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In this paper, we investigate the existence, uniqueness, and spectral stability of traveling waves arising from a single threshold neural field model with one spatial dimension, a Heaviside firing rate function, axonal propagation delay,…
Spin waves offer intriguing novel perspectives for computing and signal processing, since their damping can be lower than the Ohmic losses in conventional CMOS circuits. For controlling the spatial extent and propagation of spin waves on…
Waves propagating through weakly disordered smooth linear media undergo a universal phenomenon called branched flow. Branched flow has been observed and studied experimentally in various systems by considering coherent waves. Recent…
The structure of the axon-dendrite connections of neurons of the brain creates a rich spatial structure in which provided various combinations of signals surrounding neurons. Structure of dendritic trees and shape of dendritic spines allow…
The dynamic behavior of scalp potentials (EEG) is apparently due to some combination of global and local processes with important top-down and bottom-up interactions across spatial scales. In treating global mechanisms, we stress the…
We report a theoretical study of the electromagnetic waves (EWs) propagation through an array of superconducting qubits, i.e. coherent two-level systems, embedded in a low-dissipative transmission line. We focus on the near-resonant case as…
We study long range propagation of electromagnetic waves in random waveguides with rectangular cross-section and perfectly conducting boundaries. The waveguide is filled with an isotropic linear dielectric material, with randomly…
The human brain is one of the most complex and intriguing scientific topics. The most established theory on neuronal communication is a pure electrical model based on the propagation of intracell cationic charges along the neurons. Here we…
Electroencephalography (EEG) monitors ---by either intrusive or noninvasive electrodes--- time and frequency variations and spectral content of voltage fluctuations or waves, known as brain rhythms, which in some way uncover activity during…
We study Maxwell's equations in random media with small fluctuations of the electric permittivity. We consider a setup where the waves propagate toward a preferred direction, called range. We decompose the electromagnetic wave field in…
We consider the phenomenon of weak localization of a short wave pulse in a quasi-1D disordered waveguide. We show that the long-time decay of the average transmission coefficient is not purely exponential, in contradiction with predictions…
Wave transport in complex media is determined by the nature of quasimodes at the microscopic level. In three dimensional disordered media, waves generally undergo a phase transition from diffusion to Anderson localization, characterized by…
A mutilated model is constructed to approximate the collision term of spin Boltzmann equation that incorporates newly appearing collisional invariants i.e, the total angular momentum. With recourse to degenerate perturbation theory, the…
We study the localization of classical waves in weakly scattering 2D systems with anisotropic disorder. The analysis is based on a perturbative path-integral technique combined with a spectral filtering that accounts for the first-order…
Neural mass models are used to simulate cortical dynamics and to explain the electrical and magnetic fields measured using electro- and magnetoencephalography. Simulations evince a complex phase-space structure for these kinds of models;…
In studying structural inter-connections in the human brain, it is common to first estimate fiber bundles connecting different regions of the brain relying on diffusion MRI. These fiber bundles act as highways for neural activity and…
It is shown that asymmetric waveguides with gain and loss can support a stable propagation of optical beams. This means that the propagation constants of modes of the corresponding complex optical potential are real. A class of such…
Cortical spreading depression and spreading depolarization (CSD) are waves of neuronal depolarization that spread across the cortex, leading to a temporary saturation of brain activity. They are associated to various brain disorders such as…
Local field potentials (LFPs) are routinely measured experimentally in brain tissue, and exhibit strong low-pass frequency filtering properties, with high frequencies (such as action potentials) being visible only at very short distances…
We continue the work of a series of previous studies of a mathematical model that describes the mean-field limit behavior of a homogeneous network of excitatory point spiking neurons. Contrary to other models, here noise is intrinsic to the…