Recent content by AiRAVATA

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    Best bound for simple inequality

    Let's see if I got it. Suppose I want to find the best constant for the inequality \int_0^\mu f(x) dx \le K \int_0^1 f(x) dx, where f(x) \in C^1(0,1), f(0) = 0, f(x) \ge 0, and 0 \le \mu \le 1. Let f_n(x) = \begin{cases} \frac{n+2}{n+3} x(2\mu -x), &0 < x \le \mu, \\ \\ \frac{n+2}{n+3}...
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    Best bound for simple inequality

    I see. Thanks a lot.
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    Best bound for simple inequality

    Hello all, the problem I have is the following: Suppose f \in C^1(0,1) and f(0) = 0, then f^2(x) \le \int_0^1 f^2(x) dx, but I was wondering if 1 is the best constant for the inequality. In other words, how do I determine the best bound for f^2(x) \le K \int_0^1 f^2(x) dx...
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    What Equation Combines Laplacian and Time Derivatives of a Vector Function?

    Indeed.---EDIT--- Err, not quite. I hadn't noticed the sign of the Laplacian.
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    What Equation Combines Laplacian and Time Derivatives of a Vector Function?

    It is the Newton equation for the small displacement of a string (or membrane, etc.) considering friction.
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    Multi-region Finite Difference- Interface between materials

    Colud you please post the problem you're trying to solve? I'm not sure, but it looks like you're missing some sort of jump condition. You should check if your algorithm is correct when j = Ai, because that's where the coupling occurs.
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    Doubt regarding constants. Elastic Beam Theory.

    It thought that was implied given the equation posted in #1. Agree. I might have been unclear about this point, but boundary conditions are more complicated than "simply supported", the reason why I didn't elaborated is because they have little to do with the original question. I understand...
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    Doubt regarding constants. Elastic Beam Theory.

    Ok. After a little reading, I now know that N is the axial tension, and in my case, is equal to zero, because the beam is not under the effects of prestress.
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    Doubt regarding constants. Elastic Beam Theory.

    Sorry for late reply and thanks for your attention. I'm having the flu and that has kept me from thinking about the problem. First, Nayfeh is a classic author in perturbation theory and nonlinear oscillations, and has several papers on nonlinear beam theory. The reference I give is from his...
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    Doubt regarding constants. Elastic Beam Theory.

    Well, the unusual notation comes from the book of Nayfeh and Mook, and from the literature I've consulted. I used to think that the second derivative term had something to do with some sort of "tension", like in string theory, but now I think I'm wrong. From what I've read, it comes from...
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    Doubt regarding constants. Elastic Beam Theory.

    Hello. As a good mathematician, I'm having troubles reading some constants for a PDE. I'm modelling an elastic rod using the equation \rho A U_{tt} - N U_{xx} + E I U_{xxxx} = 0, where "\rho is the beam density, A and I are the area and moment of inertia of the beam cross section...
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    How to handle the Dirac delta function as a boundary condition

    There shouldn't be any epsilon in the equations.
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    Solving second order PDE by separation of variables (getting 2 ODE's)

    The whole point of perturbation techniques is to simplify a problem by using the small parameter. How come you ended up with a simpler problem that is still dependent of the small parameter?
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    Laser rate equation(ODE) simulation problem

    Thas far from truth. You should always adimensionalize your problem, as it will give you a general perspective on the system and (in nonlinear cases) important values to work with. Imagine you want to model the behavior of a string of infinite length, tension N and constant density \rho, with...
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    Why does separation of variables work?

    Thats right, because if you don't specify what are x and y, then that equality is ambiguous (in the context of the ode you want to solve). P.S. You can also see separation of variables as an example of the implicit function theorem.
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