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We study bandstructure properties of periodic optical systems composed of lossy and intrinsically dispersive materials. To this end, we develop an analytical framework based on adjoint modes of a lossy periodic electromagnetic system and…
We study the problem of a target search by a Brownian particle subject to stochastic resetting to a pair of sites. The mean search time is minimized by an optimal resetting rate which does not vary smoothly, in contrast with the well-known…
We solve explicitly a certain minimization problem for probability measures in one dimension involving an interaction energy that arises in the modelling of aggregation phenomena. We show that in a certain regime minimizers are absolutely…
We give an expression for the partition function of a one-dimensional log-gas comprised of particles of (possibly) different integer charge at inverse temperature {\beta} = 1 (restricted to the line in the presence of a neutralizing field)…
In this paper we study "discrete polynomial blending," a term used to define a certain discretized version of curve blending whereby one approximates from the "sum of tensor product polynomial spaces" over certain grids. Our strategy is to…
We study the existence of densities for distributions of piecewise deterministic Markov processes. We also obtain relationships between invariant densities of the continuous time process and that of the process observed at jump times. In…
We study the problem of Brownian motion in a multiscale potential. The potential is assumed to have N+1 scales (i.e. N small scales and one macroscale) and to depend periodically on all the small scales. We show that for nonseparable…
Wave propagation in architectured materials, or materials with microstructure, is known to be dependent on the ratio between the wavelength and a characteristic size of the microstructure. Indeed, when this ratio decreases (i.e. when the…
Computer simulations were done of the mean square displacement (MSD) of tracer particles in colloidal gels formed by diffusion or reaction limited aggregation of hard spheres. The diffusion coefficient was found to be determined by the…
Numerical calculation of modes in dispersive and absorptive systems is performed using the finite element method. The dispersion is tackled in the frame of an extension of Maxwell's equations where auxiliary fields are added to the…
We establish a new monotonicity formula for minimizers of the Mumford-Shah functional in planar domains. Our formula follows the spirit of Bucur-Luckhaus, but works with the David-L\'eger entropy instead of the energy. Interestingly, this…
One-point time-series measurements limit the observation of three-dimensional fully developed turbulence to one dimension. For one-dimensional models, like multiplicative branching processes, this implies that the energy flux from large to…
A Langevin process diffusing in a periodic potential landscape has a time dependent diffusion constant which means that its average mean squared displacement (MSD) only becomes linear at late times. The long time, or effective diffusion…
The entropy of the Reissner-N\"{o}rdstrom black hole is studied within the context of a brane-world scenario. Such a black hole is a solution of the Einstein field equations on the brane, possessing a tidal charge which is a reflection of…
Radiant spherical suspensions have an $\veps$-periodic distribution in a tridimensional incompressible viscous fluid governed by the Stokes-Boussinesq system. We perform the homogenization procedure when the radius of the solid spheres is…
We develop a theory to represent dislocated single crystals at the mesoscopic scale by considering concentrated effects, governed by the distribution theory combined with multiple-valued kinematic fields. Our approach gives a new…
We consider the inclusion process on the complete graph with vanishing diffusivity, which leads to condensation of particles in the thermodynamic limit. Describing particle configurations in terms of size-biased and appropriately scaled…
We present a perturbation approach to calculate the short-time propagator, or transition density, of the one-dimensional Fokker-Planck equation, to in principle arbitrary order in the time increment. Our approach preserves probability…
The Arcsine laws of Brownian motion are a collection of results describing three different statistical quantities of one-dimensional Brownian motion: the time at which the process reaches its maximum position, the total time the process…
There are not many kinetic models where it is possible to prove bifurcation phenomena for any value of the Knudsen number. Here we consider a binary mixture over a line with collisions and long range repulsive interaction between different…