How do ordered, non-chaotic patterns emerge from the Kuramoto-Sivashinsky equation with a temporally periodic parameter?

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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'?

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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

What is the most Operating System (OS) which can be INSTALL on Tiny hard devices like Raspberry Pi (RPi) hardware ?

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03 March 2021 1,931 5 View

Can we classify HV and LV lines based on line length?

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03 March 2021 4,116 4 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

Is there a classification scheme for rock cavities or caverns with respect to their size and shape?

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02 March 2021 4,511 3 View

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

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02 March 2021 4,910 3 View

Is there a powerful system for the security of the systems distributed on IoT systems?

02 March 2021 3,858 10 View

Which is suitable for use with Python? MySQL or SQL Server?

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01 March 2021 3,422 3 View

How to Eliminate cosine error and abbe error in LASER measurement system(for example Rhenishaw XL80)?

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28 February 2021 4,890 3 View

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

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27 February 2021 356 6 View

I need dataset for recommandation system?

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27 February 2021 7,063 7 View

Sukanta Basu

Mark,

Why don't you compute Lyapunov exponents from your simulation and compare with the standard K-S results? Another possibility would be to compute some measures of nonlinearity from the forced K-S simulation. If the result is close to periodic, you will not be able to detect any sign of nonlinearity.

A few references:

Kaneko, Kunihiko. "Lyapunov analysis and information flow in coupled map lattices." Physica D: Nonlinear Phenomena 23.1-3 (1986): 436-447.

Ciliberto, S., and B. Nicolaenko. "Estimating the number of degrees of freedom in spatially extended systems." EPL (Europhysics Letters) 14.4 (1991): 303.

Chaté, H. "Lyapunov analysis of spatiotemporal intermittency." EPL (Europhysics Letters) 21.4 (1993): 419.

R. Mark Bradley

Dear Sukanta,

Thanks very much for your valuable input. Can you suggest a method we could use to compute the Lyapunov exponents? Could you give an example (or examples) of a measure of nonlinearity that we might apply? Chaos is a subject that I know little about, and so your help is very much appreciated.

Best regards,

Mark

Hi Mark,

I will send you an email with information.

Sukanta

Excellent! Many thanks.