Questions tagged [laplace-transform]
Use for the Laplace integral transformation.
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Laplace transform of triple convolution involving Heaviside function — stems from multi-state random walk
I'm a bit stuck on this problem stemming from a multi-state random walk.
I have a function of the form
$$C(t) = \int_0^t dt' \theta(t'-T)A(t')B(t-t')$$ and I'd like to calculate its Laplace transform....
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0answers
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Diffusion in a Semi-Infinite Medium: Breakaup of a Duhamel Convolution Integral
For a diffusion problem in a semi-infinite domain with a transient boundary condition, the temperature profile can be obtained from Duhamel's Principle as
$$
\theta(r,t)= \int_0^t \frac{\partial \phi}...
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1answer
85 views
Diffusion equation with time-dependent boundary condition
I was trying to solve this 1D diffusion problem
\begin{equation}
\dfrac{\partial^2 T}{\partial \xi^2} = \dfrac{1}{\kappa_S}\dfrac{\partial T}{\partial t}\, , \label{eq_diff_xi}
\end{equation}
with ...
2
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1answer
205 views
Density of states for 3D simple harmonic oscillator
I have the thermal partition function and the density of states for the 3D simple harmonic oscillator, which are given below
$$
Z(\beta) = \frac { 1 } { \left( 2 \sinh \left( \frac { \beta \omega } { ...
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vote
1answer
144 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 ...
2
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1answer
84 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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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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105 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
111 views
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
87 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
240 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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64 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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votes
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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vote
1answer
4k 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
640 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 ...
