Recent content by afallingbomb

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    Graduate Proof of Zero Value for Vector Field Integral on Closed Surface

    Yes it does. Thank you very much for your time!
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    Graduate Proof of Zero Value for Vector Field Integral on Closed Surface

    So I am wrong to interpret a surface integral as the analog of a line integral to double integrals? I can think of a problem on a plane that gives me a zero line integral over the unit circle with fields of varying magnitudes. Consider the two vector fields...
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    Graduate Proof of Zero Value for Vector Field Integral on Closed Surface

    Thanks for the replies and I apologize if I wasn't clear enough. I agree with LCKurtz. The integral you presented, HallsofIvy, is over a scalar field. I was referring to a vector field which at the boundary only has normal components. LCKurtz, I did mean unit vectors, but now that I...
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    Graduate Proof of Zero Value for Vector Field Integral on Closed Surface

    What is the value of a surface integral over a closed, continuous surface of a vector field of vectors normal to the surface? The integral of ndS over S. I believe the answer is zero. Can someone direct me to a proof for an aribitrary closed surface?
    • afallingbomb
    • Thread
    • Closed Field Integral Proof Surface Value Vector Vector field Zero
    • Replies: 8
    • Forum: Calculus
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    Graduate Boussinesq Elasticity Problem Derivation

    Where can I find the derivation of the Boussinesq problem of elasticity (point load on an isotropic elastic infinite half-plane)? Besides the original 19th century paper, of course. Thanks!
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    Graduate Manipulating 2nd Order Tensor Expression: Isolating Q

    arkajad, thank you very much. You made me see that my problem was not well posed. The physical motivation of this problem stemmed from my curiosity on determining a unique material property (stiffness or compliance) from a specified stress and strain state at a material point. In the most...
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    Graduate Manipulating 2nd Order Tensor Expression: Isolating Q

    The double dot product between a fourth order tensor and a second order tensor is a second order tensor (now I'm referring to order as the number of subscripts... rank/order are used interchangeably in the literature). I can work it out using dyadics, but I'm not sure how to move around terms...
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    Graduate Manipulating 2nd Order Tensor Expression: Isolating Q

    Sure, Arkajad. The double dot product or double contraction is the inner product of the two tensors. If they were both second order tensors, their double dot product would yield a scalar. As is described...
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    Graduate Manipulating 2nd Order Tensor Expression: Isolating Q

    Given the expression \textbf{A} = \textbf{Q} : \textbf{B} where A and B are second order tensors of rank 2 and Q is a second order tensor of rank 4. How can I manipulate this expression to calculate for Q given A and B? In other words, isolate Q on one side of the equation. Thank...
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    Graduate Taylor Series Linearization of f(x) Around x0

    I am trying to linearize a function, f(x), where x is a normally distributed N(0,1) random variable. How can I perform a taylor series expansion around a deterministic value x0? Thanks.
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    Graduate Newton's laws in variable mass systems

    For a non-relativistic continuum (solid, fluid, etc) Newton's second law is simply the conservation of linear momentum expressed as: http://en.wikipedia.org/wiki/Cauchy_momentum_equation
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    Graduate Newton's laws in variable mass systems

    This may be of use here: http://articles.adsabs.harvard.edu//full/1992CeMDA..53..227P/0000227.000.html
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    MATLAB Extracting a Column from a 4D Double Array in MATLAB using Squeeze

    Thanks, Matonski. Squeeze does the trick!
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    MATLAB Extracting a Column from a 4D Double Array in MATLAB using Squeeze

    Hello, I'd like to access a column of values from the 4th dimension of a 4D Double array in MATLAB and then save them to a new matrix. For example: A = rand(3,3,3,3); A(1,1,1,:) gives me: ans(:,:,1,1) = 0.7077 ans(:,:,1,2) = 0.0669 ans(:,:,1,3) = 0.7794 I...
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    Graduate How Does an Ideal Gas Sphere Expand in a Vacuum?

    I thought of what seems to be a very classical problem but I can't find a solution for it. At t=0 you have a sphere of radius, R, made up of an ideal gas at a temperature, T, and pressure, P. The sphere is sitting in an infinite vacuum. At t>0 you allow the sphere to expand freely outward...