Science topics: Applied MathematicsNumerical Calculations
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Numerical Calculations - Science topic
Explore the latest questions and answers in Numerical Calculations, and find Numerical Calculations experts.
Questions related to Numerical Calculations
I am working on optimal control problems with state/control constraints. My current interest is to use penalty function to convert the constrained optimal control problem into an unconstrained one. Then the unconstrained problem can be solved either via indirect method or direct method. I've been trying to use indirect method to solve the problem.
The numerical difficulties have been mentioned a lot in the literature since the unconstrained optimal control problem contains a small smooth parameter or a penalty parameter. But I have not found any detailed explanation pertaining to this issue. When I use shoothing method to solve the unconstrained optimal control problem (approporiate initial guess is already provided), many issues often arise; one is the constraint may be violated even if I've adjusted the smooth parameter or penalty parameter; another is the singularity problem of the Jacobian.
However, if I use direct method with penalty function, I can get right answers sometimes. Can anyone explain my question? Penalty function works for direct method while not for indirect method? Thanks a lot!
For a 1D system, there is a way to calculate the Zak phase in the discrete form. Suppose C is some closed path in k-space (a 1D BZ). If we suppose the path is discretized into (not necessarily equidistant) ki steps with i=1,…,N and kN+1≡k1, the end result is:
(the formula exists in the appendix)
You can view this as the product (i.e. phase summation) of N small rotations of the eigenvector's phase as it's transported along C; the Im(log)-part merely picks out the phase.
If C is a non-contractible path in the BZ along a reciprocal lattice vector G, it is desirable to enforce a periodic gauge, in which case one would take:
(the formula exists in the appendix)
How we can implement the periodic gauge in numerical calculations? We know it is necessary when we talk about the berry phase. I mean how I can do a numerical calculation for considering periodic gauge mentioned above.
I did a calculation of the output power of VAWT with the following equation:
[Available output power]=([density of air]*[Swept area of blades]*[wind speed]^3)/2
[Real output power]=[Available output power]*[wind turbine efficiency]
I achieved some values, but I am not sure if it is the right way to calculate the output power.
According to VAWTs on market such as Makemu EOLO 3000, the output power is achieving 2kW at 8m/s which is 10 times bigger than my calculation, on the other hand, the output of EOLO 3000 was achieving more than the [Available output power]. Is there any other way to calculate the output power of VAWT?
A circular plasmid has three different but unique restriction sites for enzymes ‘a’, ‘b’ and ‘c.’ When enzymes ‘a’ and ‘b’ are used together, two fragments of equal size are generated. Enzyme ‘c’ creates fragments of equal size only from one of the fragments generated by those cleaved by ‘a’ and ‘b’. The plasmid is treated with a mixture of ‘a’, ‘b’ and ‘c’ and analysed by agarose gel electrophoresis. The number of bands observed in the gel is __________.
Thanks in advance !!!
Hello Researchers,
I am using Gauss Quadrature for numerical integration to obtain the stiffness and mass matrices for a plate element in my FEM code. We know that both these matrices are symmetric. However, I find that due to numerical integration the stiffness and mass matrix turns out to be asymmetric.
Kindly note that the asymmetry is not by any means large. The result of the subtraction of a symmetric matrix from its transpose is a null or zero matrix. If I subtract the stiffness and mass matrix from their respective transposes, the resulting matrix has all the non-diagonal terms of the order 10 to the power of -8 and all diagonal terms are zero (maybe for most cases it can be considered as a zero matrix).
At the point of writing this question, I am suspecting that this discrepancy (i.e asymmetry of the mass and stiffness matrices) is due to the finite precision arithmetic of floating-point numbers. (need your thoughts on whether my suspicions are true)
The end result of not having symmetric stiffness and mass matrices is that the 'eig' function in MATLAB gives incorrect eigenvectors although the eigenvalues are correct.
I would like to know if anyone has encountered such issues and how was it resolved.
I am also attaching a couple of links related to finite precision arithmetic errors below for your reference:
Thank you,
Jatin Poojary
On the basis of the Kaleman function, it is necessary to make numerical calculations for elliptical systems of equations. The results are obtained using computer packages of calculations.
For the 2D NS equation of the stream-vorticity formula:
^{$\partial w/ \partial = J(\psi,w) + (1/Re)\Delta w+f(x,y,t); w = -\Delta \psi$.}
^{Using the Fourier-Fourier basis Exp(I(k1*x+k2*y)), I got the evolution in spectral space:}
^{$dW/dt = LW+N(W,\psi_hat)$,}
^{where W, \psi_hat are complex. It has the solution W(t;W0) if the initial values W0 is given.}
^{To search the periodic orbits of this problem with a period T, I tried to solve the equation }
^{$ F(W0,T) := W(T;W0)-W0=0$,}
^{Using the Newton search, I can get:}
^{$ \partial W/\partial W0 * dW0 + \partial W/\partial T *dT = -F(W0,T)$. (*)}
^{Now the problem I meet is: both dW0 and dT are complex since the coefficient matrix of (*) is complex.}
^{SO how can I get a REAL dT?}
^{THANK YOU VERY MUCH!}
Hello everyone,
I do not know the dynamic viscosity of my material (ZrB2-SiC). It's ceramic.
Is there any way to calculate it numerically?
If you know about it, please comment. Thank You.
I have not found out any such curves by searching internet. If I try to solve it myself, then what I have is a functional differential equation, which I cannot solve. if (x,y) is a point on that curve, then (x+y''/y', y+1/y'') must be yet another point on curve (the ' indicates differentiation).
would that be a closed curve or some sort of spiral? I have not found any way to numerically solve it, for I cannot jump from (x,y) to (x+\del x, x+\del y) in small intervals. How can I, at least , numerically solve it?
Also, is there generalization of curve as 3D surface, 4D hypersurface, or in general, an (n-1) hypersurface (differential manifold)embedded in n-dimensional space?
What is seeked for a twice-differentiable curve which is expressble analytically
Hi all,
I'm interested in simulating CdTe solar cells with drift-diffusion modelling (coupled with transfer-matrix modelling). I have been able to find old papers where they explain the roll-over effect observed in J-V curves (near the Voc) due to a bad back contacts (such as the papers by Burgelman), but I haven't been able to find anything recent. I'm assuming the way CdTe layers are processed have changed a lot since back in the late 90's early 2000s.
Any pointers towards a recent 2016+ paper where they manage to model the roll-over effect due to the back contact would be greatly appreciated.
Thank you!
Jason
Hello everyone,
Using the spectral collocation method (SCM), I have successfully obtained the complex wavenumber k, displacement U and stress field S of different LAMB modes.
However, when I used the obtained k/U/S form the SCM method to solve the LAMB wave edge reflection problem, I had trouble with the calculation of energy reflection coefficients.
The sum of all the non-zero energy reflection coefficients (corresponding to the propagating modes) should be equal to 1, but I failed to get that right and the sum of those coefficients turned to be variable.
Power flux has been calculated as described in Mode-exciting method for Lamb wave-scattering analysis (JASA, 2004) by Arief Gunawan, and Sohichi Hirose in the form:
<P> = Real ( -iw/2*intgrate(sigma*·(du/dt), -h,h) )
If anyone has ever met this problem or knows how to solve it? Or, if there is any program available online for us to use and study?
I have been checking my program over and over again for half a month, but I still can't find the causes. Thank you so much for spending your time reading my question. I would really appreciate it if you can help me with this problem.
My program was written with reference to the article of Prof. Pagneux and has been attached as NromalIncident-Vincent Pagneux way.zip, in which the LambDispersionValidation.m can be run to check the basic results of my program (compared with the online program from https://www.mathworks.com/matlabcentral/fileexchange/73050-lamb-wave-dispersion-curve, as shown in the figure below).
To help you understand my program and save your time, I want to tell you some details about my codes:
- I can get the dispersion curves (as shown in the figure below). So I think the results of complex wavenumber k are right.
- For LAMB waves propagating in +x direction, the displacement field was assumed as u = U*exp(i(kx-wt)). The numerically obtained k may have the form a + bi, a - bi, -a + bi, -a - bi (a and b are positive real numbers). In the GetkInOrder.m, I have kept only those k with positive real part (+x propagating) and positive imaginary part (physically decaying with propagation).
- For LAMB waves propagating in -x direction, the displacement field was assumed as u = U*exp(i(-kx-wt)), so the k will be still kept k = a+bi.
Best regards,
Hao Qiu
I have been trying to get the spectrum for HHG based on Lewenstein model but I am not able to get the correct spectrum. Are there any matlab code available to compare?
I am using finite difference method to discretize the parabolic equation (explicit method), but confused about the chemical reaction term. Solving the generic equation for i specie involves a couple of species in the kinetic reaction equation since it is reversible ( Ex: A+B <-->C ). What is the best way to conquer the complexity in this manner? should I go with separation method and solve diffusion and reaction term separately. I am not quit sure if it is applicable. Thanks in advance.
I’m using COMSOL for circuit breaker PSS-1 2D time-dependent simulation. I have coupled all moduls: Heat Transfer in Fluids, CFD-Modul, Electric Currents, Magnetic Fields, Moving Mesh
in HT-Modul I use 3 HeatSources for Simulation of radiation, Joule-Heat(ec volumetric los), enthalpy transport.
in CFD Modul I use Force for Lorenz-Force consideration
EC and MF moduls are coupled with external current density.
MF:full field, ”in plane“ field, gauge A-fixing
boundary conditions: walls
initial values: T=293K, P=1atm(with hydrostatic correction), DC terminal 100A and ground.
between electrodes T=10000K or I tryed to use Gauss-Pulse function (quasi same effect)
Solver: fully coupled
Method: High-nonlinear Newton
Goal: to simulate plasma in switching device correct and watch internal thermo-hydrodynamics and V-A characteristics of circuit breaker.
when I start to calculate my modell, I receive no convergence in both Stationary and Time-Dependent cases.
when somebody need a comsol-file, just ask it
Nowadays, many researchers are devoting their research work to the non-singular kernel. Most of them have mentioned that "the main advantage of this kind of operators is that the singular power-law kernel is now replaced by a non-singular kernel," which is easier to use in theoretical analysis, numerical calculations, and real-world applications. But in my opinion, the singular power-law kernel is very easy to use in the mentioned above calculations and applications. Kindly share your thoughts.
I have evaluated the adsorption and desorption of two pollutants from aqueous solutions in singular and binary conditions with three different adsorbents.
In my adsorption dataset, there are four inputs, which include Initial concentration, adsorbents dosage, contact time, and temperature. Among them, only the Initial concentration of pollutants is variable and the rest of the environmental conditions are constant for all the samples.
Regarding the explained condition, is it possible and rational run a linear or non-linear regression model for my dataset?
Hello, the software I use is ANSYS Fluent. The subject of my research is the analysis of temperature distribution in the oven. At present, I have a very simple model to test, just how to try the heat of the heater to pass the dance. Or problems such as inability to converge during calculations, floating-point changes, etc. are also repeated.
1.
In the current model, the solid part has a heater, box, and door; and the fluid part has internal air, external air, and a simple cylindrical fan. There is a 0.5mm gap between the door and the box so that the internal air can be transmitted to the external air.
2.
In the cell zone condition, there is an energy parameter of 3570000 (W/m3) for setting the heater.
3.
In the boundary conditions, the six sides of the outside air, the side where the inside air connects to the outside air, and the fan exhaust are set as pressure-out. The fan inlet is set to velocity-intel, and the parameter is 1m/s. The heater, cabinet, and door surface are all set to convection, and the value of heat transfer coefficient is only 500W/m2-K for the heater, and 25W/m2-K for other parameters.
4.
In solution methods, after changing the gradient mode to green-gauss cell-based, numerical calculations are performed.
The above is a rough setting. I wonder if there are any more experienced or professional people who can help me with the problem?
I already familiar with Wolf and Sandri papers which suggest method to calculate the full spectrum of Lyapunov exponents by calculation of the Jacobin matrix, but it is too expensive for large (>1000 nodes) networks.
- Determining Lyapunov exponents from a time series, A Wolf, JB Swift, HL Swinney, JA Vastano - Physica D: Nonlinear Phenomena, 1985
- Numerical calculation of Lyapunov exponents, M Sandri - Mathematica Journal, 1996
I appreciate any guide in advance.
Hello all,
I am looking for an method / algorithm/ or logic which can help to figure out numerically whether the function is differentiable at a given point.
To give a more clear perspective, let's say while solving a fluid flow problem using CFD, I obtain some scalar field along some line with graph similar to y = |x|, ( assume x axis to be the line along which scalar field is drawn and origin is grid point, say P)
So I know that at grid point P, the function is not differentiable. But how can I check it using numeric. I thought of using directional derivative but couldn't get along which direction to compare ( the line given in example is just for explaining).
Ideally when surrounded by 8 grid points , i may be differentiable along certain direction and may not be along other. Any suggestions?
Thanks
With the limited ability of personal computers, it is often impossible to do numerical calculations because it involves a very large number of cells, for example, with 10 million cells. This problem is usually experienced when facing problems with large geometric sizes. What do we do to reduce the number of cells in a numerical simulation, but give good results?
Dear respective researchers, please give your reply for this case.
Thank you very much for your reply and contributions.
Kind regards,
Nazar
Dear Colleagues!
I ask you for cooperation in the implementation of the project
"Numerical calculation of the counterintuitive behavior of an underwater cylinder of infinite length under hydrodynamic loading"
Thank you in advance
Detailed description in attached file
I want to calculate natural convection in the horizontal rectangular enclosure (heated from below) and in the vertical rectangular enclosure by using the Nusselt correlation. However, I can not find the Nusselt correlation for the high aspect ratio and high Rayleigh number. Does anyone of you know these correlations and if yes, can you please share the references with me. Thank you.
Best Regards.
How we can compute eigenvalues of a 2*2 block matrix when each block is a square matrix?
I am modeling tailing dams, specifically studying liquefaction. I have imputed a seismographic record that has a duration of 200 seconds. When i configure the "seismic phase" using dynamic analysis, it is when my question appears. There is an option to configure the Dynamic time interval but i wanna know what specifically it is and how can i calibrate it correctly consideding that i have a Seismographic record of 200 seconds duration, or it doesnt affect??? However i want to know the meaning of that and and what is his influence in the Dynamic calculation.
Which turbulence model is most suitable for numerical calculations of flow and heat transfer in annular finned tubes geometry?
Solving Schrödinger equation numerically we will have finite size matrix, which has finite number of eigenvalues, that is - discrete spectrum. But we know, that atoms also have continuous spectrum. Is it possible somehow modify algorithm for quantum mechanic calculations to account continuous spectrum?
The wall maybe any kind of wall or shell. I mean the numerical calculation by codes and software to predict sound level and pressure. please tell me the name of the codes and the way that used to predict acoustic properties
Hello Everyone !
I want to perform FFT for the case when a rectangular wings is oscillating in direction of roll . The vertices, being generated at the tips are also changing their locations as the wings moves. In Tecplot 360 we can only specify the coordinates of the spatial position through probe or by entering the coordinates values .
So lets say if I put a point on the vortex at certain times step , in the next step the point will remain on its position but the vortex will be shifted to another position . Is there any way to move the position of probe point along with vortex at the time passes by .
Hi dear researchers,
I am currently implementing direct collocation NMPC,
However, I have a doubt on the control value for the first control u_0
that should be applied to the system once the control trajectory is found as collocation downsamples the system dynamics before solving the dynamic NLP problem.
will the control value u_0 be (u*(0)+u*(1))/2?
x_k+1 = f(x_k,u_0);
Should this be the case, will that not have a detrimental effect in the accuracy of the true control?
Kind regards
Hello! Please help to find a simple cross-shore sandy beach evolution (erosion+accretion) model for using in day-week scale (i had initial and intermediate profiles (once at month), and 3 hr forcing factors - wave height, period, wave length etc.
I need to estimate beach dynamics between my surveys (primary for getting beach width and slope).
Thanks for your advice!
General algebraic equation cannot be solved CALSSICALLY after degree 4 (Galois theory). Some case seems tracktable for the quintic using hypergeometric function and other technics. BUT I would know what is actually the best algorithm for solving numerically any algebraic equation (technic + calgorithmic complexity) ? for the two case Real and Real+Complex. Thx in advance for any answer.
HP
There are various methods that have been used in solving the fractional differential equations, but I am wondering what are the most powerful and efficient ones that can be applied effectively in solving the fractional differential equations?
When dealing with Boson system, we often meet Bogoliubov transformation, which is different from the unitary transformation. The matrix may be large that needs the numerical calculation. My question is how to perform the Bogoliubov transformation numerically?
I used differential evolution to determine the interatomic potential parameters of a model by minimizing a objective function that is the sum of the squared difference of experimental and calculated values of a set of properties. Now I'm trying to calculate the covariance matrix (and correlation matrix) for the fitted parameters. Is there a method for numerically calculate this matrix by probing the objective function? I've been able to numerically calculate the Hessian at the minimum and tried to use it's inverse as the covariance matrix, but the resulting correlation matrix has values that are outside the range (-1,1) so I'm no confident it is correct.
Hi,
Maxwell Stress Tensor (MST) method is usually used to calculate the optical force exerted on an object. However, my question is about the applicability range of this method. When do we use MST method and when we prefer to use other methods. Is there any reference that explains about different methods of optical force calculation?
Thanks in advance
I'm a little bit confused in regard of implementing MMA method. Should I transform the objective function into a Taylor series in order to use this method?
Most of tutorials explain the general theme of the technique but not how to implement it.
Hi, can we get the steady state solution directly of TPCT in Ansys / Fluent ?
Or, we should use transient solution till reach the final steady state ?
Hello all,
I want to implement Interval Newton Generalized Bisection method to find the root of a non-linear equation.
Though I have understood the overall idea ( start with an interval, evaluate new interval, if they intersect : unique solution). But I am not unable to understand when and how to bisect. I understand it's probably when there are more than 1 root.
May some one provide simple example/reference where this may have been explained.
Thanks
Up to my knowledge, I find that the simulation with regard to the simulate of two-dimensional mixed Volterra-Fredholm equatio is confined to be in a closed subset of R^n and there are several wonderful methods. However, I happen to get a integral equation in the following form (please see the attached picture). The only difference with the existing ones is that the integration with respect to x is from 0 to infinity and the boundary condition available is f(x,T)=h(x), with h() given, which is also quite weird. I desire to do a rough simulation in the last part to make a brief illustration but I get no idea and have no inspirations from the literature. Also, since I get little knowledge and experience in simulation of solutions to equations like that, I find it's hard for me to think out a practical method to do the simulation. I'm asking if I can get some useful inspirations from you, who may be experienced in numerical simulation of integral equations. Thanks a lot for your generouse help, your attention and your precious time.
It is said that approximate solutions are found where there is difficulty in finding exact solution or analytical solution. But still we calculate approximate solution for problems with exact solution or analytical solution. Being a student of computational mathematics I wanted to know the importance of finding approximate solution or numerical solutions.
Anscombe's quartet comprises four datasets that have nearly identical simple descriptive statistics, yet appear very different when graphed. Each dataset consists of eleven (x,y) points. They were constructed in 1973 by the statistician Francis Anscombe to demonstrate both the importance of graphing data before analyzing it and the effect of outliers on statistical properties. He described the article as being intended to counter the impression among statisticians that "numerical calculations are exact, but graphs are rough.
Which programming language is the best to use in CFD?
FORTRAN, MATLAB or any other?
Is there difference between the performance of these codes and applications such as OpenFOAM?
I am to numerically calculate the value of cost, for a certain optimal quadratic regulator. Cost in quadratic regulator is J=J(t)= int((x^2+u^2).dt, 0...inf). I have the numerical values of x and u as data signals. I want to calculate the total cost. Am I allowed to use Matlab syntax: sum(x.^2+u.^2), to have a nonscaled evaluation of cost for a fixed-step solver. Is it correct to evaluate J as J= sum((x.^2+u.^2).dt), where dt is the fixed-step size. The model has been simulated by Matlab syntax ode45 or similar solvers. What happens to the calculation if I don't use a fixed-step solver? And how to calculate cost for a variable-step solver?.
I have a dataset with categorical and numerical data. I want to apply clustering algorithm (e.g. K-means). As far as I know, the data should be numerical to calculate the distance between points (samples).
Any advice how to deal with the categorical data in this case? Is it allowed to change the categorical data to numerical data? If yes, how this can be done?
Thanks
I want to do some complicated numerical calculations in my research problems. Please suggest me any software to do this.
Hi,
How is it possible to calculate the DDSDDE numerically when dealing with finite strain plasticity problem.
The formula which I am using currently is:
DDSDDE= 2*(dS/dC)
Where: S- Second Piola Kirchoff stresses
C- Right Cauchy-Green deformation tensor
Is this formula correct?
Best Regards,
Ahmad
Could anybody share the source code of mathematical model of biofiltration, biosoption or adsoprtion? Usually, model is represented by system of PDE that includes mass transfer kinetic and dynamic equations, sorption isotherm and in the case of biological treatment - equation of biofilm degradation and microbiological growth.
I will appreciate any help provided. Thank you!
We live in a world of computations, there is no doubt about it. Computations that increase in terms of computarional demand every day. What do you think is the future in solving large scale numerical models? Some say OMP, others MPI and the romantics say cloud computing. What is your opinion and why?
PS: Any other methods used to solve in parallel or other techniques are more than welcome to be presented.
Take the viscous flow over a cylinder as an example. We know that for a specific range of Re number the Karman vortex appears behind the cylinder. This is due to the inequality in roughness of the lower and upper surfaces of the cylinder.
Also, in a numerical simulation in which the flow and the cylinder are 100% symmetric the Karman vortex appears.
One can say this is due to the round off error in the numerical calculations. But I'm not sure about that.
Does anybody have another theory or answer?
Thanks
Hi,
I am looking to solve an equation in three variables like
s == x*tanh(x), s == y*tanh(y), s == -sqrt(x^2+y^2)*tan(sqrt(x^2+y^2)).
Specifically, I'm only looking for the smallest non-zero value of s that satisfies this equation (there are infinite solutions in s, x, y).
I know that there should be a solution at s = 1.7089319, and that this is indeed the smallest non-zero value of s. I deduced this heuristically from an implicit plot using a program called GrafEq. (I tried the plot in Matlab but apparently it's too complicated for Matlab to handle).
However, using vpasolve can be rather problematic. Here is my code:
syms s x y
[sol_s, sol_x, sol_y] = vpasolve([s == x*tanh(x), s == y*tanh(y), s == -sqrt(x^2+y^2)*tan(sqrt(x^2+y^2))], [s, x, y], [1 2; -Inf Inf; -Inf Inf])
The output is
sol_s = Empty sym: 0-by-1
and similarly with sol_x and sol_y.
In other words, Matlab can't even find any solution for s (let alone show it is the smallest).
Apart from altering the search range for x and y (from -Inf Inf to NaN NaN or to some finite range), is there any other method or tool (in Matlab or elsewhere) I could use to solve this kind of equation numerically?
Thanks.
Can anyone please help me with Conference papers / Articles on analysis of beams using Timoshenko beam theory, effect of geometrical properties on analysis and also papers with numerical calculations to compare the results obtained using my procedure.
I’ll be very grateful for any help you can give me with this.
I am modelling a shallow foundation with midas gts nx and ı want to compare result with traditional bearing capacity method.Is there anyone know is it neccesary to apply pressure into the foundation etc.For ex after making pressure or displacement on foundation how can ı found bearing capacity?
I want to start learn CFD, I am good enough with Hoffman Computational Fluid Dynamics book but I need an starter maybe multimedia course to get my mind ready, so if you have any good free online course for start learning CFD please let me know about that. plus I'm good at programming and numerical calculation methods
hi dear all; consider 5 complex nonlinear equations with 5 variables. what is the simplest method for solution?
e.g. I calculate 4 combinations(i.e.nCr(10,1)=10,nCr(10,2)=45,(10,3)=120,(10,4)=210 using for loop).Can I get these four answers as four entries of a matrix?
The command I used is >> n=10;
>> for k=1:4
nchoosek(n,k)
end (which gives above four answers)
How to get these answers as a matrix of four entries?(1st answer as 1st entry, 2nd answer as second entry of the matrix and others accordingly).So that we can further work with that matrix
If I have to calculate 10C4(i.e. nchoosek(10,4)),10C3,10C2,10C1, Can I calculate all these four values using one command?
.e.g. in case of factorial If I have to calculate 1! 2! 3! 4! 5!, My command will be n=1:5 followed by factorial(n), which gives required factorials in one command.But in case of combination nchoosek(n,k) does not work the same way.It gives single answer for single values of n and k.If anyone has an alternative solution to my problem, kindly guide me
.In short, I want to calculate more than one combination using single code or single program or single command as in case of factorial above.
I want to solve the laplace equation on rectangle geometry.
My problem is that one axisc is much bigger than the other.
x=100 nm & y~1cm
One edge with Dirichlet boundary
Other two edges with Neumann boundaries equal zero
And the fourth edge with Neumann boundary equal to same non zero function
How can I overcome this badly scale ratio?
Which methods should I use?
Thanks in advance
Hey!!
I need to multiply viscous dissipation/heating term with a factor of 0.4( or say is as efficiency factor) and the resulting term should be further used as effective viscous dissipation term in further numerical calculations in fluent.
I searched a lot but could not find a way to implement this in fluent whereas several research papers that I am referring have implemented this in fluent.
Kindly help me in implementing this in fluent. Help will be highly appreciated.
Thanks
I'm trying to measure the pitch length of a non-perfect helix. I have some data points on that non-perfect helix for which I know (estimate) the axis and radius.
Currently, I'm sorting all the points (N points) along the axis and then measure the axial distance and also the angle of rotation for each couple of successive points (N-1 couples). So, each couple has its own pitch. Then I average all these calculated pitches, to get a single pitch for the whole helix.
The problem is that, as the helix is not perfect, so the pitch variation is significant which makes the measured pitch unreliable.
I was wondering if there is any solid and robust approach for pitch calculation of a non-perfect helix for which the axis is known?
Dear colleagues, I'm solving Poisson's equation with Neumann boundary conditions in rectangular area as you can see at the pic 1. I realized fully explicit algorithm, but it costs to much operations per time. Now I'm looking for economy algorithm in 2D.
Can you advice any? If you are using c++, maybe it's any open source librarys with poisonn's solver?
Fast Fourier Transformations are not allowed.
In some numeric calculations which concerned distillation process I found out that it can be higher than 1 so I wonder in which specific conditions this can occur. Thank you for any reply.
We define numerical reproducibility as an ability to obtain a bit-wise identical floating-point result from multiple runs of the same code. Indeed, the non-reproducibility of results often happens. But, we search for those applications where this non-reproducibility impacts significantly results or leads to completely wrong results. The accuracy of results is also of our interest, but not for very ill-conditional problems.
Dear Prof.,
We have an integral in which we have singularity. We try to use Matlab for numerical calculation. However, We have not found the correct way to calculate the integral. We use trapz or cumtrapz. However we can not remove the infinities in the integral. Please let you suggest me about this problem.
Thank you for your suggestion
thank you for taking your valuble time to answer.
i have one more question,( i am new to this field of study sorry for asking very fundamental question)
i am doing the experiment on exciting plasmon with kretschmann method.
using a 40nm gold film deposited on a slide glass.as for now im trying out water as the index matching layer between the prism and the slide gass which contains the layer.
my question is how do i calculate the plasmon excitaiton angle(with numerical calculation) for this specific setup ?
thank you
Recently I am stuty on the Numeric Calculation of 3-D translating-pulsating source(Haskind source) Green's function in Havelock form.LOBATTO rule could be used to eliminate the singulatity of of the Green's function expressed in single integration form and the Hess &Smith Polynomial Method could be adopted to calculated the complex exponentila integral.But the complex exponential integral for derivatives of Green's function oscillates with high frequency when theta=pi due to its tending to intinity.And how to deal with this singularity of partial derivative for 3-D translating-pulsating source Green's function????????
If you need a more particular knowledge of this problem ,you could read the attachment named the singularity of partial derivative.pdf
If anyone willing to tell me any method to deal with singularity of partial derivative for 3-D translating-pulsating source Green's function in Havelock form,or recommend me any material about this problem,it will be much appreciated.
Your response will be highly appreciated.
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Thanking you in advance
I have a set of measured data points that empirically defines a function of two variables. I need to fit this data set with a nonlinear analytical function that is given but it contains five adjustable fitting parameters in addition to the two variables. Let us define the error measure between the fit and the data using the traditional sum-square-error (with an optional user-selected weighting function) definition. The goal is to numerically calculate the fitting parameters that minimize this error measure, and some numerical routine is needed to do that. My problem is that all of the publicly available routines that I have tried look for relative minimums in the error measure instead of the global minimum. The routine declares success when a relative minimum is found. For my specific application there is an enormous number of relative minimums, so that almost any change in the initial guess produces an entirely different returned result. I have to manually keep track of which relative minimum (out of many because of many initial guesses) is the smallest. A smarter routine would not declare success each time a relative minimum in the error measure is found. Instead, it would remember results from prior initial guesses and recognize that if the most recent calculated relative minimum is not smaller than all prior calculations, then it needs to keep working. Does anyone know of a publicly available routine (e.g., a package in MATLAB) that does this?
I am trying to update a thermal finite element model with experimental thermography data. I use a gradient based nonlinear least square optimization algorithm using the trust-region reflective algorithm.
The objective function of my results is simplified explained the difference between the experimental measured temperature and the numerical calculated temperature. The optimized parameters are the experimental parameters as the heat pulse length and the orientation of the heat sources.
Out of my results I found out that if I optimize more than 4 different parameters, the results converge to non-unique solutions which are dependent of the initial parameter values.
I already checked the independancy of the parameters and received covariance values of less than 0.4 between the parameters.
I also checked the routine using a CMA evolution strategy based on the methodology of Hansen which delivers the same problem.
The tolerance of the optimization routine is set on 10^{-12}.
Does anybody has an idea what the problem could be?
Thank you very much for your input.
The question is about a imaginary cubic R^3 pointcoordinate-representation in which each corepoint (monade) is a basment for a graph which orientation can be defined using two angles (phi and psi).
This could have the advantage to be able to integrate functions based on tangents within the two angles defining a single line in the ordinary coordinatesystem and can solve problems like send and return values in communication systems (VSWR - r).
Once implemented - which is a very difficult quest, there could be a way to simplify functionality that can be integrated seperately - isn't it ?
The two angled representation in sort of cubes of the R^3 can then be used for magnetic and electric waves or for example building a function for calculating the evolutionvelocity of pointamout-mathematical functions for numerical sciences.
Using the Taylor-rows with the bernoulli-numbers for tangential calculations an amount of points or mathematical elements could be paralellized and the precision could be adapted fluently!
Is there someone having this expertise already giving me an advice about the concept?
Vertical electric field is using to tune the electrical properties of channel in FETs. In new 2D material this is referred to the shifting of electrochemical potential. In contrast in simple Nonequilibrium Green function formulism applying voltage to the gate or gates (DG/double gate channels) does not influenced Fermi level position in numerical calculation. Instead, it will change the shape of conduction band.
Is there any mathematical relation or physics formula that can explain the displacement or shifting of the Fermi level with respect to Fermi level on the time that no external voltage applied to the gate or gates, (considering martial properties)?
Anybody can explain this paradox? Is there any good literatures on the shifting of Fermi level due to applying electric field?
And what are the benefits of calculation r squared for linear regression ?
One of my task is connected with numerical calculation of the following kind of integrals
NIntegrate[g[x] Exp[n f[x]],{x,a,b}]
where g[x] and f[x] are given function, n=10,…,10000.
I can assume that f[x]<=0 in this range and g[x]>0 and can be limited by polynomial x^k.
I am searching for the most accurate way how to solve this problem. Exp[n f[x]] can be a very small value about 10^(-800).