Stability Definition and 524 Threads

What is stability of Hawking Mass and how to calculate it? Any references will be appreciated. Thanks

dear sir, i heard that that proton spins about itselfand this helps in stability of nucleus. i also heard from the a friend that neutron has a proton and electron within it. this electron moves out from neuton making it proton and entering proton to form a neutron. sir i need to know...

Hello, I am reading the book, The Quantum Theory of Fields II by Weinberg. In page 426 of this book (about soliton, domain wall stuffs), we have Eq(23.1.5) as the solution that minimizes Eq(23.1.3). The paragraph below Eq(23.1.5), the author said "The advantage of the derivation based on...

i have this system x'=y-x3-xy2 y'=-x-x2y-y3 i worked it out and found the equilibrium point to be 0. how do i determine whether it is stable, assymp stable or not stable

Might be a stupid question but got to ask. The bonds of benzene have a bond dissociation energy in between that of a single C-C bond and an alkene yet its stability is much higher that expected due to aromaticity/e- delocalization. Is stability not necessarily reflected in bond dissociation...

Hello everyone, Recently I've been looking at quadcopter technology. While looking through literature, I noticed that most people mention that a quadcopter is inherently unstable but no reasoning is provided. I looked a bit at the EOMs but that's a big mess that I don't have time for yet. I...

Homework Statement Show that the stability condition for a circular orbit of radius a, i.e. f(a) + \frac{a}{3} (\frac{df}{dr})_{r=a} < 0 is equivalent to the condition \frac{d^2V(r)}{dr^2} > 0 for r=a where V(r) is the effective potential given by V(r) = U(r) +...

For the function fc(x)= (6/x) + (x/2) -c, generate an estimate of the Lyapunov exponent for at least one c value chosen from each of the following intervals : (note 0 <= c <= 3) a) the interval of stability of the fixed point b) the interval of stability of the 2-cycle c) the interval of...

Investing function fc(x) = (6/x)+(x/2)-c where 0<= c <=3 a) Use alegbra to find the positive fixed point (in terms of c) and identify its exact interval of existence b) Use algebra and calculus to find the exact interval of stability of the fixed point c) Use algebra to find the points of the 2...

If a system transfer function has a pole equal with 1 , j, cos(pi/4)+j*sin(pi/4) in other words its location is on the margin of the unit circle, it`s the system stable? In my opinion it`s not stable because we have a sum of 1 which doesn't converge but I am not sure. Everywhere I've read it...

Hi all. I am new to boundary layers. Do the stability region of viscous Laminar and inviscid flow overlap? Why? Thanks :)

A predictor-corrector method for the approximate solution of y'=f(t,y) uses \begin{equation} y_{n+1}-y_{n}=hf_{n} \tag P \end{equation} as predictor and \begin{equation} y_{n+1}-y_{n}=\frac{h}{2}(f_{n+1}-f_{n}) \tag C \end{equation} IF (P) and (C) are used in PECE mode on the...

A predictor-corrector method for the approximate solution of $y'=f(t,y)$ uses \begin{equation} y_{n+1}-y_{n}=hf_{n} \tag P \end{equation} as predictor and \begin{equation} y_{n+1}-y_{n}=\frac{h}{2}(f_{n+1}-f_{n}) \tag C \end{equation} IF $(P)$ and $(C)$ are used in PECE mode on the...

Find the fixed points of the implicit Euler scheme \begin{equation} y_{n+1}-y_{n}= hf(t_{n+1},y_{n+1}) \end{equation} when applied to the differential equation y'=y(1-y) and investigate their stability? => implicit Euler scheme \begin{equation} y_{n+1}-y_{n}= hf(t_{n+1},y_{n+1})...

Find the fixed points of the implicit Euler scheme \begin{equation} y_{n+1}-y_{n}= hf(t_{n+1},y_{n+1}) \end{equation} when applied to the differential equation $y'=y(1-y)$ and investigate their stability? => implicit Euler scheme \begin{equation} y_{n+1}-y_{n}= hf(t_{n+1},y_{n+1}) \end{equation}...

The Finite difference scheme: \begin{equation} y_{n+3}-y_{n+1}= \frac {h}{3}(f_{n}-2f_{n+1}+7f_{n+2}) \end{equation} Deduce that the scheme is convergent and find its interval of absolute stability(if any) => the first characteristic polynomial is then \begin{equation} ρ(r)= r^3 -r...

Show that the explicit Runge-Kutta scheme \begin{equation} \frac {y_{n+1} -y_{n}}{h}= \frac{1}{2} [f(t,y_{n} + f(t+h, y_{n}+hk_{1})] \end{equation} where $k_{1} = f(t,y_{n})$applied to the equation $y'= y(1-y)$ has two spurious fixed points if $h>2$.Briefy describe how you would investigate...

Hello everyone, I am having a little difficulty understand precisely what Gibbs free energy is. I have read in my textbook that a negative change in Gibbs free energy implies that the substance under consideration will react/change spontaneously. As such, the more negative the Gibbs free...

Hi all, I would be greatful is someone could kindly enlighten me as to the correct interpretation of the appended bode plots. My understanding when interpreting bode plots is that we desire 0 gain where the phase is equal to or exceeds 180 degrees (marginally stable / unstable). In...

Homework Statement The transfer function of an LTI system H(s) = (s^2 + 2)/(s^3+2s^2+2s+1) Find the followings i) pole-zero pattern of H(s) ii) Stability of the system iii) Impulse response h(t) Homework Equations Zero for which H(s) = 0 & Pole is for which H(s) = ∞ The...

The enthalpies of creating a cyclohexene radical isomers are: ORTHO: 444 kJ/mol META: 361 kJ/mol PARA: 401 kJ/mol The meta-isomer is most stable (that is the reason for the formation of meta product in radical addition). Para/meta isomers energies seem obvious - both carbons...

Homework Statement Given G(s) = 1/[(s^2+s+4)(s+6)] and C(s) = k, find the limit of stability of k. Also, what is the range of k such that the settling time is between 10 and 20 seconds. Homework Equations Provided above The Attempt at a Solution I have attempted to set this...

Homework Statement I'm having to figure out if a system is asymptotically stable, stable, or unstable. I am given the system block diagram. However, each constant block is actually a matrix. Also, there is an integral block thrown in there... Homework Equations The Attempt at a Solution In a...

I know there are other things that fail about the rutherford atom but as the electron is accelerating and radiating away energy it would fall into the nucleus, my question is how much energy would the electron need to gain so that the classical atom could be stable a hydrogen atom for example

Hi all, I need a model of a pneumatic pressure regulator. The model should be as simplest as possible and use an optimization solver to identify the regulator parameters in order to fit the performance I find in the datasheet of a commercial pressure regulator. I have already done a model...

I have a general question about the solution to the Diffusion equation using the explicit finite difference method. Now, it is known the solution is stable when D*dt/dx^2 is less than 0.5, based on the choice of time and space steps. However, how does the choice of the time and space steps...

I remember reading something, long ago, to the effect that any attempt at creating a CTC would be doomed by energy from vacuum fluctuations piling up through it and leading to explosive behavior (I think the idea originated in work done by Misner and Taub in 1969?). Does anyone know what is...

I'm a new comer to study the hadron physics.Why light quarks are more stable than heavy quarks and which one is easy to study? why? Thank you

Homework Statement Example: x'=y-x^3 y'=-x-y^3 Homework Equations The Attempt at a Solution Linear system x'=y y'=-x Is stable because Det(P-\lambdaE)=\lambda2+1 \lambda1,2=+-i So if I am not mistaken,than Ishould use Lyapunov stability,because the linear system is stable and I can't say...

Hi, I'm working on an invention that eliminates liquid slosh in partially filled liquid containers and allows for center of gravity control. I'm wondering if there is a market for such an apparatus where elimination of all slosh is needed. I am aware of baffles, sponges, and diaphragms. A...

Disclaimer: I'm not a physicist I've never quite grasped interstellar gas clouds (i.e. the material for new stars) and how they work. If they were too sparse, then you'd expect them to just dissipate. If they were too dense, then you'd expect them to collapse spontaneously. But yet they seem...

A question I am doing hints that the solution (y,\dot{y}) = (0,0) of \ddot{y} - \frac{2}{t}\dot{y} + y = 0 is unstable. I believe (although I am not 100% sure) that is true however I am struggling to prove it. I can rewrite the equation as a system of equations in matrix form to get \dot{x} =...

Hi, Homework Statement How may I determine whether a system is stable if its input is equal to its output, hence yielding a system(transfer) function equal to 1? Furthermore, could an eigenvalue zero characterize a stable system? I am attaching three examples where I am asked to determine...

hi, I'm measuring my laser pointing stability with a focusing lens and a CCD. Could you guys tell me what would the relationship be between the offset from focal point in CCD and the angle with which the beam exits the laser? CCD is in focus.

U = Th + alpha rays 92p 90p 146n 144n I have heard that if n/p ratio exceeds 1.56, the substance becomes radioactive. Now, for Uranium, n/p ratio is 1.59. It gives out alpha rays in order to gain stability and in turn forms Thorium. n/p...

I have always been under the impression that I totally understood the mechanics working behind the stability of a bicycle i.e. i) the gyroscopic effect of the spinning wheel ii) weight of cycle and rider and iii) the centrifugal force acting on the CG when the bicycle follows a curve path. If...

How can I plot the runge kutta 4 stability region? I know on the i axis the max is \(\pm 2\sqrt{2}\). The plot makes a heart type shape. I don't know how to plot it though but would like to.

This question was prompted by reflecting after reading the standard textbook explanation that "the greater acidity of RCOOH vs ROH is due to the greater stability of the delocalised RCOO- ion causing the position of equilibrium to be further to the right". The equilibria can be written as...

I took a CFD class last semester (had to leave school though due to personal garbage). I am making a come back this fall and as some extra credit I am trying to numerically solve the unsteady laminar flow equation in a pipe. The equation is \dot{U} + U'' + K = 0 where dots denote the time...

I've heard this expression in nuclear physics: the "island of stability." I know it has to do with the stability of a heavy transuranium atom (at least i think so), but what precisely does that expression mean? And what does it have to do with quantum mechanics? Why is this "island" there...

I'm in my last year of college as an undergraduate physics B.S. and have so far tried astronomy and materials science research internships and haven't liked either of them that much. I enjoy the theory behind astrophysics but don't enjoy programming all day. On the other hand, I like the...

Suppose we have a matrix A that has eigenvalues λ1, λ2, λ3,... Matrix B is a matrix that has "very small" matrix elements. Then we could expect that the eigenvalues of sum matrix A + B would be very close to the eigenvalues λi. But this is not the case. The eigenvalues of a matrix are not...

Minkowski space and deSitter space have been shown to be stable in GR under small perturbations. Perturbations do not intensify in higher frequency modes--these solutions don't go haywire and develop black holes all over the place. Piotr Bizon has shown that Anti-deSitter (AdS) space is not...

I am stuck with another one -- Assume that f(x) has the following graph: (for graph please see the attachment) Consider the (1-dimensional) ODE: X’ = f(x): (a) Find all the xed points, and study their stability. (b) Draw the phase portrait of the system, as well as the graphs of the...

Hi PF, I've been wondering why lattice structures form in metals and in salts. Why do fcc or bcc structures reduce the energy of a system so that regular lattices are favorable over those whose atoms are randomly placed? Thanks, Pillow

Stability, Helmholtz free energy mathematical relation "proof" Homework Statement I must show that \left ( \frac{\partial ^2 F}{\partial V ^2} \right ) _T=\frac{\frac{\partial ^2 U}{\partial S^2} \frac{\partial ^2 U}{\partial V ^2} - \left ( \frac{\partial ^2 U}{\partial S \partial V} \right...

About 6 years ago, I made a precipitate of Lead Iodide in water by mixing Potassium Iodide and Lead Nitrate. I have kept the precipitate in a test tube. Would anybody know how stable is the precipitate over time. The temperature has been mostly between 20 and 32 degrees depending on the...

It is often stated that quantum mechanics is able to explain the stability of atoms. I think most explanations are cheating b/c the compare apples and oranges. There are two reasons in classical theory which indicate that atoms should be unstable: A) there is no minimum for the orbit; the...

Hello everyone! This is my first post here, and I'm a recent graduate (within 1yr) of a BS in Mechanical Engineering. I have always been a car nut, and I'm interested in designing, or installing and tuning, a stability control system for my car. I recently purchased a 2012 Subaru...

Hello, I'm currently modeling the profile of a droplet (sessile drop, axisymmetric) in matlab. I've coded differential equations, applied the solver, and I get a reasonable result, except that it spirals continuously. The ODE's in question are: \frac{dx}{ds}=cos(\theta)...