Questions tagged [laplace-transform]
Use for the Laplace integral transformation.
46 questions
3 votes
1 answer
227 views
How to derive Fourier-Laplace transform of random walk master equation on 2D lattice (Part 2)?
This question is linked with this question and is related to this paper. The Fourier-Laplace transform is given by: $$P(q,r,s)=\sum_{t=0}^{\infty}\sum_{m,n=-\infty}^{\infty}\frac{e^{iqm+irn}}{(1 + s)^{...
- 291
1 vote
2 answers
160 views
How to derive Fourier-Laplace transform of random walk master equation on 2D lattice (Part 1)?
I have certain gaps in clearly understanding the derivation given in this paper. Suppose a particle moves on a 2D lattice randomly. The probability of going in any one direction outb of four available ...
- 291
1 vote
1 answer
186 views
Units when solving with Laplace Transforms
I've worked with Laplace transforms to solve systems for a long time but never thought too deeply about the units of the output. Recently, I checked the units after solving a problem and it seemed ...
- 15
9 votes
3 answers
739 views
Relation between Legendre and Laplace transforms in statistical mechanics
I am working off of these lecture notes by Stephen Teitel for his spring 2025 Statistical Mechanics course to study the canonical ensemble in statistical mechanics. In doing so, I have come across the ...
- 2,015
3 votes
1 answer
237 views
Laplace transform and initial conditions harmonic oscillator [duplicate]
I am having trouble understanding Laplace transforms and initial conditions in the case of a forced harmonic oscillator of general equation of motion $$x'' + \omega_{0}^{2} x = \frac{f(t)}{m}.$$ In ...
- 242
0 votes
0 answers
83 views
How to read the axis on a bode plot?
I'm looking at a tutorial on bode plots. One of the poles is at 50. To find the frequency at 50, I assumed that I would start at 10 and then count grid-lines until I hit the 5th one. However, in all ...
- 101
3 votes
1 answer
254 views
Real time correlation function from inverse Fourier/Laplace transform
In a diffusive system described by Maxwell-Cattaneo equation $$\tau \partial_t^2 n+\partial_t n- D \nabla^2 n=0,$$ which reduces to simple diffusion at $\tau=0$, I have calculated the correlation ...
- 1,038
0 votes
1 answer
99 views
Laplace Transform of time evolution of Amplitudes involving correlation functions
The correlation function is given by $$ G_{ij}(t-t')= g_{i} g_{j} e^{(i\omega_{i0}-\frac{\Gamma_{0}}{2})t-(i\omega_{j0}-\frac{\Gamma_{0}}{2})t'} $$ With the time evolution of amplitudes being given by ...
0 votes
0 answers
133 views
What is the difference between scaling property when scaling factor is $-1$ and the time reversal property of Laplace transform?
I came across this question when one of my students asked me about it. Suppose that $L$ denotes the Laplace transform and that $L\{F(t)\}=f(s)$. By scaling property, we have $L\{F(-t)\}=-f(-s)$. The ...
0 votes
0 answers
89 views
Laplace transform: How to evaluate partial derivative in the denominator of a fraction?
I am solving a differential equation using the Laplace transform. However, to evaluate it I need to evaluate some strange terms. Specifically, I have a partial derivative in the denominator of the ...
- 105
0 votes
1 answer
145 views
Unique distribution of charge on a conductor
If i place some charge on a conductor then it will distribute itself in such a way that electric field everywhere inside is zero. My text book says that only one kind of such charge distribution is ...
- 363
1 vote
0 answers
70 views
PI controller - output calculation [closed]
The propeller of an airship is connected to a DC motor. The motor is being controlled using a PI controller. The PI controller has a proportional gain of Kp = 2, and an integral gain of Ki = 0.5, and ...
- 31
20 votes
5 answers
8k views
Fourier vs. Laplace transforms
Electronics books often use Laplace to analyze circuits, while in physics we use Fourier, most of the times... if not always: from complex impedances to electromagnetism, quantum mechanics, Green ...
- 601
1 vote
2 answers
654 views
What is the physical meaning of sigma in the Laplace transform?
Let’s use a simple harmonic oscillator as an example. When we calculate the Fourier Transform (a special case of the Laplace transform) of that system we get a function that shows which frequencies of ...
- 11
1 vote
1 answer
191 views
What is the intuitive interpretation of the transfer function of this system?
If I have the system that could be observed in the next Image: I want to know the transfer function, where the external force $f$ is the entry and $x_1$ is the output. The direction and positive ...
