Related papers: Probability distribution function for reorientatio…
This paper explores the reconstruction of drift or diffusion coefficients of a scalar stochastic diffusion processes as it starts from an initial value and reaches, for the first time, a threshold value. We show that the distribution…
Since the advent of quantum mechanics different approaches to find analytical solutions of the Schr\"odinger equation have been successfully developed. Here we follow and generalize the approach pioneered by Natanzon and others by which the…
The problem of the flux to a spherical trap in one and three dimensions, for diffusing particles undergoing discrete-time jumps with a given radial probability distribution, is solved in general, verifying the Smoluchowski-like solution in…
We compute the effective diffusion coefficient of a Brownian particle in a piece-wise linear periodic potential and subject of spatially inhomogeneous temperature, otherwise known as the B{\"u}ttiker-Landauer motor. We obtain analytical…
This paper deals with the distributed order time-fractional diffusion equations with non-homogeneous Dirichlet (Nuemann) boundary condition. We first prove the wellposedness of the weak solution to the initial boundary value problem for the…
We introduce a new factorized and resummed waveform for circularized, nonspinning, compact binaries that leverages on the solution of the Teukolsky equation once mapped into a confluent Heun equation. The structure of the solution allows…
We consider a class of external potentials on the complex plane $\mathbb{C}$ for which the coincidence set to the obstacle problem contains a Jordan curve in the exterior of the droplet. We refer to this curve as a spectral outpost. We…
This paper stidies the first passage times to constant boundaries for mixed-exponential jump diffusion processes. Explicit solutions of the Laplace transforms of the distribution of the first passage times, the joint distribution of the…
The problem of anomalous diffusion in momentum (velocity) space is considered based on the master equation and the appropriate probability transition function (PTF). The approach recently developed by the author for coordinate space, is…
The issue of analytical derivation of the mean velocity profile in a near-wall turbulent flow is revisited in the context of a two-dimensional channel flow. An approach based on the use of dispersion relations for the flow velocity is…
The solution of the one-dimensional Schr\"odinger equation for a potential involving an attractive $x^\frac{2}{3}$ and a repulsive centrifugal-barrier $\sim x^{-2}$ terms is presented in terms of the non-integer-order Hermite functions. The…
We show that there exist infinitely many nontrivial choices of parameters of the single confluent Heun equation for which the three-term recurrence relations governing the expansions of the solutions in terms of the confluent hypergeometric…
We present an exact calculation of the mean first-passage time to a target on the surface of a 2D or 3D spherical domain, for a molecule alternating phases of surface diffusion on the domain boundary and phases of bulk diffusion. The…
We report on recent progress in the study of nonlinear diffusion equations involving nonlocal, long-range diffusion effects. Our main concern is the so-called fractional porous medium equation, $\partial_t u +(-\Delta)^{s}(u^m)=0$, and some…
In this work, we consider the numerical solution of an initial boundary value problem for the distributed order time fractional diffusion equation. The model arises in the mathematical modeling of ultra-slow diffusion processes observed in…
Given a random quantum state of multiple distinguishable or indistinguishable particles, we provide an effective method, rooted in symplectic geometry, to compute the joint probability distribution of the eigenvalues of its one-body reduced…
In this paper, we generalize the weighted Fourier transform with respect to a function, originally proposed for the one-dimensional case in \cite{Dorrego}, to the $n$-dimensional Euclidean space $\mathbb{R}^{n}$. We develop a comprehensive…
We use Maxwell's equations in a sourceless, inhomogeneous medium with continuous permeability $\mu (\mathbf{r}) $ and permittivity $% \epsilon (\mathbf{r}) $ to study the wave propagation. The general form of the wave equation is derived…
Diffusion models learn to reverse the progressive noising of a data distribution to create a generative model. However, the desired continuous nature of the noising process can be at odds with discrete data. To deal with this tension…
For suspensions of permeable particles, the short-time translational and rotational self-diffusion coefficients, and collective diffusion and sedimentation coefficients are evaluated theoretically. An individual particle is modeled as a…