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Periodic Boundary Conditions (periodic + boundary_condition)
Selected AbstractsThird and fourth Stokes parameters in polarimetric passive microwave remote sensing of rough surfaces over layered mediaMICROWAVE AND OPTICAL TECHNOLOGY LETTERS, Issue 12 2008Leung Tsang Abstract We consider the four Stokes parameters in microwave emission from a layered medium with the top interface being a rough surface. The rough surface varies in one horizontal direction so that azimuthal asymmetry exists in the 3-D problem. Dyadic Green's functions of multilayered media are used to formulate the surface integral equations. Periodic boundary conditions are used. The numerical results show that the presence of the layered media below the rough surface reduces the vertical and horizontal brightness temperatures. The interaction between the rough surface and the layered media also enhance the third and fourth Stokes parameters. In particular, the fourth Stokes parameter can be large for such geometrical configurations. Results show that the nonzero third and fourth Stokes parameters exist for all frequencies and are particularly large when the rough surface has large slope. © 2008 Wiley Periodicals, Inc. Microwave Opt Technol Lett 50: 3063,3069, 2008; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.23892 [source] The embedded ion method: A new approach to the electrostatic description of crystal lattice effects in chemical shielding calculationsCONCEPTS IN MAGNETIC RESONANCE, Issue 5 2006Dirk Stueber Abstract The nuclear magnetic shielding anisotropy of NMR active nuclei is highly sensitive to the nuclear electronic environment. Hence, measurements of the nuclear magnetic shielding anisotropy represent a powerful tool in the elucidation of molecular structure for a wide variety of materials. Quantum mechanical ab initio nuclear magnetic shielding calculations effectively complement the experimental NMR data by revealing additional structural information. The accuracy and capacity of these calculations has been improved considerably in recent years. However, the inherent problem of the limitation in the size of the systems that may be studied due to the relatively demanding computational requirements largely remains. Accordingly, ab initio shielding calculations have been performed predominantly on isolated molecules, neglecting the molecular environment. This approach is sufficient for neutral nonpolar systems, but leads to serious errors in the shielding calculations on polar and ionic systems. Conducting ab initio shielding calculations on clusters of molecules (i.e., including the nearest neighbor interactions) has improved the accuracy of the calculations in many cases. Other methods of simulating crystal lattice effects in shielding calculations that have been developed include the electrostatic representation of the crystal lattice using point charge arrays, full ab initio methods, ab initio methods under periodic boundary conditions, and hybrid ab initio/molecular dynamics methods. The embedded ion method (EIM) discussed here follows the electrostatic approach. The method mimics the intermolecular and interionic interactions experienced by a subject molecule or cluster in a given crystal in quantum mechanical shielding calculations with a large finite, periodic, and self-consistent array of point charges. The point charge arrays in the EIM are generated using the Ewald summation method and embed the molecule or ion of interest for which the ab initio shielding calculations are performed. The accuracy with which the EIM reproduces experimental nuclear magnetic shift tensor principal values, the sensitivity of the EIM to the parameters defining the point charge arrays, as well as the strengths and limitations of the EIM in comparison with other methods that include crystal lattice effects in chemical shielding calculations, are presented. © 2006 Wiley Periodicals, Inc. Concepts Magn Reson Part A 28A: 347,368, 2006 [source] Heat-Transfer Coefficient for Cellular Materials Modelled as an Array of Elliptic Rods,ADVANCED ENGINEERING MATERIALS, Issue 10 2009Marcelo J. S. de Lemos Convective heat-transfer coefficients in foam-like materials, modelled as an array of elliptic rods, are numerically determined. An incompressible fluid is considered, flowing through an infinite foam-like material with an arbitrary solid temperature. A repetitive cell is identified and periodic boundary conditions are applied. Turbulence is handled with both low and high Reynolds number formulations. The interfacial heat-transfer coefficient is obtained by volume integrating the distributed variables obtained within the cell. The results indicate that, for the same mass-flow rate, materials formed by elliptic rods have a lower interfacial heat-transfer coefficient compared to other media modelled as staggered arrays of square rods. [source] Estimation of effective exchange integral value of polyradical systems based on the band calculationINTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 15 2009Yasuyuki Nakanishi Abstract Effective exchange integral (Jab) values calculated by cluster models were compared with values calculated under the periodic boundary conditions. So far, to estimate the Jab value of a macro system, we have considered that of the corresponding to cluster one. However, they will get absolutely nothing out of it if a cluster model and the periodic boundary conditions method give different results to us. The main aim of this report is to give an opinion to this issue using a one-dimensional polyhydrogen system as example. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2009 [source] Density functional crystal orbital study of cyano-substituted poly(para -phenylene-vinylene) and poly(quinoxaline-vinylene)INTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 8 2006F. Bartha Abstract We have calculated the optical and electronic properties of several conjugated organic polymers: poly(p -phenylene-vinylene) (PPV) and its derivatives. Cyano substitutions on the phenylene ring: poly(2,5-dicyano- p -phenylene-vinylene) (2,5-DCN-PPV) and on the vinylene linkage: poly(p -phenylene-7(,8)-(di)cyano-vinylene) are considered. In addition, poly(quinoxaline-vinylene) (PQV) is studied. The infinite isolated quasi-1D chains are treated with periodic boundary conditions, using atomic basis sets. In a comparative study of PPV, some issues regarding the selection of the functionals and basis sets are discussed and excitation energies derived from time-dependent and from ordinary methods are compared. It is concluded that for these polymers the calculations are informative at the B3LYP/6-31G** density functional theory (DFT) level. The absolute values might change with improved methods, but the similarity of the polymers suggests that the relative characterization is adequate. Band structures are communicated along with characteristics of the highest occupied and the lowest unoccupied crystal orbitals (HOCO and LUCO). Electron affinities, ionization potentials, valence and conduction bandwidths, and effective masses at the bandgap are given. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2006 [source] Analysis and design of band-pass frequency-selective surfaces using the FEM CAD toolINTERNATIONAL JOURNAL OF RF AND MICROWAVE COMPUTER-AIDED ENGINEERING, Issue 5 2004P. T. Teo Abstract Three-dimensional (3D) full-wave analysis and design of bandpass frequency-selective surfaces (FSSs) is presented. By using the unique features of a unit cell and the periodic boundary conditions, infinite FSSs can be simulated. Wave propagation through FSSs, which is otherwise difficult to quantify, can be visualised by using a commercial CAD tool. The creation of the simulation model, interpretation and analysis of the outcome, and comparison with experimental results are presented for the square-slot and the square-loop-slot band-pass FSS. © 2004 Wiley Periodicals, Inc. Int J RF and Microwave CAE 14, 391,397, 2004. [source] Dynamic Charge Equilibration-Morse stretch force field: Application to energetics of pure silica zeolitesJOURNAL OF COMPUTATIONAL CHEMISTRY, Issue 16 2002Jan Sefcik Abstract We present the Dynamic Charge Equilibration (DQEq) method for a self-consistent treatment of charge transfer in force field modeling, where atomic charges are designed to reproduce electrostatic potentials calculated quantum mechanically. Force fields coupled with DQEq allow charges to readjust as geometry changes in classical simulations, using appropriate algorithms for periodic boundary conditions. The full electrostatic energy functional is used to derive the corresponding forces and the second derivatives (hessian) for vibrational calculations. Using DQEq electrostatics, we develop a simple nonbond force field for simulation of silica molecular sieves, where nonelectrostatic interactions are described by two-body Morse stretch terms. Energy minimization calculations with the new force field yield accurate unit cell geometries for siliceous zeolites. Relative enthalpies with respect to quartz and third-law entropies calculated from harmonic vibrational analysis agree very well with available calorimetric data: calculated SiO2 enthalpies relative to ,-quartz are within 2 kJ/mol and entropies at 298 K are within 3 J/mol K of the respective experimental values. Contributions from the zero point energy and vibrational degrees of freedom were found to be only about 1 kJ/mol for the free energy of mutual transformations between microporous silica polymorphs. The approach presented here can be applied to interfaces and other oxides as well and it is suitable for development of force fields for accurate modeling of geometry and energetics of microporous and mesoporous materials, while providing a realistic description of electrostatic fields near surfaces and inside pores of adsorbents and catalysts. © 2002 Wiley Periodicals, Inc. J Comput Chem 23: 1507,1514, 2002 [source] Computational alanine scanning of the 1:1 human growth hormone,receptor complexJOURNAL OF COMPUTATIONAL CHEMISTRY, Issue 1 2002Shuanghong Huo Abstract The MM-PBSA (Molecular Mechanics,Poisson,Boltzmann surface area) method was applied to the human Growth Hormone (hGH) complexed with its receptor to assess both the validity and the limitations of the computational alanine scanning approach. A 400-ps dynamical trajectory of the fully solvated complex was simulated at 300 K in a 101 Å×81 Å×107 Å water box using periodic boundary conditions. Long-range electrostatic interactions were treated with the particle mesh Ewald (PME) summation method. Equally spaced snapshots along the trajectory were chosen to compute the binding free energy using a continuum solvation model to calculate the electrostatic desolvation free energy and a solvent-accessible surface area approach to treat the nonpolar solvation free energy. Computational alanine scanning was performed on the same set of snapshots by mutating the residues in the structural epitope of the hormone and the receptor to alanine and recomputing the ,Gbinding. To further investigate a particular structure, a 200-ps dynamical trajectory of an R43A hormone,receptor complex was simulated. By postprocessing a single trajectory of the wild-type complex, the average unsigned error of our calculated ,,Gbinding is ,1 kcal/mol for the alanine mutations of hydrophobic residues and polar/charged residues without buried salt bridges. When residues involved in buried salt bridges are mutated to alanine, it is demonstrated that a separate trajectory of the alanine mutant complex can lead to reasonable agreement with experimental results. Our approach can be extended to rapid screening of a variety of possible modifications to binding sites. © 2002 Wiley Periodicals, Inc. J Comput Chem 23: 15,27, 2002 [source] Exponential attractor for a planar shear-thinning flowMATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 17 2007Dalibor Pra Abstract We study the dynamics of an incompressible, homogeneous fluid of a power-law type, with the stress tensor T = ,(1 + µ|Dv|)p,2Dv, where Dv is a symmetric velocity gradient. We consider the two-dimensional problem with periodic boundary conditions and p , (1, 2). Under these assumptions, we estimate the fractal dimension of the exponential attractor, using the so-called method of ,,-trajectories. Copyright © 2007 John Wiley & Sons, Ltd. [source] On non-stationary viscous incompressible flow through a cascade of profilesMATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 16 2006Miloslav Feistauer Abstract The paper deals with theoretical analysis of non-stationary incompressible flow through a cascade of profiles. The initial-boundary value problem for the Navier,Stokes system is formulated in a domain representing the exterior to an infinite row of profiles, periodically spaced in one direction. Then the problem is reformulated in a bounded domain of the form of one space period and completed by the Dirichlet boundary condition on the inlet and the profile, a suitable natural boundary condition on the outlet and periodic boundary conditions on artificial cuts. We present a weak formulation and prove the existence of a weak solution. Copyright © 2006 John Wiley & Sons, Ltd. [source] On singular mono-energetic transport equations in slab geometryMATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 13 2002Mohamed Chabi In this paper we establish the well posedness of the Cauchy problem associated to transport equations with singular cross-sections (i.e. unbounded collisions frequencies and unbounded collision operators) in L1 spaces for specular reflecting boundary conditions. In addition, we discuss the weak compactness of the second-order remainder term of the Dyson,Phillips expansion. This allows us to estimate the essential type of the transport semigroup from which the asymptotic behaviour of the solution is derived. The case of singular transport equations with periodic boundary conditions is also discussed. The proofs make use of the Miyadera perturbation theory of positive semigroups on AL -spaces. Copyright © 2002 John Wiley & Sons, Ltd. [source] Stability and convergence of optimum spectral non-linear Galerkin methodsMATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 5 2001He Yinnian Abstract Our objective in this article is to present some numerical schemes for the approximation of the 2-D Navier,Stokes equations with periodic boundary conditions, and to study the stability and convergence of the schemes. Spatial discretization can be performed by either the spectral Galerkin method or the optimum spectral non-linear Galerkin method; time discretization is done by the Euler scheme and a two-step scheme. Our results show that under the same convergence rate the optimum spectral non-linear Galerkin method is superior to the usual Galerkin methods. Finally, numerical example is provided and supports our results. Copyright © 2001 John Wiley & Sons, Ltd. [source] A conceptually simple method for incorporating periodic boundary conditions into the FDTD methodMICROWAVE AND OPTICAL TECHNOLOGY LETTERS, Issue 6 2005R. Todd Lee Abstract A straightforward, conceptually simple technique is presented for incorporating periodic boundary conditions into the FDTD method. The method is valid over a wide range of angles of incidence (for the scattering case) or angles of scan (for the antenna case). The method is verified through comparison with results calculated using a frequency-domain, mode-matching method. © 2005 Wiley Periodicals, Inc. Microwave Opt Technol Lett 45: 472,476, 2005; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.20856 [source] Parametric study and synthesis of 60-GHz Fabry,Perot resonatorsMICROWAVE AND OPTICAL TECHNOLOGY LETTERS, Issue 4 2002R. Sauleau Abstract The analysis and the synthesis of plane-parallel Fabry,Perot (FP) resonators, illuminated by a normally incident plane wave, are investigated theoretically and experimentally in the 60-GHz band. The reflecting mirrors are inductive metal meshes with square apertures. The frequency response of symmetrical and asymmetric FP cavities is studied (a) approximately with the transmission-line theory (TL), and (b) and rigorously with the Finite-difference,time-domain (FDTD) technique combined with periodic boundary conditions. Then, the inverse problem is solved with the use of an iterative procedure based on the FDTD method. In particular, it is shown theoretically and checked experimentally that the thickness of the cavity is the most critical parameter in the design, although the grid dimensions enable a precise adjustment of the module and of the phase of the internal reflection coefficients. © 2002 Wiley Periodicals, Inc. Microwave Opt Technol Lett 34: 247,252, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.10429 [source] Extension theorems for Stokes and Lamé equations for nearly incompressible media and their applications to numerical solution of problems with highly discontinuous coefficientsNUMERICAL LINEAR ALGEBRA WITH APPLICATIONS, Issue 2 2002N. S. Bakhvalov Abstract We prove extension theorems in the norms described by Stokes and Lamé operators for the three-dimensional case with periodic boundary conditions. For the Lamé equations, we show that the extension theorem holds for nearly incompressible media, but may fail in the opposite limit, i.e. for case of absolutely compressible media. We study carefully the latter case and associate it with the Cosserat problem. Extension theorems serve as an important tool in many applications, e.g. in domain decomposition and fictitious domain methods, and in analysis of finite element methods. We consider an application of established extension theorems to an efficient iterative solution technique for the isotropic linear elasticity equations for nearly incompressible media and for the Stokes equations with highly discontinuous coefficients. The iterative method involves a special choice for an initial guess and a preconditioner based on solving a constant coefficient problem. Such preconditioner allows the use of well-known fast algorithms for preconditioning. Under some natural assumptions on smoothness and topological properties of subdomains with small coefficients, we prove convergence of the simplest Richardson method uniform in the jump of coefficients. For the Lamé equations, the convergence is also uniform in the incompressible limit. Our preliminary numerical results for two-dimensional diffusion problems show fast convergence uniform in the jump and in the mesh size parameter. Copyright © 2002 John Wiley & Sons, Ltd. [source] Discontinuous Galerkin methods for periodic boundary value problemsNUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 3 2007Kumar Vemaganti Abstract This article considers the extension of well-known discontinuous Galerkin (DG) finite element formulations to elliptic problems with periodic boundary conditions. Such problems routinely appear in a number of applications, particularly in homogenization of composite materials. We propose an approach in which the periodicity constraint is incorporated weakly in the variational formulation of the problem. Both H1 and L2 error estimates are presented. A numerical example confirming theoretical estimates is shown. © 2006 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2007 [source] Finite element analysis of plain weave composites for flexural failurePOLYMER COMPOSITES, Issue 4 2010Ömer Soykasap This article presents finite element analysis for flexural behavior of woven composites considering the fiber and the matrix and their interactions. Finite element model using Abaqus program is developed to predict the homogenized properties of plain-weave T300/LTM45 composite. Initially, curved beam elements are used to model each resin-infiltrated fiber bundle. Geometrically, nonlinear analyses of the model with periodic boundary conditions are carried out to obtain effective in-plane and bending properties of the composite. Statistical analysis is presented to study the stiffness variability. The flexural failure of a single-ply composite is estimated based on the homogenized material properties, and is compared with previously published data. The model is able to correct the significant errors in the stiffnesses of the composite and captures the failure behavior accurately. POLYM. COMPOS., 2010. © 2009 Society of Plastics Engineers [source] X-ray study and structure simulation of amorphous tungsten oxideACTA CRYSTALLOGRAPHICA SECTION B, Issue 4 2002L. A. Lugovskaya In this work, X-ray studies of the amorphous oxide films obtained by thermal evaporation of WO3 powder in a vacuum and by anodic oxidation were carried out. X-ray diffraction patterns were obtained in the symmetric reflection geometry on a DRON-4 diffractometer (Mo K, radiation, LiF monochromator) in automatic mode. Molecular dynamics simulation of amorphous tungsten oxide atomic configurations has been carried out in the micro-canonical ensemble (NVE) for N,=,208 atoms and N,=,624 atoms, in a cubic cell, using pairwise Born,Mayer interaction potentials and periodic boundary conditions. One of the purposes of the present work is to analyze the influence of the parameters and the cutoff of the interaction potentials on the interatomic distances. The values obtained in the molecular dynamics simulation for the pair functions D(r) are compared with the experimental data for amorphous oxides in order to choose the most convenient aforesaid values. The values of the average interatomic distances and the coordination numbers obtained by both methods are also compared. The result shows that the tungsten subsystem can be well reproduced using the potential cutoff radius of about 4,Å, but the oxygen subsystem can be well reproduced when the cutoff of the potential for the W,O pairs is equal to 2.8,Å. The configuration built during the molecular dynamics experiment consists of distorted octahedra. These octahedra form chains, as in the WO3 phases of type ReO3, and hexagonal rings, of the same type as in the WO3(1/3)H2O phase, when we extract (1/3)O at every WO3 unit. The pair function D(r) and scattering intensity I(s) distribution curves calculated for simulation configurations show a satisfactory agreement with experiment. [source] The mean-field approximation in quantum electrodynamics: The no-photon caseCOMMUNICATIONS ON PURE & APPLIED MATHEMATICS, Issue 4 2007Christian Hainzl We study the mean-field approximation of quantum electrodynamics (QED) by means of a thermodynamic limit. The QED Hamiltonian is written in Coulomb gauge and does not contain any normal ordering or choice of bare electron/positron subspaces. Neglecting photons, we properly define this Hamiltonian in a finite box [,L/2; L/2)3, with periodic boundary conditions and an ultraviolet cutoff ,. We then study the limit of the ground state (i.e., the vacuum) energy and of the minimizers as L goes to infinity, in the Hartree-Fock approximation. In the case with no external field, we prove that the energy per volume converges and obtain in the limit a translation-invariant projector describing the free Hartree-Fock vacuum. We also define the energy per unit volume of translation-invariant states and prove that the free vacuum is the unique minimizer of this energy. In the presence of an external field, we prove that the difference between the minimum energy and the energy of the free vacuum converges as L goes to infinity. We obtain in the limit the so-called Bogoliubov-Dirac-Fock functional. The Hartree-Fock (polarized) vacuum is a Hilbert-Schmidt perturbation of the free vacuum and it minimizes the Bogoliubov-Dirac-Fock energy. © 2006 Wiley Periodicals, Inc. [source] Malliavin calculus for the stochastic 2D Navier,Stokes equationCOMMUNICATIONS ON PURE & APPLIED MATHEMATICS, Issue 12 2006Jonathan C. Mattingly We consider the incompressible, two-dimensional Navier-Stokes equation with periodic boundary conditions under the effect of an additive, white-in-time, stochastic forcing. Under mild restrictions on the geometry of the scales forced, we show that any finite-dimensional projection of the solution possesses a smooth, strictly positive density with respect to Lebesgue measure. In particular, our conditions are viscosity independent. We are mainly interested in forcing that excites a very small number of modes. All of the results rely on proving the nondegeneracy of the infinite-dimensional Malliavin matrix. © 2006 Wiley Periodicals Inc. [source] Nontopological N -vortex condensates for the self-dual Chern-Simons theoryCOMMUNICATIONS ON PURE & APPLIED MATHEMATICS, Issue 12 2003Margherita Nolasco We prove the existence of nontopological N -vortex solutions for an arbitrary number N of vortex points for the self-dual Chern-Simons-Higgs theory with 't Hooft "periodic" boundary conditions. We use a shadowing-type lemma to glue together any number of single vortices obtained as a perturbation of a radially symmetric entire solution of the Liouville equation. © 2003 Wiley Periodicals, Inc. [source] | |||||||||||||||||||