Good morning. I am researching the development of a theoretical material that behaves in a very particular way. Specifically, I am talking about a variable viscosity fluid whose properties change in function of small temperature changes and a secondary external variable (let's say an applied...
I've ended up with a variable coefficient wave equation, so I'm browsing for numerical solutions of similar problems at ScienceDirect.
A closed form solution at this point is like asking Santa Claus for Dominion Over the Universe (yeah, um... not going to happen).
JC
I have read that Brownian movement is used in certain stochastic processes, but I need further reading to be actually able to put some math into it. My research involves a stochastic process as well, but is an area of physics that so far I haven't been able to fully digest properly. Anyone who...
1. It can be either. No troubles there. Sometimes I use Fourier, sometimes a constrained poly regression.
2. I don't have the resolution to determine what u(x,0) is. It is impossible to measure. The only thing I can say for sure is that u(L,0)=S(0) and that u(0,0)=0. So u(x,0) is some function...
I don't use Mathematica, but I do have access to Matlab. I don't know there capabilities/limitations though.
The following equation would only be valid for a^2 constant:
u_{tt}=a^{2}u_{xx}
Otherwise I'm stuck with this one:
\frac{\partial^{2} u(x,t)}{\partial...
Just to clarify, the wave equation becomes:
\frac{\partial^{2} u}{\partial t^{2}}=\frac{\partial}{\partial x} (a^{2} \frac{\partial u}{\partial x})
When a is not constant. Any thoughts?
Hello exalted ones. I am working on a set of differential equations for my research and there is one that is becoming mortal.
I am solving a mechanical system whose behavior eq. is that of a one dimensional wave PDE. Namely:
u_{tt}=a^{2}u_{xx}
For which I would derive two parametrized...
Thanks.
It helped me solve the differential equation, and it also made me realize that the solution is not what I expected it to be. I believe I need to revisit the formulation.
Thanks again,
JC
I have spent hours and hours trying to solve a problem until reaching a dead point. I don't know how to solve, simplify, or proceed next with the following PDE:
m \frac{\partial^2 x}{\partial t^2} + 2 \frac{\partial m}{\partial t} \frac{\partial x}{\partial t} + x \frac{\partial^2...
I would go with the drafters. They know how to do it quickly and are better at industry drafting specs. They can even tell you what's relevant and what's not. As engineers we pay attention at the design part of the drawing, not so much to conventions. Nevertheless, it depends on the area you are...
Indeed. The problem is that at this scale everything costs so much money that it's unfair otherwise.
Maybe it's a good idea to see if there's a high precision manufacturer in your area. I remember visiting one somewhat near where I live when I was in the university. They charged large sums of...
Just as well, in the silicon industry masks are used to expose the silicon in the lithography process of manufacturing the computer chips. As the transistor gates have been getting smaller and smaller the process of creating these masks has been getting more and more complex, and so also the...
As far as I know, from an efficiency and leverage standpoint it's better to use hydraulics. However in the case of a robot I would fancy using other smaller devices depending on what it is to be used for and how much load it has to lift. I don't know about moving like muscles do, but I imagine...
Non-linear mechanics is always a pain because there are so many variables involved that we are only beginning to see and understand and there is still a long way to go.
In the mean time we are bound to do things in the way that Studiot suggests: by designing for linearity and making it easy to...