Related papers: The narrow capture problem on general Riemannian s…
We study the first passage statistics to adsorbing boundaries of a Brownian motion in bounded two-dimensional domains of different shapes and configurations of the adsorbing and reflecting boundaries. From extensive numerical analysis we…
Intracellular transport in living cells is often spatially inhomogeneous with an accelerated effective diffusion close to the cell membrane and a ballistic motion away from the centrosome due to active transport along actin filaments and…
Consider the geometric inverse problem: There is a set of delta-sources in spacetime that emit waves travelling at unit speed. If we know all the arrival times at the boundary cylinder of the spacetime, can we reconstruct the space, a…
The concept of closed trapped surface is of paramount importance in General Relativity and other gravitational theories. However, it is a purely geometrical object. With the aim of bringing this concept to closer attention by the…
We study the problem of particles undergoing Brownian motion in an expanding sphere whose surface is an absorbing boundary for the particles. The problem is akin to that of the diffusion of impurities in a grain of polycrystalline material…
We consider the initial value problem (IVP) associated to the Schr\"odinger-Debye system posed on a $d$-dimensional compact Riemannian manifold $M$ and prove local well-posedness result for given data $(u_0, v_0)\in H^s(M)\times (H^s(M)\cap…
Let M be a smooth compact oriented manifold without boundary, imbedded in a euclidean space E and let f be a smooth map of M into a Riemannian manifold N. An unknown state x in M is observed via X=x+su where s>0 is a small parameter and u…
We consider the kinetics of the imperfect narrow escape problem, i.e. the time it takes for a particle diffusing in a confined medium of generic shape to reach and to be adsorbed by a small, imperfectly reactive patch embedded in the…
An analysis is presented of a Brownian particle moving on the half-line, subject to a restoring force proportional to its displacement and an absorbing boundary at the origin. When the initial displacement is large, the central moments of…
Fix an arbitrary compact orientable surface with a boundary and consider a uniform bipartite random quadrangulation of this surface with $n$ faces and boundary component lengths of order $\sqrt n$ or of lower order. Endow this…
Under some weak conditions, the first-passage time of the Brownian motion to a continuous curved boundary is an almost surely finite stopping time. Its probability density function (pdf) is explicitly known only in few particular cases.…
We study minimal surfaces in generic sub-Riemannian manifolds with sub-Riemannian structures of co-rank one. These surfaces can be defined as the critical points of the so-called {\it horizontal} area functional associated to the canonical…
Narrow escape and narrow capture problems which describe the average times required to stop the motion of a randomly travelling particle within a domain have applications in various areas of science. While for general domains, it is known…
Given a survival distribution on the positive half-axis and a Brownian motion, a solution of the inverse first-passage problem consists of a boundary so that the first passage time over the boundary has the given distribution. We show that…
The diffusion equation is the primary tool to study the movement dynamics of a free Brownian particle, but when spatial heterogeneities in the form of permeable interfaces are present, no fundamental equation has been derived. Here we…
In one-dimensional systems, the dynamics of a Brownian particle are governed by the force derived from a potential as well as by diffusion properties. In this work, we obtain the first-passage-time statistics of a Brownian particle driven…
We construct the solution of the Riemann problem for the shallow water equations with discontinuous topography. The system under consideration is non-strictly hyperbolic and does not admit a fully conservative form, and we establish the…
We review some representative results for first-passage problems involving so-called mortal or evanescent walkers, i.e., walkers with a finite lifetime. The mortality constraint plays a key role in the modeling of many real scenarios, as it…
We introduce variational obstacle avoidance problems on Riemannian manifolds and derive necessary conditions for the existence of their normal extremals. The problem consists of minimizing an energy functional depending on the velocity and…
During a random search, resetting the searcher's position from time to time to the starting point often reduces the mean completion time of the process. Although many different resetting models have been studied over the past ten years,…