A speculative approach to quantum gravity.
A stability estimate for a solution to a three-dimensional inverse problem for the Maxwell equations.
A stability estimate for a solution to a two-dimensional inverse problem of electrodynamics.
A stability theorem of the Navier-Stokes flow past a rotating body
In this paper, a stability theorem of the Navier-Stokes flow past a rotating body is reported. Concerning the linearized problem, the proofs of the generation of a C₀ semigroup and its decay properties are sketched.
A stabilized finite element scheme for the Navier-Stokes equations on quadrilateral anisotropic meshes
It is well known that the classical local projection method as well as residual-based stabilization techniques, as for instance streamline upwind Petrov-Galerkin (SUPG), are optimal on isotropic meshes. Here we extend the local projection stabilization for the Navier-Stokes system to anisotropic quadrilateral meshes in two spatial dimensions. We describe the new method and prove an a priori error estimate. This method leads on anisotropic meshes to qualitatively better convergence behavior...
A stable class of spacetimes with naked singularities
We present a stable class of spacetimes which satisfy the conditions of the singularity theorem of Hawking & Penrose (1970), and which contain naked singularities. This offers counterexamples to a geometric version of the strong cosmic censorship hypothesis.
A stable mixed finite element method on truncated exterior domains
A stochastic lagrangian proof of global existence of the Navier-Stokes equations for flows with small Reynolds number
A stochastic phase-field model determined from molecular dynamics
The dynamics of dendritic growth of a crystal in an undercooled melt is determined by macroscopic diffusion-convection of heat and by capillary forces acting on the nanometer scale of the solid-liquid interface width. Its modelling is useful for instance in processing techniques based on casting. The phase-field method is widely used to study evolution of such microstructural phase transformations on a continuum level; it couples the energy equation to a phenomenological Allen-Cahn/Ginzburg-Landau equation...
A Stochastic Solver of the Generalized Born Model
A stochastic generalized Born (GB) solver is presented which can give predictions of energies arbitrarily close to those that would be given by exact effective GB radii, and, unlike analytical GB solvers, these errors are Gaussian with estimates that can be easily obtained from the algorithm. This method was tested by computing the electrostatic solvation energies (ΔGsolv) and the electrostatic binding energies (ΔGbind) of a set of DNA-drug complexes, a set of protein-drug complexes, a set of protein-protein...
A study of bifurcation of Kolmogorov flows with an emphasis on the singular limit.
A study of Galerkin method for the heat convection equations
The paper investigates the Galerkin method for an initial boundary value problem for heat convection equations. New error estimates for the approximate solutions and their derivatives in strong norm are obtained.
A study of the dynamic of influence through differential equations∗
The paper concerns a model of influence in which agents make their decisions on a certain issue. We assume that each agent is inclined to make a particular decision, but due to a possible influence of the others, his final decision may be different from his initial inclination. Since in reality the influence does not necessarily stop after one step, but may iterate, we present a model which allows us to study the dynamic of influence. An innovative...
A study of the dynamic of influence through differential equations∗
The paper concerns a model of influence in which agents make their decisions on a certain issue. We assume that each agent is inclined to make a particular decision, but due to a possible influence of the others, his final decision may be different from his initial inclination. Since in reality the influence does not necessarily stop after one step, but may iterate, we present a model which allows us to study the dynamic of influence. An innovative...
A study of the stationary reactive flow of a fluid cofined in -dimensional domains with holes using fixed point theory.
A supraconvergent scheme for the Korteweg-de Vries equation.
A survey of some new results in ferromagnetic thin films
A thermodynamic approach to nonisothermal phase-field models
The goal of this paper is to work out a thermodynamical setting for nonisothermal phase-field models with conserved and nonconserved order parameters in thermoelastic materials. Our approach consists in exploiting the second law of thermodynamics in the form of the entropy principle according to I. Müller and I. S. Liu, which leads to the evaluation of the entropy inequality with multipliers. As the main result we obtain a general scheme of phase-field models which involves an...
A triangular mixed finite element method for the stationary semiconductor device equations
A two-dimensional Landau-Lifshitz model in studying thin film micromagnetics.