Related papers: From the bulk electrolyte solution to the electroc…
This expository article explores the vital role of interpolation theory and Lorentz spaces in the rigorous analysis of partial differential equations (PDEs). While classical Lebesgue spaces ($L_{p}$) successfully measure the magnitude of…
The description of a conducting medium in thermal equilibrium, such as an electrolyte solution or a plasma, involves nonlinear electrostatics, a subject rarely discussed in the standard electricity and magnetism textbooks. We consider in…
The surface of a polar liquid presents a special environment for the solvation and organization of charged solutes, which differ from bulk behaviors in important ways. These differences have motivated many attempts to understand…
Within the Landau-Ginzburg-Wilson approach we derive the effective Hamiltonian governing fluctuations of an interface between two phases, one of them adsorbed on a disclike substrate. For large disc radii and for temperatures close to the…
We employ a simple and mostly accurate dimensional interpolation formula using dimensional limits $D=1$ and $D=\infty$ to obtain $D=3$ ground-state energy of metallic hydrogen. We also present results describing the phase transitions for…
The problem of the one dimensional electro-diffusion of ions in a strong binary electrolyte is considered. In such a system the solute dissociates completely into two species of ions with unlike charges. The mathematical description…
Ionic crystals, such as solid electrolytes and complex oxides, are central to modern technologies for energy storage, sensing, actuation, and other functional applications. An important fundamental issue in the atomic and quantum-scale…
These notes are based on a series of six lectures, given during my stay at the CRC 701 in June/July 2008. The lecture series intended to give a survey of some of the results for the almost Mathieu operator that have been obtained since the…
The diffuse interface model of Cahn-Hilliard-van der Waals is often used to study various aspects of multi-phase flows such as droplets coalescence and contact line dynamics. The original model of Cahn-Hilliard-van der Waals uses an…
Chemistry is about chemical reactions. Chemistry is about electrons changing their configurations as atoms and molecules react. Chemistry studies reactions as if they occurred in ideal infinitely dilute solutions. But most reactions occur…
Electrochemical ion insertion involves coupled ion-electron transfer reactions, transport of guest species, and redox of the host. The hosts are typically anisotropic solids with two-dimensional conduction planes, but can also be materials…
Short-range correlations in electrolyte solutions lead to oscillatory profiles of water polarization and ionic concentration at electrode-electrolyte interfaces. The recently developed density-potential-polarization functional theory…
The analytical solution of the equation describing diffusion of intrinsic point defects has been obtained for a one-dimensional finite-length domain. This solution is intended for investigating and modeling the changes in defect…
Isothermal interfacial zones are investigated starting from a local energy which can be considered as the sum of two terms: one corresponding to a medium with a uniform composition equal to the local one and a second one associated with the…
We investigate the diffusiophoresis of a non-polarizable droplet laden with soluble ionic surfactant, for which the surface charge arises from adsorption of surfactant at the fluid-fluid interface. Unlike previous studies that assume either…
In this paper we present a mathematical model for the electrochemical deposition aimed at the production of inverse opals. The real system consists of an arrangement of sub micrometer spheres, through which the species in an electrolytic…
Ab initio modeling of electrochemical systems is becoming a key tool for understanding and predicting electrochemical behavior. Development and careful benchmarking of computational electrochemical methods are essential to ensure their…
The interfacial tension of a liquid droplet surrounded by another liquid in the presence of microscopic ions is studied as a function of the droplet radius. An analytical expression for the interfacial tension is obtained within a linear…
The adsorption behavior of ions at liquid-vapor interfaces exhibits several unexpected yet generic features. In particular, energy and entropy are both minimum when the solute resides near the surface, for a variety of ions in a range of…
In this paper, we provide relations among the following properties: (a) the tail triviality of a probability measure $\mu$ on the configuration space ${\boldsymbol\Upsilon}$; (b) the finiteness of the $L^2$-transportation-type distance…