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A semilinear singularly perturbed reaction-diffusion equation with Dirichlet boundary conditions is considered in a convex unbounded sector. The singular perturbation parameter is arbitrarily small, and the "reduced equation" may have…
The study of time-dependent, many-body transport phenomena is increasingly within reach of ultra-cold atom experiments. We show that the introduction of spatially inhomogeneous interactions, e.g., generated by optically-controlled…
Induced-charge electro-osmosis (ICEO) is shown to control the length scale of the diffusion layer (DL), which in turn, affects the diffusion limited ion transport through the microchannel-Nafion membrane system. The ICEO vortices form at an…
We show how the nonlinear interaction effects `volume filling' and `adhesion' can be incorporated into the fractional subdiffusive transport of cells and individual organisms. To this end, we use microscopic random walk models with…
Complex biological and physical transport processes are often described through systems of interacting particles. Excluded-volume effects on these transport processes are well studied, however the interplay between volume exclusion and…
Modern electronic-structure theory defines dispersion interactions as connected intramonomer excitations. Using this definition, dispersion contributions have been shown in literature to be large relative to other contributions at van der…
Time-dependent multiphysics interactions that drive the energy transfer in electromechanical systems are poorly understood. We probe dielectric barrier discharge (DBD) with an external DC-augmented (DCA) field to reveal new mechanistic…
A modified Poisson-Nernst-Planck system in a bounded domain with mixed Dirichlet-Neumann boundary conditions is analyzed. It describes the concentrations of ions immersed in a polar solvent and the correlated electric potential due to the…
We study discrete solvent effects on the interaction of two parallel charged surfaces in ionic aqueous solution. These effects are taken into account by adding a bilinear non-local term to the free energy of Poisson-Boltzmann theory. We…
A theory is constructed for dense ionic solutions near charged planar walls that is valid for strong inter-ionic correlations. This theory predicts a fluctuation-induced, first-order transition and spontaneous charge density ordering at the…
In this paper we analyze a two-dimensional discrete model of nearest-neighbour Lennard-Jones interactions under the microscopical constraint that points on a lattice triangle maintain their order. This can be understood as a microscopical…
We present results demonstrating the space charge-mediated transition between classical, diffusion-limited current and surface-conduction dominant over-limiting current in a shallow micro-nanochannel device. The extended space charge layer…
The dynamics of various optically controlled non-equilibrium phenomena in the condensed phase are studied using the Liouville equation. We study a projection of the same in a slow moving coordinate, identified as the Reaction Coordinate…
The analytical theory of diffusive cosmic ray acceleration at parallel stationary shock waves with magnetostatic turbulence is generalized to arbitrary shock speeds $V_s=\beta_1c$, including in particular relativistic speeds. This is…
Interfacial charge transfer is widely assumed to obey Butler-Volmer kinetics. For certain liquid-solid interfaces, Marcus-Hush-Chidsey theory is more accurate and predictive, but it has not been applied to porous electrodes. Here we report…
The Debye-Falkenhagen differential equation is commonly used as a mean-field macroscopic model for describing electrochemical ionic drift and diffusion in dilute binary electrolytes when subjected to a suddenly applied potential smaller…
We reformulate and extend porous electrode theory for non-ideal active materials, including those capable of phase transformations. Using principles of non-equilibrium thermodynamics, we relate the cell voltage, ionic fluxes, and Faradaic…
We study the temperature-dependent corrections to the conductance due to electron-electron (e-e) interactions in clean two-dimensional conductors, such as lightly doped graphene or other Dirac matter. We use semiclassical Boltzmann kinetic…
We investigate the effect of small diffusion on the principal eigenvalues of linear time-periodic parabolic operators with zero Neumann boundary conditions in one dimensional space. The asymptotic behaviors of the principal eigenvalues, as…
Using the rigid dipole model, we study the translational and rotational motions of single-domain fer-romagnetic nanoparticles in a dilute suspension induced by the harmonically oscillating gradient magnetic field in the presence of a…