Why is it important that Hamilton’s equations have the four symplectic properties and what do they mean?

The symplectic properties are: time invariance conservation of energy the element of phase space volume is invariant to coordinate transformations the volume the phase space element is invariant with respect to time I’m most inerested in what 3 and 4 mean and why they are important. Answer Coordinate invariance guarantees that the phase space M … Read more

Magnetic B Field of Point Charge Not at Constant Velocity

I’m working on an N-body simulator for charged particles. I know that moving charged particles generate a magnetic field, and another moving charged particle could be effected by this magnetic field. Using the Maxwell’s Equations we can derive the magnetic field of a point charge moving at a constant velocity, which is roughly approximated by … Read more

Friction simulation in case of body moving with constant velocity and no external force

I am trying to write a simple physics simulation but have troubles with how friction works. Let’s assume a body of mass m is moving horizontally on a plane with initial velocity v0. Can someone please explain me how friction works in this case? Is there a constant friction force opposite to the direction of … Read more

Binning or just skipping values in a simulation to avoid autocorrelation

Given a set of data from a generic Montecarlo simulation xi, (1=1,…,N), autocorrelation is expected to happen between data points within relaxation time τ (correlation time) distance between each other. Now, I know that a possibile approach to reduce/avoid correlation is to set up bins much greater than the relaxation time and compute an average … Read more

Analytical solution of the thermal conductivity equation [closed]

Closed. This question needs to be more focused. It is not currently accepting answers. Want to improve this question? Update the question so it focuses on one problem only by editing this post. Closed last year. Improve this question What is the exact analytical solution of a 1D thermal conductivity PDE: ∂T∂t=α⋅∂2T∂x2, where T = … Read more

Calculating temperature from molecular dynamics simulation

My understanding is that temperature is an inherently macroscopic quantity, but I’ve seen a number of people talk about calculating the temperature of ideal-gas simulations like this one. To take one example, in the final simulation here the author, a physicist, mentions calculating the pressure and temperature of the particles in his simulation. Is it … Read more

Is our universe an emulation?

I was watching one of Neil Degrasse Tyson talks and there was a scientist (can’t recall his name sorry) who was talking about a recent discovery: “Doubly-even self-dual linear binary error-correcting block code” has been discovered embedded within the equations of superstring theory. Is this for real? Does it imply that our universe just a … Read more

System that is more efficient to simulate than to compute

I know some physics calculations require alot of computing to solve. Are there currently systems where it is more logical to do an experiment to “let the universe simulate the experiment for us” and measure the outcome instead of calculating it out of time/resource concerns? Note i do not mean the complexity of the experiment … Read more

Adiabatic turning on of coupling constant in simulation of ϕ4\phi^4 theories in the JLP algorithm

In the Quantum Algorithms for Quantum Field Theories by Jordan, Lee and Preskill they have devised an efficient algorithm to simulate ϕ4 theories. Given by the Lagrangian density L(φ)=12[∂μφ∂μφ−m2φ2]−14λφ4. During the simulation they prepare the state and then turn on the coupling parameter λ adiabatically (Edit: The simulation itself is not adiabatic, it uses the … Read more

NN-body gravity simulator: why does energy conservation break down when introducing an adaptive timestep?

I am playing with an N-body gravity simulator using the velocity-verlet algorithm. In the actual simulation I normalize everything so that it is nicely behaved numerically, but I’ll express things in real units here. My acceleration on body i is →ai=∑j≠iGmj||→rij||3→rij The basic, constant timestep implementation works well, as long as things don’t get too … Read more