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A two space dimensional active nonlinear nonlocal cochlear model is formulated in the time domain to capture nonlinear hearing effects such as compression, multi-tone suppression and difference tones. The micromechanics of the basilar…
High auditory sensitivity, sharp frequency selectivity, and otoacoustic emissions are signatures of active amplification of the cochlea. The human ear can also detect very large amplitude sound without being damaged as long as the exposed…
We investigate instabilities in a stochastic mathematical model of cochlear dynamics. The cochlea is modeled as a spatio-temporal dynamical system made up of a spatially distributed array of coupled oscillators, together with the cochlear…
The human cochlea is a remarkable device, able to discern extremely small amplitude sound pressure waves, and discriminate between very close frequencies. Simulation of the cochlea is computationally challenging due to its complex geometry,…
We develop an analytic model of the mammalian cochlea. We use a mixed physical-phenomenological approach by utilizing existing work on the physics of classical box-representations of the cochlea, and behavior of recent data-derived…
An active dissipative process organizes auditory frequency analysis in the mammalian cochlea. A minimal active beam model reveals that a spatially varying viscous coupling operator, $\partial_{xx}\kappa\partial_{xx}$, generates dissipative…
Recent advances in high-resolution imaging techniques and particle-based simulation methods have enabled the precise microscopic characterization of collective dynamics in various biological and engineered active matter systems. In…
Biologically inspired auditory models play an important role in developing effective audio representations that can be tightly integrated into speech and audio processing systems. Current computational models of the cochlea are typically…
The aim of this paper is to understand the behaviour of a large number of coupled subwavelength resonators. We use layer potential techniques in combination with numerical computations to study the acoustic pressure field due to scattering…
Cochlea displays complex and highly nonlinear behavior in response to wide-ranging auditory stimuli. While there have been many recent advancements in the modeling of cochlear dynamics, it remains unclear what mathematical structures…
The dynamics of a membrane is a coupled system comprising a moving elastic surface and an incompressible membrane fluid. We will consider a reduced elastic surface model, which involves the evolution equations of the moving surface, the…
We investigate multicellular sender receiver systems embedded in hydrogel beads, where diffusible signals mediate interactions among heterogeneous cells. Such systems are modeled by PDE ODE couplings that combine three dimensional diffusion…
In this article we propose and investigate a hierarchy of mathematical models based on partial differential equations (PDE) and ordinary differential equations (ODE) for the simulation of the biophysical phenomena occurring in the…
A sound stimulus entering the inner ear excites a deformation of the basilar membrane which travels along the cochlea towards the apex. It is well established that this wave-like disturbance is amplified by an active system. Recently, it…
Within the framework of mode-coupling theory, we present a simple model for describing dense assemblies of active (self-propelled) spherical colloidal particles. For isotropic suspensions, we demonstrate that the glass transition is shifted…
This manuscript reports the first step towards building a robust and efficient model reduction methodology to capture transient dynamics in a transmission level electric power system. Such dynamics is normally modeled on…
We propose an algorithm for approximating the solution of a strongly oscillating SDE, that is, a system in which some ergodic state variables evolve quickly with respect to the other variables. The algorithm profits from homogenization…
Noise can induce coherent oscillations in excitable systems without periodic orbits. Here, we establish a method to derive a hybrid system approximating the noise-induced coherent oscillations in excitable systems and further perform phase…
The sensitivity and frequency selectivity of hearing result from tuned amplification by an active process in the mechanoreceptive hair cells. In most vertebrates the active process stems from the active motility of hair bundles. The…
This work deals with the numerical solution of the monodomain and bidomain models of electrical activity of myocardial tissue. The bidomain model is a system consisting of a possibly degenerate parabolic PDE coupled with an elliptic PDE for…