We study the global existence and space-time asymptotics of solutions for a class of nonlocal parabolic semilinear equations. Our models include the Nernst–Planck and the Debye–Hückel drift-diffusion systems as well as parabolic-elliptic systems of chemotaxis. In the case of a model of self-gravitating particles, we also give a result on the finite time blow up of solutions with localized and o...

We study the global existence and space-time asymptotics of solutions for a class of nonlocal parabolic semilinear equations. Our models include the Nernst–Planck and the Debye–Hückel drift-diffusion systems as well as parabolic-elliptic systems of chemotaxis. In the case of a model of self-gravitating particles, we also give a result on the finite time blow up of solutions with localized and o...

Pharmacophore models play an essential role in drug discovery. Generating pharmacophore models which encode accurate molecular recognition features are highly dependent on properly defined annotations. Simplistic or ill-defined pharmacophore annotations which do not capture subtle electronic or geometric effects lead to many inaccuracies. SMARTS patterns which are often used to specify annotati...

Abstract. We study the electrostatic Casimir effect and related phenomena in equilibrium statistical mechanics of classical (non-quantum) charged fluids. The prototype model consists of two identical dielectric slabs in empty space (the pure Casimir effect) or in the presence of an electrolyte between the slabs. In the latter case, it is generally believed that the long-ranged Casimir force due...

Abstract The classical Debye-Hückel screening effect of the electrostatic field generated by isolated charged particles immersed in a plasma is reviewed. The validity of the underlying mathematical model, and particularly of the weak-field approximation, are analyzed. It is shown that the presence of the plasma sheath around test particles and the resulting effect of charge screening are essent...

We study the band gap in some semi-conducting polymers with two models: Hückel molecular orbital theory and the socalled free electron model. The two models are directly related to spectral theory on combinatorial and metric graphs. Our numerical results reproduce qualitatively experimental results and results from much more complex density-functional calculations. We show that several trends c...

Models of non-bonded interactions are crucial in structure-based drug design. “Standard” hydrogen bonds are well modelled through traditional molecular mechanics forcefields with their treatments of electrostatics, and functional forms, often based on abundant crystal structure data, to describe their geometries. But “non-standard” interactions for example, hydrogen bonds with carbon as the don...

The thermodynamics of a charge-asymmetric lattice gas of positive ions carrying charge q and negative ions with charge 2zq is investigated using Debye–Hückel theory. Explicit analytic and numerical calculations, which take into account the formation of neutral and charged clusters and cluster solvation by the residual ions, are performed for z52, 3, and 4. As charge asymmetry increases, the pre...