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In studies of the brain and the nervous system, extracellular signals - as measured by local field potentials (LFPs) or electroencephalography (EEG) - are of capital importance, as they allow to simultaneously obtain data from multiple…
We determine the local charge dynamics of a $z-z$ electrolyte embedded in a varying-section channel. By means of an expansion based on the length scale separation between the axial and transverse direction of the channel, we derive closed…
The classical theory of electrokinetic phenomena assumes a dilute solution of point-like ions in chemical equilibrium with a surface whose double-layer voltage is of order the thermal voltage, $k_BT/e = 25$ mV. In nonlinear…
The control of the dielectric and conductive properties of device-level systems is important for increasing the efficiency of energy- and information-related technologies. In some cases, such as neuromorphic computing, it is desirable to…
Electrical signaling in the brain plays a vital role to our existence but at the same time, the fundamental mechanism of this propagation is undeciphered. Notable advancements have been made in the numerical modeling supplementing the…
Electrochemical phenomena in biology often unfold in confined geometries where micrometer- to millimeter-scale domains coexist with nanometer-scale interfacial diffuse charge layers. We analyze a model lipid membrane-electrolyte system…
The conductance of domain wall structures consisting of either stripes or cylindrical domains in multi-axial ferroelectric-semiconductors is analyzed. The effects of the domain size, wall tilt and curvature, on charge accumulation, are…
Contrary to existing theoretical models, experimental evidence points out that electroporation (membrane defect formation under external electric fields) starts to occur within the range of transmembrane voltages that cells may routinely…
The transmission of correlated electrons through a domain wall in ferromagnetic quasi-one-dimensional systems is studied theoretically in the case when the domain wall width is comparable with the Fermi wavelength of the charge carriers.…
Periodic configurations of electrodes, in particular of microelectrodes, have been of interest since the advent of microfabrication. In this report, theory which is common to any periodic cell (or any cell that can be extended periodically)…
To use batteries as large-scale energy storage systems it is necessary to measure and understand their degradation \textit{in-situ} and \textit{in-operando}. As a battery's degradation is often the result of molecular processes inside the…
Continuum simulation is employed to study ion transport and fluid flow through a nanopore in a solid-state membrane under an applied potential drop. Results show the existence of concentration polarization layers on the surfaces of the…
We present theoretical models for the time-dependent voltage of an electrochemical cell in response to a current step, including effects of diffuse charge (or "space charge") near the electrodes on Faradaic reaction kinetics. The full model…
We have studied the transport properties of a molecular device composed of donor and acceptor moieties between two electrodes on either side. The device is considered to be one-dimensional with different on-site energies and the…
The spatial distribution of electric current under magnetic field and the resultant orbital magnetism have been studied for two-dimensional electrons under a harmonic confining potential $V(\vecvar{r})=m \omega_0^2 r^2/2$ in various regimes…
The voltage-conductance kinetic model for the collective behavior of neurons has been studied by scientists and mathematicians for two decades, but the rigorous analysis of its solution structure has been only partially obtained in spite of…
Ion transport in extremely narrow nanochannels has gained increasing interest in recent years due to its unique physical properties, and the technological advances that allow us to study them. It is tempting to approach this regime with the…
We consider the limit of vanishing Debye length for ionic diffusion in fluids, described by the Nernst-Planck-Navier-Stokes system. In the asymptotically stable cases of blocking (vanishing normal flux) and uniform selective (special…
The self-organized electric cell voltage of the physical circuit is calculated at etching and deposition of metals at the surface of a magnetized ferromagnetic electrode in an electrolyte without passing an external electrical current. This…
A transient Poisson-Nernst-Planck system with steric effects is analyzed in a bounded domain with no-flux boundary conditions for the ion concentrations and mixed Dirichlet-Neumann boundary conditions for the electric potential. The steric…