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Questions tagged [laplace-transform]

Use for the Laplace integral transformation.

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135 views

Density of states for 3D simple harmonic oscillator

I have the thermal partition function and the density of states for the 3D simple harmonic oscillator, which are given below $$ Z(\beta) = \frac { 1 } { \left( 2 \sinh \left( \frac { \beta \omega } { ...
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1answer
83 views

Laplace transform on thermodynamics equation

I'm trying to create a simple model of a single-flash geothermal plant which consist of 3 main parts (flash-separator, turbine, and condenser). Is there any way to create a transfer function using ...
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1answer
64 views

Why is the Laplace Transform essentially never used when dealing with problems involving resonance?

Both the Laplace Transform and the Fourier Transform can be applied to a PDE, for example the wave equation, and used to derive a solution to the equation. But I never see the Laplace Transform used ...
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0answers
103 views

Laplace Transform Density of States & Partition function

I am currently going through Pathria's Statistical Mechanics text , and under the Canonical Ensemble description, the author stresses that the partition function of a continuous system is the Laplace ...
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0answers
61 views

Fourier Transforms of Harmonic Functions

Suppose you are presented with the equation ($D=3$) \begin{equation} \nabla^2 A(x) = \nabla^2 B(x). \end{equation} Decompose $A$ and $B$ into their Fourier components, \begin{equation} A(x) = \int d^...
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3answers
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Why is there a sudden change in current between $t=0^{-}$ and $t=0^{+}$ when an active inductor is connected in series with a relaxed inductor?

Let us take the following question as an example: For the above question I drew the corresponding Laplace transform diagram, as follows (didn't draw the switch since it basically open circuit after $...
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1answer
81 views

Difference between Fourier and Laplace transforms in analyzing data

I have a set of displacement-time graphs from an experiment to convert to the frequency domain. Both the Fourier and Laplace transform seem to do this, so what's the difference between them (...
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1answer
231 views

What is this equation, written on a wall? [closed]

I've also asked this in MathOverflow, but since the equation in question is related to acceleration and physical phenomenon, I figure this is also a good place. I was asked to ID the following, but ...
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0answers
59 views

Question about the Radiative Transfer Equation (RTE) Phase function term

I am new to this subject. I am trying to understand what is the purpose of the phase function $$ ∂u/∂t=-v∘∇u-v( μ_{a}+μ_{s})u+∫vμ_s p_{s} (Ω^{'}→Ω)u(r,Ω^{'},t)ⅆΩ^{'}+q(r,Ω,t) $$ Were u= angular ...
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2answers
1k views

Why is the impedance of a resistor the same in time and frequency domains if the Laplace transform of a constant is not the same constant?

I'm sure this is a silly question, but if the Laplace transform of a constant is not a constant, e.g. $$\mathfrak{L}[1] = \frac{1}{s}$$ then how come the impedance of a resistor is the same in the ...
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1answer
3k views

Solving LR Circuit with Laplace Transform

I have a RLC circuit where the capacitor is connected in parallel with a resistance and inductance in series. The battery is connected "in parallel" with the capacitor and the RL branches. At t=0 the ...
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2answers
577 views

Express Laplace transform of voltage across a capacitor in terms of charge

In Charge Tunneling Rates in Ultrasmall Junctions section 2.1, the authors consider the problem of charge relaxation in a simple circuit shown in Figure A. The implicitly use an assumption made about ...