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Starting from the wave equation for a medium with material properties that vary periodically, we study a system of recurrence relations that describe propagation of wave packets that oscillate on the microscale (i.e. on lengths of the order…
We have developed a computational method to describe the nonlinear light propagation of an intense and ultrashort pulse at oblique incidence on a flat surface. In the method, coupled equations of macroscopic light propagation and…
Inertia does not generally affect the long-time diffusion of passive overdamped particles in fluids. Yet a model starting from the Langevin equation predicts a surprising property of particles coated with ligands, that bind reversibly to…
Long-term outcomes of experimental evaluations are necessarily observed after long delays. We develop semiparametric methods for combining the short-term outcomes of experiments with observational measurements of short-term and long-term…
The concept of the PT-symmetry, originating from the quantum field theory, has been intensively investigated in optics, stimulated by the similarity between the Schr\"odinger equation and the paraxial wave equation that governs the…
Metric spaces provide a framework for analysis and have several very useful properties. Many of these properties follow in part from the triangle inequality. However, there are several applications in which the triangle inequality does not…
Textbooks state that the successful application of Maxwell's Equations in physical optics problems requires light to interact with matter where any inhomogeneities are spaced by less than or equal to the wavelength of light; the 'dense'…
Parametric path problems arise independently in diverse domains, ranging from transportation to finance, where they are studied under various assumptions. We formulate a general path problem with relaxed assumptions, and describe how this…
General properties of linear propagation of discretized light in homogeneous and curved waveguide arrays are comprehensively investigated and compared to those of paraxial diffraction in continuous media. In particular, general laws…
Nonlinear effects are omnipresent in thin films of ion conducting materials showing up as a significant increase of the conductivity. For a disordered hopping model general physical mechanisms are identified giving rise to the occurrence of…
The theory of linear acceleration emission is developed for a large amplitude electrostatic wave in which all particles become highly relativistic in much less than a wave period. An Airy integral approximation is shown to apply near the…
Relativistic effects on dispersion in a degenerate electron gas are discussed by comparing known response functions derived relativistically (by Jancovici) and nonrelativistically (by Lindhard). The main distinguishing feature is one-photon…
Symmetries are widespread in physical, technological, biological, and social systems and networks, including power grids. The swing equation is a classic model for the dynamics of powergrid networks. The main goal of this paper is to…
The linear Boltzmann equation describes the macroscopic transport of a gas of non-interacting point particles in low-density matter. It has wide-ranging applications, including neutron transport, radiative transfer, semiconductors and ocean…
Interferometry has been used widely in sensing application. However, the technique is limited by the finite coherence time of the light sources when the interference paths are not balanced. Higher-order interference effects involve…
Among the main actors of organism development there are morphogens, which are signaling molecules diffusing in the developing organism and acting on cells to produce local responses. Growth is thus determined by the distribution of such…
We present an analysis of wave propagation in a two step-index, parallel waveguide system. The goal is to quantify the effect of scattering at randomly perturbed interfaces between the guiding layers of high index of refraction and the host…
In this work we continue the systematic study of observable effects emerging from modified dispersion relations. We study the motion of test particles subject to a general first order modification of the general relativistic dispersion…
It is shown that a light beam in free space is representable by an integral over a vectorial angular spectrum that is expressed in terms of an extension matrix, which describes the vectorial nature of the beam. A symmetry axis of the…
Modern deep learning models are highly overparameterized, resulting in large sets of parameter configurations that yield the same outputs. A significant portion of this redundancy is explained by symmetries in the parameter…