele frequencies between 2 populations.

17. XP-CLR (Chen et al., 2010): Multilocus allele frequency differentiation between two populations.

The database has been published in the NAR Database issue 2014:

Pybus M, Dall'olio GM, Luisi P, Uzkudun M, Carreño-Torres A, Pavlidis P,
Laayouni H, Bertranpetit J, Engelken J. 1000 Genomes Selection Browser 1.0: a
genome browser dedicated to signatures of natural selection in modern humans.
Nucleic Acids Res. 2014 Jan 1;42(1):D903-9. doi: 10.1093/nar/gkt1188. Epub 2013
Nov 25. PubMed PMID: 24275494. Available at http://nar.oxfordjournals.org/content/42/D1/D903.short

For completeness we also also link dbPSHP, a database of curated publications about positive selection in different human populations, which also presents the results of 15 tests for positive selection.

1000genomes selection human Forum • 13k views
1
Entering edit mode

Cool resource and nice post describing it!

1
Entering edit mode
8.4 years ago
DG 7.3k

Awesome! I can already think of some interesting things I'd like to test out with this data!

0
Entering edit mode

I am glad that you liked it :-) Feel free to ask any question you may have, to me or in the website.

1
Entering edit mode
8.4 years ago
Rubal7 ▴ 820

Great resource!

1
Entering edit mode
7.6 years ago
yfwangbm ▴ 10

Hi Giovanni, it is a great job. And I check the databases and tried to download the data for iHS score, but some question I am not quite clear. 1. Why the score here are all positive? 2. this is unstandardised or normalized iHS score, and how to do the normalization? In addition, I tried to find the corresponding genetic distance for 1000 genome variants, I saw you it was mentioned in the paper, so how to add the genetic map?

0
Entering edit mode

iHS scores are usually given as absolute values, hence all positives. The negative or positive value that this statistics can give will also depend on the equation used. On the original Voight et al (2006) paper, negative values indicated selection at derived alleles for instance. Also unstardardised iHS values are largely useless, they should always be corrected by the allele frequencies, standardised iHS values are usually reported.

0
Entering edit mode

From the supplemental information: Raw scores from ΔiHH, iHS and XP-EHH were standardized in bins of derived allele frequency (step size of 0.05) using the respective genome-wide distribution for each statistic to capture signal from ancestral SNPs that have hitchhiked to high frequency along with a selected derived variant, absolute standardized iHS scores were chosen as the end result (24).

1
Entering edit mode
6.8 years ago

I'm having trouble dumping CEU vs CHB XP-EHH. The tables are limited to a chromosome?

Also, I really dig the boosting.

1
Entering edit mode

Hi Zev,

are you downloading the file from the Table Browser? I think there is a limit on the number of rows that can be downloaded from there. For example I downloaded the whole file, and towards the end I see an error message saying "Reached output limit of 100000 data values".

The best way to get the data is to download them from this folder. The files contain both the scores and the log(pvalue).

0
Entering edit mode

perfect. thank you very much.

0
Entering edit mode

One last question, these data are hg19? I ask because I know the original xpehh was hg18.

1
Entering edit mode

Yes, everything is hg19. Feel free to ask as many questions you need ;-)

0
Entering edit mode

well, since you offered. The "p-values" for the CEU-YRI are not bounded by zero and one. Are they Z-scores? I'm trying to get the joint probability of XP-EHH and DN/DS.

Thanks.

2
Entering edit mode

Hi Zev,

the p-values are simply the -log10 of the fraction of SNPs with an higher score. For example in R, using dplyr:

> xpehh = read.table('XPEHH_CEU_vs_CHB.whole_genome.pvalues', header=T, stringsAsFactors=F, colClasses=c('character','integer', 'numeric', 'numeric', 'numeric'))
> xpehh %>%
arrange(desc(score)) %>%   # Sort SNPs by XPEHH score (descending)
mutate(
rank=row_number(),           # number of SNPs with higher scores
rank.perc=rank/n(),          # fraction of SNPs with higher score
rank.log=-log10(rank.perc)   # P-value
)
snpID chromosome position    score   pvalue  rank    rank.perc rank.log
(chr)      (int)    (dbl)    (dbl)    (dbl) (int)        (dbl)    (dbl)
1  rs116972803         15 48377866 8.018417 7.133374     1 7.355728e-08 7.133374
2   rs77517214         15 48377764 8.018099 6.832344     2 1.471146e-07 6.832344
3   rs75870250         15 48376241 7.942488 6.656253     3 2.206718e-07 6.656253
4  rs150960840         15 48379200 7.925932 6.531314     4 2.942291e-07 6.531314

So, I guess that yes, our p-values could be actually called Z-scores, sorry about the confusion :-)

0
Entering edit mode

Giovanni M Dall'Olio I've computed genome-wide iHS for the phase III One Thousand genomes project. Any interest in adding the data to the browser? It only took thousands of CPU hours ;-).

0
Entering edit mode

Hi Zev, I think it would be amazing! Let me ask back to my colleagues at UPF to see how it can be done.

0
Entering edit mode

Hey there, Any word on the phase III iHS values?

1
Entering edit mode
6.6 years ago
Krisr ▴ 470

Hi,

Great resource, thanks!

I have a quick question. Is there a way to determine an arbitrary FDR, say of 2%, or 2.5%, or 5% (instead of the default 1% in the downloads) for the boosting results? Or, are there other values/methods to lessen relax the significance thresholds derived from these datasets? So if the CEU Complete boosting threshold at 1% FDR is 0.40199. What would it be at 2.5% FDR. Would this require rerunning the analysis, or can a post threshold be determined. Thanks again for this resource!

0
Entering edit mode
6.8 years ago
Pierre ▴ 500

Glad that you dig the boosting.
About your question, I just tried it and could visualize all chromosomes. What problem do you face exactly? Is it with track visualization or tables?

Cheers

0
Entering edit mode

The viewing is fine. I'm trying to export the genome-wide XPEHH for CEU_VS_CHB. Every time I download the table it only has chr1.

0
Entering edit mode
6.1 years ago
mwhart • 0

Hi, Giovanni. Thanks this is a great tool. I'm using it to look at some unlinked SNPs in genes with epistatic interactions. One of the SNPs is rs2906999; in hg19 it should be at chr7:76069811. But in several tests focused on the interval around that SNP (iHS, Fst) that coordinate does not appear among the sites with a test statistic. That site is polymorphic in the 1000 Genomes phase 1 data, and has a high minor allele frequency, so I expected it to show up in the test results (the other SNPs I am analyzing do appear in the test results).

I am having trouble figuring out where that one missing SNP might be. Can you help me figure that out? I realize that some rare polymorphisms were filtered out in developing the database, but these are common polymorphisms. Thanks for any help or suggestions (and I hope you are still monitoring this Biostars thread).

Cheers!


text:
# Start a new discussion

## Not signed in

Want to take part in these discussions? Sign in if you have an account, or apply for one below

## Discussion Tag Cloud

Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.

• CommentRowNumber1.
• CommentAuthorUrs
• CommentTimeDec 10th 2015
• (edited Dec 10th 2015)

I am touching various entries related to equivariant stable homotopy theory, adding basics from the literature. For instance I briefly added to G-spectrum the basic definition via indexing on a universe, and added the statement of the equivariant stable Whitehead theorem, cross-linked with the relevant bits at equivariant homotopy theory, etc. I have also been expanding a little more at RO(G)-grading and cross-linked more with old material at equivariant cohomology. Tried to make the link between RO(G)-grading and equivariant suspension isomorphism more explicit.

Just in case you are watching the logs and are wondering. I am not announcing every single edit, unless there is anything noteworthy.

• CommentRowNumber2.
• CommentAuthorUrs
• CommentTimeSep 14th 2018


text:
Find all School-related info fast with the new School-Specific MBA Forum

 It is currently 31 May 2016, 03:36

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# A new commercial radio station in Greenfield plans

Author Message
TAGS:

### Hide Tags

Intern
Joined: 06 May 2013
Posts: 14
Location: United States
GMAT 1: 700 Q49 V36
Followers: 0

Kudos [?]: 7 [0], given: 2

### Show Tags

29 Jan 2014, 22:02
1
This post was
BOOKMARKED
00:00

Difficulty:

(N/A)

Question Stats:

97% (02:15) correct 3% (01:44) wrong based on 55 sessions

### HideShow timer Statistics

A new commercial radio station in Greenfield plans to play songs that were popular hits fifteen to twenty-five years ago. It hopes in this way to attract an audience made up mainly of people between thirty-five and forty-five years old and thereby to have a strong market appeal to advertisers.

Each of the following, if true, strengthens the prospects that the radio station's plan will succeed EXCEPT:

(A) People tend to remain very fond of the music that they heard when they were in their teens and early twenties.

(B) In a number of cities demographically similar to Greenfield, radio stations that play recordings of popular music from fifteen to twenty-five years ago have succeeded commercially.

(C) People in the thirty-five- to forty-five-year-old age group are more likely to listen to the radio for news than for music.

(D) The thirty-five- to forty-five-year-old age group is one in which people tend to have comparatively high levels of income and are involved in making household purchases.

(E) Among the few radio stations in the Greenfield area, there is none that plays music from this particular period for more than a few hours per week.

Hi.

Please explain how choice E strengthens the conclusion.
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 6585
Location: Pune, India
Followers: 1796

Kudos [?]: 10816 [1] , given: 213

### Show Tags

29 Jan 2014, 22:21
1
KUDOS
Expert's post
phammanhhiep wrote:
A new commercial radio station in Greenfield plans to play songs that were popular hits fifteen to twenty-five years ago. It hopes in this way to attract an audience made up mainly of people between thirty-five and forty-five years old and thereby to have a strong market appeal to advertisers.

Each of the following, if true, strengthens the prospects that the radio station's plan will succeed EXCEPT:

(A) People tend to remain very fond of the music that they heard when they were in their teens and early twenties.

(B) In a number of cities demographically similar to Greenfield, radio stations that play recordings of popular music from fifteen to twenty-five years ago have succeeded commercially.

(C) People in the thirty-five- to forty-five-year-old age group are more likely to listen to the radio for news than for music.

(D) The thirty-five- to forty-five-year-old age group is one in which people tend to have comparatively high levels of income and are involved in making household purchases.

(E) Among the few radio stations in the Greenfield area, there is none that plays music from this particular period for more than a few hours per week.

Hi.

Please explain how choice E strengthens the conclusion.

Let's analyze the given argument:

A new station plans to play songs that were popular 15-25 years ago.
It hopes to attract people between 35-45 years
It hopes to have a strong market appeal to advertisers.

There are a number of assumptions (the term is used loosely here) the author of the argument is working on... First of all, he is assuming that people would like to hear the hits of their youth. They will be attracted to this channel which plays the hits of their time. It is also assuming that others do not cater sufficiently to this segment and hence this new channel will be able to attract people. Another assumption is that if they are able to attract 35-45 yr olds, advertisers will be pleased i.e. the 35-45 yr olds are the decision makers of many products advertised on the radio.
If our option provides any one of these premises given above, it will strengthen our argument.
(A), (B), (D) and (E) strengthen the argument.

(B) strengthens by saying that the same plan has been tried at other similar places and has succeeded. This strengthens our argument that it might succeed here as well. Note that we only need to strengthen it, not prove it beyond doubt. Sure, if it has succeeded at other places, it MAY not succeed here but it does strengthen our belief in the plan.

(E) strengthens it by saying that other channels do not cater to this segment much. Hence the possibility of this channel attracting people is higher. It is providing a service to people which they would like and others are not providing. Hence the chances of success increase. That's all we want to do - INCREASE the chances of success.

(C) does not strengthen it and hence is the answer.
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for $199 Veritas Prep Reviews Intern Joined: 04 Dec 2011 Posts: 29 Followers: 0 Kudos [?]: 8 [0], given: 6 Re: A new commercial radio station in Greenfield plans [#permalink] ### Show Tags 06 Feb 2014, 20:52 Hi Mam, How D supports?Can you please explain. Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 6585 Location: Pune, India Followers: 1796 Kudos [?]: 10816 [1] , given: 213 Re: A new commercial radio station in Greenfield plans [#permalink] ### Show Tags 07 Feb 2014, 06:25 1 This post received KUDOS Expert's post sanjeebpanda wrote: Hi Mam, How D supports?Can you please explain. An argument gives us the following: A new station plans to play songs that were popular 15-25 years ago. It hopes to attract people between 35-45 years It hopes to have a strong market appeal to advertisers. What will make this argument stronger? The argument is assuming that if the station is able to attract people between 35-45 years, it will have a strong appeal to advertisers. Why is that so? This will be so if the 35-45 years old people actually are decision makers the products advertised i.e. they decide whether they/their family will buy the products. Hence (D) will make this argument stronger. _________________ Karishma Veritas Prep | GMAT Instructor My Blog Get started with Veritas Prep GMAT On Demand for$199

Veritas Prep Reviews

GMAT Club Legend
Joined: 01 Oct 2013
Posts: 7714
Followers: 713

Kudos [?]: 144 [0], given: 0

### Show Tags

30 Jan 2016, 11:59
Hello from the GMAT Club VerbalBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
Intern
Joined: 12 Nov 2014
Posts: 19
Followers: 1

Kudos [?]: 0 [0], given: 486

### Show Tags

30 Jan 2016, 12:04
I choose D, because I thought C would kind of strengthen. As 35-45 only hear news because there is no music played of their type. So when radio station would start playing then they will start listening. I kind of didn't like D either but went with D.
Intern
Joined: 17 Oct 2015
Posts: 33
Followers: 0

Kudos [?]: 2 [0], given: 433

### Show Tags

31 Jan 2016, 11:38
chetan2u, could you please edit the question and include the OA?

phammanhhiep wrote:
A new commercial radio station in Greenfield plans to play songs that were popular hits fifteen to twenty-five years ago. It hopes in this way to attract an audience made up mainly of people between thirty-five and forty-five years old and thereby to have a strong market appeal to advertisers.

Each of the following, if true, strengthens the prospects that the radio station's plan will succeed EXCEPT:

(A) People tend to remain very fond of the music that they heard when they were in their teens and early twenties.

(B) In a number of cities demographically similar to Greenfield, radio stations that play recordings of popular music from fifteen to twenty-five years ago have succeeded commercially.

(C) People in the thirty-five- to forty-five-year-old age group are more likely to listen to the radio for news than for music.

(D) The thirty-five- to forty-five-year-old age group is one in which people tend to have comparatively high levels of income and are involved in making household purchases.

(E) Among the few radio stations in the Greenfield area, there is none that plays music from this particular period for more than a few hours per week.

Hi.

Please explain how choice E strengthens the conclusion.
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 6585
Location: Pune, India
Followers: 1796

Kudos [?]: 10816 [0], given: 213

### Show Tags

31 Jan 2016, 20:57
Expert's post
alice7 wrote:
I choose D, because I thought C would kind of strengthen. As 35-45 only hear news because there is no music played of their type. So when radio station would start playing then they will start listening. I kind of didn't like D either but went with D.

Actually, option (C) tells you that 35-45 yr olds prefer to listen to radio for news, not music - it is a choice they make. Whether their choice will change when the new music channel will arrive, we don't know. Hence, (C) does not strengthen the argument.
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for \$199

Veritas Prep Reviews

Re: A new commercial radio station in Greenfield plans   [#permalink] 31 Jan 2016, 20:57
Similar topics Replies Last post
Similar
Topics:
5 Revision Project: A new commercial radio station in Greenfield 6 03 Feb 2015, 07:22
2 A new commercial radio station in Greenfield plans to play 8 29 Dec 2012, 00:11
13 Radio Stations with radio data system (RDS) technolodgy 35 16 Jun 2008, 04:18
1 Radio stations with radio data system (RDS) technology 6 10 Nov 2006, 20:49
Radio stations with radio data system (RDS) technology 5 22 Sep 2006, 09:05
Display posts from previous: Sort by


text:
plotting_positions¶

class reliability.Probability_plotting.plotting_positions

Calculates the plotting positions for plotting on probability paper.

Parameters: failures (array, list) – The failure data. Must have at least 1 element. right_censored (array, list, optional) – The right censored failure data. Optional input. Default = None. a (float, int, optional) – The heuristic constant for plotting positions of the form (k-a)/(n+1-2a) where k is the rank and n is the number of points. Optional input. Default is a = 0.3 which is the median rank method (same as the default in Minitab and Reliasoft). Must be in the range 0 to 1. For more heuristics, see: https://en.wikipedia.org/wiki/Q%E2%80%93Q_plot#Heuristics (array(x),array(y)) (tuple) – a tuple of two arrays. The arrays provide the x and y plotting positions. The x array will match the failures parameter while the y array will be the empirical estimate of the CDF at each of the failures.

Notes

This function is primarily used by the probability plotting functions. The order of the input data is preserved (not sorted).


text:
# Wikipedia:Reference desk/Archives/Science/2013 March 6

Science desk
< March 5 << Feb | March | Apr >> March 7 >
Welcome to the Wikipedia Science Reference Desk Archives
The page you are currently viewing is an archive page. While you can leave answers for any questions shown below, please ask new questions on one of the current reference desk pages.

# March 6

## Silent Supernovae

Is it right to say that when a star goes supernova, it is an acoustically silent event, even if one could (hypothetically) witness it from a close distance? And because sound cannot travel through space, this would also apply to events such as Gamma Ray bursts, and even the Big Bang itself, correct?Honeyman2010 (talk) 04:50, 6 March 2013 (UTC)

This seems to be a common question. Sound can and does travel through space, as it is not a complete vacuum. However, due to it being a pretty good vacuum, the sound propagated is not what human ears could detect, even if the human could function in that vaccuum. You would need absolutely immense ears. Go to the top of this page, and try "sound in space" and similar strings in the Search Reference Desk archives field, and you'll be entertained for quite a while. Wickwack 120.145.35.223 (talk) 05:17, 6 March 2013 (UTC)
And, when the particles blasted off during the supernova hit you, they would make quite a racket, indeed. StuRat (talk) 05:29, 6 March 2013 (UTC)
Not to mention, vapourise you in the process. I mean planets in orbit have a difficult time surviving such an event, what chance have a mere human? If our sun were to go supernova, Jupiter would be stripped entirely of its atmosphere and be left a metallic white-hot cinder only just larger than earth. The outer gas giants beyond should fare better. Plasmic Physics (talk) 08:06, 6 March 2013 (UTC)
If you were in that star system, sure. But if you were far enough away, you're spaceship would just get noisy when the particles hit. StuRat (talk) 16:30, 6 March 2013 (UTC)
Or do it the Native American way: touch your ear to the dark side of a planet. The chances of survival are still somewhat low... ;) - ¡Ouch! (hurt me / more pain) 08:04, 8 March 2013 (UTC)
As for the Big Bang, yes, you would hear it, but it would not sound like a bang. It would sound more like a very, very ,very loud, high pitched hum, which would decay both in volume and pitch in an exponential way. You'd hear it because space was not as vacuous as it is today. Plasmic Physics (talk) 07:24, 6 March 2013 (UTC)
After this much time, it has decayed to such an extent, that it is not discernable from background noise. The sound would initially have been audible for millions of years. Plasmic Physics (talk) 07:28, 6 March 2013 (UTC)
Considering a gamma ray burst, would it not create secondary sound as it irradiates the listening device, creating a large amount of static. Plasmic Physics (talk) 08:09, 6 March 2013 (UTC)

## Big Bang and light

Is it true that all matter can be converted into light? If so, is the coverse true? If that is also true, could the primeval atom have been pure light in a metastable state, which spontaneously condensed into matter, such as particle-antiparticle production from gamma radiation. How many electron volts would a single photon have to represent to contain the total universal energy and all its mass. Plasmic Physics (talk) 07:51, 6 March 2013 (UTC) "Let there be light." Plasmic Physics (talk) 07:54, 6 March 2013 (UTC)

If matter fell into a black hole, or quantum tunneled into a black hole, the hole may then decay into Hawking Radiation, which may be mostly photons. So the future of matter may the formation of cool photons. You will have to say how big is the universe to get an answer to the total energy in the universe. As the universe ages the visible universe expands, so we do not actually know the size or mass of the universe. Graeme Bartlett (talk) 09:33, 6 March 2013 (UTC)
Well, the most obvious problem is that there's no such thing as light before electroweak symmetry breaking. If you believe inflation, the energy of all the particles in the universe came from the energy of the field that caused inflation, which is similar to the present-day Higgs field or dark energy. So they did come from pure energy, in a way.
According to Google the density of the universe is around 5·10−30 g/cm³, and the radius of the visible universe is about 46 billion light years, and it's spatially flat, so the total mass in the visible universe is around (5·10−30 g/cm³) (4/3) π (46 Gly)³ ≈ 1090 eV/c². But that's just the part we can see. -- BenRG (talk) 22:13, 6 March 2013 (UTC)
What would happen to such an energetic photon if released into our universe today? Plasmic Physics (talk) 08:14, 7 March 2013 (UTC)

## Some questions about the Universe

I have some questions about the Universe.

1. Is the Universe finite or infinite? Universe is the sum total of all matter and energy. The unknown part of the Universe, i.e. the part that extends beyond the observable universe, may be finite or may be infinite. What are the current opinion regarding this?

2. If the Universe is finite, then it must have edges or boundaries. I want to know what is beyond that boundary? Is that pure vacuum?

3. If the Universe is infinite, then why is it said that the Universe is flat. An infinite object is not supposed to have any shape.

4. According to the Big Bang theory, the Universe, at its beginning (the very early Universe), was rapidly expanding and cooling, and then expanded gradually. I want to know is there any explanation how did this very early Universe originate? --PlanetEditor (talk) 13:31, 6 March 2013 (UTC)

(Q4) If I'm not wrong, Stephen Hawking said something like at the very very early stages of the Universe, it (the Universe) was just like a very small balck hole. As time does not exist in a black hole, there was no time before the Big Bang. There is no cause or origination for the Universe because there was not time for a cause to exist in. It just "popped up" like a proton, which IS possible according to some elaborate Science laws. ☯ Bonkers The Clown \(^_^)/ Nonsensical Babble ☯ 13:44, 6 March 2013 (UTC)
If you're talking about the stuff in A Brief History of Time, that was never mainstream; it was just a description of his own (highly speculative) research. -- BenRG (talk) 21:53, 6 March 2013 (UTC)
re Q2: finite does not imply edges or boundaries. The surface area of the earth is finite, for instance, but has no edges, (according to modern theories). Imagine a 4th dimensional sphere analog that we're on the 3d surface of. Now imagine that sphere expanding, and now you have the expanding universe we experience, where there is no particular center to the expansion which is uniform all over. Gzuckier (talk) 18:15, 6 March 2013 (UTC)
(Q1) According to the Shape of the universe article, the infinite flat model is currently the most popular of the models of the universe that fit the currently available data. Red Act (talk) 21:54, 6 March 2013 (UTC)
1. Nobody knows. If you asked cosmologists to guess, I suspect a majority of them would say infinite, but that doesn't mean much. 2. As Gzuckier said, it doesn't imply there's a boundary, but there could be a boundary. There would be nothing outside of it, which is not the same as vacuum. Light can't propagate through nothing. 3. An infinitely large object can have a shape. For example an infinite plane and an infinite paraboloid have different shapes. 4. Nobody knows, but if you asked cosmologists to guess, most of them would guess some kind of inflation. -- BenRG (talk) 21:53, 6 March 2013 (UTC)

Thank you everyone. --PlanetEditor (talk) 10:12, 7 March 2013 (UTC)

However I would have liked a bit more explanation of Q4. The religionists use this issue as an excuse to prove the existence of God. --PlanetEditor (talk) 10:20, 7 March 2013 (UTC)
If you haven't seen it already, Big_Bang#Speculative_physics_beyond_Big_Bang_theory. You really are stuck in a bind, there. Either you have something exist before the Big Bang, and then have to explain where that came from; or you have a theory such as Hawking's where a beginning is (allegedly) not required. Neither class of theories is likely to satisfy. Someguy1221 (talk) 10:45, 7 March 2013 (UTC)
Hawkins' explanation that time is compressed inside a black hole - and that's (effectively) what the early universe was like - may or may not be correct, but at least it offers one possible explanation for the "Origin of Everything" question that doesn't result in an infinite regress. The idea that this is an argument for the existence of God is a silly one because one only has to ask the question "So...what created God then?" to demonstrate that adding a supernatural being as the creator of the universe doesn't help to answer the ultimate question If the early universe was "caused" by something, then you're in the infinite regress of asking what that cause was and what was the cause of the cause and so forth. Hawkins' approach is elegant in that by pointing out that time inside a black hole is crunched into nothingness and therefore there is no "Before" in the case of the big bang - it was there for a literally infinity amount of time. He might not be right - but at least there are possible "ultimate origin" explanations that do not require gods and other mystical junk to make them work. SteveBaker (talk) 22:04, 7 March 2013 (UTC)
Thank you Someguy and Steve. --PlanetEditor (talk) 09:07, 8 March 2013 (UTC)

## Statistics of hysterectomies

Why are hysterectomies so common in women above tha age of 50 if its such a major operation? Clover345 (talk) 14:48, 6 March 2013 (UTC)

I think the article on Hysterectomy actually does a good job of going into some of the issues. The major downside of the surgery (aside from risk) is loss of the ability to bear children, which is usually a moot point by the age of 50. The upshot to the surgery, such as benefiting cancer risk or severe pain, will often outweigh that downside, although for sure there are a lot of these being performed. ~ Amory (utc) 15:24, 6 March 2013 (UTC)
From personal experience in the UK, if there is no good reason to remove a uterus then they won't. Fibroids or adenomyosis stop responding to oestrogen as less and less is being produced, and shrink of their own accord. I'd like to see up to date statistics on this. --TammyMoet (talk) 16:23, 6 March 2013 (UTC)

## Prove relation

Given ${\displaystyle P(x,t)=|\Psi (x,t)|^{2}}$,

and ${\displaystyle J(x,t)=-{\frac {ih}{2m}}\left(\Psi ^{*}(x,t){\frac {\partial }{\partial x}}\Psi (x,t)-\Psi (x,t){\frac {\partial }{\partial x}}\Psi ^{*}(x,t)\right)}$

I want to prove the following relation

${\displaystyle {\frac {\partial }{\partial t}}P(x,t)+{\frac {\partial }{\partial x}}J(x,t)=0}$

I denote complex conjugate with asterisk. I believe I can think of examples of functions Psi for which it's not true. Here is my working so far anyway.

${\displaystyle ={\frac {\partial }{\partial t}}|\Psi (x,t)|^{2}-{\frac {ih}{2m}}{\frac {\partial }{\partial x}}\left(\Psi ^{*}(x,t){\frac {\partial }{\partial x}}\Psi (x,t)-\Psi (x,t){\frac {\partial }{\partial x}}\Psi ^{*}(x,t)\right)}$

${\displaystyle ={\frac {\partial }{\partial t}}\left(\Psi (x,t)\Psi ^{*}(x,t)\right)-{\frac {ih}{2m}}{\frac {\partial }{\partial x}}\left(\Psi ^{*}(x,t){\frac {\partial }{\partial x}}\Psi (x,t)-\Psi (x,t){\frac {\partial }{\partial x}}\Psi ^{*}(x,t)\right)}$

${\displaystyle =\Psi ^{*}(x,t){\frac {\partial }{\partial t}}\Psi (x,t)+\Psi (x,t){\frac {\partial }{\partial t}}\Psi ^{*}(x,t)-{\frac {ih}{2m}}{\frac {\partial }{\partial x}}\left(\Psi ^{*}(x,t){\frac {\partial }{\partial x}}\Psi (x,t)-\Psi (x,t){\frac {\partial }{\partial x}}\Psi ^{*}(x,t)\right)}$

It's not clear at all that this is zero to me.

150.203.115.98 (talk) 15:19, 6 March 2013 (UTC)

maybe this is a homework question, so we should be wary. I don't know much about this area, but I'd try integrating J first. Let me know if I'm out on a limb. IBE (talk) 17:19, 6 March 2013 (UTC)
You should differentiate the expression in parentheses (by x) then you should substitute derivatives by time from the 1D Schrodinger equation in free space. After that everything will be obvious. Ruslik_Zero 18:15, 6 March 2013 (UTC)

## Reverse osmosis semipermeable membranes

Semi-permeable_membrane says that membranes used in reverse osmosis are made of polyimide while Thin-film composite membrane says that they are made of polyamide.

What's correct?--Gauravjuvekar (talk) 16:42, 6 March 2013 (UTC)

Looking through a number of suppliers of such membranes, most just describe them as "Thin Film", but Dow's datasheet states that their membranes are polyamide. On the other hand, this patent is for a polyimide membrane. I think it's safe to say that both _can_ be used. Tevildo (talk) 22:36, 6 March 2013 (UTC)
This site lists lots of polyamide membranes, a few "Thin Film" membranes, and a few cellulose acetate membranes. Polyamide seems to be the most common material. Tevildo (talk) 22:45, 6 March 2013 (UTC)

## Meteor fragments and aircraft

There is LOTS of discussion about meteors/comets/etc impacting the Earth, the History of the big ones, etc. HOWEVER, I heard somewhere that 40 TONS of material impact on the Earth's atmosphere daily. ALL discussions I've read say something like "most" of this material burns up in the Earth's atmosphere, leaving particles "smaller than grains of sand" etc. When most folks read this phrase, they say "no problem". HOWEVER, I would imagine that a particle not much bigger than a grain of sand could have a disastrous effect should it strike the wing of a flying aircraft. How come there aren't more recorded (or hypothesized) cases of aircraft being affected by meteor fragments? Thanks, Jack Murray p.s.- This is a WORLDWIDE question p.p.s. - How do I know what to search on in Wikipedia to find out if anyone addressed this? — Preceding unsigned comment added by Jaqmur (talkcontribs) 17:14, 6 March 2013 (UTC)

Regarding your last question, "How do I know what to search on in Wikipedia to find out if anyone addressed this?", knowing what search terms to use to finds the answer to a question is known as Google-fu, and it's a skill you learn through practice. If you meant where do you search, there's a search bar at the top of every reference desk page where you can search the desk archives. 90.193.232.228 (talk) 17:43, 6 March 2013 (UTC)
Particles the size of a grain of sand will rapidly decelerate to free-fall speed, due to air resistance. A grain of sand at that speed is not a problem for an aircraft. However, many such grains of sand are, and we get those by flying through a volcanic plume. StuRat (talk) 18:00, 6 March 2013 (UTC)
Just in case you're still struggling with Google, I had a go myself. I typed aircraft "meteor strike" into the search bar (the words within the "quote marks" means that Google will only show an exact match for that phrase). I found a data analysis blog called Revolutions - How much of a threat are meteors to aviation? Using some complicated calculations, the author states that the chance of a meteor strike on a single aircraft are "about 1 in a billion, give or take". However, given the number of aircraft using the sky, "there's about a 4.3% chance of a meteor strike on at least one airliner in the next 20 years". Alansplodge (talk) 18:16, 6 March 2013 (UTC)
It's called terminal velocity, not "free fall speed". μηδείς (talk) 23:28, 6 March 2013 (UTC)
"Free fall speed" is a synonym for "terminal velocity". StuRat (talk) 05:08, 7 March 2013 (UTC)
Aircraft regularly encounter hail stones. Hail is capable of stripping paint and abrading windshields so pilots use their weather radars to avoid heavy rain and hail. Despite that, damage more serious than stripped paint and abraded windshields occurs occasionally. A meteor fragment the size of a grain of sand, falling at its terminal velocity, is nowhere near as hazardous to an aircraft as a hail stone falling at its terminal velocity. Dolphin (t) 00:14, 7 March 2013 (UTC)
How do we know the fragments would be at terminal velocity? Objects only reach terminal velocity in free fall; a meteor may strike the earth at many orders of magnitude faster than its terminal free-fall velocity, and it may take some distance to slow down to terminal velocity. A meteor could be moving quite fast when it strikes the plane; there's no requirement that it be moving as slow as terminal velocity. --Jayron32 06:05, 7 March 2013 (UTC)
The OP has prefaced the question with most of this material burns up in the Earth's atmosphere, leaving particles smaller than grains of sand. The question excludes particles much larger than grains of sand. Meteors disintegrate in the Earth's upper atmosphere. By the time a fragment the size of a grain of sand falls to the altitude at which aircraft operate, a long time will have elapsed and it will be at its terminal velocity. True, the geological record shows evidence of very large meteors having reached the Earth's surface, leaving large craters, but the question doesn't extend to consideration of such large meteors. Dolphin (t) 06:17, 7 March 2013 (UTC)
Gotcha. Yeah, in that case a grain of sand at its terminal velocity is still a grain of sand at terminal velocity, and carries very little energy, certainly not enough to damage anything on an aircraft. The origin if the sand itself is irrelevant. If the sand were really hauling ass, then maybe, but sand in free fall is still sand in free fall, even if it came from space. --Jayron32 06:23, 7 March 2013 (UTC)
I interpreted the OP to be asking about a high-speed aircraft striking a particle that has no horizontal velocity and almost zero vertical velocity. Dolphin (t) 06:37, 7 March 2013 (UTC)
Re your last question. I read that as "How do I find out if anyone has answered this very question I'm asking here?". You just search for this page by its name, Wikipedia:Reference desk/Science, using the search function. Then scroll down to find the right thread. -- Jack of Oz [Talk] 00:41, 7 March 2013 (UTC)
From playing around with numbers at this impact simulator, it looks like any meteor smaller than about 50 cm in diameter is going to be moving at its terminal velocity by the time it reaches the typical airplane. For a piece of sand, that terminal velocity is a few miles per hour, so most of the impact speed will come from the airplane's movement, not the rock's movement. --Carnildo (talk) 01:56, 7 March 2013 (UTC)

Thanks for all the info. Jaqmur (talk) 14:35, 7 March 2013 (UTC)

The thing to bear in mind when thinking about meteors and such is that if you halve the diameter of a roughly symmetrical object, you reduce it's cross-sectional area by a factor of four and it's mass by a factor of eight. So the aerodynamic drag forces on small particles (which depends on their cross-sectional area and not on their mass) are much larger compared to their initial kinetic energy (which depends on their mass) than for big rocks. So these sand-grain sized meteors slow down to their terminal velocity very quickly - where a mountain-sized meteor hardly slows down at all.
Do a mental experiment - take a rock the size of your fist and imagine how far you can throw it - 20 feet maybe? How far do you think you could throw a grain of sand? A couple of feet maybe? Both objects leave your hand at about the same speed just as large and small meteors are entering the atmosphere at about the same speed.
So for meteor dust, it's going to be moving at terminal velocity - which is when the gravitational force (which is proportional to its mass) balances the drag force (which is proportional to it's cross-sectional area) - with very tiny mass and less tiny cross-section, it's moving very slowly. But the hailstone is obviously moving a lot faster because the ratio of mass to cross-sectional area is much higher than for the dust. More importantly, since kinetic energy (which is what goes into damaging the plane) is proportional to the SQUARE of the speed multiplied by the mass - these low-mass, low-speed sand-grains don't have enough energy to do much damage...and as Carnildo pointed out - the speed of the airplane is by far the biggest contributor in terms of relative velocity.
Hitting meteor dust is much less damaging than hitting even a raindrop or a snowflake...it's about as bad as hitting the smoke particles from the airplane a mile or two ahead of you.
SteveBaker (talk) 13:21, 8 March 2013 (UTC)

## Film problems

Not sure if this should go here or on the entertainment desk, but...

While watching The Aztecs (Doctor Who), I noticed two problems:

1. In episode 1, the image jerks upwards for a fraction of a second and then returns to normal.

2. There is considerable background noise, sounding a lot like rain.

Why do these effects occur? Whoop whoop pull up Bitching Betty | Averted crashes 20:19, 6 March 2013 (UTC)

1) This sounds like a problem I've sometimes seen when projecting a film. Presumably it was copied into a digital format, but, if that process involves using a film projector, and the operator is rather careless, this could be the result. Or, perhaps that happened when filming. Were they doing any hand cranking: [1] ? (This techniques was sometimes used to change the recording speed of the film, manually.)
2) This might be an original issue with the sound recording. Wind noise can sound like that, if they don't cram the microphone inside a dead cat to prevent it. British TV of that era had notoriously low production values, so it wouldn't surprise me if this happened. StuRat (talk) 20:34, 6 March 2013 (UTC)
1) Then why is the image stable for the entire episode with the exception of that momentary jerk? Whoop whoop pull up Bitching Betty | Averted crashes 20:39, 6 March 2013 (UTC)
1) Probably a torn sprocket hole or two messed up the timing, then it was able to recover. This type of thing happens more often than you might think. It's just that in a Hollywood production, as bad as the plots are, they do an extraordinary job of fixing any production quality problems like this which crop up. Watching foreign films and TV, I've been surprised to see microphones repeatedly in the frame, characters calling each other by the wrong names (possibly by the actor's name), and worse mistakes, all making it onto the final film. In a Hollywood production, this type of thing ends up on the blooper reel. StuRat (talk) 20:43, 6 March 2013 (UTC)
A 1964 Dr. Who? I wouldn't be surprised to see one of the crew wandering around the back of the frame eating a sandwich. Gzuckier (talk) 21:03, 6 March 2013 (UTC)
In Terrence Malick's The Thin Red Line, if you watch the DVD copy on a computer, you can see a crew member standing about staring at the camera holding a clipboard on the far edge of the frame in one of the love scenes. Can't be seen on a TV. – Kerαunoςcopiagalaxies 03:15, 7 March 2013 (UTC)
<coughs> No period after "Dr". See Dr. Who (the Peter Cushing Dalek movies). Tevildo (talk) 22:53, 6 March 2013 (UTC)
Our article on negative cutting doesn't say anything, but sometimes a negative cutter will foobar a splice. Projectionists have been known to cut out single frames of their favorite shots, using cheap splicing tape or cement to piece the film back together. Also damage happens to film, sometimes a single frame or sprocket can become damaged and either cut or, if unnoticed, left in the film. If the Dr Who episode was made from a print, rather than a negative, this could be what happened, though a solid jump up and down probably means there was a splice. (The thickness of the cement/tape jerks the film about in the telecine or projector.) By the way, regarding projectionists cutting out frames, there shouldn't be a problem with sound sync anymore (it's been a while) since I think sound CDs are now synchronized to code printed on the actual film edge. In the old days, though, if someone cut out a splice, you would hear a pop/jump in the sound about a second later. – Kerαunoςcopiagalaxies 03:15, 7 March 2013 (UTC)
Did the BBC actually spend the money in 1964 to shoot Dr who on film? It would have been cheaper to shoot on video tape. The first programs were lost, and The Aztecs is from several months later. I just watched it on Netflix, and it had the look of videotape. Perhaps it got converted to film at some point for distribution and rebroadcast. Doctor Who (series 1) says that the series only transitioned from videotape to film in the 2005 relaunch, which they perversely call "Series 1." Edison (talk) 04:23, 7 March 2013 (UTC)
Our article on that episode makes it clear that it was first recorded using videotape, then converted to film so that the tape could be reused (because video tape was extremely expensive at that time), then later converted back to a video format using the VidFIRE process. Looie496 (talk) 06:22, 7 March 2013 (UTC)

## Genetic disorders that come out due to inbreeding.

The article on the Amish states

Since almost all Amish descend from about 200 18th-century founders, genetic disorders that come out due to inbreeding exist in more isolated districts (an example of the founder effect).

I have always thought that inbreeding, while it does increase the incidence of certain disorders, does not create new ones by itself. Am I correct? If not, can anyone of you provide examples of genetic disorders that come out due to inbreeding? --190.19.83.213 (talk) 02:19, 7 March 2013 (UTC)

You are correct, but I think you are misreading that quotation. It is basically saying the same thing you did. StuRat (talk) 02:29, 7 March 2013 (UTC)

"Come out" is a misleading term. By far the most common type of genetic disease associated with inbreeding is autosomal recessive enzyme or other protein deficiencies. If the carrier (heterozygote) rate in the US population for an autosomal recessive mutation that causes blue hair disease in homozygotes is 1%, but the carrier rate in an intermarrying subpopulation, like Amish, or Ashkenazi Jews, or Yupik Eskimos, is 6%, then the likelihood of a carrier marrying another carrier is 6x higher, and the rate of homozygous blue hair births in that population will be 36x higher than in the general US population. alteripse (talk) 02:41, 7 March 2013 (UTC)

## Jumping from a airplane with wingtip sails

Cardinals on their way to the conclave. PrimeHunter (talk) 15:35, 6 March 2013 (UTC)

This picture is taken from the humanities.

My question is:

Is it safer to jump out from an airplane with wingtip sails because of reduced wingtip vortices? -- Toytoy (talk) 03:18, 7 March 2013 (UTC)

Maybe if the chutes are going to open immediately, as they seem to in the pic. On the other hand, if the chutes wait a bit to open, then they will be clear of the vortices before opening. StuRat (talk) 03:23, 7 March 2013 (UTC)
Our article, Wake turbulence, doesn't mention hazards to parachutes, but does say that vortices are generated when the wings are creating lift. I suspect that the pilot would take this into account when people are jumping out of his or her aircraft, but perhaps another editor has some experience in this field. Note that the RAF has been dropping paratroopers since 1941, but has never possessed one with wingtip devices until it acquired some C-17s in 2002. Alansplodge (talk) 18:01, 7 March 2013 (UTC)
On large aircraft such as the one pictured here, the wingtip vortices are too far outboard in any case to affect parachutists jumping out of that aircraft. FWIW 24.23.196.85 (talk) 04:57, 9 March 2013 (UTC)


text:
# Gauge forces and internal symmetries

1. Oct 31, 2013

### kye

gauge forces like electromagnetic, weak and strong forces have local gauge symmetry invariance in terms of u(1), su(2), su(3) because the em for example cant have the same global phase or global symmetry at all points of space. but is there no corresponding gauge forces for global symmetry?

2. Oct 31, 2013

### dauto

No, global symmetries have no gauge bosons or gauge forces associated with them. For instance, there is not gauge boson associated with baryon number conservation but there is a boson associated with electric charge conservation - the photon. That's because baryon conservation is a consequence from a global symmetry while charge conservation is a consequence from a local symmetry.

3. Oct 31, 2013

### kye

1. does global symmetry only have to do with conservations? what other conservations are there beside baryon conservation in global symmetry?

2. quantum is supposed to be random and even nonlocal. why does it have go obey local symmetry of phase for example when global simultaneous change of phase may not be problem since quantum mechanics is fundamentally nonlocal?

4. Nov 1, 2013

### K^2

Each symmetry has a conserved charge. There are four symmetries and four charges. U(1)xSU(2) gives you conserved electric and weak charges. SU(3) gives you conserved color-charge. And if you throw in a bit of GR and consider Poincare symmetry, you end up with stress-energy tensor as another conserved charge. The later is a generalization of energy, momentum, and angular momentum conservation from classical theory.

And Quantum Mechanics is actually very local. You shouldn't think of "delocalization" as particles starting to behave as diffuse clouds. They still behave as point objects. These point objects simply have ability to take all the possible paths at once, and therefore, interact at many different places at once. But interaction at each location is still strictly local.

5. Nov 1, 2013

### kye

i read the global symmetry is composed of

1. parity
2. charge conjugation
3. time reversal
4. flavor conservation laws - lepton and baryon numbers

are there others?
but you will notice all of them are not fields like em or weak fields. but why is there no global symmetry fields. what laws forbid them?

but in contextuality and bells theorem which discoung local realism, bill hobba for example in the other thread said particles dont exist before measurement, meaning the other entangled pair for example dont exist before measurement. maybe you subscribe to realism compared to others?

6. Nov 1, 2013

### K^2

Parity, charge, and time symmetries, individually, are broken. There are PC violations which suggest that T violations also exist. Together, PCT is a valid global symmetry, but since it follows from Poincare symmetry, I would expect it to have the same conservation law.

Flavors aren't strictly conserved either. Baryon and lepton numbers appear to be, but their conservation follows from super symmetry, and there is symmetry breaking there as well. Unfortunately, I know very little about the subject. You can try your luck in high energy section for that.

Because the corresponding force fields result from gauge comparators. If the gauge is global, comparator is unity throughout space, and the connection field vanishes. So you can say that there is a field corresponding to global symmetry, but it's zero everywhere. There is a bit of algebra in here that I'm glossing over. I can run through it if you are comfortable with multi-variable calculus.

7. Nov 2, 2013

### kye

K^2. I searched for "Gauge Comparators" and all references I can find are tire gauge comparators. What is the other name for this in gauge theory that I can find in the net? Anyway. I found this paper by David Gloss "Gauge: Past, Present and Future" and there is a line that mentioned "A local symmetry is much more in keeping with the lessons of field theory and relativity than a postulated global symmetry, which smells of action at a distance.". Now let me go back the quantum entanglement thing. Is quantum correlations or Bell's theorem not related to the global symmetry of Gauge theory? Or Is gauge theory nothing to do with quantum entanglement at all? It is not described by local symmetry nor global symmetry? Why? Hope others can comment too. Thanks.

8. Nov 2, 2013

### kye

Gauge Global Symmetry

I read that global symmetry is composed of

1. parity
2. charge conjugation
3. time reversal
4. flavor conservation laws - lepton and baryon numbers

Why is mass not a global symmetry? are there others global symmetry besides the above? Why them specifically?

I know local symmetry produced the gauge fields like em, electroweak, strong in the form of U(1), SU(2), SU(3)

9. Nov 3, 2013

### vanhees71

Since mass is not conserved within relativistic physics, there's no symmetry related to it.

In non-relativistic physics mass is a central charge of the Galilei group and thus not only conserved but there's also a superselection rule, according to which there are no superpositions of states with different mass. See, e.g.,

http://arxiv.org/abs/quant-ph/9508002

10. Nov 3, 2013

### fzero

Mass is a conserved quantity. The relevant global symmetry in relativistic physics is translation invariance of spacetime: $x^\mu \rightarrow x^\mu + \alpha^\mu$. Under this symmetry, 4-momentum $p_\mu$ (energy and spatial momentum) is conserved. Mass is the length squared of this 4-momentum, $p^\mu p_\mu = m^2$ and is a conserved, Lorentz-invariant quantity.