# Questions tagged [stability]

Stability theory addresses the stability of potentials, solutions of differential equations, and of trajectories of dynamical systems under small perturbations of initial conditions.

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### Is amorphous ice thermodynamically stable?

Amorphous ice is often produced by cooling liquid water below its glass transition temperature so fast that it does not have time to form ice crystals. The fact that this can only occur if the ...
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### Numerical model of 1D equations for compressible flow

The equations for 1D compressible flow are $$\frac{\partial u(x,t)}{\partial t}-A\frac{\partial v(x,t)}{\partial x}=0,$$ $$\frac{\partial v(x,t)}{\partial t}-B\frac{\partial u(x,t)}{\partial x}=0,$$ ...
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### How does the increased binding energy per nucleon help in stability?

I have some read answers on this forum, some books like Halliday Resnick and my course books. I have understood that binding energy is the energy we need to supply to break nucleus into individual ...
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### Rain drop trails on a car window prefer certain paths. Why?

Why do the raindrops always flow down in the middle? That's a question given to me by my seven year old son. Some background: We are sitting in a bus with two windscreen wiper blades. I hope that ...
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### Does every element have a critical mass?

We have all heard of critical mass for radioactive materials like Uranium, Plutonium etc. but does every element theoretically have a critical mass? If not, what determines if such a phenomena is ...
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### How can the mass of an unstable composite particle become complex?

To show where the resonances in cross sections come from, one usually considers the exact propagator in the interacting theory, which for a scalar is iG(p^2)=\frac{i}{p^2-m_R^2+\Sigma(p^2)+i\epsilon}...
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### Arrow of time as the result of a feedback loop that stabilizes an inheret unstable reversible time [closed]

I am searching to find some literature on idea i am having, regarding the "arrow of time". The main idea is an expansion of the main theme of an Asimov sci-fi novel, where he postulates ...
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### What is meant by "stable" vs. "unstable" in terms of particles?

I am reading more carefully about subatomic particles, and am on the Muon Wiki page, where it says: The muon is an unstable subatomic particle with a mean lifetime of 2.2 μs, much longer than many ...
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### Renormalization constant in unstable particle propagator

On Peskin & Schroeder's QFT, section 7.3, the book discusses the unstable particle. Before (7.57), the book gives the formula of a scalar particle propagator For unstable particle, the book ...
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### Ostrogradsky instability and fractional derivatives

Are fractional derivatives (or even more generally differentegrals) also under the scope of the Ostrogradsky instability theorem?
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### If there wasn't a weak nuclear force, what would be the heaviest stable theoretically stable isotope with equal protons and neutrons?

If there was no weak nuclear force, what would be the heaviest stable theoretically stable isotope with equal protons and Neutrons? For our universe the heaviest such isotope is calcium 40, but most ...
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### Can a bicycle whose front wheel cannot turn left/right stay upright?

Most sensible explanations of why a bicycle stays upright involve the turning left/right of the front wheel. If a bicycle's front wheel cannot turn left/right, can it stay upright while being pedalled?...
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### Convection in stratified atmosphere

In the stability analysis of stratified atmosphere in the presence of gravity, we consider a blob of atmosphere and perturb it (move it up by a small height $\Delta z$). Initially, the blob had the ...
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### It is possible to combine two heavy elements into one?

Is it possible to combine say two uranium atoms into very heavy new element? Periodic table ends around 115 today, but can it go forever technically?
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### Mass per nucleon graph

I am a high school student and am struggling with understanding the significance of the mass per nucleon graph. What does this graph show with regard to nuclear reactions? (y-axis: M/A, x-axis:A) I ...
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### Why is a star unstable if it's adiabatic exponents are less than 4/3?

In "Introduction to Stellar Structure" by Walter J. Maciel at page 76 it is said that for a partially ionized non degenerate hydrogen gas, the star is unstable if the adiabatic exponents are ...
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### Isotopes half-lives distribution - is it log-uniform?

Decay of single isotope follows exponential law. BUT decay of nuke fallout / spent nuclear fuel will follow hyperbolic law. It is easy to explain if we assume that half-lives are log-uniformly ...
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### Timescale for unstable stratification to resolve itself

The ocean is typically vertically stratified, that is the deeper you go the higher the density should be. This can be because of increased salinity or decreased temperature. If that is not the case ...
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### Why do magic number nuclei have higher first excitation energies?

I have read online that one property of stable 'magic number' nuclei is that they have higher first excitation energies. Why is this?
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### Stability of Euler-Cromer method

Euler method doesn't perform well in the context of oscillatory problems like the harmonic oscillator; the amplitude of the oscillation gets bigger with time, which clearly contradicts theory as no ...
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### Is there a "most unstable rigid body shape" when spun about its intermediate axis?

Is there a shape of a solid, that provides the quickest and most violent deviation of its axis of rotation, when spun around its intermediate axis? What would be this shape and does it depend on a ...
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### Could there be undiscovered long-lived isomers of unstable elements?

There are 80 stable elements in the periodic table. These elements have at least one stable isotope. Other elements don’t have any identified stable isotopes. The existence of stable isotopes can be ...
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I would like to show that the time it takes for a pendulum to leave the unstable equilibrium at the top is logarithmic; i.e. if the starting position of the mass is $\theta_0 = \delta$ for some small $... • 428 2 votes 1 answer 115 views ### Why isn't lead-207 radioactive? I've recently learnt from here, in an atom, the stability of an atom is described in two contexts, one according to the ratio of neutron and proton of the atom. The ratio will always be between 1 and ... 1 vote 2 answers 50 views ### Literature reference: example of stable and unstable manifolds in Henon-Heiles system There is a quite classical description of chaotic systems based on the behaviour of stable and unstable manifolds around a stationary point of the Poincaré section. It is presented, for example, [here,... 2 votes 0 answers 57 views ### Most stable shape if Newtonian gravity was proportional to$r^\alpha$Consider lots of mass in isolated 3D space, close to each other. Consider that only the gravitational force (Newtonian) exists. Also consider that there is no rotational motion. It is evident that a ... • 201 3 votes 1 answer 43 views ### Given a system, how to decide whether a closed orbit is homoclinic, not periodic, solely based on its phase portrait? Background and definitions: A system is conservative if it has at least one conserved quantity. In a phase portrait of a nonlinear conservative system, trajectories that start and end at the same ... • 313 -1 votes 2 answers 135 views ### Neutron star vs. Islands of stability "Neutron stars" are said to be almost entirely composed of neutrons. The islands of stability principle recognizes an upper limit to the number of neutrons that can be introduced to an atom. ... 5 votes 2 answers 212 views ### Were there any explanations as for the stability of matter before the advent of quantum mechanics? Reading the paper by Lieb "The stability of matter", it is clear from the start that quantum mechanics is absolutely necessary to solve this problem. However, I assume this question was ... • 1,396 13 votes 1 answer 153 views ### Why is there a sudden drop-off in half-life of isotopes at around 130 neutrons? Is there a name for this? Pertaining to the chart of nuclides, there is a region above Bismuth, in which the relatively continuous trend of stability is interrupted by a batch of isotopes all with extremely short half-lives. I ... • 141 1 vote 2 answers 25 views ### Motorcycle handle Bar vibration & Bar End Weights Pic 1 is a normal motorcycle bar end weights. My question, if I replace the bar end weights with a long threaded rod (M8x150) and the thread rod is inserted inside the handle bar(pic 2), will it ... 1 vote 1 answer 23 views ### What is the fractional frequency stability of a thermal damped harmonic oscillator? Suppose I have a lightly driven (classical) damped harmonic oscillator at temperature$T$. Suppose$\omega$and$Q$are specified as well as the mean energy$\bar{E}$in the oscillator due to the ... • 11.9k 3 votes 0 answers 30 views ### Landau Theory of a Crystal A crystal has ferroelectric and ferromagnetic properties. Suppose that the ferromagnetic transition occurs at a temperature$T_m$slightly higher than the ferroelectric transition$T_{e}$, and that ... • 1,059 3 votes 2 answers 122 views ### What limits mechanical watch precision? [closed] It seems like good mechanical watches gain or lose +/- a few seconds per day. 5 s/day corresponds to a fractional frequency stability of$5\times 10^{-5}$. What limits this stability? Obvious ... • 11.9k 0 votes 0 answers 26 views ### Why we have not observed one proton and one neutron nuclear decay? [duplicate] I'm learning about nuclear decays: Alpha (helium nucleus, +2) Beta (electron) Gamma (photon) Neutron But why helium nucleus? Why not hydrogen nucleus (deuterium)? I mean why two protons and two ... • 1,127 1 vote 1 answer 150 views ### What causes the formation of vortices in a separated flow? Consider flow over a cylinder. At a high enough Reynold's Number, the strength of the adverse pressure gradient becomes too large for the boundary layer to be able to remain attached to the cylinder. ... 0 votes 0 answers 23 views ### Is an element necessarily more stable if the no. of protons and neutrons are equal? [duplicate] This question came in the Rajshahi University admission exam 2017-18 Q) An element is more stable if in its atom- (a) Protons and neutrons are equal in number (b) Protons and electrons are equal in ... 0 votes 2 answers 89 views ### Buoyancy and stability I don't understand how does a rotating moment caused by the weight force form when a submerged object is tilted like this. I understand that the buoyancy force produce a moment about CG because of the ... 0 votes 0 answers 94 views ### On the impossibility of stable equilibrium of a charge in an electric field I had read from my textbook that a positive charge cannot be in stable equilibrium as if we take a gaussian surface surrounding the charge then assuming that the charge is in equilibrium then using ... 1 vote 0 answers 28 views ### If there was no weak nuclear force, what would be the heaviest stable theoretically stable isotope with equal protons and neutrons? If there was no weak nuclear force, what would be the heaviest stable theoretically stable isotope with equal protons and Neutrons? For our universe the heaviest such isotope is calcium 40, but most ... • 1,598 0 votes 0 answers 27 views ### What's the minimum possible mass of a stable neutron star? [duplicate] What's the minimum possible mass of a stable neutron star? Let's say you have a neutron star and slowly take away it's mass, e.g., either by firing a stream of anti-neutrons or by proton decay, since ... • 1,598 2 votes 1 answer 70 views ### How compact can a thin shell be without collapsing? I've heard of https://en.wikipedia.org/wiki/Buchdahl%27s_theorem. It states that as the ratio between a spheres radius a it's Schwarzschild radius approaches$9/8$. the pressure at the center tends to ... • 1,598 0 votes 1 answer 84 views ### About why electrons in atom don't radiate(considering wave nature also) [duplicate] It's said in textbooks that electrons won't radiate and fall into nucleus because matter wave of it's form a standing wave but could somebody explain why being a standing wave it doesn't radiate, even ... 81 votes 2 answers 7k views ### Why doesn't a nucleus-like body made up of just neutrons exist? We know that neutrons exert short ranged nuclear forces over other nucleons in a nucleus, and these forces are only attractive in nature. Also this force is universal and doesn't differentiate between ... • 783 3 votes 2 answers 944 views ### Why do elements, as they have more protons, need a higher amount of neutrons to stabilise them? [duplicate] I've seen the graphs of the stability line but I can't find any reason as to why this happens, I understand radiation, just not why radiation needs to occur in the first place if that makes sense. 0 votes 1 answer 84 views ### Why does the stability of a nucleus depend on the binding energy$\textit{per nucleon}\$ instead of the total binding energy?

The larger the total binding energy of a nucleus, the greater the minimum energy that must be added to infinitely separate the constituent nucleons. Shouldn't the total binding energy, then, be used ...
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### Current status and reference request for the Black Hole Stability Conjecture

The Black Hole Stability Conjecture is one of the most important open problems in the field of General Relativity, and remains open in spite of the advances in the past half century. To test Einstein’...
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### Are atoms still unstable in 4 spatial dimensions when the physical size of nuclei is accounted for?

Per this answer, depending on a dimensionless parameter hydrogen atoms in 4 spatial dimensions can be either unbound (i.e., nonexistent), stably bound dependent on boundary conditions, or unstable ...
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