# Questions tagged [numerical-modelling]

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### stability issues - how to find and fix them? [closed]

When reading about the stability of the softmax function, I found a nice trick one can use during implementation: subtracting the maximal element from all elements. That way none of elements "...
1 vote
104 views

### Educational Purpose: How to synchronize chaotic systems

The graph plots the X coordinate of the synchronized Lorenz chaotic system. I am self learning by reading research articles on how to synchronize identical chaotic systems. But as seen from the figure,...
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236 views

### Roadmap for Career Transition to Computational Science

What sort of path should I follow to make a the transition from high school physics to computational science? Context 15 years teaching experience in physics and general science. Maths is currently ...
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1 vote
125 views

### Best finite difference scheme in 2D for the mixed derivative

The are good methods to deduce finite difference schemes for derivatives of functions of one variable. But how to get a good one for the mixed derivative of a function of two variables $u=u(x,y)$, ...
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1 vote
81 views

### Does anyone know how to add a forcing term at the center of a cicular membrane?

I am here once again searching for wisdom, as some of you might notice I asked a related question a few days ago. And now I am struggling to add a forcing term at the center of the membrane, in order ...
138 views

### How is entropy taken into account in a FV solver?

When solving for a given PDE, how is the entropy taken into account? Does the fluxes has another form? Or is the entropy PDE for a given entropy-flux included in the solver?
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### In electromagnetic simulation, how much does the feed model impact an antenna's directivity performance and E-field phase readings?

Question: How much would a simplified feed model in an EM simulation alter an antenna's directivity and the E-field phase reading when compared to using a more complicated/realistic feed model? I am ...
138 views

### Solving system of ODEs, where time derivative approaches infinity due top initial condition

I am trying to solve a problem in python using scipy's solve_ivp. The system of ODEs I am trying to solve is for coupled where I am solving for two time-dependent ...
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104 views

### What is the difference between approximations of mixed derivative and how to implement it

currently I am solving 2D nonlinear second order differential equation containing mixed derivative. I started searching how to descretisize it and found two formulas for 4th order approximation. First ...
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147 views

### Shallow water model for year-round watershed runoff

I have an (maybe not so clever) idea to apply the shallow water model for computing the year-round watershed runoff of a catchment. It means using of real topography with variable slopes and roughness,...
1 vote
92 views

### Improved euler on hybrid methods where both time and space are discretized?

I am trying to understand how to use the improved euler method on MPM simulations. In the kind of MPM simulation I am doing with forward euler the order of operations is as follows: Write particle ...
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124 views

### How do the navier stoke equations model materials who "forget" their original form?

Sorry for the screenshot but I don't want to try to format this on latex: We have this annotation of the Navier-Stokes equations: I am particularly puzzled by the viscosity/stress term. For an ...
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1 vote
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### Numerical diagonalization of Hamiltonian

Framework I am trying to diagonalize the Bogoliubov-de Gennes Hamiltonian. The problem is that the Hamiltonian contains a Laplacian. This could be solved by using a discretized Laplacian. How I tried ...
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