# Tagged Questions

**5**

votes

**1**answer

800 views

### Mathematical study of Mpemba effect?

It has been known since the days of Aristotle and Descartes that under certain circumstances warm water freezes faster than cold water. This effect is now commonly known as the Mpemba effect, named ...

**32**

votes

**2**answers

1k views

### Recent fundamental new directions in PDEs

My main interests are in modern geometry/topology, algebra and mathematical physics. I observe that there is a raising communication, language and social barrier between this community and the ...

**3**

votes

**1**answer

129 views

### Using Fourier Transform to speed up calculation of forces following an inverse square law

Suppose I have $n$ electric point charges in, say, two dimensions. Is there any algorithm (and I have a hunch that it might be related to the Fourier transform) to compute the net forces that act on ...

**4**

votes

**1**answer

445 views

### Solution of Helmholtz-Equation where Phase is restricted by additional PDE

Hello!
Let's say I have
$(\partial_x^2 + \partial_y^2 + a)f(x,y)=0$
with $f(x,y) \in \mathbb{C}$, ($\lim_{x,y \to \infty} f(x,y)=0$).
Now separate the Amplitude and Phase of the solution:
...

**6**

votes

**4**answers

589 views

### Applications of Hodge-de Rham Laplacian on p-forms ($p\neq 0,n$) in physics or engineering

The Hodge-de Rham Laplacian $L=(d+d^*)^2$, where $d$ is the boundary operator of the de Rham complex, is well-known in the math community. Recently, I tried very hard to search for examples of its use ...

**1**

vote

**1**answer

224 views

### Stieltjes convolution with white noise

I'm looking for a reference that would discuss a Stieltjes convolution between a wiener process and a function of bounded variation. Additionally, I had a question about this sort of convolution.
Is ...

**2**

votes

**0**answers

300 views

### Gaussian type integral with inverse square root

Hi,
I have encountered an integral of the following type in an engineering application:
$\int_{-\infty}^\infty dx \frac{1}{\sqrt{x^2+a^2}}\exp(-x^2/2+i x b)$,
where $a$ and $b$ are real ($a$ could ...

**7**

votes

**2**answers

456 views

### Efficiently computing a few localized eigenvectors

Let $H = \triangle + V(x) : \mathbb{R}^2 \rightarrow \mathbb{R}^2$. I am interested in domain decomposition for an eigenproblem involving $H$.
The lowest 1000 eigenfunctions of $H$, $ \psi_i $, can ...

**5**

votes

**3**answers

411 views

### Traceless GUE : Four Centered Fermions

The proof of the Wigner Semicircle Law comes from studying the GUE Kernel
\[ K_N(\mu, \nu)=e^{-\frac{1}{2}(\mu^2+\nu^2)} \cdot \frac{1}{\sqrt{\pi}} \sum_{j=0}^{N-1}\frac{H_j(\lambda)H_j(\mu)}{2^j j!} ...

**2**

votes

**0**answers

658 views

### Bessel functions in wave propagation and scattering

Is there a way to scale Bessel J(n,.) (Bessel of first kind) and Bessel H(n,.) (Bessel of third kind or Hankel)? I am having computer problems with higher orders (higher vlaues of n) and small ...

**8**

votes

**2**answers

251 views

### Computational methods for dealing with geometrically complicated solid boundaries in fluid-air interface problems

Hello,
I am a PhD student who does not have extensive computational experience seeking advice from those experienced with computational modelling as to which method would be most appropriate for ...

**10**

votes

**1**answer

566 views

### Regge calculus: Questions of consistency resolved?

Hello,
Regge calculus is an approximation scheme for General Relativity, which has been introduced in early-sixties and has been adopted both in numerical relativity and numerical quantum relativity. ...

**4**

votes

**1**answer

274 views

### Schrodinger's equation over a randomized grid

I am interested in solutions to
$$
\frac{d}{dt} \Psi = -iH \Psi
$$
for $H$ hermitian and time independent. This boils down to evaluating
$$
\Psi(t) = e^{-iHt}\Psi_0
$$
at points of interest $t_n$. I ...

**0**

votes

**1**answer

470 views

### Delta notation used for describing numerical stencil

While reading some papers translated from the Russian literature, I've noticed that a delta symbol can be used to denote a FDTD stencil that discretizes a PDE. For example, in [1], a fourth order ...

**0**

votes

**0**answers

379 views

### Splitting wave equation for application of CPML

A recent paper (Roden and Gedney, 2000) proposed the application of a Convolutional Perfectly Matched Layer (CPML) to approximate free-field conditions for Finite-Difference Time-Domain (FDTD) ...

**10**

votes

**2**answers

828 views

### Are there any known quantum algorithms that clearly fall outside a few narrow classes?

I'm trying to refresh myself on quantum algorithms and have been skimming Childs and van Dam's 2008 RMP paper among other things. From my preliminary surfing it looks like the known quantum algorithms ...

**2**

votes

**2**answers

648 views

### Application of coordinate-stretching transformation for Perfectly Matched Layer

A Perfectly Matched Layer (PML) is an absorbing boundary condition (ABC) which can be used to approximate free-field conditions for the numerical solution of wave equation problems.
PML note
The PML ...

**1**

vote

**1**answer

1k views

### Boundary conditions of wave equation near infinity

For the following wave equation
$
\frac{{\partial ^2 p}}{{\partial ^2 x}} + \frac{{\partial ^2 p}}{{\partial ^2 y}} = A\frac{{\partial ^2 p}}{{\partial ^2 t}} + B\frac{{\partial p}}{{\partial t}}
$
...

**0**

votes

**0**answers

222 views

### What's a good approach to model this system?

Edited 15 Jul 2010
Willie's points are well-taken. I apologize for the wordy description. It turns out have a relative who is quite knowledgeable about numerical problems like this and has offered ...

**3**

votes

**2**answers

511 views

### Asymptotic Matching of an logarithmic Outer solution to an exponential growing inner solution

Hi,
I'm studying an ODE with a small parameter $\epsilon$ and I'm trying to find the solution in terms of a zeroth-order term and a boundary layer. The zeroth-order term has a logarithmic behavior ...