Lorenz Definition and 57 Threads

hi guys one of my friends asked me about the origin of the electromagnetic induction, I know somehow that its related to the Lorenz force as the electrons in the conduction band of say the coil interact with the magnetic field ,which results in separation of electrons and positive ions which...

@Dale : “The COP of a heat pump and the efficiency of a heat engine both depend strongly on the temperatures of the hot and cold reservoirs. For this calculation you need to go back and check the sources for the temperatures corresponding to each of these numbers. You will find that the Stirling...

I was dealing with nonlinear systems of differential equations like the Lorenz equations (https://en.wikipedia.org/wiki/Lorenz_system). Now there is a trapping region of this system defined by the ellipsoid ρx^2+σy^2+σ(z-2ρ)^2<R. I wondered how this region is found and I found out that a...

The Klein-Gordon equation is based on the relation (E-eΦ)2-(pc-eA)2=m2^2c2, which is the magnitude of the difference between the momentum four-vector and the four-potential. Since the magnitude of the momentum four-vector is given by E2-p2c2=m2c4, does it follow that the magnitude of the...

Fμν = ∂μAν- ∂νAμ ∂μFμν = ∂2μAν - ∂ν(∂μAμ) = ∂2μAνWhy ∂ν(∂μAμ) and not ∂μ∂νAμ ? And why does ∂ν(∂μAμ) drop out? thank you

From Weinberg, The Quantum Theory of Fields, Vol. 1, there is the statement that "the only way" to merge Lorentz invariance with the cluster decomposition property (a.k.a. locality) is through a field theory. He uses this argument basically to justify that any quantum theory at low energies...

I wonder these equations can satisfy the Lorenz condition?? I mean.. how above equations can satisfy the divergence A + 1/c^2 dϕ/dt =0.

Features: No external dependencies. Arbitrary order simulation (accuracy limited by float precision). No finite difference errors. Can be extended to arbitrary precision with gmpy2 and two more lines. Enjoy! Parameters: order step size number of steps initial conditions (x, y, z) parameters...

For example, Lorenz transformation of time means That measurement of time changes from one observer to another. I have read that this means moving clocks run slower. But this can't be true because Lorenz transformation of time depends on both of the seed of the observer and the object he...

Hi. Here, somebody apparently derives Maxwell's equations using only symmetry of second derivatives and the Lorenz gauge condition. Unfortunately it's in German, but I think the basic ideas are clear from the maths only. In this derivation, the magnetic field turns out to be divergence-free...

Can someone explain to me (or point me towards a source) how is the Lorenz Gauge derived? I am reading the Griffiths book and from what I understand we can do the transformation ##A' = A + \nabla \lambda## and at the same time ##V' = V - \frac{\partial \lambda}{\partial t}## and B and E remain...

I am given the equations of Lorenz with respect to deterministic non-periodic flow: \frac{dX}{dt} = Pr(Y-X), X(0)=X_{0} \frac{dY}{dt} = -XZ + rX - Y, Y(0) = Y_{0} \frac{dZ}{dt} = XY-bZ, Z(0) = Z_{0} where Pr is the Prandtl number, r = Ra/Rac is the ratio of the Rayleigh number to its...

Hello, friends! My textbook, Gettys's Physics, says that the Lorenz gauge choice uses the magnetic vector potential $$\mathbf{A}(\mathbf{x},t):=\frac{\mu_0}{4\pi}\int \frac{\mathbf{J}(\mathbf{y},t-c^{-1}\|\mathbf{x}-\mathbf{y}\|)}{\|\mathbf{x}-\mathbf{y}\|}d^3y $$and the electric potential...

Is it correct to say that the Lorenz curve is the normalized integral of the quantile function with respect to the x-axis?

Homework Statement A Lorenz system is given by x' = sy - sx y' = 3sx - y - xz z' = xy - bz In the vicinity of point x = y = 2s, z=4s , for s>>b, show motion is aligned with the y,z plane (sub these values in and x' is 0). By considering the evolution of vectors [2,0,1+sqrt(5)] , [0,1,0]...

Hi. I'm trying to get the Lyapunov coeficient for a Lorenz System (namely, a laser, using the Lorenz-Haken model) but I'm not getting the plots that would be expected. This is how two trajectories with near identical initial conditions behave (only one of the variables): And here's the...

As more wind turbines are installed worldwide, I was wondering how much of an impact on weather they could/would have. (Full disclosure: I am not trained, merely an interested non-scientist) Collectively, wind turbines are collecting considerably more energy than Lorenz's butterfly, so could...

Why is it that in SR we always seem to jump to the Lorenz equations when there is a simpler way. This is the concept of an interval. The interval is defined as the square root of ( T squared minus X squared) . In Special relativity the time and distance are different for different...

Homework Statement Cooling of a food from 293K (20 ⁰C), freezing it at 272K (-1⁰C), and further cooling to 253K (-20 ⁰C); using cooling water rising in temperature from 293K (20 ⁰C) to 303K (30 ⁰C) to accept heat. The specific heat of the unfrozen food is taken as 3.2 kJ/kg K, that of the...

I'm having trouble reproducing some of the results regarding gravitational waves in the Wald's General Relativity In section 4.4 of gravitational radiation, eq.4.4.49 shows the far-field generated by a variable mass quadrupole: $$ \gamma_{i j}(t,r)=\frac{2}{3R} \frac{d^2 q_{i j}}{dt^2}...

I have 2 questions about the Lorenz attractor: 1)Is the Lorenz attractor considered to be a fractal set? 2)If it is so, then what is its topological dimension? Thanks.:)

Take the Lorenz equations x'=σ(y-x) y'=rx-y-xz z'=xy-bz with σ=10, b=8/3 and r=28 as a typical example of chaos (I am using primes to indicate total time derivatives in this post). A basic property of a chaotic system (where the flow in phase space is a strange attractor) is that if you pick...

A highly accelerated object near the speed of light,should be seen contracting faster,than the speed of light.Maybe the contraction could not be observed?

I have been studying history of relativity theory and now it seems to me, that it is wrong to automatically assume that proofs of Lorentz covariance are proofs of Special relativity theory. It seems to me, that there is broader group of theories, that are compatible with Lorentz covariance but...

Length contraction velocity question. Suppose there are two sets of binary neutron stars in mirrored synchronous orbits one light year apart with zero differential velocity between the orbits center of mass. Both sets of binary stars are orbiting very fast causing velocities with respect...

This is Problem 10.6 in page 422 of "Introduction to Electrodynamics" Edition 2 by David Griffiths. The question is: Which of the potentials in the following is in the Coulomb gauge? Which is in Lorenz Gauge?( Notice that these gauges are not mutually exclusive.) This is what the solution...

i am searching the physical significance of lorenz and coloumb gauge but can't find anything besides that coloumb gauge is used for finding time independent potentials while lorenz is for finding time dependent potentials. and i'll be really grateful if u give me applications of then in any field.

Homework Statement Show that there is a certain ellipsoidal region E of the form rx2 + σy2 + σ(z-2r)2 ≤ C such that all trajectories of the Lorenz equations eventually enter E and stay in there forever. Homework Equations Lorenz Equations: \dot{x} = \sigma (y - x) \dot{y} = rx -...

Hi! I've seen it stated that because of Lorenz and translational invariance \langle 0| \phi(x) |0 \rangle has to be a constant and I wondered how to formally verify this?

Newtons third law states that there is a counter force to every force. Unfortunately this doesn't seem to work for moving point charges. The Coulomb force cancels out but the B-Field of a moving point charge is: \mathbf{B}=\frac{\mu_0}{4\pi}q...

Lorenz Curve question. HELP HELP! Urgent? If a country has a coefficient of inequality (CI) of 0.99, describe the graph of the Lorenz function in relation to the line y=x. Hence comment on the income distribution.

In the Lorenz gauge, the Maxwell equations reduce to four inhomogenous wave equations, with the charge density acting as the source for V, and the current density for A. For now, just take a static charge distribution -- say, a point charge at the origin. It is well known that a static...

Homework Statement http://imageshack.us/photo/my-images/535/newpicture3.jpg/ Homework Equations Honestly i used the equation in Strogatz 10.3.3 so I am not sure how to do it for others. The Attempt at a Solution http://imageshack.us/photo/my-images/406/worke.png/...

Thanks for reading! Homework Statement I have been given a proof for the lorentz transformations (which I only partly understand) that relied on the two relativity postulates (equivalence of inertial systems and the speed of light being constant) for the case of two standard inertial...

I have created a physics simulation for the famous Lorenz Waterwheel that also graphs its velocity, acceleration, and water distribution in real time. Thus, the Lorenz attractor emerges. https://www.youtube.com/watch?v=http://www.youtube.com/watch?v=9VwQhF7tjoQ I posted this here...

Homework Statement the particles in a high energy accelerator experiment are approaching each other head on, each with speed of 0.9520c as measured in laboratory. what is the magnitude of the velocity of one particle relative to the other? Homework Equations vx = vx' + u / 1 + (uvx' /...

The string theory is believed to take the form of a Calabi–Yau manifold. But the exact shape is not yet known. Is there any possibility that Lorenz attractor equations can define its shape?

π²³ ∞ ° → ~ µ ρ σ τ ω ∑ … √ ∫ ≤ ≥ ± ∃ · θ φ ψ Ω α β γ δ ∂ ∆ ∇ ε λ Λ Γ ô Homework Statement Show that Lorentz' gauge equation ∇.A = -µ(jωε+σe)φ is the equation of continuity ∇ .Ji = (jωε+σe)/ε P(R) Homework Equations The Attempt at a Solution I tried taking curl, div of...

It's not clear to me why the Lorenz model shows us that the apparent unpredictability of turbulent fluid dynamics is deterministic. Can anyone explain?

My teacher told me that in columb gauge we have div A = 0 along with d/dt(Ao) = 0 where A is the vector potential and Ao is its time component , and time & space are not on equal footing , so these are two degrees of freedom and in lorenz gauge we have 4 dimensional divA = 0 where space & time...

I started to read a bit of Konrads Lorent work, since he was pointed to me in this thread by Andre: https://www.physicsforums.com/showthread.php?p=2437331#post2437331 Ive come across on this...

Homework Statement A clock is moving past us at speed v=\frac{c}{2} reads t^{'}=0 when our clock read t=0. Using the Lorentz tranformation, find out what our clock will read when the moving clock reads 10s. Homework Equations t=\gamma(x^{'}+\frac{Vt^{'}}{c^{2}}) The Attempt at a...

Is corretct, that a general lorenz transformation don't satisfaction axioms of group structure? Let, GL(A,B) is general Lorenz transformacion from a frame A to frame B, which B is moveing a velocity V with respect to A. And GL(B,C) is likewise G. L. from B to C. A frame C has a valocity U...

Homework Statement I'm using the textbook "Nonlinear Dynamics and Chaos" by Strogratz. So far, it's been terrific. However, I got to the section on the Lorenz attractor and got stuck. The author has a picture and an explanation that eludes me. The picture in question can be seen on this...

I understand the concept of a gauge transform, and I understand why it is that the magnetic field would be unchanged with the addition of the gradient of an arbitrary scalar potential onto the magnetic vector potential A, and I understand why the electric field E would be invariant under the...

I have made a new version of Faraday's homopolar motor. This was the first device to demonstrate the connection between electricity, magnetism and motion. Faraday's motor included a beaker of mercury as the outer conductor. This has been demonstrated in classes. My motor comprises gold-plated...

Homework Statement Using the Liapunov function V=1/2(x^2+\sigma y^2 + \sigma z^2), obtain conditions on sigma, rho, beta sufficient for global asymptotic stability of the origin in the Lorenz equation. Homework Equations The Lorenz equation \dot{x}=\sigma (y-x); \dot{y}=\rho...

If I am watching spherical mass A that is traveling away from me at close to light speeds it lorenz contracts like I am looking down at a plate. Does the distance mass A is from me contract also or does it stay the same distance away ?

I didn't know where to put this notice, but the father of chaos theory died yesterday at his home in Cambridge at the age of 90.

I've gotten out most of this question, it's really just the last part that's getting to me at this stage. I'd never seen the http://mathworld.wolfram.com/DeltaFunction.html" before so it might be because of that. I've an idea how to do it but I just end up in a mess of partial derivatives. I'd...