Vahid Mosallanejad

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• PhD
• Assistant Prof at Westlake University

I have found the logic behind python way of coding is different from MATLAB. for example it is hard to accept a "for" loop has no "end" in the Python.

I need a book where the implementation of basic mathematical operations in Python is explained concisely. Basically I am looking for a learning materials where coding explained back and forth between MATLAB and python. Or authors assumes readers have a mindset of coding (numerical solution) using MATLAB but want to translate their MATLAB code to Python

Thanks for your answers in advance.

Regards

Vahid

Dear all chemists and physicists,

How to (deeply) understand Markov approximation? I did not satisfy by what was given on page (132) of the book "THE THEORY OF OPEN QUANTUM SYSTEMS" by Breuer, Petruccione. I have attached that page in the following.

I appreciate it if anybody can make it clear to me? Sadly, there is no justification for why this assumption can be correct.

Regards

Vahid

Just assume an arbitrary ( not pi or pi/2) phase is added to the sin or cos on the integral definition of Bessel function.

You can find the integral form here :

int ( exp[-i*(n \phi -x*sin(\phi-\phi_0)] ) on the domain [-pi pi]

here we have added "\phi_0 ".

Check the following integral attached as a pdf

I used to derive math equations by Mathtype. It seems Mathtype has not a version for Mac catalina yet. I appreciate if you guys can recommend me an alternative.

Hi,

I am looking for a 3D solver which is specifically based on finite-volume method preferably using unstructured mesh. It is a bless if the code or the software allows me to include a nonlinear source in form of

D. [ c(x,y,z) D (x,y,z) ]=f(u,x,y,z), where “D” refers to the vector differential operator.

On a MOS(metal-oxid-semiconductor) system, an energy splitting (shifting) exist between two-fold degenerate and four-fold degenerate conduction bands of silicon, perhaps when interaface is parallel to the [1 0 0] crystal orientation. Anisotropy in effecitve mass is blamed to be the reseason for such shifting. Later, a biased top gate will form a 2DEG (or a 1DEG) beneath the gate. It seems forming the Quantum Well (2DEG/1DEG) will lift the two-fold degeneracy and valley splitting occurs. The shape of quantum well and electron density 2DEG can be simulated by self-consistent solution using effective single band approximation for the hamiltoninan.

Is it possible to use some type of two band (6 band) effective mass hamilitonian and through the similar process of Self-Consistant solution of schrodinger-poisson equations observe the small splitting of lower valleies ( or observe combination of shifting and splitting of four-fold upper valleys)?

Many thanks for spending your time on above question.

Vahid

I have noticed, it is possible to evaluate one eigenvalue and the coresponding eigenvector by newton's method as it has been explained on :

https://www.vulcanhammer.org/2012/12/30/use-of-netwons-method-to-determine-matrix-eigenvalues/

Iteration in a loop, knowing the jacobian matrix, converge an initial guess to the closest "vector of answer".

The equation to solve is as: M[x]=\lambda [x] but the [vector of answer] arranged as X(i)=[x1(i) x2(i) x3(i) ... xn(i) \lambda (i)] and [x]=[x1(i) x2(i) x3(i) ... xn(i)]. M is a n by n matrix. It has been mentioned " The method is better at finding eigenvalues than finding eigenvectors".

I need to know if this method has been developed to acheive (correct by iteration) all eigenvalue-eigenvectors simultaneously. I believe the simulatenous correction in Newton's method is the most strongest point about this wonderful numerical method.

I would appreciate, if experts would kindly express their opinions on this problem.

Regards

Vahid

Dear experts

I need to generate mesh for a rectangular box with an empty area as it can be seen in the attachment. It must use the hexagonal cells. I need a MATLAB code. Inputs would be the vertices and faces of the 3D geometry. I believe 1D mesh on each independent direction, x, y, z can be used to control the fineness of mesh in each direction independently.

Anybody knows about a free code in this regard?

Thanks for your time and considerations in advance.

Dear people in the field of Quantum mechanics,

There are many online explanations about the semi-analytical solution for the problem of particle in a 1D finite potential well as well analytical solution for particle in a 2D box with infinite potential on barriers.

Basically, the continuity of wavefunction determines the eigen energies in such problems. However, online resources seems to be empty when it comes to the problem of particle in 2D finite potential well. I have only found a question in a physics forum which I have found the given answers unclear.

https://physics.stackexchange.com/questions/73571/how-to-solve-bound-states-of-2d-finite-rectangular-square-well

Anybody can recommend textbook (or a robust explanation ) where I can follow a semi-analytical solution of bounding states in a 2D rectangular (Not the square) finite potential well?

I do know that the first bonding states are not far from bounding states in a 2D box with infinite potential on barriers. However, here I require very accurate eigen energies and I need a semi-analytical answers {if it exists as a general answer} and not interested in numerical approaches.

thanks in advance.

Hi, to all experts on the Finite Volume method.

Is it absolutely essential to linearize a non-linear source ,term, of a non-linear PDE during the process of solving a PDE with finite volume method (FVM)?

Few times in textbooks and online lectures, I have saw, experts tend to linearize the non-linear source terms( for example in a 2D Poisson equation. Lets say u"-exp(u)=0 ) during the process of the discretization of a PDE with finite volume method.

However, considering the approximation of the piece-wise constant , I expect the non-linear source will add non-linear terms to discretized equations (i.e., exp( u (x_p,y_p) ), where x_p and y_p are coordination of the center of the control volume) and one can use the Newton's method to solve a set of nonlinear algebraic equation.

For example, we could have a final set of the algebraic equation as Au - diag( exp(u) )=b, where "A" is the coefficient matrix, resulting of discretization and "b" is a constant vector containing the information of boundary conditions.

What harm it could have, on the conservative nature of FVM, if one processed similar to what I have explained on above example.

Many thanks of you, if you stop by and take look at my question. :-)

Vahid