All Questions
Tagged with nonlinear-dynamics fluid-dynamics
7
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Realizing a modified transport equation
Stated somewhat informally, the continuity equation or transport equation $\partial_t\rho_t = -\nabla\cdot(\rho_t v_t)$ describes the evolution of a density where each particle flows along a vector ...
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Topologically Transitive Flow on $R^n$
I have been looking but cannot find the following: an example of a topologically transitive map on $\mathbb{S}^n$ or on $\mathbb{R}^n$ (for arbitrary $n$). Here, by a topologically transitive flow, I ...
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While solving the motion in plane problems (dynamics) how to figure out whether the radial accelration is 0 or mgsin(theta)?
There is a problem : A straight smooth tube revolves with constant angular velocity W in a horizontal plane about one extremity which is fixed. If at zero time the tube be horizonal and a particle ...
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Calculation of Symmetry generator of cylindrical KdV equation
I have calculated the generators of the cylindrical $KdV$ equation $$u_t+(u/2t)+uu_x+u_{xxx}=0,$$
but I got three generators, $$X_1=\partial_x,\\ X_2=2t^{1/2}\partial_x+\left(1/2t^{1/2}\right)\...
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Fourier Series Ansatz for 3D Rayleigh-Benard Convection
I'm trying to follow the derivation of a 9D Lorenz type system in the following paper by Reiterer et al (1998), and am having difficulties:
https://www.academia.edu/17449586/A_nine-...
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Extension of Burgers' equation
I recently encountered a viscous Burgers' equation type PDE, but with the addition of a derivative-squared nonlinear term (in dimensionless form):
$u_t - u_{xx} + uu_x - u_x^2 = 0\,,$
where the ...
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Trial solution for modulational instability
I have a simple linear differential equation of the following form:
$\frac{\partial a}{\partial z} + i\beta_2\frac{\partial^2 a}{\partial t^2} = i\gamma P(a+a^*)$
I seek the solution to $a(z,t)$, ...
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