text:
## CryptoDB

### Paper: An Enhanced One-round Pairing-based Tripartite Authenticated Key Agreement Protocol

Authors: Meng-Hui Lim Sanggon Lee Youngho Park Hoonjae Lee URL: http://eprint.iacr.org/2007/142 Search ePrint Search Google A tripartite authenticated key agreement protocol is generally designed to accommodate the need of three specific entities in communicating over an open network with a shared secret key, which is used to preserve data confidentiality and integrity. Since Joux proposed the first pairing-based one-round tripartite key agreement protocol in 2000, numerous authenticated protocols have been proposed after then. However, most of them have turned out to be flawed due to their inability in achieving some desirable security attributes. In 2005, Lin-Li had identified the weaknesses of Shim's protocol and subsequently proposed their improved scheme by introducing an extra verification process. In this paper, we prove that Lin-Li's improved scheme remains insecure due to its susceptibility to the insider impersonation attack. Based on this, we propose an enhanced scheme which will not only conquer their defects, but also preserves the desired security attributes of a key agreement protocol.
##### BibTeX
@misc{eprint-2007-13424,
title={An Enhanced One-round Pairing-based Tripartite Authenticated Key Agreement Protocol},
booktitle={IACR Eprint archive},
keywords={Tripartite authentication, Key Agreement Protocol, Pairing},
url={http://eprint.iacr.org/2007/142},
note={Not published. meng17121983@yahoo.com 13624 received 20 Apr 2007, last revised 20 Apr 2007},
author={Meng-Hui Lim and Sanggon Lee and Youngho Park and Hoonjae Lee},
year=2007
}


text:
# Revision history of "Logistic map"

• (cur | prev) 09:06, 29 June 2019  . . (359 bytes) (+359). . (Created page with "The logistic map $x \to r x (1 - x)$ with $x \in [0,1] \subset \mathbb{R}$ and $r \in [0,4] \subset \mathbb{R}$ is a simple equation that exh...")

format: plain


text:
# Fourier Transformation integral

1. Jan 19, 2009

### rugapark

I'm trying to integrate a function which is given as

$$F(u)= \int f(x)e^{-2}^{\pi} ^{i} ^{x} ^{u} dx$$

with limits of +ve and -ve infinity

integrating by parts gives me

$$\frac{1}{2} f(x)^{2}e^{-2}^{\pi}^{i}^{x}^{u}-\frac{1}{2} \int f(x)^{2}xe^{-2}^{\pi}^{i}^{x}^{u}dx$$

fisrt off, is the $$i$$ in the equation an imaginary number ( I am pretty sure it is)
and after integration how do I apply the infinite limits, also is my integration correct?

cheers

2. Jan 20, 2009

### Unco

Hi Ruga,

Yes, $$i = \sqrt{-1}$$.

Without knowing what f(x) is, your integral is not correct. In general, $$\int{f(x)} dx$$ will not resemble $$\frac{1}{2}f(x)^2$$ (or do you know that $$f(x) = x$$?), so choosing v' = f(x) in the integration by parts method does not yield $$v = \frac{1}{2}f(x)^2$$.

Could you provide some context (e.g., the complete problem statement) as we may find the requisite expression for f(x) there. If you're just trying to evaluate the integral in full generality, then we're out of luck!


text:
Skip to main content

# Molecular jets and outflows from young stellar objects in Cygnus-X, Auriga, and Cassiopeia

Makin, Sally Victoria (2019) Molecular jets and outflows from young stellar objects in Cygnus-X, Auriga, and Cassiopeia. Doctor of Philosophy (PhD) thesis, University of Kent,. (KAR id:72857)

 PDF Language: English This work is licensed under a Creative Commons Attribution 4.0 International License. Download (10MB) Preview Preview This file may not be suitable for users of assistive technology. Request an accessible format

## Abstract

An unbiased, systematic survey for jets and outflows from young stars has been performed in two distinct and different regions in the Galactic plane. It utilised the 1 - 0 S(1) near-infrared line of molecular hydrogen (H2) to trace shock-excited emission, using data from the UKIRT Widefield Infrared Survey for H2 (UWISH2) survey. A total of 572 outflows were found in the high-mass star forming complex of Cygnus-X, and 98 in the low-mass regions of Auriga and Cassiopeia. Of these outflows found, 84% are entirely new discoveries, and now 40% of all the currently known H2 outflows are a result of the UWISH2 survey. The properties of the outflows were consistently measured and a large statistical sample has been built. Similarities and differences between the outflow populations in the two regions were explored in order to discover which properties are universal and which depend on local factors. In both regions, most outflows are located in isolated

(60%) and not clustered environments, but those from clusters are longer and more luminous. Almost fifty new infrared cluster candidates have also been discovered as a result of this work, and the typical cluster is around 0.5 pc in diameter. About 10% of outflows form crossing pairs of outflows, and 40% of these show signs of precession compared to 20% in the general population. The outflow position angles are in agreement with a homogeneous distribution. Most of the

outflows are driven by protostars (Class 0/I) rather than the more evolved young stellar objects (Class II), as determined using their mid-infrared magnitudes. The typical outflow has a length of < 0.4 pc, and is slightly asymmetric with one lobe around 30% longer than the other. The length distribution follows an exponential behaviour and there appears to be a maximum length. The typical outflow luminosity is faint (1×10$^?3$ Lsolar) and most of the outflows are driven by low

or intermediate-luminosity protostars. The lobe luminosity ratios (the faint lobe over the bright lobe) are highly asymmetric in H2. There is a correlation between the length and luminosity of an outflow, and these do not depend on the evolutionary stage of the driving source. There is also a correlation between the luminosity of the driving source and the outflow luminosity, but the length

distribution does not follow their behaviour. Therefore, the outflow lengths must also, to some extent, be governed by the density distribution of the local environment.

Item Type: Thesis (Doctor of Philosophy (PhD)) Froebrich, Dirk Galactic plane surveys astronomy star formation jets outflows Divisions > Division of Natural Sciences > Physics and Astronomy System Moodle System Moodle 05 Mar 2019 15:30 UTC 03 Sep 2021 14:00 UTC https://kar.kent.ac.uk/id/eprint/72857 (The current URI for this page, for reference purposes)
• Depositors only (login required):


text:
# Set delimiter between short title–year citations in Biblatex

Biblatex provides a \nameyeardelim command for setting the delimiter in name–year citations. I use this as follows to add a comma:

\renewcommand*{\nameyeardelim}{\addcomma\space}

I need to cite some references which have neither an author nor an editor. In this case Biblatex defaults to using the title (or shorttitle) and year, which is fine, except that there doesn't seem to be any way of setting the delimiter. (There's no corresponding \titleyeardelim or \shorttitleyeardelim command.)

Can someone tell me what I need to do so that the following minimal working example produces "(Proceedings of SENSEVAL-3, 2004)" instead of "(Proceedings of SENSEVAL-3 2004)"?

\documentclass{article}

\usepackage[backend=biber,style=authoryear-comp]{biblatex}

\begin{filecontents}{bibliography.bib}
@Proceedings{senseval2004,
title = {Proceedings of SENSEVAL-3, the Third International Workshop on the Evaluation of Systems for the Semantic Analysis of Text},
shorttitle = {Proceedings of SENSEVAL-3},
year = {2004},
}
\end{filecontents}

\begin{document}
\autocite{senseval2004}
\end{document}

You only need

\DeclareDelimFormat{nonameyeardelim}{\addcomma\space}

MWE

\documentclass{article}

\usepackage[backend=biber,style=authoryear-comp]{biblatex}
\begin{filecontents}{\jobname.bib}
@Proceedings{senseval2004,
title = {Proceedings of SENSEVAL-3, the Third International Workshop on the Evaluation of Systems for the Semantic Analysis of Text},
shorttitle = {Proceedings of SENSEVAL-3},
year = {2004},
}
\end{filecontents}

\begin{document}
\autocite{senseval2004,sigfridsson,kant:kpv}
\end{document}

This answer was edited with a much simpler solution for newer biblatex versions. If you are using an ancient version of biblatex and the above does not work for you, consider an update. And if you can't update, have a look at the edit history for a solution that should work with older versions as well.


text:
Tiling rectangles with N pentomino plus rectangles

Also in this series: Tiling rectangles with F pentomino plus rectangles

Tiling rectangles with T pentomino plus rectangles

Tiling rectangles with U pentomino plus rectangles

Tiling rectangles with V pentomino plus rectangles

Tiling rectangles with W pentomino plus rectangles

Tiling rectangles with X pentomino plus rectangles

The goal is to tile rectangles as small as possible with the N pentomino. Of course this is impossible, so we allow the addition of copies of a rectangle. For each rectangle $a\times b$, find the smallest area larger rectangle that copies of $a\times b$ plus at least one N-pentomino will tile. Example shown, with the $1\times 1$, you can tile a $2\times 4$ as follows:

Now we don't need to consider $1\times 1$ any longer as we have found the smallest rectangle tilable with copies of N plus copies of $1\times 1$.

There are at least 22 more solutions. More expected. I tagged it 'computer-puzzle' but you can certainly work some of these out by hand. The larger ones might be a bit challenging.

• My program found another tiling for this one. So now there are thirteen left to find. Should I put hints on these as to the rectangles which have tilings? – theonetruepath Apr 26 '18 at 10:54
• This is identical to mine challenges, however, let it be. I decided not to post them, because they do not have so much solutions or have infinitely many. This one has infinitely many. – Somnium May 7 '18 at 22:14

Here is my (now improved) solution for $2\times3$ rectangles plus N-pentomino(s):

It is a $7\times8$ rectangle, using four N-pentominoes and six $2\times3$ rectangles.

And here is my solution for $2\times5$ rectangles plus N-pentomino(s):

It is a $7\times10$ rectangle, using two N-pentominoes and six $2\times5$ rectangles.

Here are some more solutions, though for these I used computer assistance.

$1\times6$ rectangles plus N-pentomino(s):

It is an $8\times13$ rectangle, using 16 N-pentominoes and four $1\times6$ rectangles.

The solutions given by others for $1\times3$ and $1\times5$ generalise to give solutions for $1\times(5k+3)$ rectangles and $1\times 5k$ rectangles.

A $(5k+4)\times(10k+5)$ rectangle can be filled with $2k+1$ N-pentominoes and $10k+5$ rectangles of size $1\times(5k+3)$.
Similarly, a $(5k+1)\times 10k$ rectangle can be filled with $2k$ N-pentominoes and $10k$ rectangles of size $1\times 5k$.

Here is a solution for the $1\times7$ rectangle plus N-pentomino(s), which also generalises in the same way to $1\times(5k+2)$ :

It is an $(5k+3)\times(10k+5)$ rectangle, using $2k+1$ N-pentominoes and $10k+5$ rectangles of size $1\times(5k+2)$ .

There is also a family of solutions for $2\times(10k+7)$ rectangles.

A $(20k+16)\times(20k+15)$ rectangle can be filled with $8k+6$ N-pentominoes and $20k+15$ rectangles of size $2\times(10k+7)$.

• The 2x5 is minimal, but the 2x3 is not. So 12 left to find. – theonetruepath Apr 27 '18 at 0:27
• @theonetruepath I have now improved the $2\times3$ solution. – Jaap Scherphuis Apr 28 '18 at 7:03
• 2x3 now minimal, as is the 1x6. There is a smaller 1x7. Your 1x3 generalisation to 1x8 (9x15) is minimal too. In fact a very similar design will give you the minimal 1x7 tiling. I'll do a summary at some point. – theonetruepath Apr 29 '18 at 8:19
• Your 2x7 is not minimal either, although it's not far off. – theonetruepath Apr 29 '18 at 8:25
• 1x(5k+2) and 2x(10k+5) should be easily generalizable as well. – phenomist May 8 '18 at 6:51

2x2

This is smallest rectangle with N pentomino and O tetromino.

$8 \times 20$:

2x4

This is smallest rectangle with N pentomino and 2x4 rectangle:

$16 \times 16$:

3x4

This is smallest rectangle with N pentomino and 3x4 rectangle:

$14 \times 16$:

3x5

$16 \times 30$:

In general, there exists solution for each $2 \times n$ rectangle (note that these also give implicit solutions for all $1 \times n$ rectangles):

Generalized solution for $2 \times n$ for odd $n$:
Resulting rectangle will be $2n \times (2 + lcm(5, n))$

Generalized solution for $2 \times n$ for even $n$:
Resulting rectangle will be $(4 + n + kn) \times (2 + n + 2mn)$ where $k \equiv 2n^{-1} \pmod{5}$ and $m \equiv 3n^{-1} \pmod{5}$
This one also solves for odd $n$ because you can join two rectangles to get even length, so for now this is most general solution.

General solution for any rectangle with coprime sides $a \times b, a>1,b>1$:

Resulting rectangle will be $(an + bm) \times (an + bm - 1 + lcm(5, a, b))$ where $n \equiv a^{-1}\pmod{b}$ and $m \equiv b^{-1}\pmod{a}$

This gives $16 \times 30$ solution for $3 \times 5$, $22 \times 126$ solution for $3 \times 7$ and $21 \times 40$ solution for $3 \times 4$

• Those general solutions are really great. – Jaap Scherphuis May 8 '18 at 9:57
• 2x2, 2x4, 3x4 all minimal. Minimality of the generalisations unclear... until my program gets a bit further – theonetruepath May 8 '18 at 12:29
• @theonetruepath Added 3x5, cannot check for minimality for now. Also added very general solution. – Somnium May 9 '18 at 8:19
• Your 3x5 is probably minimal, my program is up to area 456 now and a few more rectangles to check before I can confirm it. Progress is slow at these sizes... I like the general solution for axb with a,b co-prime. – theonetruepath May 9 '18 at 9:40

Here's an attempt for 1x4:

11x5 = 55 squares

and another one for 1x5:

10x6 = 60 squares

and one for 1x9:

14x14 = 196

and one for 1x10, smaller than the generalized 1x5k solution:

12x15 = 180

and one for 1x11; it looks like this sequence is somehow generalizable as well. N has a nice shape, it seems.

13x18 = 234

1x12:

18x16 = 288

Here is the minimal solution for $2 \times 7$, which generalizes to $2 \times (10k + 7)$ and is just a little bit smaller than the one discovered by Jaap:

15x15 = 255 (generalized: $(20k + 15) \times (20k + 15)$)

• Both optimal. My tiling for the 1x4 is slightly different (still a 5x11). Most of these tilings are unique. – theonetruepath Apr 23 '18 at 16:33
• 1x9 and 1x10 both optimal. 1x11 probably optimal... I will have to run my program on that to check, I went only to 10x10 – theonetruepath May 8 '18 at 9:44
• 13x18 for the 1x11 is optimal too. – theonetruepath May 8 '18 at 11:09
• 16x18 for the 1x12 also minimal – theonetruepath May 8 '18 at 12:00

Let's give it a try:

$1 \times 2$

Area: $2 \times 7 = 14$

$1 \times 3$

Area: $4 \times 5 = 20$

• Yup both are minimal. Nice colours! Only 14 to go... – theonetruepath Apr 17 '18 at 8:07

A 4 x 4 area can be tiled by two N pentominos and three 1 x 2 rectangles.

1 1 n n
n n n 2
N N N 2
3 3 N N

A 5 x 5 area can be tiled by two N pentominos and five 1 x 3 rectangles.

1 1 1 n n
2 n n n 5
2 3 3 3 5
2 N N N 5
4 4 4 N N

• [Add spoiler tags please.] Neither of these is optimal. – theonetruepath Apr 17 '18 at 6:24

Since the solutions are so widely spread across the answers, here's an attempt to put them all together in a Community Wiki answer. If somebody has a better way of formatting this inside a spoiler, be my guest.

$1 \times n$

1 x n solution found by, image
1 x 1 2 x 4 = 8 .theonetruepath
1 x 2 2 x 7 = 14 .athin
1 x 3 4 x 5 = 20 .athin
1 x 4 5 x 11 = 55 .Glorfindel
1 x 5 6 x 10 = 60 .Glorfindel
1 x 6 8 x 13 = 104 .Jaap Scherphuis
1 x 7 8 x 15 = 120 .Jaap Scherphuis
1 x 9 14 x 14 = 196 .Glorfindel
1 x 10 12 x 15 = 180 .Glorfindel
1 x 11 13 x 18 = 234 .Glorfindel
1 x 12 16 x 18 = 288 .Glorfindel
1 x 5k 5k+1 x 10k .Jaap Scherphuis
1 x 5k+2 5k+3 x 10k+5 .Jaap Scherphuis
1 x 5k+3 5k+4 x 10k+5 .Jaap Scherphuis

$2 \times n$

2 x n solution found by, image
2 x 2 8 x 20 = 160 .Somnium
2 x 3 7 x 8 = 56 .Jaap Scherphuis
2 x 4 16 x 16 = 256 .Somnium
2 x 5 7 x 10 = 70 .Jaap Scherphuis
2 x 7 15 x 15 = 225 .Glorfindel
2 x 2k see below (*) .Somnium
2 x 2k+1 4k+2 x 2+lcm(5,2k) .Somnium
2 x 10k+7 20k+15 x 20k+15 .Glorfindel

(*): solution size for $2 \times 2k$ is $(4 + 2k + 2lk) \times (2 + 2k + 4mk)$ where $l \equiv 4k^{-1} \pmod{5}$ and $m \equiv 6k^{-1} \pmod{5}$.

$3 \times n$ and others

3 x n solution found by, image
3 x 4 14 x 16 = 224 .Somnium
3 x 5 16 x 30 = 480 .Somnium
a x b (*) see below (*) .Somnium

(*): $a$ and $b$ must be coprime and greater than 1. The solution size is $(an + bm) \times (an + bm - 1 + lcm(5, a, b))$ where $n \equiv a^{-1}\pmod{b}$ and $m \equiv b^{-1}\pmod{a}$.

• The 1x8 is missing, but the smallest solution is the generalized one for 1x5k+3 found by Jaap Scherphuis. – Glorfindel Jun 5 '18 at 21:24
• (I know the alignment doesn't work on mobile; please view this answer in full site mode.) – Glorfindel Jun 5 '18 at 21:32


text:
# Concept of Area

#### definition

Area: The amount of surface enclosed by a closed figure is called its area.

# Area:

• The amount of surface enclosed by a closed figure is called its area.

• A polygon is a plane shape with straight sides. The area of a polygon measures the size of the region enclosed by the polygon.

• It is measured in units squared.

## Area of Regular Shapes

Area of shapes such as circle, triangle, square, rectangle, parallelogram, etc. are the region occupied by them in space. Polygon shape: A polygon is a two-dimensional shape that is formed by straight lines. The examples of polygons are triangles, hexagons and pentagons.

Area of Square

Area of Rectangle

Area of Triangle

## Visualisation of covered Area on the graph:

It is difficult to tell the area of the figure just by looking at the figure.

Place them on a squared paper or graph paper where every square measure 1 cm × 1 cm.

Make an outline of the figure.

Look at the squares enclosed by the figure. Some of them are completely enclosed, some half, some less than half and some more than half.

The area is the number of centimeter squares that are needed to cover it

But there is a small problem: the squares do not always fit exactly into the area you measure. We get over this difficulty by adopting a convention:

• The area of one full square is taken as 1 sq unit. If it is a centimeter

• square sheet, then the area of one full square will be 1 sq cm.

• Ignore portions of the area that are less than half a square.

• If more than half of a square is in a region, just count it as one square.

• If exactly half the square is counted, take its area as 1/2sq unit.

Such a convention gives a fair estimate of the desired area.

 Covered area Number Area estimate (sq. units) (i) Fully-filled squares 101 101 (ii) Half-filled squares 4 4 × 1/2 (iii) More than half-filled squares 21 21 (iv) Less than half-filled squares 23 0

Total area = 101 + 4 × 1/2 + 21 = 1261/2 sq. Units.

#### Example

By counting squares, estimate the area of the figure.

 Covered area Number Area estimate (sq units) (i) Fully-filled squares 11 11 (ii) Half-filled squares 3 3 xx 1/2 (iii) More than half-filled squares 7 7 (iv) Less than half-filled squares 5 0

Total area = 11 + 3 × 1/2 + 7 = 19 1/2 sq units.

#### Example

By counting squares, estimate the area of the figure.

 Covered area Number Area estimate (sq units) (i) Fully-filled squares 1 1 (ii) Half-filled squares - - (iii) More than half-filled squares 7 7 (iv) Less than half-filled squares 9 0

Total area = 1 + 7 = 8 sq units.

If you would like to contribute notes or other learning material, please submit them using the button below.

### Shaalaa.com

Area Part-1 [00:21:56]
S
0%


text:
Página 1 dos resultados de 1988 itens digitais encontrados em 0.009 segundos

## Análise numérica de escoamentos turbulentos não reativos com transferência de calor por convecção e radiação térmica em meios participantes; Numerical analysis of non-reactive turbulent flows with convection and thermal radiation heat transfer in participanting media

Santos, Elizaldo Domingues dos
Tipo: Tese de Doutorado Formato: application/pdf
POR
Relevância na Pesquisa
46.6%
O presente trabalho apresenta um estudo numérico sobre escoamentos turbulentos combinando os mecanismos de transferência de calor por convecção e radiação térmica em meios participantes. Os principais propósitos são obter um melhor entendimento a respeito da relevância das interações Turbulência-Radiação (TRI) em escoamentos turbulentos não reativos, bem como, investigar o efeito da radiação térmica sobre o comportamento transiente, médio e estatístico dos campos térmicos. Para investigar a relevância das interações TRI em escoamentos turbulentos internos, realiza-se uma comparação entre os fluxos temporais médios por convecção e radiação térmica obtidos através da simulação de grandes escalas (LES) e da modelagem clássica da turbulência (RANS) para escoamentos no regime permanente com as seguintes espessuras ópticas: τ0 = 0.01, 0.10, 1.0, 10.0 e 100.0, que representam desde meios opticamente muito finos até meios muito espessos. Para todos os casos, o número de Reynolds baseado na velocidade de fricção e o número de Prandtl são mantidos fixos: Reτ = 180 e Pr = 0.71. A abordagem da turbulência é realizada a partir dos modelos submalha dinâmico de Smagorinsky (DSSGS) e k – ε padrão no âmbito de LES e RANS...

## A Reynolds stress model for turbulent flows of viscoelastic fluids

Resende, P. R.; Pinho, F. T.; Cruz, D. O.
Fonte: Taylor & Francis Ltd Publicador: Taylor & Francis Ltd
Tipo: Artigo de Revista Científica Formato: 1-36
ENG
Relevância na Pesquisa
46.49%
A second-order closure is developed for predicting turbulent flows of viscoelastic fluids described by a modified generalised Newtonian fluid model incorporating a nonlinear viscosity that depends on a strain-hardening Trouton ratio as a means to handle some of the effects of viscoelasticity upon turbulent flows. Its performance is assessed by comparing its predictions for fully developed turbulent pipe flow with experimental data for four different dilute polymeric solutions and also with two sets of direct numerical simulation data for fluids theoretically described by the finitely extensible nonlinear elastic - Peterlin model. The model is based on a Newtonian Reynolds stress closure to predict Newtonian fluid flows, which incorporates low Reynolds number damping functions to properly deal with wall effects and to provide the capability to handle fluid viscoelasticity more effectively. This new turbulence model was able to capture well the drag reduction of various viscoelastic fluids over a wide range of Reynolds numbers and performed better than previously developed models for the same type of constitutive equation, even if the streamwise and wall-normal turbulence intensities were underpredicted.

## Turbulent dispersion via fan-generated flows

Halloran, Siobhan K.; Wexler, Anthony S.; Ristenpart, William D.
Fonte: AIP Publishing LLC Publicador: AIP Publishing LLC
Tipo: Artigo de Revista Científica
EN
Relevância na Pesquisa
46.52%
Turbulent dispersion of passive scalar quantities has been extensively studied in wind tunnel settings, where the flow is carefully conditioned using flow straighteners and grids. Much less is known about turbulent dispersion in the “unconditioned” flows generated by fans that are ubiquitous in indoor environments, despite the importance of these flows to pathogen and contaminant transport. Here, we demonstrate that a point source of scalars released into an airflow generated by an axial fan yields a plume whose width is invariant with respect to the fan speed. The results point toward a useful simplification in modeling of disease and pollution spread via fan-generated flows.

## Numerical investigation of turbulent forced convective flows over a pair of circular cylinders

Santos, Elizaldo Domingues dos; Silva, Fábio de Moraes Vaz da; Acunha Junior, Ivoni Carlos; Galarça, Marcelo Moraes; Isoldi, Liércio André; Rocha, Luiz Alberto Oliveira
Tipo: Artigo de Revista Científica
ENG
Relevância na Pesquisa
56.38%
The present study presents large eddy simulation (LES) of forced convective heat transfer in transient, two-dimensional, incompressible turbulent flows over a pair of cylinders with two different arrangements: 1) with two circular cylinders in tandem (both cylinders are in line with the streamwise direction of the flow, β = 0º) and 2) two side-by-side circular cylinders (where both cylinders are placed transversally to the streamwise direction of the flow, β = 90º). The dynamic Smagorinsky model is employed for the sub-grid treatment. The simulations are based on the finite volume method solution for the conservation equations of mass, momentum and energy. Both simulations are performed with Reynolds and Prandtl numbers of ReD = 22000 and Pr = 0.71, respectively. The results showed that the transient fluid dynamic and thermal patterns are strongly affected by the configuration of circular cylinders. The kind of arrangement led to a difference of nearly 20 % for time-averaged Nusselt number (NuD).

## A numerical study of combined convective and radiative heat transfer in non-reactive turbulent channel flows with several optical thicknesses: a comparison between LES and RANS

Santos, Elizaldo Domingues dos; Isoldi, Liércio André; Petry, Adriane Prisco; França, Francis Henrique Ramos
Tipo: Artigo de Revista Científica
ENG
Relevância na Pesquisa
46.52%
This work presents a numerical study of turbulent channel flows with combined convective and radiative heat transfer in participating media by means of large Eddy simulation and Reynolds averaged Navier–Stokes (RANS) with k–ε model. The main purpose is to evaluate the employment of the traditional modeling (RANS without TRI) for the prediction of time-averaged parameters of turbulent non-reactive flows with convective and radiative heat transfer. All cases are investigated with Re τ = 180, Pr = 0.71 and for various optical thicknesses: τ 0 = 0.01, 0.1, 1.0, 10 and 100. In spite of the consideration of non-relevance of turbulence–radiation interactions for non-reactive turbulent flows, the results shown that for τ 0 ≥10 the employment of RANS with k–ε model led to considerable deviations for the prediction of time-averaged radiative fluxes and divergence of the radiative fluxes. For τ 0 = 100, both models also led to different results for the time-averaged convective fluxes.

## Large eddy simulation of turbulent forced convective flows over a pair of circular cylinders with different arrangements

Santos, Elizaldo Domingues dos; Silva, Fábio de Moraes Vaz da; Acunha Junior, Ivoni Carlos; Galarça, Marcelo Moraes; Isoldi, Liércio André; Rocha, Luiz Alberto Oliveira
Tipo: Conferência ou Objeto de Conferência
ENG
Relevância na Pesquisa
56.38%
The present study presents large eddy simulation (LES) of forced convective heat transfer in transient, twodimensional, incompressible turbulent flows over a pair of cylinders with two different arrangements: 1) with two circular cylinders in tandem (both cylinders are in line with the streamwise direction of the flow, α = 0º) and 2) two side-by-side circular cylinders (where both cylinders are placed transversally to the streamwise direction of the flow, α = 90º). The dynamic Smagorinsky model is employed for the sub-grid treatment. The simulations are based on the finite volume method solution for the conservation equations of mass, momentum and energy. Both simulations are performed with Reynolds and Prandtl numbers of ReD = 22000 and Pr = 0.71, respectively. The results showed that the transient fluid dynamic and thermal patterns are strongly affected by the configuration of circular cylinders. The kind of arrangement led to a difference of nearly 20 % for time-averaged Nusselt number (NuD).

## Finite element analysis of laminar and turbulent flows using LES and subgrid-scale models

Popiolek, Tales Luiz; Awruch, Armando Miguel; Teixeira, Paulo Roberto de Freitas
Tipo: Artigo de Revista Científica
ENG
Relevância na Pesquisa
66.52%
Numerical simulations of laminar and turbulent flows in a lid driven cavity and over a backward-facing step are presented in this work. The main objectives of this research are to know more about the structure of turbulent flows, to identify their three-dimensional characteristic and to study physical effects due to heat transfer. The filtered Navier–Stokes equations are used to simulate large scales, however they are supplemented by subgrid-scale (SGS) models to simulate the energy transfer from large scales toward subgridscales, where this energy will be dissipated by molecular viscosity. Two SGS models are applied: the classical Smagorinsky s model and the Dynamic model for large eddy simulation (LES). Both models are implemented in a three-dimensional finite element code using linear tetrahedral elements. Qualitative and quantitative aspects of two and three-dimensional flows in a lid-driven cavity and over a backward-facing step, using LES, are analyzed comparing numerical and experimental results obtained by other authors.

## Dynamics of large turbulent structures in a steady breaker

Rodríguez-Rodríguez, Javier; Marugán-Cruz, C.; Aliseda, Alberto; Lasheras, Juan C.
Tipo: info:eu-repo/semantics/acceptedVersion; info:eu-repo/semantics/article Formato: application/pdf; text/plain
Relevância na Pesquisa
56.36%
The flow near the leading edge of a steady breaker has been studied experimentally using Bubble Image Velocimetry (BIV) with the aim of characterizing the dynamics of the large eddies responsible for air entrainment. It is well reported in the literature, and confirmed by our measurements of the instantaneous velocity field, that this flow shares some important features with the turbulent shear-layer formed between two parallel semi-infinite streams with different velocities. Namely, the formation of a periodic array of coherent vortices, the constant convective velocity of those vortices, the linear relation between their size and their downstream position and the self-similar structure of both mean velocity profiles and Reynolds shear stresses. Nonetheless, important differences exists between the dynamics of the large eddies in a steady breaker and those in a free shear-layer. Particularly, the convective velocity of these large structures is slower in a steady breaker and, consistent with this, their growth rates are larger. A physical interpretation of these differences is provided together with a discussion of their implications. To support our measurements and conclusions, we present a careful analysis of the accuracy of the BIV technique in turbulent flows with large bubbles; The authors wish to thank Professor Emil J. Hopfinger for his valuable suggestions on the interpretation of the experimental data. This work was supported by the ONR through Grant N00014-05-1-0121 and by the Spanish Ministry of Science (MICINN) through Grant DPI2008-06369

## Mathematical and Numerical Modeling of Turbulent Flows

Vedovoto,João M.; Serfaty,Ricardo; Silveira Neto,Aristeu Da
Tipo: Artigo de Revista Científica Formato: text/html
Relevância na Pesquisa
66.56%
The present work is devoted to the development and implementation of a computational framework to perform numerical simulations of low Mach number turbulent flows over complex geometries. The algorithm under consideration is based on a classical predictor-corrector time integration scheme that employs a projection method for the momentum equations. The domain decomposition strategy is adopted for distributed computing, displaying very satisfactory levels of speed-up and efficiency. The Immersed Boundary Methodology is used to characterize the presence of a complex geometry. Such method demands two separate grids: An Eulerian, where the transport equations are solved with a Finite Volume, second order discretization and a Lagrangian domain, represented by a non-structured shell grid representing the immersed geometry. The in-house code developed was fully verified by the Method of Manufactured Solu- tions, in both Eulerian and Lagrangian domains. The capabilities of the resulting computational framework are illustrated on four distinct cases: a turbulent jet, the Poiseuille flow, as a matter of validation of the implemented Immersed Boundary methodology, the flow over a sphere covering a wide range of Reynolds numbers, and finally, with the intention of demonstrating the applicability of Large Eddy Simulations - LES - in an industrial problem...

## Direct Numerical Simulation of Compressible and Incompressible Wall Bounded Turbulent Flows with Pressure Gradients

Wei, Liang
Fonte: Quens University Publicador: Quens University
Tipo: Tese de Doutorado Formato: 3555645 bytes; application/pdf
EN; EN
Relevância na Pesquisa
56.56%
This thesis is focused on direct numerical simulation (DNS) of compressible and incompressible fully developed and developing turbulent flows between isothermal walls using a discontinuous Galerkin method (DGM). Three cases (Ma = 0.2, 0.7 and 1.5) of DNS of turbulent channel flows between isothermal walls with Re ~ 2800, based on bulk velocity and half channel width, have been carried out. It is found that a power law seems to scale mean streamwise velocity with Ma slightly better than the more usual log-law. Inner and outer scaling of second-order and higher-order statistics have been analyzed. The linkage between the pressure gradient and vorticity flux on the wall has been theoretically derived and confirmed and they are highly correlated very close to the wall. The correlation coefficients are influenced by Ma, and viscosity when Ma is high. The near-wall spanwise streak spacing increases with Ma. Isosurfaces of the second invariant of the velocity gradient tensor are more sparsely distributed and elongated as Ma increases. DNS of turbulent isothermal-wall bounded flow subjected to favourable and adverse pressure gradient (FPG, APG) at Ma ~ 0.2 and Reref ~ 428000, based on the inlet bulk velocity and the streamwise length of the bottom wall...

## Validation of the Lattice Boltzmann Method for Direct Numerical Simulation of Wall-Bounded Turbulent Flows

BESPALKO, DUSTIN JOHN
Fonte: Quens University Publicador: Quens University
EN; EN
Relevância na Pesquisa
46.56%
In this work, the lattice Boltzmann method (LBM) was validated for direct numerical simulation (DNS) of wall-bounded turbulent flows. The LBM is a discrete-particle-based method that numerically solves the Boltzmann equation as opposed to conventional DNS methods that are based on the Navier-Stokes (NS) equations. The advantages of the LBM are its simple implementation, its ability to handle complex geometries, and its scalability on modern high-performance computers. An LBM code was developed and used to simulate fully-developed turbulent channel flow. In order to validate the results, the turbulence statistics were compared to those calculated from a conventional NS-based finite difference (FD) simulation. In the present study, special care was taken to make sure the computational domains for LBM and FD simulations were the same. Similar validation studies in the literature have used LBM simulations with smaller computational domains in order to reduce the computational cost. However, reducing the size of the computational domain affects the turbulence statistics and confounds the results of the validation. The turbulence statistics calculated from the LBM and FD simulations were found to agree qualitatively; however, there were several significant deviations...

## Um esquema \"upwind\" para leis de conservação e sua aplicação na simulação de escoamentos incompressíveis 2D e 3D laminares e turbulentos com superfícies livres; The \"upwind\" scheme to the conservation laws and their application in simulation of 2D and 3D incompressible laminar and turbulent flows with free surfaces

Kurokawa, Fernando Akira
Fonte: Biblioteca Digitais de Teses e Dissertações da USP Publicador: Biblioteca Digitais de Teses e Dissertações da USP
Tipo: Tese de Doutorado Formato: application/pdf
Relevância na Pesquisa
56.34%
Apesar de as EDPS que modelam leis de conservação e problemas em dinâmica dos fluídos serem bem estabelecidas, suas soluções numéricas continuam ainda desafiadoras. Em particular, há dois desafios associados à computação e ao entendimento desses problemas: um deles é a formação de descontinuidades (choques) e o outro é o fenômeno turbulência. Ambos os desafios podem ser atribuídos ao tratamento dos termos advectivos não lineares nessas equações de transporte. Dentro deste canário, esta tese apresenta o estudo do desenvolvimento de um novo esquema \"upwind\" de alta resolução e sua associação com modelagem da turbulência. O desempenho do esquema é investigado nas soluções da equação de advecção 1D com dados iniciais descontínuos e de problemas de Riemann 1D para as equações de Burgers, Euler e águas rasas. Além disso, são apresentados resultados numéricos de escoamentos incompressíveis 2D e 3D no regime laminar a altos números de Reynolds. O novo esquema é então associado à modelagem \'capa\' - \'epsilon\' da turbulência para a simulação numérica de escoamentos incompressíveis turbulentos 2D e 3D com superfícies livres móveis. Aplicação, verificação e validação dos métodos numéricos são também fornecidas; Althought the PDEs that model conservation laws and fluid dynamics problems are well established...

## Feasible domain of Walker's unsteady wall-layer model for the velocity profile in turbulent flows

MIKHAILOV,MIKHAIL D.; FREIRE,ATILA P. SILVA
Tipo: Artigo de Revista Científica Formato: text/html
Relevância na Pesquisa
56.3%
The present work studies, in detail, the unsteady wall-layer model of Walker et al. (1989, AIAA J., 27, 140 – 149) for the velocity profile in turbulent flows. Two new terms are included in the transcendental non-linear system of equations that is used to determine the three main model parameters. The mathematical and physical feasible domains of the model are determined as a function of the non-dimensional pressure gradient parameter (p+). An explicit parameterization is presented for the average period between bursts (), the origin of time () and the integration constant of the time dependent equation (A0) in terms of p+. In the present procedure, all working systems of differential equations are transformed, resulting in a very fast computational procedure that can be used to develop real-time flow simulators.

## Irreversibility and small-scale generation in 3D turbulent flows

Pumir, Alain; Xu, Haitao; Grauer, Rainer; Bodenschatz, Eberhard
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
46.56%
In three-dimensional turbulent flows energy is supplied at large scales and cascades down to the smallest scales where viscosity dominates. The flux of energy through scales implies the generation of small scales from larger ones, which is the fundamental reason for the irreversibility of the dynamics of turbulent flows. As we showed recently, this irreversibility manifests itself by an asymmetry of the probability distribution of the instantaneous power $p$ of the forces acting on fluid elements. In particular, the third moment of $p$ was found to be negative. Yet, a physical connection between the irreversibility manifested in the distribution of $p$ and the energy flux or small-scale generation in turbulence has not been established. Here, with analytical calculations and support from numerical simulations of fully developed turbulence, we connect the asymmetry in the power distribution, {\it i.e.}, the negative value of $\langle p^3 \rangle$, to the generation of small scales, or more precisely, to the amplification (stretching) of vorticity in turbulent flows. Our result is the first step towards a quantitative understanding of the origin of the irreversibility observed at the level of individual Lagrangian trajectories in turbulent flows.; Comment: 13 pages...

## Macroscopic effects of the spectral structure in turbulent flows

Tran, Tuan; Chakraborty, Pinaki; Guttenberg, Nicholas; Prescott, Alisia; Kellay, Hamid; Goldburg, Walter; Goldenfeld, Nigel; Gioia, Gustavo
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
46.67%
Two aspects of turbulent flows have been the subject of extensive, split research efforts: macroscopic properties, such as the frictional drag experienced by a flow past a wall, and the turbulent spectrum. The turbulent spectrum may be said to represent the fabric of a turbulent state; in practice it is a power law of exponent \alpha (the "spectral exponent") that gives the revolving velocity of a turbulent fluctuation (or "eddy") of size s as a function of s. The link, if any, between macroscopic properties and the turbulent spectrum remains missing. Might it be found by contrasting the frictional drag in flows with differing types of spectra? Here we perform unprecedented measurements of the frictional drag in soap-film flows, where the spectral exponent \alpha = 3 and compare the results with the frictional drag in pipe flows, where the spectral exponent \alpha = 5/3. For moderate values of the Reynolds number Re (a measure of the strength of the turbulence), we find that in soap-film flows the frictional drag scales as Re^{-1/2}, whereas in pipe flows the frictional drag scales as Re^{-1/4} . Each of these scalings may be predicted from the attendant value of \alpha by using a new theory, in which the frictional drag is explicitly linked to the turbulent spectrum. Our work indicates that in turbulence...

## A connection between the Camassa-Holm equations and turbulent flows in channels and pipes

Chen, S.; Foias, C.; Holm, D. D.; Olson, E.; Titi, E. S.; Wynne, S.
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
46.59%
In this paper we discuss recent progress in using the Camassa-Holm equations to model turbulent flows. The Camassa-Holm equations, given their special geometric and physical properties, appear particularly well suited for studying turbulent flows. We identify the steady solution of the Camassa-Holm equation with the mean flow of the Reynolds equation and compare the results with empirical data for turbulent flows in channels and pipes. The data suggests that the constant $\alpha$ version of the Camassa-Holm equations, derived under the assumptions that the fluctuation statistics are isotropic and homogeneous, holds to order $\alpha$ distance from the boundaries. Near a boundary, these assumptions are no longer valid and the length scale $\alpha$ is seen to depend on the distance to the nearest wall. Thus, a turbulent flow is divided into two regions: the constant $\alpha$ region away from boundaries, and the near wall region. In the near wall region, Reynolds number scaling conditions imply that $\alpha$ decreases as Reynolds number increases. Away from boundaries, these scaling conditions imply $\alpha$ is independent of Reynolds number. Given the agreement with empirical and numerical data, our current work indicates that the Camassa-Holm equations provide a promising theoretical framework from which to understand some turbulent flows.; Comment: tex file...

## On the meaning of mixing efficiency for buoyancy driven mixing in stratified turbulent flows

Wykes, Megan S. Davies; Hughes, Graham O.; Dalziel, Stuart B.
Fonte: Cambridge University Press Publicador: Cambridge University Press
Tipo: Article; accepted version
EN
Relevância na Pesquisa
56.38%
This is the author accepted manuscript. The final version is available from Cambridge University Press via http://dx.doi.org/10.1017/jfm.2015.462; This article is Crown Copyright.; The concept of a mixing efficiency is widely used to relate the amount of irreversible diabatic mixing in a stratified flow to the amount of energy available to support mixing. This common measure of mixing in a flow is based on the change in the background potential energy, which is the minimum gravitational potential energy of the fluid that can be achieved by an adiabatic rearrangement of the instantaneous density field. However, this paper highlights examples of mixing that is primarily ?buoyancy-driven? (i.e. energy is released to the flow predominantly from a source of available potential energy) to demonstrate that the mixing efficiency depends not only on the specific characteristics of the turbulence in the region of the flow that is mixing, but also on the density profile in regions remote from where mixing physically occurs. We show that this behaviour is due to the irreversible and direct conversion of available potential energy into background potential energy in those remote regions (a mechanism not previously described). This process (here termed ?relabelling?) occurs without requiring either a local flow or local mixing...

## On the full lagrangian approach and thermophoretic deposition in gas-particle flows

Healy, David Patrick
Fonte: University of Cambridge; Department of Engineering; Clare College Publicador: University of Cambridge; Department of Engineering; Clare College
Tipo: Thesis; doctoral; PhD
EN
Relevância na Pesquisa
46.51%
Theoretical and experimental studies of particle deposition in turbulent pipe flow have been carried out for over forty years, but some of the most important transport mechanisms are still not well understood. The first part of this thesis is concerned with the calculation of particle density when using Lagrangian methods to predict inertial particle transport in two-dimensional laminar fluid flows. Traditionally, Lagrangian calculations involve integrating the particle equations of motion along particle pathlines, and the particle density is obtained by applying a statistical averaging procedure to those pathlines which intersect a particular computational grid cell. Unfortunately, extremely large numbers of particles are required to reduce the statistical errors to acceptable levels, and this makes the method computationally expensive. Recently, the Full Lagrangian approach has been developed, which allows the direct calculation of the particle density along particle pathlines. This method had previously been applied only to simple analytical flow fields. The application of the method to CFD generated fluid velocity fields was shown to be possible, and the results obtained using the Full Lagrangian approach were compared to those from a traditional Lagrangian approach. It was found that better quality solutions could be obtained with the use of far fewer particle pathlines. An analysis of the manner in which the Full Lagrangian approach deals with particles whose paths cross each other (and the resulting discontinuity in particle density) was also undertaken...

## Entrainment of fine sediments by turbulent flows

Sutherland, Alexander James
Fonte: California Institute of Technology Publicador: California Institute of Technology
Tipo: Report or Paper; PeerReviewed Formato: application/pdf


text:
On computer role-playing forums, I have seen a lot of general strategy advice regarding difficult group battles ("attack the boss monster first", "start with the highest-damage enemies", etc.). I have decided to see for myself which the optimal tactics is. The answer requires some basic (school-level but nontrivial) mathematics: see http://www.mathlinks.ro/viewtopic.php?t=326811 , scroll down to the remark (the problem turned out to be more or less identical to an American Math. Monthly question which is older than CRPG).

Is it possible to brute-force a combination lock by repeatedly changing a digit without checking one and the same combination several times? (Yes, by induction, at least if you can cycle every digit all the way from 0, 1, 2, ... to 9 and back to 0. If you cannot move between 9 and 0 without going through the intermediate digits, then no, by a semi-invariant argument. The keyword here is Hamiltonian path. If none exists, the next natural question is how to find a path through every vertex of minimal length...) And as we are talking about Hamiltonian paths, Euler paths can be interesting as well...

You want to encrypt a message in a way that each of $n$ persons gets a key such that any $k$ of them can, in a joint effort, unambiguously decrypt the it, while any $k-1$ will not have the slightest idea about the message (i. e., every possible message including gibberish will be equiprobable). It's called Shamir's Secret Sharing.


text:
### Archive

Posts Tagged ‘HAT-P-7’

## M for all and all for M

I’m always impressed by the efficiency with which red dwarfs pack hydrogen, the stuff of flammable zeppelins, into such a small space: Gliese 1214 is more than twice as dense as led. The density of the Sun, on the other hand, is bubblegum by comparison.

Gliese 1214b’s orbital period is a mere 1.58 days. Its 0.014 AU separation from the system barycenter is the smallest yet measured for any planet. Yet because of the high red dwarf density, the star-planet configuration is actually rather spacious. Here’s the system to scale:

It’s interesting to compare this diagram with that of a genuinely close-in planet such as HAT-P-7b, which actually has a somewhat longer 2.2 day orbital period:

At a given period, a red dwarf fills much less of a planetary orbit than does a Sun-like star. If the occurrence rate of planets at a specified period is the same for stars of different masses, then one needs to look at $\sim(M_{\odot}/M_{\rm RD})^{2/3}$ times more red dwarfs than Sun-like stars to find a given number of transits with a particular period.

Gliese 1214b lies at enough stellar radii from Gliese 1214 that its a-priori transit probability was only about 7%. The Mearth survey currently covers only ~2000 stars, and so the fact that the discovery was made so quickly was probably not luck, but rather points to the existence of a very large number of low-mass planets orbiting small stars.

Let’s face it. The big dough goes to chase potentially habitable transiting planets. With this metric, the red dwarfs come out way ahead. If red dwarfs and Sun-like stars have equal occurrence fractions for planets with Earth’s mass and insolation, then a low-mass red dwarf has roughly four times the probability of a Sun-like star of harboring a transiting potentially habitable planet. Twice the temperature means one-sixteenth the area and the square root of sixteen is four. The red dwarfs also present a number of other advantages, see e.g. here, here, and here.

Ryan Montgomery and I have a recent paper out which foreshadows what I think is the inevitability of transit surveys that use the Mearth strategy to target true-Earth analogs the habitable zones of the lowest-mass red dwarf stars. Mearth  is itself very well-positioned to expand in this direction. I also think that a lot of effort will continue to shift toward improved Doppler-velocity capability in the near-infrared (see, e.g. this recent paper by Jacob Bean and collaborators which describes the use of ammonia gas in a glass cell to imprint a forest of fixed reference lines on a K-band stellar spectrum).

A last note: Twelve-Fourteen-b is likely to become a favorite target for small-telescope observers, so I made sure to add it to the Transitsearch.org candidates table. Now that classes are done for the quarter, I’ve been going through the literature and adding or updating one or two planets a day. It’s tedious work, but I’ve noticed some interesting upcoming opportunities, which I’ll be writing about soon. For transit-themed ephemera and the latest celebrity gossip, look no further than the transitsearch twitter stream: http://twitter.com/Transitsearch.

And a postscript: In the comments, reader cwmagee points out that the implication of the post is that the HAT-P-7 and Gl1214 diagrams are to scale which eachother, but that’s not the case. He attached a version which shows a to-scale comparison of both systems:

Red dwarfs are small!

Categories: worlds Tags:

August 18th, 2009 1 comment

Turn your world upside-down and you’re looking at a very different planet. Antarctica, ringed by the vast exapse of the Southern Ocean, draws all the attention. Viewed from beneath, I think Earth might better resemble the habitable planets that are out there in the local galactic neighborhood, waiting to be found.

Speaking of upside-down planets, last week brought a curious back-to-back development. Three separate papers (one, two, three), posted to astro-ph on two successive days, presented strong Rossiter-McLaughlin-based evidence that both WASP-17b and HAT-P-7b are on severely misaligned, potentially retrograde orbits around their parent stars. Winn et al.’s data for HAT-P-7 are a near-exact inversion of the familiar sawtooth produced by well-behaved hot Jupiters such as HD 209458b or HD 189733b. It would appear that Dr. Kozai exerted a heavy hand during HAT-P-7b’s early days:

The HAT-P-7 system is alarmingly compact. The star is roughly 80% larger than the Sun, and the orbit of the transiting planet is only about four times larger than the star itself. It looks, in fact, when drawn to scale and tilted to the proper inclination, like a schematic cartoon of a transiting system.

Remarkably, HAT-P-7 lies in the Kepler field, and was the subject of a teaser-like “brevia” published in Science a few weeks ago. In the folded Kepler light curve for HAT-P-7b it’s easy to see the phase function of the orbiting planet, along with the primary transit and the secondary eclipse. The well-resolved depth of the secondary eclipse indicates that the spacecraft is performing up to spec and will be able to detect the transits of Earth-sized planets orbiting Sun-sized stars.

Interestingly, a near-perfectly inverted Rossiter-McLaughlin waveform doesn’t necessarily mean that the planetary orbit is retrograde, but rather only that the angle between the planet’s orbital angular momentum vector and the sky-projected spin axis of the star is close to 180 degrees. If the star’s polar axis is pointing nearly in our direction, then the planetary orbit is close to polar. The small vsin(i) for HAT-P-7 provides a piece of evidence that HAT-P-7b’s orbit might in fact be close to polar.

Categories: worlds Tags:


text:
# American Institute of Mathematical Sciences

• Previous Article
Existence and multiplicity of positive solutions for a class of quasilinear Schrödinger equations in $\mathbb R^N$$^\diamondsuit$
• DCDS-S Home
• This Issue
• Next Article
Existence criteria of ground state solutions for Schrödinger-Poisson systems with a vanishing potential

## Stability and bifurcation analysis in a delay-induced predator-prey model with Michaelis-Menten type predator harvesting

 School of Mathematical Sciences, Qufu Normal University, Qufu 273165, Shandong, China

*Corresponding author: Fanwei Meng

Received  May 2019 Revised  September 2019 Published  February 2020

The present paper considers a delay-induced predator-prey model with Michaelis-Menten type predator harvesting. The existence of the nontrivial positive equilibria is discussed, and some sufficient conditions for locally asymptotically stability of one of the positive equilibria are developed. Meanwhile, the existence of Hopf bifurcation is discussed by choosing time delays as the bifurcation parameters. Furthermore, the direction of Hopf bifurcation and the stability of the bifurcated periodic solutions are determined by the normal form theory and the center manifold theorem for functional differential equations. Finally, some numerical simulations are carried out to support the analytical results.

Citation: Ming Liu, Dongpo Hu, Fanwei Meng. Stability and bifurcation analysis in a delay-induced predator-prey model with Michaelis-Menten type predator harvesting. Discrete & Continuous Dynamical Systems - S, doi: 10.3934/dcdss.2020259
##### References:

show all references

##### References:
The diagram (a) shows the time series of $x(t)$, $y(t)$ and the diagram (b) shows the phase portrait of model (3) with $\tau_1 = \tau_2 = 0$. The positive equilibrium point $E_2(0.68, 0.32)$ is locally asymptotically stable. Here the initial value is $(0.8, 0.6)$
The diagram (a) shows the time series of $x(t)$, $y(t)$ and the diagram (b) shows the phase portrait of model (3) with $\tau_1 = 0$, $\tau_2 = 2.8 < \tau_{20} = 2.91$. The positive equilibrium point $E_2(0.48, 0.52)$ is locally asymptotically stable. Here the initial value is $(0.5,0.5)$
The diagram (a) shows the time series of $x(t)$, $y(t)$ and the diagram (b) shows the phase portrait of model (3) with $\tau_1 = 0$, $\tau_2 = 2.92 > \tau_{20} = 2.91$. The positive equilibrium point $E_2(0.48, 0.52)$ is unstable. Here the initial value is $(0.5,0.5)$
The diagram (a) shows the time series of $x(t)$, $y(t)$ and the diagram (b) shows the phase portrait of model (3) with $\tau_1 = 2.0 < \tau_{30} = 2.11$, $\tau_2 = 0$. The positive equilibrium point $E_2(0.53, 0.47)$ is locally asymptotically stable. Here the initial value is $(0.5,0.5)$
The diagram (a) shows the time series of $x(t)$, $y(t)$ and the diagram (b) shows the phase portrait of model (3) with $\tau_1 = 2.1185 > \tau_{30} = 2.11$, $\tau_2 = 0$. The positive equilibrium point $E_2(0.53, 0.47)$ is unstable. Here the initial value is $(0.5,0.5)$
The diagram (a) shows the time series of $x(t)$, $y(t)$ and the diagram (b) shows the phase portrait of model (3) with $\tau_1 = \tau_2 = 1.85 < \tau_{40} = 1.92$. The positive equilibrium point $E_2(0.53, 0.47)$ is locally asymptotically stable. Here the initial value is $(0.55,0.6)$
The diagram (a) shows the time series of $x(t)$, $y(t)$ and the diagram (b) shows the phase portrait of model (3) with $\tau_1 = \tau_2 = 1.926 > \tau_{40} = 1.92$. The positive equilibrium point $E_2(0.53, 0.47)$ is unstable. Here the initial value is $(0.55,0.6)$
The diagram (a) shows the time series of $x(t)$, $y(t)$ and the diagram (b) shows the phase portrait of model (3) with $\tau_1 = 3 < \tau_{50} = 4.90$, $\tau_2 = 1.8$. The positive equilibrium point $E_2(0.48, 0.52)$ is locally asymptotically stable. Here the initial value is $(0.55,0.6)$
The diagram (a) shows the time series of $x(t)$, $y(t)$ and the diagram (b) shows the phase portrait of model (3) with $\tau_1 = 6 > \tau_{50} = 4.90$, $\tau_2 = 1.8$. The positive equilibrium point $E_2(0.48, 0.52)$ is unstable. Here the initial value is $(0.55,0.6)$
 [1] Demou Luo, Qiru Wang. Dynamic analysis on an almost periodic predator-prey system with impulsive effects and time delays. Discrete & Continuous Dynamical Systems - B, 2021, 26 (6) : 3427-3453. doi: 10.3934/dcdsb.2020238 [2] Shiwen Niu, Hongmei Cheng, Rong Yuan. A free boundary problem of some modified Leslie-Gower predator-prey model with nonlocal diffusion term. Discrete & Continuous Dynamical Systems - B, 2021  doi: 10.3934/dcdsb.2021129 [3] Qian Cao, Yongli Cai, Yong Luo. Nonconstant positive solutions to the ratio-dependent predator-prey system with prey-taxis in one dimension. Discrete & Continuous Dynamical Systems - B, 2021  doi: 10.3934/dcdsb.2021095 [4] Nhu N. Nguyen, George Yin. Stochastic partial differential equation models for spatially dependent predator-prey equations. Discrete & Continuous Dynamical Systems - B, 2020, 25 (1) : 117-139. doi: 10.3934/dcdsb.2019175 [5] Guirong Jiang, Qishao Lu. The dynamics of a Prey-Predator model with impulsive state feedback control. Discrete & Continuous Dynamical Systems - B, 2006, 6 (6) : 1301-1320. doi: 10.3934/dcdsb.2006.6.1301 [6] Prabir Panja, Soovoojeet Jana, Shyamal kumar Mondal. Dynamics of a stage structure prey-predator model with ratio-dependent functional response and anti-predator behavior of adult prey. Numerical Algebra, Control & Optimization, 2021, 11 (3) : 391-405. doi: 10.3934/naco.2020033 [7] Qigang Yuan, Jingli Ren. Periodic forcing on degenerate Hopf bifurcation. Discrete & Continuous Dynamical Systems - B, 2021, 26 (5) : 2857-2877. doi: 10.3934/dcdsb.2020208 [8] Rui Hu, Yuan Yuan. Stability, bifurcation analysis in a neural network model with delay and diffusion. Conference Publications, 2009, 2009 (Special) : 367-376. doi: 10.3934/proc.2009.2009.367 [9] Martin Bohner, Sabrina Streipert. Optimal harvesting policy for the Beverton--Holt model. Mathematical Biosciences & Engineering, 2016, 13 (4) : 673-695. doi: 10.3934/mbe.2016014 [10] Yahui Niu. A Hopf type lemma and the symmetry of solutions for a class of Kirchhoff equations. Communications on Pure & Applied Analysis, , () : -. doi: 10.3934/cpaa.2021027 [11] Andrea Signori. Penalisation of long treatment time and optimal control of a tumour growth model of Cahn–Hilliard type with singular potential. Discrete & Continuous Dynamical Systems, 2021, 41 (6) : 2519-2542. doi: 10.3934/dcds.2020373 [12] Akio Matsumoto, Ferenc Szidarovszky. Stability switching and its directions in cournot duopoly game with three delays. Discrete & Continuous Dynamical Systems - B, 2021  doi: 10.3934/dcdsb.2021069 [13] Pengyu Chen, Xuping Zhang, Zhitao Zhang. Asymptotic behavior of time periodic solutions for extended Fisher-Kolmogorov equations with delays. Discrete & Continuous Dynamical Systems - B, 2021  doi: 10.3934/dcdsb.2021103 [14] Michael Grinfeld, Amy Novick-Cohen. Some remarks on stability for a phase field model with memory. Discrete & Continuous Dynamical Systems, 2006, 15 (4) : 1089-1117. doi: 10.3934/dcds.2006.15.1089 [15] Quan Hai, Shutang Liu. Mean-square delay-distribution-dependent exponential synchronization of chaotic neural networks with mixed random time-varying delays and restricted disturbances. Discrete & Continuous Dynamical Systems - B, 2021, 26 (6) : 3097-3118. doi: 10.3934/dcdsb.2020221 [16] Elimhan N. Mahmudov. Second order discrete time-varying and time-invariant linear continuous systems and Kalman type conditions. Numerical Algebra, Control & Optimization, 2021  doi: 10.3934/naco.2021010 [17] Martial Agueh, Reinhard Illner, Ashlin Richardson. Analysis and simulations of a refined flocking and swarming model of Cucker-Smale type. Kinetic & Related Models, 2011, 4 (1) : 1-16. doi: 10.3934/krm.2011.4.1 [18] Yongqiang Fu, Xiaoju Zhang. Global existence and asymptotic behavior of weak solutions for time-space fractional Kirchhoff-type diffusion equations. Discrete & Continuous Dynamical Systems - B, 2021  doi: 10.3934/dcdsb.2021091 [19] Zengyun Wang, Jinde Cao, Zuowei Cai, Lihong Huang. Finite-time stability of impulsive differential inclusion: Applications to discontinuous impulsive neural networks. Discrete & Continuous Dynamical Systems - B, 2021, 26 (5) : 2677-2692. doi: 10.3934/dcdsb.2020200 [20] Xiongxiong Bao, Wan-Tong Li. Existence and stability of generalized transition waves for time-dependent reaction-diffusion systems. Discrete & Continuous Dynamical Systems - B, 2021, 26 (7) : 3621-3641. doi: 10.3934/dcdsb.2020249

2019 Impact Factor: 1.233

## Tools

Article outline

Figures and Tables


text:
## Wednesday, July 30, 2008 ... //

### LHC: FAQ

Update: Physics World spreads a rumor about the first proton beams to be injected on August 9th into parts of the tunnel and on September 2nd-3rd to the whole ring.
Original text from July 28th: Martin Coles at The (Montreal) Gazette wrote a couple of excellent articles about the Large Hadron Collider. Click at the following:
Frequently asked questions (illuminating, a lot of understandable numbers!)
Deep thinking (from Galileo to the LHC, a story)
In their realm, outside Canada (Montrealers at CERN)
For a photographer and a journalist, these sensible articles are extraordinary and deserve an explanation. The main explanation is probably that Martin Coles has studied math and philosophy in Cambridge, Old England, so he is not quite just a photographer or a journalist. ;-)

Incidentally, all eight sectors of the LHC except for "78" are already below the temperature of 5 K, usually close to the final 1.9 K. Only the "78" sector is at 15 K in average (update, July 30th: close to 5 K, too). It should be cooled down soon.

I don't really like rap but if you do, play the video above. Ms Alpinekat explains the basic purpose of the four LHC experiments very well.

Hat tip: Tommaso Dorigo.

#### snail feedback (0) :

(function(i,s,o,g,r,a,m){i['GoogleAnalyticsObject']=r;i[r]=i[r]||function(){ (i[r].q=i[r].q||[]).push(arguments)},i[r].l=1*new Date();a=s.createElement(o), m=s.getElementsByTagName(o)[0];a.async=1;a.src=g;m.parentNode.insertBefore(a,m) })(window,document,'script','//www.google-analytics.com/analytics.js','ga'); ga('create', 'UA-1828728-1', 'auto'); ga('send', 'pageview');


text:
# How do you write 350000 in scientific notation?

Aug 31, 2017

$3.5 \cdot {10}^{5}$

#### Explanation:

Start by writing your number in standard notation

three hundred fifty thousand $\to 350 , 000$

Now, a number written in scientific notation will take the form

$\textcolor{w h i t e}{a a} \textcolor{b l u e}{m} \times {10}^{\textcolor{p u r p \le}{n} \textcolor{w h i t e}{a} \stackrel{\textcolor{w h i t e}{a a a a a a}}{\leftarrow}} \textcolor{w h i t e}{a \textcolor{b l a c k}{\text{the")acolor(purple)("exponent}} a a}$
$\textcolor{w h i t e}{\frac{a}{a} \textcolor{b l a c k}{\uparrow} a a a a}$
$\textcolor{w h i t e}{\textcolor{b l a c k}{\text{the")acolor(blue)("mantissa}} a}$

For normalized scientific notation, which is what you'll be dealing with in the vast majority of cases, you need to have

$1 \le | \textcolor{b l u e}{m} | < 10$

$350 , 000 \cdot {10}^{0}$

so you can say that you have

$\textcolor{b l u e}{m} = 350 , 000 \text{ "and " } \textcolor{p u r p \le}{n} = 0$

In order to write the number in scientific notation, you must divide it $10$ as many times as you need in order to get

$1 \le \textcolor{b l u e}{m} < 10$

For every time you divide the number by $10$, you must also multiply it by $10$ in order to keep its value unchanged.

The trick here is that you divide the mantissa by $10$ and you multiply by $10$ by increasing the exponent by $1$.

So, divide the mantissa by $10$ and multiply

$\frac{350 , 000}{10} \cdot {10}^{0} \cdot 10 = 35 , 000 \cdot {10}^{1}$

Since

$1 \le 35 , 000 \textcolor{red}{\cancel{\textcolor{b l a c k}{<}}} 10$

you must repeat the procedure.

$\frac{35 , 000}{10} \cdot {10}^{1} \cdot 10 = 3 , 500 \cdot {10}^{2}$

Once again, you have

$1 \le 3 , 500 \textcolor{red}{\cancel{\textcolor{b l a c k}{<}}} 10$

so you must repeat the procedure again

$\frac{3 , 500}{10} \cdot {10}^{2} \cdot 10 = 350 \cdot {10}^{3}$

Repeat it again

$\frac{350}{10} \cdot {10}^{3} \cdot 10 = 35 \cdot {10}^{4}$

Repeat it again

$\frac{35}{10} \cdot {10}^{4} \cdot 10 = 3.5 \cdot {10}^{5}$

This time, you have

$1 \le 3.5 < 10 \text{ } \textcolor{g r e e n}{\sqrt{}}$

so you can say that your original number written in scientific notation will look like this

$350 , 000 = 3.5 \cdot {10}^{5}$

Notice that the mantissa keeps the same number of sig figs as the number written in standard form, i.e. $2$ sig figs.