Related papers: On "the complete basis set limit" and plane-wave m…

First principles calculations based on density functional theory are having an incerasing impact on our understanding of molecule-surface interactions. For example, calculations of the multi-dimensional potential energy surface have…

Using first principles simulations we have investigated the structural and bonding properties of dense fluid oxygen up to 180 GPa. We have found that band gap closure occurs in the molecular liquid, with a "slow" transition from a…

In this chapter, we illustrate the advantage of variational principles for modeling water waves from an elementary practical viewpoint. The method is based on a `relaxed' variational principle, i.e., on a Lagrangian involving as many…

The local structure of liquid water as a function of temperature is a source of intense research. This structure is intimately linked to the dynamics of water molecules, which can be measured using Raman and infrared spectroscopies. The…

We prove a dispersive estimate for the solutions of the linearized Water-Waves equations in dimension 1 in presence of a flat bottom. We prove a decay with respect to time t of order 1/3 for solutions with initial data in weighted Sobolev…

We develop structure-preserving numerical methods for the Serre-Green-Naghdi equations, a model for weakly dispersive free-surface waves. We consider both the classical form, requiring the inversion of a non-linear elliptic operator, and a…

We explore the plane-wave limit of homogeneous spacetimes. For plane-wave limits along homogeneous geodesics the limit is known to be homogeneous and we exhibit the limiting metric in terms of Lie algebraic data. This simplifies many…

The projection of the eigenfunctions obtained in standard plane-wave first-principle electronic-structure calculations into atomic-orbital basis sets is proposed as a formal and practical link between the methods based on plane waves and…

We have developed x-ray diffraction measurements with high energy-resolution and accuracy to study water structure at three different temperatures (7, 25 and 66 C) under normal pressure. Using a spherically curved Ge crystal an energy…

The application of newly developed first-principle modeling techniques to liquid water deepens our understanding of the microscopic origins of its unusual macroscopic properties and behaviour. Here, we review two novel ab initio…

Despite the simplicity of its molecular unit, water is a challenging system because of its uniquely rich polymorphism and predicted but yet unconfirmed features. Introducing a novel space of generalized coordinates that capture changes in…

Motivated by numerically modeling surface waves for inviscid Euler equations, we analyze linear models for damped water waves and establish decay properties for the energy for sufficiently regular initial configurations. Our findings give…

We study the behavior of shallow water waves over periodically-varying bathymetry, based on the first-order hyperbolic Saint-Venant equations. Although solutions of this system are known to generally exhibit wave breaking, numerical…

In this paper we investigate the dispersive properties of the solutions of the two dimensional water-waves system. First we prove Strichartz type estimates with loss of derivatives at the same low level of regularity we were able to…

This paper describes a method for deriving approximate equations for irrotational water waves. The method is based on a 'relaxed' variational principle, i.e., on a Lagrangian involving as many variables as possible. This formulation is…

The toolbox for time-resolved direct measurements of electron dynamics covers a variety of methods. Since the experimental effort is increasing rapidly with achievable time resolution, there is an urge for simple and robust measurement…

In this paper we present and analyse a high accuracy method for computing wave directions defined in the geometrical optics ansatz of Helmholtz equation with variable wave number. Then we define an "adaptive" plane wave space with small…

We derive upper bounds to free-space concentration of electromagnetic waves, mapping out the limits to maximum intensity for any spot size and optical beam-shaping device. For sub-diffraction-limited optical beams, our bounds suggest the…

Water adopts many different crystal structures in its solid form. These provide insight into potential structures of water even in its liquid phase, and they can be used to calibrate pair potentials used for simulation of water. In crowded…

We present the results of Car-Parrinello (CP) simulations of water at ambient conditions and under pressure, using a rigid molecule approximation. Throughout our calculations, water molecules were maintained at a fixed intramolecular…