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arXiv2013

Application of the Space-Time Method to Stimulated Raman Adiabatic Passage on the Simple Harmonic Oscillator

The space-time method is applied to a model system-the Simple Harmonic Oscillator in a laser field to simulate the Stimulated Raman Adiabatic Passage (STIRAP) process. The Space-Time method is a computational theory first introduced by Weatherford et. al. to solve Time-Dependent Systems with one boundary value and applied to electron spin system with invariant Hamiltonian [Journal of Molecular Structure {\bf 592} 47]. The implementation in the present work provides an efficient and general way to solve the Time-Dependent Schr{ö}dinger Equation and can be applied to multi-state systems. The algorithm for simulating the Simple Harmonic Oscillator STIRAP can be applied to solve STIRAP problems for complex systems.

physics.comp-ph↗

arXiv2016

MathGR: a tensor and GR computation package to keep it simple

We introduce the MathGR package, written in Mathematica. The package can manipulate tensor and GR calculations with either abstract or explicit indices, simplify tensors with permutational symmetries, decompose tensors from abstract indices to partially or completely explicit indices and convert partial derivatives into total derivatives. Frequently used GR tensors and a model of FRW universe with ADM type perturbations are predefined. The package is built around the philosophy to "keep it simple", and makes use of latest tensor technologies of Mathematica.

cs.MS↗

arXiv2013

An algebraic RF sheath model for all excitation waveforms and amplitudes, and all levels of collisionality

The boundary sheath of a low temperature plasma comprises typically only a small fraction of its volume but is responsible for many aspects of the macroscopic behavior. A thorough understanding of the sheath dynamics is therefore of theoretical and practical importance. This work focusses on the so-called "algebraic" approach which strives to describe the electrical behavior of RF modulated boundary sheaths in closed analytical form, i.e., without the need to solve differential equations. A mathematically simple, analytical expression for the charge-voltage relation of a sheath is presented which holds for all excitation wave forms and amplitudes and covers all regimes from the collision-less motion at low gas pressure to the collision dominated motion at gas high pressure. A comparison with the results of self-consistent particle-in-cell simulations is also presented.

physics.plasm-ph↗

arXiv2013

Symbolic-numerical algorithm for generating cluster eigenfunctions: identical particles with pair oscillator interactions

The quantum model of a cluster, consisting of A identical particles, coupled by the internal pair interactions and affected by the external field of a target, is considered. A symbolic-numerical algorithm for generating A-1-dimensional oscillator eigenfunctions, symmetric or antisymmetric with respect to permutations of A identical particles in the new symmetrized coordinates, is formulated and implemented using the MAPLE computer algebra system. Examples of generating the symmetrized coordinate representation for A-1 dimensional oscillator functions in one-dimensional Euclidean space are analyzed. The approach is aimed at solving the problem of tunnelling the clusters, consisting of several identical particles, through repulsive potential barriers of a target.

physics.comp-ph↗

arXiv2013

Performance of a GPU-based Direct Summation Algorithm for Computation of Small Angle Scattering Profile

Small Angle Scattering (SAS) of X-rays or neutrons is an experimental technique that provides valuable structural information for biological macromolecules under physiological conditions and with no limitation on the molecular size. In order to refine molecular structure against experimental SAS data, ab initio prediction of the scattering profile must be recomputed hundreds of thousands of times, which involves the computation of the sinc kernel over all pairs of atoms in a molecule. The quadratic computational complexity of predicting the SAS profile limits the size of the molecules and and has been a major impediment for integration of SAS data into structure refinement protocols. In order to significantly speed up prediction of the SAS profile we present a general purpose graphical processing unit (GPU) algorithm, written in OpenCL, for the summation of the sinc kernel (Debye summation) over all pairs of atoms. This program is an order of magnitude faster than a parallel CPU algorithm, and faster than an FMM-like approximation method for certain input domains. We show that our algorithm is currently the fastest method for performing SAS computation for small and medium size molecules (around 50000 atoms or less). This algorithm is critical for quick and accurate SAS profile computation of elongated structures, such as DNA, RNA, and sparsely spaced pseudo-atom molecules.

q-bio.BM↗

arXiv2013

Finesse, Frequency domain INterferomEter Simulation SoftwarE

Finesse is a fast interferometer simulation program. For a given optical setup, it computes the light field amplitudes at every point in the interferometer assuming a steady state. To do so, the interferometer description is translated into a set of linear equations that are solved numerically. For convenience, a number of standard analyses can be performed automatically by the program, namely computing modulation-demodulation error signals, transfer functions, shot-noise-limited sensitivities, and beam shapes. Finesse can perform the analysis using the plane-wave approximation or Hermite-Gauss modes. The latter allows computation of the properties of optical systems like telescopes and the effects of mode matching and mirror angular positions.

physics.comp-ph↗

arXiv2013

Investigation of the transfer and dissipation of energy in isotropic turbulence

A parallel pseudospectral code for the direct numerical simulation (DNS) of isotropic turbulence has been developed. The code has been extensively benchmarked using established results from literature. The code has been used to conduct a series of runs for freely-decaying turbulence. We explore the use of power-law decay of the total energy to determine an evolved time and compare with the use of dynamic quantities such as the peak dissipation rate, maximum transport power and velocity derivative skewness. Stationary turbulence has also been investigated, where we ensure that the energy input rate remains constant for all runs. We present results for Reynolds numbers up to Rλ = 335 on a 1024^3 lattice. An exploitation of the pseudospectral technique is used to calculate second and third-order structure functions from the energy and transfer spectra, with a comparison presented to the real-space calculation. An alternative to ESS is discussed, with the second-order exponent found to approach 2/3. The dissipation anomaly is considered for forced and free-decay. The Kármán-Howarth equation (KHE) is studied and a derivation of a new work term presented. The balance of energy represented by the KHE is then investigated. Based on the KHE, we develop a model for the behaviour of the dimensionless dissipation coefficient that predicts Cε = Cε(\infty) + C_L/R_L, with Cε(\infty) = 0.47 and C_L = 19.1 obtained from DNS data. Theoretical methods based on RG and statistical closures are still being developed to study turbulence. The dynamic RG procedure used by Forster, Nelson and Stephen (FNS) is considered in some detail and a disagreement in the literature is resolved here. The application of statistical closure and renormalized perturbation theory is discussed and a new two-time model probability density functional presented.

physics.flu-dyn↗

arXiv2013

RDCI: A novel method of cluster analysis and applications thereof in sample molecular simulations

A novel method, termed Reduced Dimensionality Cluster Identification, RDCI, is presented, for the identification and quantitative description of clusters formed by N objects in three dimensional space. The method consists of finding a path, as short as possible, connecting the objects, and then tracking down the size s, of a subgroup i-n, i-n+1, ..., i+n, of 2n+1 < N particles for i varying from n+1 to N-n. Clusters are located where local minima of s(i) occur whereas local maxima serve as delimiters partitioning the path in subsets containing the clusters. Minimal post-processing allows for the removal of outliers on the basis of user-defined criteria and the identification of clearly defined clusters. The advantage of the method is that it requires no predetermined input or criteria of "clusterness" such as number of objects or size of aggregates. Among the numerous possible applications of the method, results are herein reported, from Molecular Dynamics simulations of a binary mixture of Lennard-Jones fluids and of a model polymeric system with a gas-like substance dispersed in it. The method is shown to allow the extraction of meaningful quantitative information regarding the tendency of molecules to cluster or de-cluster and the dynamics of the clustering processes.

cond-mat.other↗

arXiv2013

Nonmonotonic Relaxation as a Result of Spatial Heterogeneity in the Model of In-series Blocks Chain

Recently the materials possessing structure of molecular and supramolecular matrix are more and more actively studied. They are relative to many polymeric materials of a technological origin, such as rubber, and living biological tissues. Processes of mechanical deformation of these continuous media have peculiarities connected, first, with accounting for internal friction and dissipation of energy, and secondly, with nonlinearity of their elastic and viscous properties, that is with violation of Hook and Newtons laws. Traditional approaches to mechanics of viscoelastic bodies sometimes are excessively difficult, and more evident and available representations are necessary. The invaluable role in studying of the operating processes mechanisms of elastic deformation and motility of biological materials is played by the mathematical modeling. New effect obtained by means of computer experiment of nonmonotonic relaxation of deformation in heterogeneous media is considered in the present work. Rheological properties of described media are governed by the differential equations of the first order on time (the evolution equations), as well as a huge variety of other physical processes. The physical phenomena in nonlinear systems with dissipation have a big community, including such it would seem far areas, as dynamics of magnetization in ferrite. Therefore the problem of studying new effects of viscous friction in the conditions of nonlinearity and heterogeneity, is very actual as in respect of fundamental research nonlinear and non-uniform environments, and in many areas of materials science, design of new materials, engineering of biological substitutes of living tissues and development of the micromagnetic devices using essentially new opportunities.

nlin.AO↗

arXiv2013

Effects of Gas Dynamics on Rapidly Collapsing Bubbles

The dynamics of rapidly collapsing bubbles are of great interest due to the high degree of energy focusing that occurs withing the bubble. Molecular dynamics provides a way to model the interior of the bubble and couple the gas dynamics with the equations governing the bubble wall. While much theoretical work has been done to understand how a bubble will respond to an external force, the internal dynamics of the gas system are usually simplified greatly in such treatments. This paper shows how the gas system dynamics affect bubble collapse and illustrates what effects various modeling assumptions can have on the motion of the bubble wall. In addition, we present a method of adaptively partitioning space to improve the performance of collision intersection calculations when using an energy dependent collision cross section.

physics.comp-ph↗

arXiv2013

A New Description of Quantum Behaviors for a Simple Harmonic Oscillator

We describe quantum behaviors of a simple harmonic oscillator, starting from the classical mechanics. By imposing two conditions on the phase points generated from a symplectic algorithm, we obtain discrete energy levels, satisfying $E_n τ_n = h$ where $E_n$ is the total energy of the oscillator and $τ_n$ is the time step for the closed orbit of $n$-polygon in phase space. We can thus successfully integrate classical and quantum mechanics into a single frame, if we assume that time is discrete.

quant-ph↗

arXiv2015

Extraction of the Solvation Structure on a Solid Plate from a force curve measured by Surface Force Apparatus in a hard-sphere fluid

We propose a method of transformation from a force curve obtained with a surface force apparatus (SFA) to a density distribution of a liquid near a surface. The method is based on the statistical mechanics of liquids. As a first step, we show the method for a rigid system in which two cylinders are immersed in a hard-sphere fluid as the force probes. We found that the method works well, especially in the lower density solvent. The accuracy of the transformed result increases as the distance between the circular surface of the cylinder and the solvent sphere increases.

physics.data-an↗

arXiv2013

Reliable SPICE Simulations of Memristors, Memcapacitors and Meminductors

Memory circuit elements, namely memristive, memcapacitive and meminductive systems, are gaining considerable attention due to their ubiquity and use in diverse areas of science and technology. Their modeling within the most widely used environment, SPICE, is thus critical to make substantial progress in the design and analysis of complex circuits. Here, we present a collection of models of different memory circuit elements and provide a methodology for their accurate and reliable modeling in the SPICE environment. We also provide codes of these models written in the most popular SPICE versions (PSpice, LTspice, HSPICE) for the benefit of the reader. We expect this to be of great value to the growing community of scientists interested in the wide range of applications of memory circuit elements.

physics.comp-ph↗

arXiv2013

Novel linear algebraic theory and one-hundred-million-atom electronic structure calculation on the K computer

A novel linear-algebraic algorithm, multiple Arnoldi method, was developed in an interdisciplinary study between physics and applied mathematics and realized one-hundred-million-atom (100-nm-scale) electronic state calculations on the K computer. The algorithms are Krylov-subspace solvers for generalized shifted linear equations and were implemented in our order-N calculation code ELSES (http://www.elses.jp/). Moreover, a method for calculating eigen states is presented as a theoretical extension.

cond-mat.mtrl-sci↗

arXiv2013

Excitation of high-amplitude localized nonlinear waves as a result of interaction of kink with attractive impurity in sine-Gordon equation

We study properties of the localized solitons to the sine-Gordon equation excited on the attractive impurity by a moving kink. The cases of one- and two-dimensional spatially extended impurities are considered. For the case of one-dimensional impurity the possibility of excitation of the first even and odd high-amplitude impurity modes by the moving kink is demonstrated. For the case of two-dimensional impurity we show the possibility of excitation of the nonlinear high-amplitude waves of new type called here breathing pulson and breathing 2D soliton. We suggest different analytical expressions to model these nonlinear excitations. The dependencies of the oscillation frequency and the amplitude of the excited impurity modes on the impurity parameters are reported.

nlin.PS↗

arXiv2013

Partition Function of the Ising Model via Factor Graph Duality

The partition function of a factor graph and the partition function of the dual factor graph are related to each other by the normal factor graph duality theorem. We apply this result to the classical problem of computing the partition function of the Ising model. In the one-dimensional case, we thus obtain an alternative derivation of the (well-known) analytical solution. In the two-dimensional case, we find that Monte Carlo methods are much more efficient on the dual graph than on the original graph, especially at low temperature.

cs.IT↗

arXiv2013

Review of simulating four classes of window materials for daylighting with non-standard BSDF using the simulation program Radiance

This review describes the currently available simulation models for window material to calculate daylighting with the program "Radiance". The review is based on four abstract and general classes of window materials, depending on their scattering and redirecting properties (bidirectional scatter distribution function, BSDF). It lists potential and limits of the older models and includes the most recent additions to the software. All models are demonstrated using an exemplary indoor scene and two typical sky conditions. It is intended as clarification for applying window material models in project work or teaching. The underlying algorithmic problems apply to all lighting simulation programs, so the scenarios of materials and skies are applicable to other lighting programs.

physics.comp-ph↗

arXiv2013

Influence of media on collective debates

The information system (T.V., newspapers, blogs, social network platforms) and its inner dynamics play a fundamental role on the evolution of collective debates and thus on the public opinion. In this work we address such a process focusing on how the current inner strategies of the information system (competition, customer satisfaction) once combined with the gossip may affect the opinions dynamics. A reinforcement effect is particularly evident in the social network platforms where several and incompatible cultures coexist (e.g, pro or against the existence of chemical trails and reptilians, the new world order conspiracy and so forth). We introduce a computational model of opinion dynamics which accounts for the coexistence of media and gossip as separated but interdependent mechanisms influencing the opinions evolution. Individuals may change their opinions under the contemporary pressure of the information supplied by the media and the opinions of their social contacts. We stress the effect of the media communication patterns by considering both the simple case where each medium mimics the behavior of the most successful one (in order to maximize the audience) and the case where there is polarization and thus competition among media reported information (in order to preserve and satisfy their segmented audience). Finally, we first model the information cycle as in the case of traditional main stream media (i.e, when every medium knows about the format of all the others) and then, to account for the effect of the Internet, on more complex connectivity patterns (as in the case of the web based information). We show that multiple and polarized information sources lead to stable configurations where several and distant opinions coexist.

physics.soc-ph↗