Can anyone suggest a good numerical method to study a system of linear ODE's with periodic coefficients?

We are studying a system of the form dx/dt = A(t) x, where x(t) is a two-component column vector and A(t) is a 2x2 matrix with the property A(t + \tau) = A(t) for all t. Floquet theory can be...

06 July 2014 5,437 10 View

How can I solve this nonautonomous system exactly?

I would like to find the exact solution to the system dA/dt = B - ikv cos(wt) A dB/dt = -B - ik cos(wt) A, where A=A(t) and B=B(t) are complex and v, k and w are real constants. Got any ideas?

05 June 2014 4,904 31 View

Time-dependent perturbation theory for a non-Hermitian Hamiltonian?

Is anyone familiar with a version of time-dependent perturbation theory in which both the unperturbed Hamiltonian and the perturbation are not Hermitian? The unperturbed Hamiltonian is constant...

05 June 2014 5,502 7 View

If you scatter X-rays from a bulk polycrystalline material, how do you determine the mean crystallite size?

I imagine that experts in the field will find this question trivial, but I'm not one of the cognescenti. Thanks in advance for your help.

05 June 2014 3,122 8 View

How can I solve the second order ODE \sqrt(y)(1 + cy'') = x(x^2-1) with boundary conditions y(1) = y(-1) = 0?

Consider the boundary value problem \sqrt(y)(1 + cy'') = x(x^2-1) with boundary conditions y(1) = y(-1) = 0. Here y = y(x), the primes denote derivatives with respect to x, and c is a positive...

02 March 2014 9,463 7 View

Is this nonlinear diffusion equation exactly solvable?

Can anyone suggest a method to solve the nonlinear diffusion equation u_t = -u_xxxx + (u^2)_xx subject to the initial condition u(x,0)=delta(x) and the boundary conditions u, u_x -> 0 as x ->...

10 November 2013 5,548 9 View

Can a certain little-known 2+1 dimensional generalization of the KdV equation be solved using the inverse scattering transformation?

The system of equations u_t + (\partial_x^2 + \partial_y^2)u_x + u u_x/2 = -(p_x u_x + p_y u_y)/2 (Eq. 1) p_xx + p_yy = u_x (Eq. 2) reduces to the KdV equation if u and p are independent of...

10 November 2013 9,121 2 View

Does this ODE have a solution?

Does the nonautonomous nonlinear ODE [y''' - (y')^2 + xy]' = 0 have a nonzero solution that is bounded everywhere? If there is a solution, can it be found in analytical form? Note that there is...

10 November 2013 9,894 13 View

How can I solve a^2 y = y^3 - y''' - y'?

Can anyone suggest an analytical method to solve the ODE a^2 y = y^3 - y''' - y', where a is a positive constant? The solution should have y(0) = 0. Also y -> a and y' -> 0 as x -> infinity.

10 November 2013 774 63 View

Why do under-compressive shocks form?

Is there a way to see intuitively and physically why under-compressive shocks form? The formation of compressive (Lax) shocks makes perfect sense to me, but I can't see why under-compressive...

10 November 2013 1,042 6 View

Resistor definition in Piezoelectric bimorph with ANSYS workbench

Hello, good day! I am trying to simulate similar bimorph piezoelectric harvester with below commands. However, the output power doesn't change with resistor value. Please help to find the reason. ET,10,CIRCU94,0 !SET UP RESISTOR R,1,100000 !RESISTANCE VALUE TYPE,10 !SET ELEMENT TYPE E,1,2 !CREATE RESISTOR BETWEEN NODES 1 AND 2 Thanks in advance Regards,

02 March 2021 0 0 View

Gel electrophoresis result for total RNA samples, 1.5 Agarose gel was used, How to improve the integrity of RNA?

Gel electrophoresis, RNA degradation, RNA extraction from fresh tissue

02 March 2021 5,433 5 View

Why are the velocities so high in my Boussinesq approximation Fluent simulation?

Hello, I have a mechanism where air rises due to convective flows. In this simulation, nothing is driving the air except this. I understand that the Boussinesq approximation only works for small...

02 March 2021 4,910 3 View

Any specific pipeline or parameter to analyse total transcriptomics study of brain tissue samples?

I have two groups of brain samples, control and treated for example. It was total RNA nova seq sequencing. I tried all the available pipeline like: star+rsem+deseq2, Hista+stringtie+cuffdiff,...

27 February 2021 356 6 View

What are the application of Fixed points thoery in Chemistry.?

It is said that fixed point theory has lot of applications not in the field of mathematics only but also in various areas. So I am looking for applications in Chemistry only..

26 February 2021 3,533 1 View

Has anyone used the Illumina ITS1 primer sets?

Hi everyone, Illumina provides a list of primers to amplify with high taxonomic coverage the ITS1 region for further fungal sequencing, but I cannot find the exact amount necessary of each...

25 February 2021 6,969 3 View

How do you mesh a thin solid in Fluent?

Hello, I have used the shell function on SpaceClaim to create thin solids for the model I am studying. These are contained within an enclosure for my study. I chose this approach as it avoids the...

24 February 2021 8,856 3 View

Standard curve shifting over time. How do I stabilise the ELISA?

24 February 2021 1,365 3 View

Can we recognize signs of the "volatility clustering" property of a time series in its time domain plot?

My purpose is to recognize the volatility clustering property without statistical tests such as The Lagrange Multiplier (LM) test.

24 February 2021 4,150 3 View

Is is possible to pole with corona poling pellets of the sample material instead of thin films?

As it is highly probable that pellets will have a higher degree of air gaps and voids than thin films, is it possible to pole the samples with corona poling nevertheless? Or is there the...

24 February 2021 1,349 1 View