Dimensional Periodic Systems Research Articles

Laplace transformed MP2 for three dimensional periodic materials using stochastic orbitals in the plane wave basis and correlated sampling.

We present an implementation and analysis of a stochastic high performance algorithm to calculate the correlation energy of three-dimensional periodic systems in second-order Møller-Plesset perturbation theory (MP2). In particular we measure the scaling behavior of the sample variance and probe whether this stochastic approach is competitive if accuracies well below 1 meV per valence orbital are required, as it is necessary for calculations of adsorption, binding, or surface energies. The algorithm is based on the Laplace transformed MP2 (LTMP2) formulation in the plane wave basis. The time-dependent Hartree-Fock orbitals, appearing in the LTMP2 formulation, are stochastically rotated in the occupied and unoccupied Hilbert space. This avoids a full summation over all combinations of occupied and unoccupied orbitals, as inspired by the work of Neuhauser, Rabani, and Baer [J. Chem. Theory Comput. 9, 24 (2013)]. Additionally, correlated sampling is introduced, accelerating the statistical convergence significantly.

Light localization and SERS in tip-shaped silicon metasurface.

Optical properties of two dimensional periodic system of the silicon micro-cones are investigated. The metasurface, composed of the silicon tips, shows enhancement of the local optical field. Finite element computer simulations as well as real experiment reveal anomalous optical response of the dielectric metasurface due to excitation of the dielectric resonances. Various electromagnetic resonances are considered in the dielectric cone. The metal-dielectric resonances, which are excited between metal nanoparticles and dielectric cones, are also considered. The resonance local electric field can be much larger than the field in the usual surface plasmon resonances. To investigate local electric field the signal molecules are deposited on the metal nanoparticles. We demonstrate enhancement of the electromagnetic field and Raman signal from the complex of DTNB acid molecules and gold nanoparticles, which are distributed over the metasurface. The metasurfaces composed from the dielectric resonators can have quasi-continuous spectrum and serve as an efficient SERS substrates.

Dynamic effective medium theory for periodic structures with application to acoustic cloaking metamaterials

Expressions are presented for the fully dynamic effective material parameters governing the spatially averaged fields in three dimensional periodic systems. The results, which are valid at any frequency and wavenumber, are obtained by using the plane wave expansion (PWE) method. The effective equations are of Willis form with coupling between momentum and stress. Applications to layered fluids are first illustrated, showing that the effective density must be anisotropic and frequency dependent. A metamaterial proposed for cloaking - Metal Water - will be considered in detail as a function of frequency.

Flow-History-Dependent Behavior of Entangled Polymer Melt Flow Analyzed by Multiscale Simulation

Polymer melts represent the flow-history-dependent behavior. To clearly show this behavior, we have investigated flow behavior of an entangled polymer melt around two cylinders placed in tandem along the flow direction in a two dimensional periodic system. In this system, the polymer states around a cylinder in downstream side are different from the ones around another cylinder in upstream side because the former ones have a memory of a strain experienced when passing around the cylinder in upstream side but the latter ones do not have the memory. Therefore, the shear stress distributions around two cylinders are found to be different from each other. Moreover, we have found that the averaged flow velocity decreases accordingly with increasing the distance between two cylinders while the applied external force is constant. While this behavior is consistent with that of the Newtonian fluid, the flow-history-dependent behavior enhances the reduction of the flow resistance.

On the existence of periodic solutions to higher dimensional periodic system with delay

In this paper, higher dimensional periodic systems with delay of the form $$\begin{gathered} x'\left( t \right) = A\left( {t,x\left( t \right)} \right)x\left( t \right) + f\left( {t,x\left( {t - \tau } \right)} \right), \hfill \\ x'\left( t \right) = grad G\left( {x\left( t \right)} \right) + f\left( {t,x\left( {t - \tau } \right)} \right) \hfill \\ \end{gathered} $$ are considered. Using the coincidence degree method, some sufficient conditions to guarantee the existence of periodic solution for these systems are obtained. As an application of the results, the existence of a positive periodic solution for a logarithmic population model is proved.

Three Dimensional Periodic Systems with Trivial Dynamics, II

Ž . 3 Ž . where t g R, u s u , u , u g V; V ; R is open and F t, u [ 1 2 3 Ž Ž . Ž . Ž .. f t, u , u , f t, u , f t, u , u is continuous in V, is T-periodic in the i 1 2 2 3 2 3 time t, and has continuous partial derivative ­ Fr­ u defined on R = V. We also assume that the following hypotheses hold. Ž . H ­ f r­ u , ­ f r­ u , ­ f r­ u , and ­ f r­ u 0 on R = V. 1 1 2 2 1 2 3 3 2 Ž . 3 H F has a continuous extension F : R = V a R such that 2 0 0 ­ F r­ u is defined and continuous in a neighborhood V of V. 0 0

Activated Complex Theory of Barite Scale Control Processes

A theoretical framework useful for the estimation of scale dissolution rate constants is introduced. The model consists of (a) a dissolution mechanism, (b) a quantum mechanical force field capable of describing the bulk and surface properties of barite, (c) a complete study of the structure of the dissolver molecule complex in solution, (d) a three dimensional periodic system useful for mapping the barite-dissolver interactions, including the localization of the activated complex and (e) a rate expression to estimate the dissolution rate constants from the properties of the activated complex. Our results show that molecular modeling, through a combination of molecular mechanics and high level quantum mechanical calculations, provide a new and insightful information about scale control processes.

Theory of classical diffusion in two dimensional periodic systems

Theory of classical diffusion in two dimensional periodic systems

Theory of classical diffusion in two dimensional periodic systems

The diffusion of a classical particle in a 2D periodic field of force is studied, solving a Fokker-Planck equation in the high friction limit (Wilemski equation) with a simple cosine potential. The quasi-elastic dynamic structure factor is expressed as a series of Lorentzian functions and its FWHM is calculated for an extended range of the surface momentum transfer ℏQ. Jump and free diffusion are recovered as limiting cases dependent on the temperature. A comparison with neutron scattering data from premelted surfaces is made without any free parameter and a good agreement up to temperatures next to the bulk melting temperature is obtained.

Higher dimensional crystal models: A theory of thermal accommodation coefficients

New mathematical techniques for solving higher dimensional periodic systems are developed. The system is reduced to an equivalent set of one dimensional systems, which are solved by finite difference transform calculus. The resulting solutions are synthesized in the general integral of an associated partial differential equation to form the desired solution. These techniques maintain a higher degree of analytic integrity than the normal mode series expansion method, and allow the handling of sophisticated boundary conditions in an operational manner. The techniques are used to solve physically interesting models of molecules colliding with crystals. The model presented here is a three dimensional, semi-infinite, cubic lattice. The particles obey classical mechanics and interact harmonically with their nearest neighbors. The particle displacement is normal to the surface, and the ratio of the strengths of the longitudinal and transverse harmonic interactions is arbitrary. Lame's constants λ, μ, of the crystal determine this ratio. A normally incident particle of arbitrary mass interacts with the lattice through a truncated harmonic potential of arbitrary strength. The relative motion between this particle and the lattice is determined analytically from the resulting integro-differential equation in the form of a Neumann series. Accommodation coefficients are calculated for the rare gases on tungsten in a range of 100–300 °K. Experimental agreement is quantitative, especially for the heavier gases, A, Kr, Xe.