The exact eigenfunctions and eigenvalues of a two-dimensional rigid rotor obtained using Gaussian wave packet dynamics

NASA Technical Reports Server (NTRS)

Reimers, J. R.; Heller, E. J.

1985-01-01

Exact eigenfunctions for a two-dimensional rigid rotor are obtained using Gaussian wave packet dynamics. The wave functions are obtained by propagating, without approximation, an infinite set of Gaussian wave packets that collectively have the correct periodicity, being coherent states appropriate to this rotational problem. This result leads to a numerical method for the semiclassical calculation of rovibrational, molecular eigenstates. Also, a simple, almost classical, approximation to full wave packet dynamics is shown to give exact results: this leads to an a posteriori justification of the De Leon-Heller spectral quantization method.

An investigation of the accuracy of the Merkel equation for evaporative cooling tower calculations. Waste heat management

DOE Office of Scientific and Technical Information (OSTI.GOV)

Yadigaroglu, G.; Pastor, E.J.

1974-01-01

The exact differential equations governing heat and mass transfer and air flow in an evaporative, natural-draft cooling tower are presented. The Merkel equation is then derived starting from this exact formulation and showing all the approximations involved. The Merkel formulation lumps the sensible and the latent heat transfer together and considers a single enthalpy-difference driving force for the total heat transfer. The effect of the approximations inherent in the Merkel equation is investigated and analyzed by a series of parametric numerical calculations of cooling tower performance under various ambient conditions and load conditions.

Calculating corner singularities by boundary integral equations.

PubMed

Shi, Hualiang; Lu, Ya Yan; Du, Qiang

2017-06-01

Accurate numerical solutions for electromagnetic fields near sharp corners and edges are important for nanophotonics applications that rely on strong near fields to enhance light-matter interactions. For cylindrical structures, the singularity exponents of electromagnetic fields near sharp edges can be solved analytically, but in general the actual fields can only be calculated numerically. In this paper, we use a boundary integral equation method to compute electromagnetic fields near sharp edges, and construct the leading terms in asymptotic expansions based on numerical solutions. Our integral equations are formulated for rescaled unknown functions to avoid unbounded field components, and are discretized with a graded mesh and properly chosen quadrature schemes. The numerically found singularity exponents agree well with the exact values in all the test cases presented here, indicating that the numerical solutions are accurate.

A new exact method for line radiative transfer

NASA Astrophysics Data System (ADS)

Elitzur, Moshe; Asensio Ramos, Andrés

2006-01-01

We present a new method, the coupled escape probability (CEP), for exact calculation of line emission from multi-level systems, solving only algebraic equations for the level populations. The CEP formulation of the classical two-level problem is a set of linear equations, and we uncover an exact analytic expression for the emission from two-level optically thick sources that holds as long as they are in the `effectively thin' regime. In a comparative study of a number of standard problems, the CEP method outperformed the leading line transfer methods by substantial margins. The algebraic equations employed by our new method are already incorporated in numerous codes based on the escape probability approximation. All that is required for an exact solution with these existing codes is to augment the expression for the escape probability with simple zone-coupling terms. As an application, we find that standard escape probability calculations generally produce the correct cooling emission by the CII 158-μm line but not by the 3P lines of OI.

Critical frontier of the Potts and percolation models on triangular-type and kagome-type lattices. II. Numerical analysis

NASA Astrophysics Data System (ADS)

Ding, Chengxiang; Fu, Zhe; Guo, Wenan; Wu, F. Y.

2010-06-01

In the preceding paper, one of us (F. Y. Wu) considered the Potts model and bond and site percolation on two general classes of two-dimensional lattices, the triangular-type and kagome-type lattices, and obtained closed-form expressions for the critical frontier with applications to various lattice models. For the triangular-type lattices Wu’s result is exact, and for the kagome-type lattices Wu’s expression is under a homogeneity assumption. The purpose of the present paper is twofold: First, an essential step in Wu’s analysis is the derivation of lattice-dependent constants A,B,C for various lattice models, a process which can be tedious. We present here a derivation of these constants for subnet networks using a computer algorithm. Second, by means of a finite-size scaling analysis based on numerical transfer matrix calculations, we deduce critical properties and critical thresholds of various models and assess the accuracy of the homogeneity assumption. Specifically, we analyze the q -state Potts model and the bond percolation on the 3-12 and kagome-type subnet lattices (n×n):(n×n) , n≤4 , for which the exact solution is not known. Our numerical determination of critical properties such as conformal anomaly and magnetic correlation length verifies that the universality principle holds. To calibrate the accuracy of the finite-size procedure, we apply the same numerical analysis to models for which the exact critical frontiers are known. The comparison of numerical and exact results shows that our numerical values are correct within errors of our finite-size analysis, which correspond to 7 or 8 significant digits. This in turn infers that the homogeneity assumption determines critical frontiers with an accuracy of 5 decimal places or higher. Finally, we also obtained the exact percolation thresholds for site percolation on kagome-type subnet lattices (1×1):(n×n) for 1≤n≤6 .

Exact analytic solutions of Maxwell's equations describing propagating nonparaxial electromagnetic beams.

PubMed

Garay-Avendaño, Roger L; Zamboni-Rached, Michel

2014-07-10

In this paper, we propose a method that is capable of describing in exact and analytic form the propagation of nonparaxial scalar and electromagnetic beams. The main features of the method presented here are its mathematical simplicity and the fast convergence in the cases of highly nonparaxial electromagnetic beams, enabling us to obtain high-precision results without the necessity of lengthy numerical simulations or other more complex analytical calculations. The method can be used in electromagnetism (optics, microwaves) as well as in acoustics.

Use of a variational moment method in calculating propagation constants for waveguides with an arbitrary index profile.

PubMed

Hardy, A; Itzkowitz, M; Griffel, G

1989-05-15

A variational moment method is used to calculate propagation constants of 1-D optical waveguides with an arbitrary index profile. The method is applicable to 2-D waveguides as well, and the index profiles need not be symmetric. Examples are given for the lowest-order and the next higher-order modes and are compared with exact numerical solutions.

Trajectory And Heating Of A Hypervelocity Projectile

NASA Technical Reports Server (NTRS)

Tauber, Michael E.

1992-01-01

Technical paper presents derivation of approximate, closed-form equation for relationship between velocity of projectile and density of atmosphere. Results of calculations based on approximate equation agree well with results from numerical integrations of exact equations of motion. Comparisons of results presented in series of graphs.

Rectification of thermal fluctuations in ideal gases.

PubMed

Meurs, P; Van den Broeck, C; Garcia, A

2004-11-01

We calculate the systematic average speed of the adiabatic piston and a thermal Brownian motor, introduced by C. Van den Broeck, R, Kawai and P. Meurs [Phys. Rev. Lett. 93, 090601 (2004)], by an expansion of the Boltzmann equation and compare with the exact numerical solution.

Large-scale structure perturbation theory without losing stream crossing

DOE PAGES

McDonald, Patrick; Vlah, Zvonimir

2018-01-10

Here, we suggest an approach to perturbative calculations of large-scale clustering in the Universe that includes from the start the stream crossing (multiple velocities for mass elements at a single position) that is lost in traditional calculations. Starting from a functional integral over displacement, the perturbative series expansion is in deviations from (truncated) Zel’dovich evolution, with terms that can be computed exactly even for stream-crossed displacements. We evaluate the one-loop formulas for displacement and density power spectra numerically in 1D, finding dramatic improvement in agreement with N-body simulations compared to the Zel’dovich power spectrum (which is exact in 1D upmore » to stream crossing). Beyond 1D, our approach could represent an improvement over previous expansions even aside from the inclusion of stream crossing, but we have not investigated this numerically. In the process we show how to achieve effective-theory-like regulation of small-scale fluctuations without free parameters.« less

Large-scale structure perturbation theory without losing stream crossing

DOE Office of Scientific and Technical Information (OSTI.GOV)

McDonald, Patrick; Vlah, Zvonimir

Here, we suggest an approach to perturbative calculations of large-scale clustering in the Universe that includes from the start the stream crossing (multiple velocities for mass elements at a single position) that is lost in traditional calculations. Starting from a functional integral over displacement, the perturbative series expansion is in deviations from (truncated) Zel’dovich evolution, with terms that can be computed exactly even for stream-crossed displacements. We evaluate the one-loop formulas for displacement and density power spectra numerically in 1D, finding dramatic improvement in agreement with N-body simulations compared to the Zel’dovich power spectrum (which is exact in 1D upmore » to stream crossing). Beyond 1D, our approach could represent an improvement over previous expansions even aside from the inclusion of stream crossing, but we have not investigated this numerically. In the process we show how to achieve effective-theory-like regulation of small-scale fluctuations without free parameters.« less

Localization and mobility edges in one-dimensional deterministic potentials

NASA Astrophysics Data System (ADS)

Tong, Peiqing

1994-10-01

In this paper, we study the localization properties of the wave function of a one-dimensional tight-binding electron moving in an asymptotic periodic potential, Vn=λ cos(2πQn+παnν), where n is the site index and 0<ν<1. For Q rational, the electronic energy band consists of many subbands, and the number of subbands is determined by Q. For λ<2, there are two mobility edges where the eigenstates at the subband center are all extended, whereas the subband-edge states are all localized in every subband. We develop some heuristic arguments to calculate exactly the mobility edges for this model and carry out numerical work to study the localization properties of the model. Our theoretical results are essentially in exact agreement with the numerical results. We calculate the critical exponents δ and β at mobility edges. We also study the nature of the localized, extended eigenstates and mobility edges of this system as a function of λ, α, and ν.

A hybrid stochastic hierarchy equations of motion approach to treat the low temperature dynamics of non-Markovian open quantum systems

NASA Astrophysics Data System (ADS)

Moix, Jeremy M.; Cao, Jianshu

2013-10-01

The hierarchical equations of motion technique has found widespread success as a tool to generate the numerically exact dynamics of non-Markovian open quantum systems. However, its application to low temperature environments remains a serious challenge due to the need for a deep hierarchy that arises from the Matsubara expansion of the bath correlation function. Here we present a hybrid stochastic hierarchical equation of motion (sHEOM) approach that alleviates this bottleneck and leads to a numerical cost that is nearly independent of temperature. Additionally, the sHEOM method generally converges with fewer hierarchy tiers allowing for the treatment of larger systems. Benchmark calculations are presented on the dynamics of two level systems at both high and low temperatures to demonstrate the efficacy of the approach. Then the hybrid method is used to generate the exact dynamics of systems that are nearly impossible to treat by the standard hierarchy. First, exact energy transfer rates are calculated across a broad range of temperatures revealing the deviations from the Förster rates. This is followed by computations of the entanglement dynamics in a system of two qubits at low temperature spanning the weak to strong system-bath coupling regimes.

A hybrid stochastic hierarchy equations of motion approach to treat the low temperature dynamics of non-Markovian open quantum systems.

PubMed

Moix, Jeremy M; Cao, Jianshu

2013-10-07

The hierarchical equations of motion technique has found widespread success as a tool to generate the numerically exact dynamics of non-Markovian open quantum systems. However, its application to low temperature environments remains a serious challenge due to the need for a deep hierarchy that arises from the Matsubara expansion of the bath correlation function. Here we present a hybrid stochastic hierarchical equation of motion (sHEOM) approach that alleviates this bottleneck and leads to a numerical cost that is nearly independent of temperature. Additionally, the sHEOM method generally converges with fewer hierarchy tiers allowing for the treatment of larger systems. Benchmark calculations are presented on the dynamics of two level systems at both high and low temperatures to demonstrate the efficacy of the approach. Then the hybrid method is used to generate the exact dynamics of systems that are nearly impossible to treat by the standard hierarchy. First, exact energy transfer rates are calculated across a broad range of temperatures revealing the deviations from the Förster rates. This is followed by computations of the entanglement dynamics in a system of two qubits at low temperature spanning the weak to strong system-bath coupling regimes.

Large-scale exact diagonalizations reveal low-momentum scales of nuclei

NASA Astrophysics Data System (ADS)

Forssén, C.; Carlsson, B. D.; Johansson, H. T.; Sääf, D.; Bansal, A.; Hagen, G.; Papenbrock, T.

2018-03-01

Ab initio methods aim to solve the nuclear many-body problem with controlled approximations. Virtually exact numerical solutions for realistic interactions can only be obtained for certain special cases such as few-nucleon systems. Here we extend the reach of exact diagonalization methods to handle model spaces with dimension exceeding 1010 on a single compute node. This allows us to perform no-core shell model (NCSM) calculations for 6Li in model spaces up to Nmax=22 and to reveal the 4He+d halo structure of this nucleus. Still, the use of a finite harmonic-oscillator basis implies truncations in both infrared (IR) and ultraviolet (UV) length scales. These truncations impose finite-size corrections on observables computed in this basis. We perform IR extrapolations of energies and radii computed in the NCSM and with the coupled-cluster method at several fixed UV cutoffs. It is shown that this strategy enables information gain also from data that is not fully UV converged. IR extrapolations improve the accuracy of relevant bound-state observables for a range of UV cutoffs, thus making them profitable tools. We relate the momentum scale that governs the exponential IR convergence to the threshold energy for the first open decay channel. Using large-scale NCSM calculations we numerically verify this small-momentum scale of finite nuclei.

Perpendicular susceptibility and geometrical frustration in two-dimensional Ising antiferromagnets: Exact solutions

NASA Astrophysics Data System (ADS)

Muttalib, K. A.; Khatun, M.; Barry, J. H.

2017-11-01

Discovery of new materials and improved experimental as well as numerical techniques have led to a renewed interest in geometrically frustrated spin systems. However, there are very few exact results available that can provide a benchmark for comparison. In this work, we calculate exactly the perpendicular susceptibility χ⊥ for an Ising antiferromagnet with (i) nearest-neighbor pair interaction on a kagome lattice where strong frustration prevents long-range ordering and (ii) elementary triplet interactions on a kagome lattice which has no frustration but the system remains disordered down to zero temperature. By comparing with other known exact results with and without frustration, we propose that an appropriately temperature-scaled χ⊥ can be used as a quantitative measure of the degree of frustration in Ising spin systems.

Outstanding performance of configuration interaction singles and doubles using exact exchange Kohn-Sham orbitals in real-space numerical grid method

NASA Astrophysics Data System (ADS)

Lim, Jaechang; Choi, Sunghwan; Kim, Jaewook; Kim, Woo Youn

2016-12-01

To assess the performance of multi-configuration methods using exact exchange Kohn-Sham (KS) orbitals, we implemented configuration interaction singles and doubles (CISD) in a real-space numerical grid code. We obtained KS orbitals with the exchange-only optimized effective potential under the Krieger-Li-Iafrate (KLI) approximation. Thanks to the distinctive features of KLI orbitals against Hartree-Fock (HF), such as bound virtual orbitals with compact shapes and orbital energy gaps similar to excitation energies; KLI-CISD for small molecules shows much faster convergence as a function of simulation box size and active space (i.e., the number of virtual orbitals) than HF-CISD. The former also gives more accurate excitation energies with a few dominant configurations than the latter, even with many more configurations. The systematic control of basis set errors is straightforward in grid bases. Therefore, grid-based multi-configuration methods using exact exchange KS orbitals provide a promising new way to make accurate electronic structure calculations.

Optics of Water Microdroplets with Soot Inclusions: Exact Versus Approximate Results

NASA Technical Reports Server (NTRS)

Liu, Li; Mishchenko, Michael I.

2016-01-01

We use the recently generalized version of the multi-sphere superposition T-matrix method (STMM) to compute the scattering and absorption properties of microscopic water droplets contaminated by black carbon. The soot material is assumed to be randomly distributed throughout the droplet interior in the form of numerous small spherical inclusions. Our numerically-exact STMM results are compared with approximate ones obtained using the Maxwell-Garnett effective-medium approximation (MGA) and the Monte Carlo ray-tracing approximation (MCRTA). We show that the popular MGA can be used to calculate the droplet optical cross sections, single-scattering albedo, and asymmetry parameter provided that the soot inclusions are quasi-uniformly distributed throughout the droplet interior, but can fail in computations of the elements of the scattering matrix depending on the volume fraction of soot inclusions. The integral radiative characteristics computed with the MCRTA can deviate more significantly from their exact STMM counterparts, while accurate MCRTA computations of the phase function require droplet size parameters substantially exceeding 60.

Numerical calculation of flow fields about rectangular wings of finite thickness in supersonic flow. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Vogel, J. M.

1973-01-01

The calculation of the outer inviscid flow about a rectangular wing moving at supersonic speeds is reported. The inviscid equations of motion governing the flow generated by the wing form a set of hyperbolic differential equations. The flow field about the rectangular wing is separated into three regions consisting of the forebody, the afterbody, and the wing wake. Solutions for the forebody are obtained using conical flow techniques while the afterbody and the wing wake regions are treated as initial value problems. The numerical solutions are compared in the two dimensional regions with known exact solutions.

Conservative self-force correction to the innermost stable circular orbit: Comparison with multiple post-Newtonian-based methods

DOE Office of Scientific and Technical Information (OSTI.GOV)

Favata, Marc

2011-01-15

Barack and Sago [Phys. Rev. Lett. 102, 191101 (2009)] have recently computed the shift of the innermost stable circular orbit (ISCO) of the Schwarzschild spacetime due to the conservative self-force that arises from the finite-mass of an orbiting test-particle. This calculation of the ISCO shift is one of the first concrete results of the self-force program, and provides an exact (fully relativistic) point of comparison with approximate post-Newtonian (PN) computations of the ISCO. Here this exact ISCO shift is compared with nearly all known PN-based methods. These include both 'nonresummed' and 'resummed' approaches (the latter reproduce the test-particle limit bymore » construction). The best agreement with the exact (Barack-Sago) result is found when the pseudo-4PN coefficient of the effective-one-body (EOB) metric is fit to numerical relativity simulations. However, if one considers uncalibrated methods based only on the currently known 3PN-order conservative dynamics, the best agreement is found from the gauge-invariant ISCO condition of Blanchet and Iyer [Classical Quantum Gravity 20, 755 (2003)], which relies only on the (nonresummed) 3PN equations of motion. This method reproduces the exact test-particle limit without any resummation. A comparison of PN methods with the ISCO in the equal-mass case (computed via sequences of numerical relativity initial-data sets) is also performed. Here a (different) nonresummed method also performs very well (as was previously shown). These results suggest that the EOB approach - while exactly incorporating the conservative test-particle dynamics and having several other important advantages - does not (in the absence of calibration) incorporate conservative self-force effects more accurately than standard PN methods. I also consider how the conservative self-force ISCO shift, combined in some cases with numerical relativity computations of the ISCO, can be used to constrain our knowledge of (1) the EOB effective metric, (2) phenomenological inspiral-merger-ringdown templates, and (3) 4PN- and 5PN-order terms in the PN orbital energy. These constraints could help in constructing better gravitational-wave templates. Lastly, I suggest a new method to calibrate unknown PN terms in inspiral templates using numerical-relativity calculations.« less

Exact Solutions of Linear Reaction-Diffusion Processes on a Uniformly Growing Domain: Criteria for Successful Colonization

PubMed Central

Simpson, Matthew J

2015-01-01

Many processes during embryonic development involve transport and reaction of molecules, or transport and proliferation of cells, within growing tissues. Mathematical models of such processes usually take the form of a reaction-diffusion partial differential equation (PDE) on a growing domain. Previous analyses of such models have mainly involved solving the PDEs numerically. Here, we present a framework for calculating the exact solution of a linear reaction-diffusion PDE on a growing domain. We derive an exact solution for a general class of one-dimensional linear reaction—diffusion process on 0

Exact solutions of linear reaction-diffusion processes on a uniformly growing domain: criteria for successful colonization.

PubMed

Simpson, Matthew J

2015-01-01

Many processes during embryonic development involve transport and reaction of molecules, or transport and proliferation of cells, within growing tissues. Mathematical models of such processes usually take the form of a reaction-diffusion partial differential equation (PDE) on a growing domain. Previous analyses of such models have mainly involved solving the PDEs numerically. Here, we present a framework for calculating the exact solution of a linear reaction-diffusion PDE on a growing domain. We derive an exact solution for a general class of one-dimensional linear reaction-diffusion process on 0

Assessment of numerical techniques for unsteady flow calculations

NASA Technical Reports Server (NTRS)

Hsieh, Kwang-Chung

1989-01-01

The characteristics of unsteady flow motions have long been a serious concern in the study of various fluid dynamic and combustion problems. With the advancement of computer resources, numerical approaches to these problems appear to be feasible. The objective of this paper is to assess the accuracy of several numerical schemes for unsteady flow calculations. In the present study, Fourier error analysis is performed for various numerical schemes based on a two-dimensional wave equation. Four methods sieved from the error analysis are then adopted for further assessment. Model problems include unsteady quasi-one-dimensional inviscid flows, two-dimensional wave propagations, and unsteady two-dimensional inviscid flows. According to the comparison between numerical and exact solutions, although second-order upwind scheme captures the unsteady flow and wave motions quite well, it is relatively more dissipative than sixth-order central difference scheme. Among various numerical approaches tested in this paper, the best performed one is Runge-Kutta method for time integration and six-order central difference for spatial discretization.

Green's function enriched Poisson solver for electrostatics in many-particle systems

NASA Astrophysics Data System (ADS)

Sutmann, Godehard

2016-06-01

A highly accurate method is presented for the construction of the charge density for the solution of the Poisson equation in particle simulations. The method is based on an operator adjusted source term which can be shown to produce exact results up to numerical precision in the case of a large support of the charge distribution, therefore compensating the discretization error of finite difference schemes. This is achieved by balancing an exact representation of the known Green's function of regularized electrostatic problem with a discretized representation of the Laplace operator. It is shown that the exact calculation of the potential is possible independent of the order of the finite difference scheme but the computational efficiency for higher order methods is found to be superior due to a faster convergence to the exact result as a function of the charge support.

Correlated Light-Matter Interactions in Cavity QED

NASA Astrophysics Data System (ADS)

Flick, Johannes; Pellegrini, Camilla; Ruggenthaler, Michael; Appel, Heiko; Tokatly, Ilya; Rubio, Angel

2015-03-01

In the last decade, time-dependent density functional theory (TDDFT) has been successfully applied to a large variety of problems, such as calculations of absorption spectra, excitation energies, or dynamics in strong laser fields. Recently, we have generalized TDDFT to also describe electron-photon systems (QED-TDDFT). Here, matter and light are treated on an equal quantized footing. In this work, we present the first numerical calculations in the framework of QED-TDDFT. We show exact solutions for fully quantized prototype systems consisting of atoms or molecules placed in optical high-Q cavities and coupled to quantized electromagnetic modes. We focus on the electron-photon exchange-correlation (xc) contribution by calculating exact Kohn-Sham potentials using fixed-point inversions and present the performance of the first approximated xc-potential based on an optimized effective potential (OEP) approach. Max Planck Institute for the Structure and Dynamics of Matter, Hamburg, and Fritz-Haber-Institut der MPG, Berlin

Treatment of pairing correlations based on the equations of motion for zero-coupled pair operators

NASA Astrophysics Data System (ADS)

Andreozzi, F.; Covello, A.; Gargano, A.; Ye, Liu Jian; Porrino, A.

1985-07-01

The pairing problem is treated by means of the equations of motion for zero-coupled pair operators. Exact equations for the seniority-v states of N particles are derived. These equations can be solved by a step-by-step procedure which consists of progressively adding pairs of particles to a core. The theory can be applied at several levels of approximation depending on the number of core states which are taken into account. Some numerical applications to the treatment of v=0, v=1, and v=2 states in the Ni isotopes are performed. The accuracy of various approximations is tested by comparison with exact results. For the seniority-one and seniority-two problems it turns out that the results obtained from the first-order theory are very accurate, while those of higher order calculations are practically exact. Concerning the seniority-zero problem, a fifth-order calculation reproduces quite well the three lowest states.

Solutal Convection Around Growing Protein Crystal and Diffusional Purification in Space

NASA Technical Reports Server (NTRS)

Chernov, A. A.; Lee, C. P.

2002-01-01

This work theoretically addressed two subjects: 1) onset of convection, 2) distribution of impurities. Onset of convection was considered analytically and numerically. Crystal growth was characterized by slow surface incorporation kinetics, i.e. growth kinetic coefficient beta (cm/s) small as compared to the typical bulk diffusion rate, D(sub 1)/h, where D(sub 1) is diffusivity of major crystallizing protein and h is the crystal size. Scaling type analysis predicted two laws on how the convection rate, v, essentially the Peclet number, Pe exactly equal to vh/D(sub 1), depends on dimensionless kinetic coefficient a exactly equal to beta h/D(sub 1). Namely: Pe = C(sub 2/5)(aRa(sup 2/5)) and Pe = C(sub 1) aRa. Here, Reynolds number Ra = rho(sub 1)(sup 0)gh(sup 3)(rho(sub p) - rho(sub w))/rho(sup p)rho(sub 1)vD(sub 1), v being solution viscosity. The constants C(sub 2/5), exactly equal to 0.28 and C(sub 1) exactly equal to 10(exp -2) found from the full scale computer simulation for a cylindrical crystal inside big cylindrical vessel. The linear boundary conditions connecting protein and impurity concentration at the interface with the flux to/from the interface was applied. No-slip condition for Navier-Shocker equations was employed. With these conditions, flow and concentration distributions were calculated. Validity of the Pe(Ra) dependencies follows for wide range of parameters for which numerical calculations have been accomplished and presented by various points.

Monotonic Derivative Correction for Calculation of Supersonic Flows

ERIC Educational Resources Information Center

Bulat, Pavel V.; Volkov, Konstantin N.

2016-01-01

Aim of the study: This study examines numerical methods for solving the problems in gas dynamics, which are based on an exact or approximate solution to the problem of breakdown of an arbitrary discontinuity (the Riemann problem). Results: Comparative analysis of finite difference schemes for the Euler equations integration is conducted on the…

Exact numerical calculation of fixation probability and time on graphs.

PubMed

Hindersin, Laura; Möller, Marius; Traulsen, Arne; Bauer, Benedikt

2016-12-01

The Moran process on graphs is a popular model to study the dynamics of evolution in a spatially structured population. Exact analytical solutions for the fixation probability and time of a new mutant have been found for only a few classes of graphs so far. Simulations are time-expensive and many realizations are necessary, as the variance of the fixation times is high. We present an algorithm that numerically computes these quantities for arbitrary small graphs by an approach based on the transition matrix. The advantage over simulations is that the calculation has to be executed only once. Building the transition matrix is automated by our algorithm. This enables a fast and interactive study of different graph structures and their effect on fixation probability and time. We provide a fast implementation in C with this note (Hindersin et al., 2016). Our code is very flexible, as it can handle two different update mechanisms (Birth-death or death-Birth), as well as arbitrary directed or undirected graphs. Copyright © 2016 Elsevier Ireland Ltd. All rights reserved.

A fast numerical scheme for causal relativistic hydrodynamics with dissipation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Takamoto, Makoto, E-mail: takamoto@tap.scphys.kyoto-u.ac.jp; Inutsuka, Shu-ichiro

2011-08-01

Highlights: {yields} We have developed a new multi-dimensional numerical scheme for causal relativistic hydrodynamics with dissipation. {yields} Our new scheme can calculate the evolution of dissipative relativistic hydrodynamics faster and more effectively than existing schemes. {yields} Since we use the Riemann solver for solving the advection steps, our method can capture shocks very accurately. - Abstract: In this paper, we develop a stable and fast numerical scheme for relativistic dissipative hydrodynamics based on Israel-Stewart theory. Israel-Stewart theory is a stable and causal description of dissipation in relativistic hydrodynamics although it includes relaxation process with the timescale for collision of constituentmore » particles, which introduces stiff equations and makes practical numerical calculation difficult. In our new scheme, we use Strang's splitting method, and use the piecewise exact solutions for solving the extremely short timescale problem. In addition, since we split the calculations into inviscid step and dissipative step, Riemann solver can be used for obtaining numerical flux for the inviscid step. The use of Riemann solver enables us to capture shocks very accurately. Simple numerical examples are shown. The present scheme can be applied to various high energy phenomena of astrophysics and nuclear physics.« less

Two-phase flows in the formed tornado funnel

NASA Astrophysics Data System (ADS)

Sinkevich, O. A.; Bortsova, A. A.

2017-10-01

At present, it is obvious that the problem of the tornado is important not only for our planetЮ to determine the conditions for the formation of a tornado, it is required to take into account a number of hydrodynamic and plasma processes [1 - 6]. Along to prediction of a tornado generation conditions [1 - 3] it is necessary to evaluate the characteristics of its quasi-stationary motion in a formed funnel: the mass of the moving moist air involved in the funnel and the size and form of the funnel. For a complete description of the phenomena, it is necessary to involve numerical calculations. We note that even for numerical calculations using powerful computers, the problem is very difficult because of the need to calculate multiphase turbulent flows with free, self-organizing boundaries [1, 6]. However, “strict” numerical calculations, it is impossible to do without the use of many, often mutually exclusive, models. For example, how to choice an adequate model of turbulence (algebraic, k-ε model, etc.) or the use of additional, often not accepted, hypotheses about certain processes used in calculations (mechanisms on the nature of moisture condensation, etc.). Therefore, along with numerical calculations of such flows, modeling problems that allow an exact solution and allow to determine the most important and observed characteristics of a tornado.

Intrinsic Carrier Concentration and Electron Effective Mass in Hg(1-x) Zn(x) Te

NASA Technical Reports Server (NTRS)

Sha, Yi-Gao; Su, Ching-Hua; Lehoczky, S. L.

1997-01-01

In this work, the intrinsic carrier concentration and electron effective mass in Hg(l-x)Zn(x)Te were numerically calculated. We adopt the procedures similar to those used by Su et. al. for calculating intrinsic carrier concentrations in Hg(1-x)Cd(x)Te which solve the exact dispersion relation in Kane model for the calculation of the conduction band electron concentrations and the corresponding electron effective masses. No approximation beyond those inherent in the k centered dot p model was used here.

Computer modeling of test particle acceleration at oblique shocks

NASA Technical Reports Server (NTRS)

Decker, Robert B.

1988-01-01

The present evaluation of the basic techniques and illustrative results of charged particle-modeling numerical codes suitable for particle acceleration at oblique, fast-mode collisionless shocks emphasizes the treatment of ions as test particles, calculating particle dynamics through numerical integration along exact phase-space orbits. Attention is given to the acceleration of particles at planar, infinitessimally thin shocks, as well as to plasma simulations in which low-energy ions are injected and accelerated at quasi-perpendicular shocks with internal structure.

Uniform semiclassical sudden approximation for rotationally inelastic scattering

DOE Office of Scientific and Technical Information (OSTI.GOV)

Korsch, H.J.; Schinke, R.

1980-08-01

The infinite-order-sudden (IOS) approximation is investigated in the semiclassical limit. A simplified IOS formula for rotationally inelastic differential cross sections is derived involving a uniform stationary phase approximation for two-dimensional oscillatory integrals with two stationary points. The semiclassical analysis provides a quantitative description of the rotational rainbow structure in the differential cross section. The numerical calculation of semiclassical IOS cross sections is extremely fast compared to numerically exact IOS methods, especially if high ..delta..j transitions are involved. Rigid rotor results for He--Na/sub 2/ collisions with ..delta..j< or approx. =26 and for K--CO collisions with ..delta..j< or approx. =70 show satisfactorymore » agreement with quantal IOS calculations.« less

Dynamical spin structure factors of α-RuCl3

NASA Astrophysics Data System (ADS)

Suzuki, Takafumi; Suga, Sei-ichiro

2018-03-01

Honeycomb-lattice magnet α-RuCl3 is considered to be a potential candidate of realizing Kitaev spin liquid, although this material undergoes a phase transition to the zigzag magnetically ordered state at T N ∼ 7 K. Quite recently, inelastic neutron-scattering experiments using single crystal α-RuCl3 have unveiled characteristic dynamical properties. We calculate dynamical spin structure factors of three ab-initio models for α-RuCl3 with an exact numerical diagonalization method. We also calculate temperature dependences of the specific heat by employing thermal pure quantum states. We compare our numerical results with the experiments and discuss characteristics obtained by using three ab-initio models.

Biological production models as elements of coupled, atmosphere-ocean models for climate research

NASA Technical Reports Server (NTRS)

Platt, Trevor; Sathyendranath, Shubha

1991-01-01

Process models of phytoplankton production are discussed with respect to their suitability for incorporation into global-scale numerical ocean circulation models. Exact solutions are given for integrals over the mixed layer and the day of analytic, wavelength-independent models of primary production. Within this class of model, the bias incurred by using a triangular approximation (rather than a sinusoidal one) to the variation of surface irradiance through the day is computed. Efficient computation algorithms are given for the nonspectral models. More exact calculations require a spectrally sensitive treatment. Such models exist but must be integrated numerically over depth and time. For these integrations, resolution in wavelength, depth, and time are considered and recommendations made for efficient computation. The extrapolation of the one-(spatial)-dimension treatment to large horizontal scale is discussed.

Hamilton's principle and normal mode coupling in an aspherical planet with a fluid core

NASA Astrophysics Data System (ADS)

Al-Attar, David; Crawford, Ophelia; Valentine, Andrew P.; Trampert, Jeannot

2018-04-01

We apply Hamilton's principle to obtain the exact equations of motion for an elastic planet that is rotating, self-gravitating, and comprises both fluid and solid regions. This variational problem is complicated by the occurrence of tangential slip at fluid-solid boundaries, but we show how this can be accommodated both directly and using the method of Lagrange multipliers. A novelty of our approach is that the planet's motion is described relative to an arbitrary reference configuration, with this generality offering advantages for numerical calculations. In particular, aspherical topography on the free surface or internal boundaries of the planet's equilibrium configuration can be converted exactly into effective volumetric heterogeneities within a geometrically spherical reference body by applying a suitable particle relabelling transformation. The theory is then specialised to consider the linearised motion of a planet about a steadily rotating equilibrium configuration, with these results having applications to normal mode coupling calculations used within studies of long period seismology, tidal deformation, and related fields. In particular, we explain how our new theory will, for the first time, allow aspherical boundary topography to be incorporated exactly within such coupling calculations.

Exact solution of some linear matrix equations using algebraic methods

NASA Technical Reports Server (NTRS)

Djaferis, T. E.; Mitter, S. K.

1979-01-01

Algebraic methods are used to construct the exact solution P of the linear matrix equation PA + BP = - C, where A, B, and C are matrices with real entries. The emphasis of this equation is on the use of finite algebraic procedures which are easily implemented on a digital computer and which lead to an explicit solution to the problem. The paper is divided into six sections which include the proof of the basic lemma, the Liapunov equation, and the computer implementation for the rational, integer and modular algorithms. Two numerical examples are given and the entire calculation process is depicted.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Doebling, Scott William

This paper documents the escape of high explosive (HE) products problem. The problem, first presented by Fickett & Rivard, tests the implementation and numerical behavior of a high explosive detonation and energy release model and its interaction with an associated compressible hydrodynamics simulation code. The problem simulates the detonation of a finite-length, one-dimensional piece of HE that is driven by a piston from one end and adjacent to a void at the other end. The HE equation of state is modeled as a polytropic ideal gas. The HE detonation is assumed to be instantaneous with an infinitesimal reaction zone. Viamore » judicious selection of the material specific heat ratio, the problem has an exact solution with linear characteristics, enabling a straightforward calculation of the physical variables as a function of time and space. Lastly, implementation of the exact solution in the Python code ExactPack is discussed, as are verification cases for the exact solution code.« less

The escape of high explosive products: An exact-solution problem for verification of hydrodynamics codes

DOE PAGES

Doebling, Scott William

2016-10-22

This paper documents the escape of high explosive (HE) products problem. The problem, first presented by Fickett & Rivard, tests the implementation and numerical behavior of a high explosive detonation and energy release model and its interaction with an associated compressible hydrodynamics simulation code. The problem simulates the detonation of a finite-length, one-dimensional piece of HE that is driven by a piston from one end and adjacent to a void at the other end. The HE equation of state is modeled as a polytropic ideal gas. The HE detonation is assumed to be instantaneous with an infinitesimal reaction zone. Viamore » judicious selection of the material specific heat ratio, the problem has an exact solution with linear characteristics, enabling a straightforward calculation of the physical variables as a function of time and space. Lastly, implementation of the exact solution in the Python code ExactPack is discussed, as are verification cases for the exact solution code.« less

Embedded-cluster calculations in a numeric atomic orbital density-functional theory framework.

PubMed

Berger, Daniel; Logsdail, Andrew J; Oberhofer, Harald; Farrow, Matthew R; Catlow, C Richard A; Sherwood, Paul; Sokol, Alexey A; Blum, Volker; Reuter, Karsten

2014-07-14

We integrate the all-electron electronic structure code FHI-aims into the general ChemShell package for solid-state embedding quantum and molecular mechanical (QM/MM) calculations. A major undertaking in this integration is the implementation of pseudopotential functionality into FHI-aims to describe cations at the QM/MM boundary through effective core potentials and therewith prevent spurious overpolarization of the electronic density. Based on numeric atomic orbital basis sets, FHI-aims offers particularly efficient access to exact exchange and second order perturbation theory, rendering the established QM/MM setup an ideal tool for hybrid and double-hybrid level density functional theory calculations of solid systems. We illustrate this capability by calculating the reduction potential of Fe in the Fe-substituted ZSM-5 zeolitic framework and the reaction energy profile for (photo-)catalytic water oxidation at TiO2(110).

Embedded-cluster calculations in a numeric atomic orbital density-functional theory framework

DOE Office of Scientific and Technical Information (OSTI.GOV)

Berger, Daniel, E-mail: daniel.berger@ch.tum.de; Oberhofer, Harald; Reuter, Karsten

2014-07-14

We integrate the all-electron electronic structure code FHI-aims into the general ChemShell package for solid-state embedding quantum and molecular mechanical (QM/MM) calculations. A major undertaking in this integration is the implementation of pseudopotential functionality into FHI-aims to describe cations at the QM/MM boundary through effective core potentials and therewith prevent spurious overpolarization of the electronic density. Based on numeric atomic orbital basis sets, FHI-aims offers particularly efficient access to exact exchange and second order perturbation theory, rendering the established QM/MM setup an ideal tool for hybrid and double-hybrid level density functional theory calculations of solid systems. We illustrate this capabilitymore » by calculating the reduction potential of Fe in the Fe-substituted ZSM-5 zeolitic framework and the reaction energy profile for (photo-)catalytic water oxidation at TiO{sub 2}(110)« less

Conformal anomaly of some 2-d Z (n) models

NASA Astrophysics Data System (ADS)

William, Peter

1991-01-01

We describe a numerical calculation of the conformal anomaly in the case of some two-dimensional statistical models undergoing a second-order phase transition, utilizing a recently developed method to compute the partition function exactly. This computation is carried out on a massively parallel CM2 machine, using the finite size scaling behaviour of the free energy.

Time-domain simulation of constitutive relations for nonlinear acoustics including relaxation for frequency power law attenuation media modeling

NASA Astrophysics Data System (ADS)

Jiménez, Noé; Camarena, Francisco; Redondo, Javier; Sánchez-Morcillo, Víctor; Konofagou, Elisa E.

2015-10-01

We report a numerical method for solving the constitutive relations of nonlinear acoustics, where multiple relaxation processes are included in a generalized formulation that allows the time-domain numerical solution by an explicit finite differences scheme. Thus, the proposed physical model overcomes the limitations of the one-way Khokhlov-Zabolotskaya-Kuznetsov (KZK) type models and, due to the Lagrangian density is implicitly included in the calculation, the proposed method also overcomes the limitations of Westervelt equation in complex configurations for medical ultrasound. In order to model frequency power law attenuation and dispersion, such as observed in biological media, the relaxation parameters are fitted to both exact frequency power law attenuation/dispersion media and also empirically measured attenuation of a variety of tissues that does not fit an exact power law. Finally, a computational technique based on artificial relaxation is included to correct the non-negligible numerical dispersion of the finite difference scheme, and, on the other hand, improve stability trough artificial attenuation when shock waves are present. This technique avoids the use of high-order finite-differences schemes leading to fast calculations. The present algorithm is especially suited for practical configuration where spatial discontinuities are present in the domain (e.g. axisymmetric domains or zero normal velocity boundary conditions in general). The accuracy of the method is discussed by comparing the proposed simulation solutions to one dimensional analytical and k-space numerical solutions.

Quasi-exact solvability and entropies of the one-dimensional regularised Calogero model

NASA Astrophysics Data System (ADS)

Pont, Federico M.; Osenda, Omar; Serra, Pablo

2018-05-01

The Calogero model can be regularised through the introduction of a cutoff parameter which removes the divergence in the interaction term. In this work we show that the one-dimensional two-particle regularised Calogero model is quasi-exactly solvable and that for certain values of the Hamiltonian parameters the eigenfunctions can be written in terms of Heun’s confluent polynomials. These eigenfunctions are such that the reduced density matrix of the two-particle density operator can be obtained exactly as well as its entanglement spectrum. We found that the number of non-zero eigenvalues of the reduced density matrix is finite in these cases. The limits for the cutoff distance going to zero (Calogero) and infinity are analysed and all the previously obtained results for the Calogero model are reproduced. Once the exact eigenfunctions are obtained, the exact von Neumann and Rényi entanglement entropies are studied to characterise the physical traits of the model. The quasi-exactly solvable character of the model is assessed studying the numerically calculated Rényi entropy and entanglement spectrum for the whole parameter space.

Recent Selected Papers of Northwestern Polytechnical University in Two Parts. Part I. 1979.

DTIC Science & Technology

1981-08-20

pressure coefficient is calculated by the exact Bernoulli equation. Two numerical examples are included, and the results agree fairly well with known... Bernoulli equation is applied to cal- culate the pressure coefficient: ft. 2 2, Lq32) In the above expression, all the derivatives are calculated by...0.14: R Olt(6) The real part on the unit circle in ecuation (2) is used. Making use of equations (5) and (6), both sides of equation (2) are expanded

Calculation of transonic aileron buzz

NASA Technical Reports Server (NTRS)

Steger, J. L.; Bailey, H. E.

1979-01-01

An implicit finite-difference computer code that uses a two-layer algebraic eddy viscosity model and exact geometric specification of the airfoil has been used to simulate transonic aileron buzz. The calculated results, which were performed on both the Illiac IV parallel computer processor and the Control Data 7600 computer, are in essential agreement with the original expository wind-tunnel data taken in the Ames 16-Foot Wind Tunnel just after World War II. These results and a description of the pertinent numerical techniques are included.

Analytic Method for Computing Instrument Pointing Jitter

NASA Technical Reports Server (NTRS)

Bayard, David

2003-01-01

A new method of calculating the root-mean-square (rms) pointing jitter of a scientific instrument (e.g., a camera, radar antenna, or telescope) is introduced based on a state-space concept. In comparison with the prior method of calculating the rms pointing jitter, the present method involves significantly less computation. The rms pointing jitter of an instrument (the square root of the jitter variance shown in the figure) is an important physical quantity which impacts the design of the instrument, its actuators, controls, sensory components, and sensor- output-sampling circuitry. Using the Sirlin, San Martin, and Lucke definition of pointing jitter, the prior method of computing the rms pointing jitter involves a frequency-domain integral of a rational polynomial multiplied by a transcendental weighting function, necessitating the use of numerical-integration techniques. In practice, numerical integration complicates the problem of calculating the rms pointing error. In contrast, the state-space method provides exact analytic expressions that can be evaluated without numerical integration.

Non-additive non-interacting kinetic energy of rare gas dimers

NASA Astrophysics Data System (ADS)

Jiang, Kaili; Nafziger, Jonathan; Wasserman, Adam

2018-03-01

Approximations of the non-additive non-interacting kinetic energy (NAKE) as an explicit functional of the density are the basis of several electronic structure methods that provide improved computational efficiency over standard Kohn-Sham calculations. However, within most fragment-based formalisms, there is no unique exact NAKE, making it difficult to develop general, robust approximations for it. When adjustments are made to the embedding formalisms to guarantee uniqueness, approximate functionals may be more meaningfully compared to the exact unique NAKE. We use numerically accurate inversions to study the exact NAKE of several rare-gas dimers within partition density functional theory, a method that provides the uniqueness for the exact NAKE. We find that the NAKE decreases nearly exponentially with atomic separation for the rare-gas dimers. We compute the logarithmic derivative of the NAKE with respect to the bond length for our numerically accurate inversions as well as for several approximate NAKE functionals. We show that standard approximate NAKE functionals do not reproduce the correct behavior for this logarithmic derivative and propose two new NAKE functionals that do. The first of these is based on a re-parametrization of a conjoint Perdew-Burke-Ernzerhof (PBE) functional. The second is a simple, physically motivated non-decomposable NAKE functional that matches the asymptotic decay constant without fitting.

Determining linear vibration frequencies of a ferromagnetic shell

NASA Astrophysics Data System (ADS)

Bagdoev, A. G.; Vardanyan, A. V.; Vardanyan, S. V.; Kukudzhanov, V. N.

2007-10-01

The problems of determining the roots of dispersion equations for free bending vibrations of thin magnetoelastic plates and shells are of both theoretical and practical interest, in particular, in studying vibrations of metallic structures used in controlled thermonuclear reactors. These problems were solved on the basis of the Kirchhoff hypothesis in [1-5]. In [6], an exact spatial approach to determining the vibration frequencies of thin plates was suggested, and it was shown that it completely agrees with the solution obtained according to the Kirchhoff hypothesis. In [7-9], this exact approach was used to solve the problem on vibrations of thin magnetoelastic plates, and it was shown by cumbersome calculations that the solutions obtained according to the exact theory and the Kirchhoff hypothesis differ substantially except in a single case. In [10], the equations of the dynamic theory of elasticity in the axisymmetric problem are given. In [11], the equations for the vibration frequencies of thin ferromagnetic plates with arbitrary conductivity were obtained in the exact statement. In [12], the Kirchhoff hypothesis was used to obtain dispersion relations for a magnetoelastic thin shell. In [5, 13-16], the relations for the Maxwell tensor and the ponderomotive force for magnetics were presented. In [17], the dispersion relations for thin ferromagnetic plates in the transverse field in the spatial statement were studied analytically and numerically. In the present paper, on the basis of the exact approach, we study free bending vibrations of a thin ferromagnetic cylindrical shell. We obtain the exact dispersion equation in the form of a sixth-order determinant, which can be solved numerically in the case of a magnetoelastic thin shell. The numerical results are presented in tables and compared with the results obtained by the Kirchhoff hypothesis. We show a large number of differences in the results, even for the least frequency.

Time's arrow: A numerical experiment

NASA Astrophysics Data System (ADS)

Fowles, G. Richard

1994-04-01

The dependence of time's arrow on initial conditions is illustrated by a numerical example in which plane waves produced by an initial pressure pulse are followed as they are multiply reflected at internal interfaces of a layered medium. Wave interactions at interfaces are shown to be analogous to the retarded and advanced waves of point sources. The model is linear and the calculation is exact and demonstrably time reversible; nevertheless the results show most of the features expected of a macroscopically irreversible system, including the approach to the Maxwell-Boltzmann distribution, ergodicity, and concomitant entropy increase.

Strip Yield Model Numerical Application to Different Geometries and Loading Conditions

NASA Technical Reports Server (NTRS)

Hatamleh, Omar; Forman, Royce; Shivakumar, Venkataraman; Lyons, Jed

2006-01-01

A new numerical method based on the strip-yield analysis approach was developed for calculating the Crack Tip Opening Displacement (CTOD). This approach can be applied for different crack configurations having infinite and finite geometries, and arbitrary applied loading conditions. The new technique adapts the boundary element / dislocation density method to obtain crack-face opening displacements at any point on a crack, and succeeds by obtaining requisite values as a series of definite integrals, the functional parts of each being evaluated exactly in a closed form.

Numerical studies of the topological Chern numbers in two dimensional electron system

NASA Astrophysics Data System (ADS)

Sheng, Donna

2004-03-01

I will report on the numerical results of the exact calculation of the topological Chern numbers in fractional and bilayer quantum Hall systems[1]. I will show that following the evolution of the Chern numbers as a function of the disorder strength and/or layer separations, various quantum phase transitions as well as the characteristic transport properties of the phases, can be determined. The hidden topological ordering in other two dimensional electron systems will also be discussed. 1. D. N. Sheng et. al., Phys. Rev. Lett. 90, 256802 (2003).

Calculation of the second term of the exact Green's function of the diffusion equation for diffusion-controlled chemical reactions

NASA Astrophysics Data System (ADS)

Plante, Ianik

2016-01-01

The exact Green's function of the diffusion equation (GFDE) is often considered to be the gold standard for the simulation of partially diffusion-controlled reactions. As the GFDE with angular dependency is quite complex, the radial GFDE is more often used. Indeed, the exact GFDE is expressed as a Legendre expansion, the coefficients of which are given in terms of an integral comprising Bessel functions. This integral does not seem to have been evaluated analytically in existing literature. While the integral can be evaluated numerically, the Bessel functions make the integral oscillate and convergence is difficult to obtain. Therefore it would be of great interest to evaluate the integral analytically. The first term was evaluated previously, and was found to be equal to the radial GFDE. In this work, the second term of this expansion was evaluated. As this work has shown that the first two terms of the Legendre polynomial expansion can be calculated analytically, it raises the question of the possibility that an analytical solution exists for the other terms.

Numerical Exact Ab Initio Four-Nucleon Scattering Calculations: from Dream to Reality

NASA Astrophysics Data System (ADS)

Fonseca, A. C.; Deltuva, A.

2017-03-01

In the present manuscript we review the work of the last ten years on the pursuit to obtain numerical exact solutions of the four-nucleon scattering problem using the most advanced force models that fit two nucleon data up to pion production threshold with a χ ^2 per data point approximately one, together with the Coulomb interaction between protons; three- and four-nucleon forces are also included in the framework of a meson exchange potential model where NN couples to NΔ. Failure to describe the world data on four-nucleon scattering observables in the framework of a non relativistic scattering approach falls necessarily on the force models one uses. Four-nucleon observables pose very clear challenges, particular in the low energy region where there are a number of resonances whose position and width needs to be dynamically generated by the nucleon-nucleon (NN) interactions one uses. In addition, our calculations constitute the most advance piece of work where observables for all four-nucleon reactions involving isospin I=0, I=0 coupled to I=1 and isospin I=1 initial states are calculated at energies both below and above breakup threshold. We also present a very extensive comparison between calculated results and data for cross sections and spin observables. Therefore the present work reveals both the shortcomings and successes of some of the present NN force models in describing four-nucleon data and serve as a benchmark for future developments.

A note on sound radiation from distributed sources

NASA Technical Reports Server (NTRS)

Levine, H.

1979-01-01

The power output from a normally vibrating strip radiator is expressed in alternative general forms, one of these being chosen to refine and correct some particular estimates given by Heckl for different numerical ratios of strip width to wave length. An exact and explicit calculation is effected for sinusoidal velocity profiles when the strip width equals an integer number of half wave lengths.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Derrida, B.; Nadal, J.P.

It is possible to construct diluted asymmetric models of neural networks for which the dynamics can be calculated exactly. The authors test several learning schemes, in particular, models for which the values of the synapses remain bounded and depend on the history. Our analytical results on the relative efficiencies of the various learning schemes are qualitatively similar to the corresponding ones obtained numerically on fully connected symmetric networks.

General theory for calculating disorder-averaged Green's function correlators within the coherent potential approximation

NASA Astrophysics Data System (ADS)

Zhou, Chenyi; Guo, Hong

2017-01-01

We report a diagrammatic method to solve the general problem of calculating configurationally averaged Green's function correlators that appear in quantum transport theory for nanostructures containing disorder. The theory treats both equilibrium and nonequilibrium quantum statistics on an equal footing. Since random impurity scattering is a problem that cannot be solved exactly in a perturbative approach, we combine our diagrammatic method with the coherent potential approximation (CPA) so that a reliable closed-form solution can be obtained. Our theory not only ensures the internal consistency of the diagrams derived at different levels of the correlators but also satisfies a set of Ward-like identities that corroborate the conserving consistency of transport calculations within the formalism. The theory is applied to calculate the quantum transport properties such as average ac conductance and transmission moments of a disordered tight-binding model, and results are numerically verified to high precision by comparing to the exact solutions obtained from enumerating all possible disorder configurations. Our formalism can be employed to predict transport properties of a wide variety of physical systems where disorder scattering is important.

Properties of quantum systems via diagonalization of transition amplitudes. II. Systematic improvements of short-time propagation

NASA Astrophysics Data System (ADS)

Vidanović, Ivana; Bogojević, Aleksandar; Balaž, Antun; Belić, Aleksandar

2009-12-01

In this paper, building on a previous analysis [I. Vidanović, A. Bogojević, and A. Belić, preceding paper, Phys. Rev. E 80, 066705 (2009)] of exact diagonalization of the space-discretized evolution operator for the study of properties of nonrelativistic quantum systems, we present a substantial improvement to this method. We apply recently introduced effective action approach for obtaining short-time expansion of the propagator up to very high orders to calculate matrix elements of space-discretized evolution operator. This improves by many orders of magnitude previously used approximations for discretized matrix elements and allows us to numerically obtain large numbers of accurate energy eigenvalues and eigenstates using numerical diagonalization. We illustrate this approach on several one- and two-dimensional models. The quality of numerically calculated higher-order eigenstates is assessed by comparison with semiclassical cumulative density of states.

An efficient method for the computation of Legendre moments.

PubMed

Yap, Pew-Thian; Paramesran, Raveendran

2005-12-01

Legendre moments are continuous moments, hence, when applied to discrete-space images, numerical approximation is involved and error occurs. This paper proposes a method to compute the exact values of the moments by mathematically integrating the Legendre polynomials over the corresponding intervals of the image pixels. Experimental results show that the values obtained match those calculated theoretically, and the image reconstructed from these moments have lower error than that of the conventional methods for the same order. Although the same set of exact Legendre moments can be obtained indirectly from the set of geometric moments, the computation time taken is much longer than the proposed method.

Coherent Backscattering by Polydisperse Discrete Random Media: Exact T-Matrix Results

NASA Technical Reports Server (NTRS)

Mishchenko, Michael I.; Dlugach, Janna M.; Mackowski, Daniel W.

2011-01-01

The numerically exact superposition T-matrix method is used to compute, for the first time to our knowledge, electromagnetic scattering by finite spherical volumes composed of polydisperse mixtures of spherical particles with different size parameters or different refractive indices. The backscattering patterns calculated in the far-field zone of the polydisperse multiparticle volumes reveal unequivocally the classical manifestations of the effect of weak localization of electromagnetic waves in discrete random media, thereby corroborating the universal interference nature of coherent backscattering. The polarization opposition effect is shown to be the least robust manifestation of weak localization fading away with increasing particle size parameter.

Path integral approach to the Wigner representation of canonical density operators for discrete systems coupled to harmonic baths.

PubMed

Montoya-Castillo, Andrés; Reichman, David R

2017-01-14

We derive a semi-analytical form for the Wigner transform for the canonical density operator of a discrete system coupled to a harmonic bath based on the path integral expansion of the Boltzmann factor. The introduction of this simple and controllable approach allows for the exact rendering of the canonical distribution and permits systematic convergence of static properties with respect to the number of path integral steps. In addition, the expressions derived here provide an exact and facile interface with quasi- and semi-classical dynamical methods, which enables the direct calculation of equilibrium time correlation functions within a wide array of approaches. We demonstrate that the present method represents a practical path for the calculation of thermodynamic data for the spin-boson and related systems. We illustrate the power of the present approach by detailing the improvement of the quality of Ehrenfest theory for the correlation function C zz (t)=Re⟨σ z (0)σ z (t)⟩ for the spin-boson model with systematic convergence to the exact sampling function. Importantly, the numerically exact nature of the scheme presented here and its compatibility with semiclassical methods allows for the systematic testing of commonly used approximations for the Wigner-transformed canonical density.

Calculating pH-dependent free energy of proteins by using Monte Carlo protonation probabilities of ionizable residues.

PubMed

Huang, Qiang; Herrmann, Andreas

2012-03-01

Protein folding, stability, and function are usually influenced by pH. And free energy plays a fundamental role in analysis of such pH-dependent properties. Electrostatics-based theoretical framework using dielectric solvent continuum model and solving Poisson-Boltzmann equation numerically has been shown to be very successful in understanding the pH-dependent properties. However, in this approach the exact computation of pH-dependent free energy becomes impractical for proteins possessing more than several tens of ionizable sites (e.g. > 30), because exact evaluation of the partition function requires a summation over a vast number of possible protonation microstates. Here we present a method which computes the free energy using the average energy and the protonation probabilities of ionizable sites obtained by the well-established Monte Carlo sampling procedure. The key feature is to calculate the entropy by using the protonation probabilities. We used this method to examine a well-studied protein (lysozyme) and produced results which agree very well with the exact calculations. Applications to the optimum pH of maximal stability of proteins and protein-DNA interactions have also resulted in good agreement with experimental data. These examples recommend our method for application to the elucidation of the pH-dependent properties of proteins.

Extension and applications of switching model: Range theory, multiple scattering model of Goudsmit-Saunderson, and lateral spread treatment of Marwick-Sigmund

NASA Astrophysics Data System (ADS)

Ikegami, Seiji

2017-09-01

The switching model (PSM) developed in the previous paper is extended to obtain an ;extended switching model (ESM). In the ESM, the mixt electronic-and-nuclear energy-loss region, in addition to the electronic and nuclear energy-loss regions in PSM, is taken into account analytically and appropriately. This model is combined with a small-angle multiple scattering range theory considering both nuclear and electronic stopping effects developed by Marwick-Sigmund and Valdes-Arista to formulate a improved range theory. The ESM is also combined with the multiple scattering theory with non-small angle approximation by Goudsmit-Saunderson. Furthermore, we applied ESM to lateral spread model of Marwick-Sigmund. Numerical calculations of the entire distribution functions including one of the mixt region are roughly and approximately possible. However, exact numerical calculation may be impossible. Consequently, several preliminary numerical calculations of the electronic, mixt, and nuclear regions are performed to examine their underlying behavior with respect to the incident energy, the scattering angle, the outgoing projectile intensity, and the target thickness. We show the numerical results not only of PSM and but also of ESM. Both numerical results are shown in the present paper for the first time. Since the theoretical relations are constructed using reduced variables, the calculations are made only on the case of C colliding on C.

Computing exact bundle compliance control charts via probability generating functions.

PubMed

Chen, Binchao; Matis, Timothy; Benneyan, James

2016-06-01

Compliance to evidenced-base practices, individually and in 'bundles', remains an important focus of healthcare quality improvement for many clinical conditions. The exact probability distribution of composite bundle compliance measures used to develop corresponding control charts and other statistical tests is based on a fairly large convolution whose direct calculation can be computationally prohibitive. Various series expansions and other approximation approaches have been proposed, each with computational and accuracy tradeoffs, especially in the tails. This same probability distribution also arises in other important healthcare applications, such as for risk-adjusted outcomes and bed demand prediction, with the same computational difficulties. As an alternative, we use probability generating functions to rapidly obtain exact results and illustrate the improved accuracy and detection over other methods. Numerical testing across a wide range of applications demonstrates the computational efficiency and accuracy of this approach.

FEAST fundamental framework for electronic structure calculations: Reformulation and solution of the muffin-tin problem

NASA Astrophysics Data System (ADS)

Levin, Alan R.; Zhang, Deyin; Polizzi, Eric

2012-11-01

In a recent article Polizzi (2009) [15], the FEAST algorithm has been presented as a general purpose eigenvalue solver which is ideally suited for addressing the numerical challenges in electronic structure calculations. Here, FEAST is presented beyond the “black-box” solver as a fundamental modeling framework which can naturally address the original numerical complexity of the electronic structure problem as formulated by Slater in 1937 [3]. The non-linear eigenvalue problem arising from the muffin-tin decomposition of the real-space domain is first derived and then reformulated to be solved exactly within the FEAST framework. This new framework is presented as a fundamental and practical solution for performing both accurate and scalable electronic structure calculations, bypassing the various issues of using traditional approaches such as linearization and pseudopotential techniques. A finite element implementation of this FEAST framework along with simulation results for various molecular systems is also presented and discussed.

Condensate statistics and thermodynamics of weakly interacting Bose gas: Recursion relation approach

NASA Astrophysics Data System (ADS)

Dorfman, K. E.; Kim, M.; Svidzinsky, A. A.

2011-03-01

We study condensate statistics and thermodynamics of weakly interacting Bose gas with a fixed total number N of particles in a cubic box. We find the exact recursion relation for the canonical ensemble partition function. Using this relation, we calculate the distribution function of condensate particles for N=200. We also calculate the distribution function based on multinomial expansion of the characteristic function. Similar to the ideal gas, both approaches give exact statistical moments for all temperatures in the framework of Bogoliubov model. We compare them with the results of unconstraint canonical ensemble quasiparticle formalism and the hybrid master equation approach. The present recursion relation can be used for any external potential and boundary conditions. We investigate the temperature dependence of the first few statistical moments of condensate fluctuations as well as thermodynamic potentials and heat capacity analytically and numerically in the whole temperature range.

Exact cone beam reconstruction formulae for functions and their gradients for spherical and flat detectors

NASA Astrophysics Data System (ADS)

Louis, Alfred K.

2016-11-01

We derive unified inversion formulae for the cone beam transform similar to the Radon transform. Reinterpreting Grangeat’s formula we find a relation between the Radon transform of the gradient of the searched-for function and a quantity computable from cone beam data. This gives a uniqueness result for the cone beam transform of compactly supported functions under much weaker assumptions than the Tuy-Kirillov condition. Furthermore this relation leads to an exact formula for the direct calculation of derivatives of the density distribution; but here, similar to the classical Radon transform, complete Radon data are needed, hence the Tuy-Kirillov condition has to be imposed. Numerical experiments reported in Hahn B N et al (2013 Meas. Sci. Technol. 24 125601) indicate that these calculations are less corrupted by beam-hardening noise. Finally, we present flat detector versions for these results, which are mathematically less attractive but important for applications.

Variational calculations of subbands in a quantum well with uniform electric field - Gram-Schmidt orthogonalization approach

NASA Technical Reports Server (NTRS)

Ahn, Doyeol; Chuang, S. L.

1986-01-01

Variational calculations of subband eigenstates in an infinite quantum well with an applied electric field using Gram-Schmidt orthogonalized trial wave functions are presented. The results agree very well with the exact numerical solutions even up to 1200 kV/cm. It is also shown that, for increasing electric fields, the energy of the ground state decreases, while that of higher subband states increases slightly up to 1000 kV/cm and then decreases for a well size of 100 A.

The Oscillating Circular Airfoil on the Basis of Potential Theory

NASA Technical Reports Server (NTRS)

Schade, T.; Krienes, K.

1947-01-01

Proceeding from the thesis by W. Kinner the present report treats the problem of the circular airfoil in uniform airflow executing small oscillations, the amplitudes of which correspond to whole functions of the second degree in x and y. The pressure distribution is secured by means of Prandtl's acceleration potential. It results in a system of linear equations the coefficients of which can be calculated exactly with the aid of exponential functions and Hankel's functions. The equations necessary are derived in part I; the numerical calculation follows in part II.

Binary data corruption due to a Brownian agent

NASA Astrophysics Data System (ADS)

Newman, T. J.; Triampo, Wannapong

1999-05-01

We introduce a model of binary data corruption induced by a Brownian agent (active random walker) on a d-dimensional lattice. A continuum formulation allows the exact calculation of several quantities related to the density of corrupted bits ρ, for example, the mean of ρ and the density-density correlation function. Excellent agreement is found with the results from numerical simulations. We also calculate the probability distribution of ρ in d=1, which is found to be log normal, indicating that the system is governed by extreme fluctuations.

Distillability of Werner states using entanglement witnesses and robust semidefinite programs

DOE Office of Scientific and Technical Information (OSTI.GOV)

Vianna, Reinaldo O.; Departamento de Fisica, ICEX, Universidade Federal de Minas Gerais, Av. Antonio Carlos 6627, 31270-901 Belo Horizonte, Minas Gerais; Doherty, Andrew C.

2006-11-15

We use robust semidefinite programs and entanglement witnesses to study the distillability of Werner states. We perform exact numerical calculations that show two-undistillability in a region of the state space, which was previously conjectured to be undistillable. We also introduce bases that yield interesting expressions for the distillability witnesses and for a tensor product of Werner states with an arbitrary number of copies.

The analytical transfer matrix method for PT-symmetric complex potential

NASA Astrophysics Data System (ADS)

Naceri, Leila; Hammou, Amine B.

2017-07-01

We have extended the analytical transfer matrix (ATM) method to solve quantum mechanical bound state problems with complex PT-symmetric potentials. Our work focuses on a class of models studied by Bender and Jones, we calculate the energy eigenvalues, discuss the critical values of g and compare the results with those obtained from other methods such as exact numerical computation and WKB approximation method.

Hyperfine coupling constants of the nitrogen and phosphorus atoms: A challenge for exact-exchange density-functional and post-Hartree-Fock methods

NASA Astrophysics Data System (ADS)

Kaupp, Martin; Arbuznikov, Alexei V.; Heßelmann, Andreas; Görling, Andreas

2010-05-01

The isotropic hyperfine coupling constants of the free N(S4) and P(S4) atoms have been evaluated with high-level post-Hartree-Fock and density-functional methods. The phosphorus hyperfine coupling presents a significant challenge to both types of methods. With large basis sets, MP2 and coupled-cluster singles and doubles calculations give much too small values for the phosphorus atom. Triple excitations are needed in coupled-cluster calculations to achieve reasonable agreement with experiment. None of the standard density functionals reproduce even the correct sign of this hyperfine coupling. Similarly, the computed hyperfine couplings depend crucially on the self-consistent treatment in exact-exchange density-functional theory within the optimized effective potential (OEP) method. Well-balanced auxiliary and orbital basis sets are needed for basis-expansion exact-exchange-only OEP approaches to come close to Hartree-Fock or numerical OEP data. Results from the localized Hartree-Fock and Krieger-Li-Iafrate approximations deviate notably from exact OEP data in spite of very similar total energies. Of the functionals tested, only full exact-exchange methods augmented by a correlation functional gave at least the correct sign of the P(S4) hyperfine coupling but with too low absolute values. The subtle interplay between the spin-polarization contributions of the different core shells has been analyzed, and the influence of even very small changes in the exchange-correlation potential could be identified.

Theory and Circuit Model for Lossy Coaxial Transmission Line

DOE Office of Scientific and Technical Information (OSTI.GOV)

Genoni, T. C.; Anderson, C. N.; Clark, R. E.

2017-04-01

The theory of signal propagation in lossy coaxial transmission lines is revisited and new approximate analytic formulas for the line impedance and attenuation are derived. The accuracy of these formulas from DC to 100 GHz is demonstrated by comparison to numerical solutions of the exact field equations. Based on this analysis, a new circuit model is described which accurately reproduces the line response over the entire frequency range. Circuit model calculations are in excellent agreement with the numerical and analytic results, and with finite-difference-time-domain simulations which resolve the skindepths of the conducting walls.

A note on improved F-expansion method combined with Riccati equation applied to nonlinear evolution equations.

PubMed

Islam, Md Shafiqul; Khan, Kamruzzaman; Akbar, M Ali; Mastroberardino, Antonio

2014-10-01

The purpose of this article is to present an analytical method, namely the improved F-expansion method combined with the Riccati equation, for finding exact solutions of nonlinear evolution equations. The present method is capable of calculating all branches of solutions simultaneously, even if multiple solutions are very close and thus difficult to distinguish with numerical techniques. To verify the computational efficiency, we consider the modified Benjamin-Bona-Mahony equation and the modified Korteweg-de Vries equation. Our results reveal that the method is a very effective and straightforward way of formulating the exact travelling wave solutions of nonlinear wave equations arising in mathematical physics and engineering.

A note on improved F-expansion method combined with Riccati equation applied to nonlinear evolution equations

PubMed Central

Islam, Md. Shafiqul; Khan, Kamruzzaman; Akbar, M. Ali; Mastroberardino, Antonio

2014-01-01

The purpose of this article is to present an analytical method, namely the improved F-expansion method combined with the Riccati equation, for finding exact solutions of nonlinear evolution equations. The present method is capable of calculating all branches of solutions simultaneously, even if multiple solutions are very close and thus difficult to distinguish with numerical techniques. To verify the computational efficiency, we consider the modified Benjamin–Bona–Mahony equation and the modified Korteweg-de Vries equation. Our results reveal that the method is a very effective and straightforward way of formulating the exact travelling wave solutions of nonlinear wave equations arising in mathematical physics and engineering. PMID:26064530

Exact geodesic distances in FLRW spacetimes

NASA Astrophysics Data System (ADS)

Cunningham, William J.; Rideout, David; Halverson, James; Krioukov, Dmitri

2017-11-01

Geodesics are used in a wide array of applications in cosmology and astrophysics. However, it is not a trivial task to efficiently calculate exact geodesic distances in an arbitrary spacetime. We show that in spatially flat (3 +1 )-dimensional Friedmann-Lemaître-Robertson-Walker (FLRW) spacetimes, it is possible to integrate the second-order geodesic differential equations, and derive a general method for finding both timelike and spacelike distances given initial-value or boundary-value constraints. In flat spacetimes with either dark energy or matter, whether dust, radiation, or a stiff fluid, we find an exact closed-form solution for geodesic distances. In spacetimes with a mixture of dark energy and matter, including spacetimes used to model our physical universe, there exists no closed-form solution, but we provide a fast numerical method to compute geodesics. A general method is also described for determining the geodesic connectedness of an FLRW manifold, provided only its scale factor.

An approach for generating trajectory-based dynamics which conserves the canonical distribution in the phase space formulation of quantum mechanics. II. Thermal correlation functions.

PubMed

Liu, Jian; Miller, William H

2011-03-14

We show the exact expression of the quantum mechanical time correlation function in the phase space formulation of quantum mechanics. The trajectory-based dynamics that conserves the quantum canonical distribution-equilibrium Liouville dynamics (ELD) proposed in Paper I is then used to approximately evaluate the exact expression. It gives exact thermal correlation functions (of even nonlinear operators, i.e., nonlinear functions of position or momentum operators) in the classical, high temperature, and harmonic limits. Various methods have been presented for the implementation of ELD. Numerical tests of the ELD approach in the Wigner or Husimi phase space have been made for a harmonic oscillator and two strongly anharmonic model problems, for each potential autocorrelation functions of both linear and nonlinear operators have been calculated. It suggests ELD can be a potentially useful approach for describing quantum effects for complex systems in condense phase.

An exact solution for R2,eff in CPMG experiments in the case of two site chemical exchange

PubMed Central

Baldwin, Andrew J.

2014-01-01

The Carr–Purcell–Meiboom–Gill (CPMG) experiment is widely used to quantitatively analyse the effects of chemical exchange on NMR spectra. In a CPMG experiment, the effective transverse relaxation rate, R2,eff, is typically measured as a function of the pulse frequency, νCPMG. Here, an exact expression for how R2,eff varies with νCPMG is derived for the commonly encountered scenario of two-site chemical exchange of in-phase magnetisation. This result, summarised in Appendix A, generalises a frequently used equation derived by Carver and Richards, published in 1972. The expression enables more rapid analysis of CPMG data by both speeding up calculation of R2,eff over numerical methods by a factor of ca. 130, and yields exact derivatives for use in data analysis. Moreover, the derivation provides insight into the physical principles behind the experiment. PMID:24852115

Representing exact number visually using mental abacus.

PubMed

Frank, Michael C; Barner, David

2012-02-01

Mental abacus (MA) is a system for performing rapid and precise arithmetic by manipulating a mental representation of an abacus, a physical calculation device. Previous work has speculated that MA is based on visual imagery, suggesting that it might be a method of representing exact number nonlinguistically, but given the limitations on visual working memory, it is unknown how MA structures could be stored. We investigated the structure of the representations underlying MA in a group of children in India. Our results suggest that MA is represented in visual working memory by splitting the abacus into a series of columns, each of which is independently stored as a unit with its own detailed substructure. In addition, we show that the computations of practiced MA users (but not those of control participants) are relatively insensitive to verbal interference, consistent with the hypothesis that MA is a nonlinguistic format for exact numerical computation.

Electron-cyclotron absorption in high-temperature plasmas: quasi-exact analytical evaluation and comparative numerical analysis

NASA Astrophysics Data System (ADS)

Albajar, F.; Bertelli, N.; Bornatici, M.; Engelmann, F.

2007-01-01

On the basis of the electromagnetic energy balance equation, a quasi-exact analytical evaluation of the electron-cyclotron (EC) absorption coefficient is performed for arbitrary propagation (with respect to the magnetic field) in a (Maxwellian) magneto-plasma for the temperature range of interest for fusion reactors (in which EC radiation losses tend to be important in the plasma power balance). The calculation makes use of Bateman's expansion for the product of two Bessel functions, retaining the lowest-order contribution. The integration over electron momentum can then be carried out analytically, fully accounting for finite Larmor radius effects in this approximation. On the basis of the analytical expressions for the EC absorption coefficients of both the extraordinary and ordinary modes thus obtained, (i) for the case of perpendicular propagation simple formulae are derived for both modes and (ii) a numerical analysis of the angular distribution of EC absorption is carried out. An assessment of the accuracy of asymptotic expressions that have been given earlier is also performed, showing that these approximations can be usefully applied for calculating EC power losses from reactor-grade plasmas. Presented in part at the 14th Joint Workshop on Electron Cyclotron Emission and Electron Cyclotron Resonance Heating, Santorini, Greece, 9-12 May 2006.

The special case of the 2 × 2 table: asymptotic unconditional McNemar test can be used to estimate sample size even for analysis based on GEE.

PubMed

Borkhoff, Cornelia M; Johnston, Patrick R; Stephens, Derek; Atenafu, Eshetu

2015-07-01

Aligning the method used to estimate sample size with the planned analytic method ensures the sample size needed to achieve the planned power. When using generalized estimating equations (GEE) to analyze a paired binary primary outcome with no covariates, many use an exact McNemar test to calculate sample size. We reviewed the approaches to sample size estimation for paired binary data and compared the sample size estimates on the same numerical examples. We used the hypothesized sample proportions for the 2 × 2 table to calculate the correlation between the marginal proportions to estimate sample size based on GEE. We solved the inside proportions based on the correlation and the marginal proportions to estimate sample size based on exact McNemar, asymptotic unconditional McNemar, and asymptotic conditional McNemar. The asymptotic unconditional McNemar test is a good approximation of GEE method by Pan. The exact McNemar is too conservative and yields unnecessarily large sample size estimates than all other methods. In the special case of a 2 × 2 table, even when a GEE approach to binary logistic regression is the planned analytic method, the asymptotic unconditional McNemar test can be used to estimate sample size. We do not recommend using an exact McNemar test. Copyright © 2015 Elsevier Inc. All rights reserved.

Time-Accurate, Unstructured-Mesh Navier-Stokes Computations with the Space-Time CESE Method

NASA Technical Reports Server (NTRS)

Chang, Chau-Lyan

2006-01-01

Application of the newly emerged space-time conservation element solution element (CESE) method to compressible Navier-Stokes equations is studied. In contrast to Euler equations solvers, several issues such as boundary conditions, numerical dissipation, and grid stiffness warrant systematic investigations and validations. Non-reflecting boundary conditions applied at the truncated boundary are also investigated from the stand point of acoustic wave propagation. Validations of the numerical solutions are performed by comparing with exact solutions for steady-state as well as time-accurate viscous flow problems. The test cases cover a broad speed regime for problems ranging from acoustic wave propagation to 3D hypersonic configurations. Model problems pertinent to hypersonic configurations demonstrate the effectiveness of the CESE method in treating flows with shocks, unsteady waves, and separations. Good agreement with exact solutions suggests that the space-time CESE method provides a viable alternative for time-accurate Navier-Stokes calculations of a broad range of problems.

Detecting many-body-localization lengths with cold atoms

NASA Astrophysics Data System (ADS)

Guo, Xuefei; Li, Xiaopeng

2018-03-01

Considering ultracold atoms in optical lattices, we propose experimental protocols to study many-body-localization (MBL) length and criticality in quench dynamics. Through numerical simulations with exact diagonalization, we show that in the MBL phase the perturbed density profile following a local quench remains exponentially localized in postquench dynamics. The size of this density profile after long-time-dynamics defines a localization length, which tends to diverge at the MBL-to-ergodic transition as we increase the system size. The determined localization transition point agrees with previous exact diagonalization calculations using other diagnostics. Our numerical results provide evidence for violation of the Harris-Chayes bound for the MBL criticality. The critical exponent ν can be extracted from our proposed dynamical procedure, which can then be used directly in experiments to determine whether the Harris-Chayes-bound holds for the MBL transition. These proposed protocols to detect localization criticality are justified by benchmarking to the well-established results for the noninteracting three-dimensional Anderson localization.

Protecting a quantum state from environmental noise by an incompatible finite-time measurement

DOE Office of Scientific and Technical Information (OSTI.GOV)

Brasil, Carlos Alexandre; Castro, L. A. de; Napolitano, R. d. J.

We show that measurements of finite duration performed on an open two-state system can protect the initial state from a phase-noisy environment, provided the measured observable does not commute with the perturbing interaction. When the measured observable commutes with the environmental interaction, the finite-duration measurement accelerates the rate of decoherence induced by the phase noise. For the description of the measurement of an observable that is incompatible with the interaction between system and environment, we have found an approximate analytical expression, valid at zero temperature and weak coupling with the measuring device. We have tested the validity of the analyticalmore » predictions against an exact numerical approach, based on the superoperator-splitting method, that confirms the protection of the initial state of the system. When the coupling between the system and the measuring apparatus increases beyond the range of validity of the analytical approximation, the initial state is still protected by the finite-time measurement, according with the exact numerical calculations.« less

Numerical simulations of epitaxial growth process in MOVPE reactor as a tool for design of modern semiconductors for high power electronics

NASA Astrophysics Data System (ADS)

Skibinski, Jakub; Caban, Piotr; Wejrzanowski, Tomasz; Kurzydlowski, Krzysztof J.

2014-10-01

In the present study numerical simulations of epitaxial growth of gallium nitride in Metal Organic Vapor Phase Epitaxy reactor AIX-200/4RF-S is addressed. Epitaxial growth means crystal growth that progresses while inheriting the laminar structure and the orientation of substrate crystals. One of the technological problems is to obtain homogeneous growth rate over the main deposit area. Since there are many agents influencing reaction on crystal area such as temperature, pressure, gas flow or reactor geometry, it is difficult to design optimal process. According to the fact that it's impossible to determine experimentally the exact distribution of heat and mass transfer inside the reactor during crystal growth, modeling is the only solution to understand the process precisely. Numerical simulations allow to understand the epitaxial process by calculation of heat and mass transfer distribution during growth of gallium nitride. Including chemical reactions in numerical model allows to calculate the growth rate of the substrate and estimate the optimal process conditions for obtaining the most homogeneous product.

Using monomer vibrational wavefunctions to compute numerically exact (12D) rovibrational levels of water dimer

NASA Astrophysics Data System (ADS)

Wang, Xiao-Gang; Carrington, Tucker

2018-02-01

We compute numerically exact rovibrational levels of water dimer, with 12 vibrational coordinates, on the accurate CCpol-8sf ab initio flexible monomer potential energy surface [C. Leforestier et al., J. Chem. Phys. 137, 014305 (2012)]. It does not have a sum-of-products or multimode form and therefore quadrature in some form must be used. To do the calculation, it is necessary to use an efficient basis set and to develop computational tools, for evaluating the matrix-vector products required to calculate the spectrum, that obviate the need to store the potential on a 12D quadrature grid. The basis functions we use are products of monomer vibrational wavefunctions and standard rigid-monomer basis functions (which involve products of three Wigner functions). Potential matrix-vector products are evaluated using the F matrix idea previously used to compute rovibrational levels of 5-atom and 6-atom molecules. When the coupling between inter- and intra-monomer coordinates is weak, this crude adiabatic type basis is efficient (only a few monomer vibrational wavefunctions are necessary), although the calculation of matrix elements is straightforward. It is much easier to use than an adiabatic basis. The product structure of the basis is compatible with the product structure of the kinetic energy operator and this facilitates computation of matrix-vector products. Compared with the results obtained using a [6 + 6]D adiabatic approach, we find good agreement for the inter-molecular levels and larger differences for the intra-molecular water bend levels.

Using monomer vibrational wavefunctions to compute numerically exact (12D) rovibrational levels of water dimer.

PubMed

Wang, Xiao-Gang; Carrington, Tucker

2018-02-21

We compute numerically exact rovibrational levels of water dimer, with 12 vibrational coordinates, on the accurate CCpol-8sf ab initio flexible monomer potential energy surface [C. Leforestier et al., J. Chem. Phys. 137, 014305 (2012)]. It does not have a sum-of-products or multimode form and therefore quadrature in some form must be used. To do the calculation, it is necessary to use an efficient basis set and to develop computational tools, for evaluating the matrix-vector products required to calculate the spectrum, that obviate the need to store the potential on a 12D quadrature grid. The basis functions we use are products of monomer vibrational wavefunctions and standard rigid-monomer basis functions (which involve products of three Wigner functions). Potential matrix-vector products are evaluated using the F matrix idea previously used to compute rovibrational levels of 5-atom and 6-atom molecules. When the coupling between inter- and intra-monomer coordinates is weak, this crude adiabatic type basis is efficient (only a few monomer vibrational wavefunctions are necessary), although the calculation of matrix elements is straightforward. It is much easier to use than an adiabatic basis. The product structure of the basis is compatible with the product structure of the kinetic energy operator and this facilitates computation of matrix-vector products. Compared with the results obtained using a [6 + 6]D adiabatic approach, we find good agreement for the inter-molecular levels and larger differences for the intra-molecular water bend levels.

Continuum Level Density of a Coupled-Channel System in the Complex Scaling Method

NASA Astrophysics Data System (ADS)

Suzuki, R.; Kruppa, A. T.; Giraud, B. G.; Katō, K.

2008-06-01

We study the continuum level density (CLD) in the formalism of the complex scaling method (CSM) for coupled-channel systems. We apply the formalism to the ^{4}He = [^{3}H + p] + [^3{He} + n] coupled-channel cluster model where there are resonances at low energy. Numerical calculations of the CLD in the CSM with a finite number of L^{2} basis functions are consistent with the exact result calculated from the S-matrix by solving coupled-channel equations. We also study channel densities. In this framework, the extended completeness relation (ECR) plays an important role.

Universal formulation of excitonic linear absorption spectra in all semiconductor microstructures

NASA Astrophysics Data System (ADS)

Lefebvre, Pierre; Christol, Philippe; Mathieu, Henry

1995-01-01

We present a generalization of the well-known exciton absorption calculations of Elliott [Phys. Rev. 108, 1384 (1957)], in the 3-dimensional case, and of Shinada and Sugano [J. Phys. Soc. Japan 21, 1936 (1966)], for 2-dimensional media: We calculate the optical absorption spectra of bound and unbound exciton states, by using a metric space with a noninteger dimension α (1 < α), obtaining almost exactly the same theoretical lineshapes as those resulting from accurate but costly numerical approaches [Chuang et al. Phys. Rev. B, 43, 1500 (1991); Benner and Haug, Phys. Rev. B 47, 15750 (1993)].

Numerical simulation of vortical ideal fluid flow through curved channel

NASA Astrophysics Data System (ADS)

Moshkin, N. P.; Mounnamprang, P.

2003-04-01

A numerical algorithm to study the boundary-value problem in which the governing equations are the steady Euler equations and the vorticity is given on the inflow parts of the domain boundary is developed. The Euler equations are implemented in terms of the stream function and vorticity. An irregular physical domain is transformed into a rectangle in the computational domain and the Euler equations are rewritten with respect to a curvilinear co-ordinate system. The convergence of the finite-difference equations to the exact solution is shown experimentally for the test problems by comparing the computational results with the exact solutions on the sequence of grids. To find the pressure from the known vorticity and stream function, the Euler equations are utilized in the Gromeka-Lamb form. The numerical algorithm is illustrated with several examples of steady flow through a two-dimensional channel with curved walls. The analysis of calculations shows strong dependence of the pressure field on the vorticity given at the inflow parts of the boundary. Plots of the flow structure and isobars, for different geometries of channel and for different values of vorticity on entrance, are also presented.

Exact milestoning

PubMed Central

Bello-Rivas, Juan M.; Elber, Ron

2015-01-01

A new theory and an exact computer algorithm for calculating kinetics and thermodynamic properties of a particle system are described. The algorithm avoids trapping in metastable states, which are typical challenges for Molecular Dynamics (MD) simulations on rough energy landscapes. It is based on the division of the full space into Voronoi cells. Prior knowledge or coarse sampling of space points provides the centers of the Voronoi cells. Short time trajectories are computed between the boundaries of the cells that we call milestones and are used to determine fluxes at the milestones. The flux function, an essential component of the new theory, provides a complete description of the statistical mechanics of the system at the resolution of the milestones. We illustrate the accuracy and efficiency of the exact Milestoning approach by comparing numerical results obtained on a model system using exact Milestoning with the results of long trajectories and with a solution of the corresponding Fokker-Planck equation. The theory uses an equation that resembles the approximate Milestoning method that was introduced in 2004 [A. K. Faradjian and R. Elber, J. Chem. Phys. 120(23), 10880-10889 (2004)]. However, the current formulation is exact and is still significantly more efficient than straightforward MD simulations on the system studied. PMID:25747056

A time-accurate high-resolution TVD scheme for solving the Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Kim, Hyun Dae; Liu, Nan-Suey

1992-01-01

A total variation diminishing (TVD) scheme has been developed and incorporated into an existing time-accurate high-resolution Navier-Stokes code. The accuracy and the robustness of the resulting solution procedure have been assessed by performing many calculations in four different areas: shock tube flows, regular shock reflection, supersonic boundary layer, and shock boundary layer interactions. These numerical results compare well with corresponding exact solutions or experimental data.

Experimental and numerical research on forging with torsion

NASA Astrophysics Data System (ADS)

Petrov, Mikhail A.; Subich, Vadim N.; Petrov, Pavel A.

2017-10-01

Increasing the efficiency of the technological operations of blank production is closely related to the computer-aided technologies (CAx). On the one hand, the practical result represents reality exactly. On the other hand, the development procedure of new process development demands unrestricted resources, which are limited on the SMEs. The tools of CAx were successfully applied for development of new process of forging with torsion and result analysis as well. It was shown, that the theoretical calculations find the confirmation both in praxis and during numerical simulation. The mostly used constructional materials were under study. The torque angles were stated. The simulated results were evaluated by experimental procedure.

Development of analytical methods of predicting the pressure distribution about a nacelle at transonic speeds: Exact solution

NASA Technical Reports Server (NTRS)

Grossman, B.; Moretti, G.

1973-01-01

A computer program to predict the inviscid, transonic flow field about isolated nacelles was developed. The problem was to be formulated to solve Euler's equations without any approximation (such as small disturbances) and hence the terminology exact solution. The flow field was complicated by the presence of imbedded shock waves, an engine-inlet interface, and exhaust plumes. Furthermore, the transonic nacelles of interest had a very slender but blunt cowl lip. This created two distinct length scales, the length of the nacelle and the cowl lip radius that can differ by several orders of magnitude. These aspects of the flow field presented many numerical difficulties. The approach to the problem was to calculate the nacelle flow field using the method of time-dependent computations (TDC). Although at the time of the issuance of this contract, other approaches to transonic flow calculations existed, it was felt that TDC offered the most effective means of meeting the goals of the contract.

Exact Solutions of Coupled Multispecies Linear Reaction–Diffusion Equations on a Uniformly Growing Domain

PubMed Central

Simpson, Matthew J.; Sharp, Jesse A.; Morrow, Liam C.; Baker, Ruth E.

2015-01-01

Embryonic development involves diffusion and proliferation of cells, as well as diffusion and reaction of molecules, within growing tissues. Mathematical models of these processes often involve reaction–diffusion equations on growing domains that have been primarily studied using approximate numerical solutions. Recently, we have shown how to obtain an exact solution to a single, uncoupled, linear reaction–diffusion equation on a growing domain, 0 < x < L(t), where L(t) is the domain length. The present work is an extension of our previous study, and we illustrate how to solve a system of coupled reaction–diffusion equations on a growing domain. This system of equations can be used to study the spatial and temporal distributions of different generations of cells within a population that diffuses and proliferates within a growing tissue. The exact solution is obtained by applying an uncoupling transformation, and the uncoupled equations are solved separately before applying the inverse uncoupling transformation to give the coupled solution. We present several example calculations to illustrate different types of behaviour. The first example calculation corresponds to a situation where the initially–confined population diffuses sufficiently slowly that it is unable to reach the moving boundary at x = L(t). In contrast, the second example calculation corresponds to a situation where the initially–confined population is able to overcome the domain growth and reach the moving boundary at x = L(t). In its basic format, the uncoupling transformation at first appears to be restricted to deal only with the case where each generation of cells has a distinct proliferation rate. However, we also demonstrate how the uncoupling transformation can be used when each generation has the same proliferation rate by evaluating the exact solutions as an appropriate limit. PMID:26407013

Exact Solutions of Coupled Multispecies Linear Reaction-Diffusion Equations on a Uniformly Growing Domain.

PubMed

Simpson, Matthew J; Sharp, Jesse A; Morrow, Liam C; Baker, Ruth E

2015-01-01

Embryonic development involves diffusion and proliferation of cells, as well as diffusion and reaction of molecules, within growing tissues. Mathematical models of these processes often involve reaction-diffusion equations on growing domains that have been primarily studied using approximate numerical solutions. Recently, we have shown how to obtain an exact solution to a single, uncoupled, linear reaction-diffusion equation on a growing domain, 0 < x < L(t), where L(t) is the domain length. The present work is an extension of our previous study, and we illustrate how to solve a system of coupled reaction-diffusion equations on a growing domain. This system of equations can be used to study the spatial and temporal distributions of different generations of cells within a population that diffuses and proliferates within a growing tissue. The exact solution is obtained by applying an uncoupling transformation, and the uncoupled equations are solved separately before applying the inverse uncoupling transformation to give the coupled solution. We present several example calculations to illustrate different types of behaviour. The first example calculation corresponds to a situation where the initially-confined population diffuses sufficiently slowly that it is unable to reach the moving boundary at x = L(t). In contrast, the second example calculation corresponds to a situation where the initially-confined population is able to overcome the domain growth and reach the moving boundary at x = L(t). In its basic format, the uncoupling transformation at first appears to be restricted to deal only with the case where each generation of cells has a distinct proliferation rate. However, we also demonstrate how the uncoupling transformation can be used when each generation has the same proliferation rate by evaluating the exact solutions as an appropriate limit.

Numeric calculation of celestial bodies with spreadsheet analysis

NASA Astrophysics Data System (ADS)

Koch, Alexander

2016-04-01

The motion of the planets and moons in our solar system can easily be calculated for any time by the Kepler laws of planetary motion. The Kepler laws are a special case of the gravitational law of Newton, especially if you consider more than two celestial bodies. Therefore it is more basic to calculate the motion by using the gravitational law. But the problem is, that by gravitational law it is not possible to calculate the state of motion with only one step of calculation. The motion has to be numerical calculated for many time intervalls. For this reason, spreadsheet analysis is helpful for students. Skills in programmes like Excel, Calc or Gnumeric are important in professional life and can easily be learnt by students. These programmes can help to calculate the complex motions with many intervalls. The more intervalls are used, the more exact are the calculated orbits. The sutdents will first get a quick course in Excel. After that they calculate with instructions the 2-D-coordinates of the orbits of Moon and Mars. Step by step the students are coding the formulae for calculating physical parameters like coordinates, force, acceleration and velocity. The project is limited to 4 weeks or 8 lessons. So the calcualtion will only include the calculation of one body around the central mass like Earth or Sun. The three-body problem can only be shortly discussed at the end of the project.

Computation of the asymptotic states of modulated open quantum systems with a numerically exact realization of the quantum trajectory method

NASA Astrophysics Data System (ADS)

Volokitin, V.; Liniov, A.; Meyerov, I.; Hartmann, M.; Ivanchenko, M.; Hänggi, P.; Denisov, S.

2017-11-01

Quantum systems out of equilibrium are presently a subject of active research, both in theoretical and experimental domains. In this work, we consider time-periodically modulated quantum systems that are in contact with a stationary environment. Within the framework of a quantum master equation, the asymptotic states of such systems are described by time-periodic density operators. Resolution of these operators constitutes a nontrivial computational task. Approaches based on spectral and iterative methods are restricted to systems with the dimension of the hosting Hilbert space dim H =N ≲300 , while the direct long-time numerical integration of the master equation becomes increasingly problematic for N ≳400 , especially when the coupling to the environment is weak. To go beyond this limit, we use the quantum trajectory method, which unravels the master equation for the density operator into a set of stochastic processes for wave functions. The asymptotic density matrix is calculated by performing a statistical sampling over the ensemble of quantum trajectories, preceded by a long transient propagation. We follow the ideology of event-driven programming and construct a new algorithmic realization of the method. The algorithm is computationally efficient, allowing for long "leaps" forward in time. It is also numerically exact, in the sense that, being given the list of uniformly distributed (on the unit interval) random numbers, {η1,η2,...,ηn} , one could propagate a quantum trajectory (with ηi's as norm thresholds) in a numerically exact way. By using a scalable N -particle quantum model, we demonstrate that the algorithm allows us to resolve the asymptotic density operator of the model system with N =2000 states on a regular-size computer cluster, thus reaching the scale on which numerical studies of modulated Hamiltonian systems are currently performed.

Computation of the asymptotic states of modulated open quantum systems with a numerically exact realization of the quantum trajectory method.

PubMed

Volokitin, V; Liniov, A; Meyerov, I; Hartmann, M; Ivanchenko, M; Hänggi, P; Denisov, S

2017-11-01

Quantum systems out of equilibrium are presently a subject of active research, both in theoretical and experimental domains. In this work, we consider time-periodically modulated quantum systems that are in contact with a stationary environment. Within the framework of a quantum master equation, the asymptotic states of such systems are described by time-periodic density operators. Resolution of these operators constitutes a nontrivial computational task. Approaches based on spectral and iterative methods are restricted to systems with the dimension of the hosting Hilbert space dimH=N≲300, while the direct long-time numerical integration of the master equation becomes increasingly problematic for N≳400, especially when the coupling to the environment is weak. To go beyond this limit, we use the quantum trajectory method, which unravels the master equation for the density operator into a set of stochastic processes for wave functions. The asymptotic density matrix is calculated by performing a statistical sampling over the ensemble of quantum trajectories, preceded by a long transient propagation. We follow the ideology of event-driven programming and construct a new algorithmic realization of the method. The algorithm is computationally efficient, allowing for long "leaps" forward in time. It is also numerically exact, in the sense that, being given the list of uniformly distributed (on the unit interval) random numbers, {η_{1},η_{2},...,η_{n}}, one could propagate a quantum trajectory (with η_{i}'s as norm thresholds) in a numerically exact way. By using a scalable N-particle quantum model, we demonstrate that the algorithm allows us to resolve the asymptotic density operator of the model system with N=2000 states on a regular-size computer cluster, thus reaching the scale on which numerical studies of modulated Hamiltonian systems are currently performed.

Spreading of correlations in the Falicov-Kimball model

NASA Astrophysics Data System (ADS)

Herrmann, Andreas J.; Antipov, Andrey E.; Werner, Philipp

2018-04-01

We study dynamical properties of the one- and two-dimensional Falicov-Kimball model using lattice Monte Carlo simulations. In particular, we calculate the spreading of charge correlations in the equilibrium model and after an interaction quench. The results show a reduction of the light-cone velocity with interaction strength at low temperature, while the phase velocity increases. At higher temperature, the initial spreading is determined by the Fermi velocity of the noninteracting system and the maximum range of the correlations decreases with increasing interaction strength. Charge order correlations in the disorder potential enhance the range of the correlations. We also use the numerically exact lattice Monte Carlo results to benchmark the accuracy of equilibrium and nonequilibrium dynamical cluster approximation calculations. It is shown that the bias introduced by the mapping to a periodized cluster is substantial, and that from a numerical point of view, it is more efficient to simulate the lattice model directly.

Optics of Water Cloud Droplets Mixed with Black-Carbon Aerosols

NASA Technical Reports Server (NTRS)

Mishchenko, Michael I.; Liu, Li; Cairns, Brian; Mackowski, Daniel W.

2014-01-01

We use the recently extended superposition T-matrix method to calculate scattering and absorption properties of micrometer-sized water droplets contaminated by black carbon. Our numerically exact results reveal that, depending on the mode of soot-water mixing, the soot specific absorption can vary by a factor exceeding 6.5. The specific absorption is maximized when the soot material is quasi-uniformly distributed throughout the droplet interior in the form of numerous small monomers. The range of mixing scenarios captured by our computations implies a wide range of remote sensing and radiation budget implications of the presence of black carbon in liquid-water clouds. We show that the popular Maxwell-Garnett effective-medium approximation can be used to calculate the optical cross sections, single-scattering albedo, and asymmetry parameter for the quasi-uniform mixing scenario, but is likely to fail in application to other mixing scenarios and in computations of the elements of the scattering matrix.

Exact Dispersion Study of an Asymmetric Thin Planar Slab Dielectric Waveguide without Computing {d^2}β/{d{k^2}} Numerically

NASA Astrophysics Data System (ADS)

Raghuwanshi, Sanjeev Kumar; Palodiya, Vikram

2017-08-01

Waveguide dispersion can be tailored but not the material dispersion. Hence, the total dispersion can be shifted at any desired band by adjusting the waveguide dispersion. Waveguide dispersion is proportional to {d^2}β/d{k^2} and need to be computed numerically. In this paper, we have tried to compute analytical expression for {d^2}β/d{k^2} in terms of {d^2}β/d{k^2} accurately with numerical technique, ≈ 10^{-5} decimal point. This constraint sometimes generates the error in calculation of waveguide dispersion. To formulate the problem we will use the graphical method. Our study reveals that we can compute the waveguide dispersion enough accurately for various modes by knowing - β only.

Reliable before-fabrication forecasting of normal and touch mode MEMS capacitive pressure sensor: modeling and simulation

NASA Astrophysics Data System (ADS)

Jindal, Sumit Kumar; Mahajan, Ankush; Raghuwanshi, Sanjeev Kumar

2017-10-01

An analytical model and numerical simulation for the performance of MEMS capacitive pressure sensors in both normal and touch modes is required for expected behavior of the sensor prior to their fabrication. Obtaining such information should be based on a complete analysis of performance parameters such as deflection of diaphragm, change of capacitance when the diaphragm deflects, and sensitivity of the sensor. In the literature, limited work has been carried out on the above-stated issue; moreover, due to approximation factors of polynomials, a tolerance error cannot be overseen. Reliable before-fabrication forecasting requires exact mathematical calculation of the parameters involved. A second-order polynomial equation is calculated mathematically for key performance parameters of both modes. This eliminates the approximation factor, and an exact result can be studied, maintaining high accuracy. The elimination of approximation factors and an approach of exact results are based on a new design parameter (δ) that we propose. The design parameter gives an initial hint to the designers on how the sensor will behave once it is fabricated. The complete work is aided by extensive mathematical detailing of all the parameters involved. Next, we verified our claims using MATLAB® simulation. Since MATLAB® effectively provides the simulation theory for the design approach, more complicated finite element method is not used.

The method of characteristics for the determination of supersonic flow over bodies of revolution at small angles of attack

NASA Technical Reports Server (NTRS)

Ferri, Antonio

1951-01-01

The method of characteristics has been applied for the determination of the supersonic-flow properties around bodies of revolution at a small angle of attack. The system developed considers the effect of the variation of entropy due to the curved shock and determines a flow that exactly satisfies the boundary conditions in the limits of the simplifications assumed. Two practical methods for numerical calculations are given. (author)

Fast calculation method of computer-generated hologram using a depth camera with point cloud gridding

NASA Astrophysics Data System (ADS)

Zhao, Yu; Shi, Chen-Xiao; Kwon, Ki-Chul; Piao, Yan-Ling; Piao, Mei-Lan; Kim, Nam

2018-03-01

We propose a fast calculation method for a computer-generated hologram (CGH) of real objects that uses a point cloud gridding method. The depth information of the scene is acquired using a depth camera and the point cloud model is reconstructed virtually. Because each point of the point cloud is distributed precisely to the exact coordinates of each layer, each point of the point cloud can be classified into grids according to its depth. A diffraction calculation is performed on the grids using a fast Fourier transform (FFT) to obtain a CGH. The computational complexity is reduced dramatically in comparison with conventional methods. The feasibility of the proposed method was confirmed by numerical and optical experiments.

Responses to applied forces and the Jarzynski equality in classical oscillator systems coupled to finite baths: an exactly solvable nondissipative nonergodic model.

PubMed

Hasegawa, Hideo

2011-07-01

Responses of small open oscillator systems to applied external forces have been studied with the use of an exactly solvable classical Caldeira-Leggett model in which a harmonic oscillator (system) is coupled to finite N-body oscillators (bath) with an identical frequency (ω(n) = ω(o) for n = 1 to N). We have derived exact expressions for positions, momenta, and energy of the system in nonequilibrium states and for work performed by applied forces. A detailed study has been made on an analytical method for canonical averages of physical quantities over the initial equilibrium state, which is much superior to numerical averages commonly adopted in simulations of small systems. The calculated energy of the system which is strongly coupled to a finite bath is fluctuating but nondissipative. It has been shown that the Jarzynski equality is valid in nondissipative nonergodic open oscillator systems regardless of the rate of applied ramp force.

Exact combinatorial approach to finite coagulating systems

NASA Astrophysics Data System (ADS)

Fronczak, Agata; Chmiel, Anna; Fronczak, Piotr

2018-02-01

This paper outlines an exact combinatorial approach to finite coagulating systems. In this approach, cluster sizes and time are discrete and the binary aggregation alone governs the time evolution of the systems. By considering the growth histories of all possible clusters, an exact expression is derived for the probability of a coagulating system with an arbitrary kernel being found in a given cluster configuration when monodisperse initial conditions are applied. Then this probability is used to calculate the time-dependent distribution for the number of clusters of a given size, the average number of such clusters, and that average's standard deviation. The correctness of our general expressions is proved based on the (analytical and numerical) results obtained for systems with the constant kernel. In addition, the results obtained are compared with the results arising from the solutions to the mean-field Smoluchowski coagulation equation, indicating its weak points. The paper closes with a brief discussion on the extensibility to other systems of the approach presented herein, emphasizing the issue of arbitrary initial conditions.

Exact mode volume and Purcell factor of open optical systems

NASA Astrophysics Data System (ADS)

Muljarov, E. A.; Langbein, W.

2016-12-01

The Purcell factor quantifies the change of the radiative decay of a dipole in an electromagnetic environment relative to free space. Designing this factor is at the heart of photonics technology, striving to develop ever smaller or less lossy optical resonators. The Purcell factor can be expressed using the electromagnetic eigenmodes of the resonators, introducing the notion of a mode volume for each mode. This approach allows an analytic treatment, reducing the Purcell factor and other observables to sums over eigenmode resonances. Calculating the mode volumes requires a correct normalization of the modes. We introduce an exact normalization of modes, not relying on perfectly matched layers. We present an analytic theory of the Purcell effect based on this exact mode normalization and the resulting effective mode volume. We use a homogeneous dielectric sphere in vacuum, which is analytically solvable, to exemplify these findings. We furthermore verify the applicability of the normalization to numerically determined modes of a finite dielectric cylinder.

The sagitta and lens thickness: the exact solution and a matrix approximation for lenses with toric, spherical, and cylindrical surfaces.

PubMed

Harris, W F

1989-03-01

The exact equation for sagitta of spherical surfaces is generalized to toric surfaces which include spherical and cylindrical surfaces as special cases. Lens thickness, therefore, can be calculated accurately anywhere on a lens even in cases of extreme spherical and cylindrical powers and large diameters. The sagittae of tire- and barrel-form toric surfaces differ off the principal meridians, as is shown by a numerical example. The same holds for pulley- and capstan-form toric surfaces. A general expression is given for thickness at an arbitrary point on a toric lens. Approximate expressions are derived and re-expressed in terms of matrices. The matrix provides an elegant means of generalizing equations for spherical surfaces and lenses to toric surfaces and lenses.

Aging and coarsening in isolated quantum systems after a quench: Exact results for the quantum O(N) model with N → ∞.

PubMed

Maraga, Anna; Chiocchetta, Alessio; Mitra, Aditi; Gambassi, Andrea

2015-10-01

The nonequilibrium dynamics of an isolated quantum system after a sudden quench to a dynamical critical point is expected to be characterized by scaling and universal exponents due to the absence of time scales. We explore these features for a quench of the parameters of a Hamiltonian with O(N) symmetry, starting from a ground state in the disordered phase. In the limit of infinite N, the exponents and scaling forms of the relevant two-time correlation functions can be calculated exactly. Our analytical predictions are confirmed by the numerical solution of the corresponding equations. Moreover, we find that the same scaling functions, yet with different exponents, also describe the coarsening dynamics for quenches below the dynamical critical point.

Algebraic Construction of Exact Difference Equations from Symmetry of Equations

NASA Astrophysics Data System (ADS)

Itoh, Toshiaki

2009-09-01

Difference equations or exact numerical integrations, which have general solutions, are treated algebraically. Eliminating the symmetries of the equation, we can construct difference equations (DCE) or numerical integrations equivalent to some ODEs or PDEs that means both have the same solution functions. When arbitrary functions are given, whether we can construct numerical integrations that have solution functions equal to given function or not are treated in this work. Nowadays, Lie's symmetries solver for ODE and PDE has been implemented in many symbolic software. Using this solver we can construct algebraic DCEs or numerical integrations which are correspond to some ODEs or PDEs. In this work, we treated exact correspondence between ODE or PDE and DCE or numerical integration with Gröbner base and Janet base from the view of Lie's symmetries.

Estimating statistical isotropy violation in CMB due to non-circular beam and complex scan in minutes

DOE Office of Scientific and Technical Information (OSTI.GOV)

Pant, Nidhi; Das, Santanu; Mitra, Sanjit

Mild, unavoidable deviations from circular-symmetry of instrumental beams along with scan strategy can give rise to measurable Statistical Isotropy (SI) violation in Cosmic Microwave Background (CMB) experiments. If not accounted properly, this spurious signal can complicate the extraction of other SI violation signals (if any) in the data. However, estimation of this effect through exact numerical simulation is computationally intensive and time consuming. A generalized analytical formalism not only provides a quick way of estimating this signal, but also gives a detailed understanding connecting the leading beam anisotropy components to a measurable BipoSH characterisation of SI violation. In this paper,more » we provide an approximate generic analytical method for estimating the SI violation generated due to a non-circular (NC) beam and arbitrary scan strategy, in terms of the Bipolar Spherical Harmonic (BipoSH) spectra. Our analytical method can predict almost all the features introduced by a NC beam in a complex scan and thus reduces the need for extensive numerical simulation worth tens of thousands of CPU hours into minutes long calculations. As an illustrative example, we use WMAP beams and scanning strategy to demonstrate the easability, usability and efficiency of our method. We test all our analytical results against that from exact numerical simulations.« less

A harmonic adiabatic approximation to calculate highly excited vibrational levels of ``floppy molecules''

NASA Astrophysics Data System (ADS)

Lauvergnat, David; Nauts, André; Justum, Yves; Chapuisat, Xavier

2001-04-01

The harmonic adiabatic approximation (HADA), an efficient and accurate quantum method to calculate highly excited vibrational levels of molecular systems, is presented. It is well-suited to applications to "floppy molecules" with a rather large number of atoms (N>3). A clever choice of internal coordinates naturally suggests their separation into active, slow, or large amplitude coordinates q', and inactive, fast, or small amplitude coordinates q″, which leads to an adiabatic (or Born-Oppenheimer-type) approximation (ADA), i.e., the total wave function is expressed as a product of active and inactive total wave functions. However, within the framework of the ADA, potential energy data concerning the inactive coordinates q″ are required. To reduce this need, a minimum energy domain (MED) is defined by minimizing the potential energy surface (PES) for each value of the active variables q', and a quadratic or harmonic expansion of the PES, based on the MED, is used (MED harmonic potential). In other words, the overall picture is that of a harmonic valley about the MED. In the case of only one active variable, we have a minimum energy path (MEP) and a MEP harmonic potential. The combination of the MED harmonic potential and the adiabatic approximation (harmonic adiabatic approximation: HADA) greatly reduces the size of the numerical computations, so that rather large molecules can be studied. In the present article however, the HADA is applied to our benchmark molecule HCN/CNH, to test the validity of the method. Thus, the HADA vibrational energy levels are compared and are in excellent agreement with the ADA calculations (adiabatic approximation with the full PES) of Light and Bačić [J. Chem. Phys. 87, 4008 (1987)]. Furthermore, the exact harmonic results (exact calculations without the adiabatic approximation but with the MEP harmonic potential) are compared to the exact calculations (without any sort of approximation). In addition, we compare the densities of the bending motion during the HCN/CNH isomerization, computed with the HADA and the exact wave function.

Given a one-step numerical scheme, on which ordinary differential equations is it exact?

NASA Astrophysics Data System (ADS)

Villatoro, Francisco R.

2009-01-01

A necessary condition for a (non-autonomous) ordinary differential equation to be exactly solved by a one-step, finite difference method is that the principal term of its local truncation error be null. A procedure to determine some ordinary differential equations exactly solved by a given numerical scheme is developed. Examples of differential equations exactly solved by the explicit Euler, implicit Euler, trapezoidal rule, second-order Taylor, third-order Taylor, van Niekerk's second-order rational, and van Niekerk's third-order rational methods are presented.

Statistical computation of tolerance limits

NASA Technical Reports Server (NTRS)

Wheeler, J. T.

1993-01-01

Based on a new theory, two computer codes were developed specifically to calculate the exact statistical tolerance limits for normal distributions within unknown means and variances for the one-sided and two-sided cases for the tolerance factor, k. The quantity k is defined equivalently in terms of the noncentral t-distribution by the probability equation. Two of the four mathematical methods employ the theory developed for the numerical simulation. Several algorithms for numerically integrating and iteratively root-solving the working equations are written to augment the program simulation. The program codes generate some tables of k's associated with the varying values of the proportion and sample size for each given probability to show accuracy obtained for small sample sizes.

Numerical studies of the Bethe-Salpeter equation for a two-fermion bound state

NASA Astrophysics Data System (ADS)

de Paula, W.; Frederico, T.; Salmè, G.; Viviani, M.

2018-03-01

Some recent advances on the solution of the Bethe-Salpeter equation (BSE) for a two-fermion bound system directly in Minkowski space are presented. The calculations are based on the expression of the Bethe-Salpeter amplitude in terms of the so-called Nakanishi integral representation and on the light-front projection (i.e. the integration of the light-front variable k - = k 0 - k 3). The latter technique allows for the analytically exact treatment of the singularities plaguing the two-fermion BSE in Minkowski space. The good agreement observed between our results and those obtained using other existing numerical methods, based on both Minkowski and Euclidean space techniques, fully corroborate our analytical treatment.

On physical optics for calculating scattering from coated bodies

NASA Technical Reports Server (NTRS)

Baldauf, J.; Lee, S. W.; Ling, H.; Chou, R.

1989-01-01

The familiar physical optics (PO) approximation is no longer valid when the perfectly conducting scatterer is coated with dielectric material. This paper reviews several possible PO formulations. By comparing the PO formulation with the moment method solution based on the impedance boundary condition for the case of the coated cone-sphere, a PO formulation using both electric and magnetic currents consistently gives the best numerical results. Comparisons of the exact moment method with the PO formulations using the impedance boundary condition and the PO formulation using the Fresnel reflection coefficient for the case of scattering from the cone-ellipsoid demonstrate that the Fresnel reflection coefficient gives the best numerical results in general.

The calculation of transport properties in quantum liquids using the maximum entropy numerical analytic continuation method: Application to liquid para-hydrogen

PubMed Central

Rabani, Eran; Reichman, David R.; Krilov, Goran; Berne, Bruce J.

2002-01-01

We present a method based on augmenting an exact relation between a frequency-dependent diffusion constant and the imaginary time velocity autocorrelation function, combined with the maximum entropy numerical analytic continuation approach to study transport properties in quantum liquids. The method is applied to the case of liquid para-hydrogen at two thermodynamic state points: a liquid near the triple point and a high-temperature liquid. Good agreement for the self-diffusion constant and for the real-time velocity autocorrelation function is obtained in comparison to experimental measurements and other theoretical predictions. Improvement of the methodology and future applications are discussed. PMID:11830656

Calculating qP-wave traveltimes in 2-D TTI media by high-order fast sweeping methods with a numerical quartic equation solver

NASA Astrophysics Data System (ADS)

Han, Song; Zhang, Wei; Zhang, Jie

2017-09-01

A fast sweeping method (FSM) determines the first arrival traveltimes of seismic waves by sweeping the velocity model in different directions meanwhile applying a local solver. It is an efficient way to numerically solve Hamilton-Jacobi equations for traveltime calculations. In this study, we develop an improved FSM to calculate the first arrival traveltimes of quasi-P (qP) waves in 2-D tilted transversely isotropic (TTI) media. A local solver utilizes the coupled slowness surface of qP and quasi-SV (qSV) waves to form a quartic equation, and solve it numerically to obtain possible traveltimes of qP-wave. The proposed quartic solver utilizes Fermat's principle to limit the range of the possible solution, then uses the bisection procedure to efficiently determine the real roots. With causality enforced during sweepings, our FSM converges fast in a few iterations, and the exact number depending on the complexity of the velocity model. To improve the accuracy, we employ high-order finite difference schemes and derive the second-order formulae. There is no weak anisotropy assumption, and no approximation is made to the complex slowness surface of qP-wave. In comparison to the traveltimes calculated by a horizontal slowness shooting method, the validity and accuracy of our FSM is demonstrated.

Dissociation between exact and approximate addition in developmental dyslexia.

PubMed

Yang, Xiujie; Meng, Xiangzhi

2016-09-01

Previous research has suggested that number sense and language are involved in number representation and calculation, in which number sense supports approximate arithmetic, and language permits exact enumeration and calculation. Meanwhile, individuals with dyslexia have a core deficit in phonological processing. Based on these findings, we thus hypothesized that children with dyslexia may exhibit exact calculation impairment while doing mental arithmetic. The reaction time and accuracy while doing exact and approximate addition with symbolic Arabic digits and non-symbolic visual arrays of dots were compared between typically developing children and children with dyslexia. Reaction time analyses did not reveal any differences across two groups of children, the accuracies, interestingly, revealed a distinction of approximation and exact addition across two groups of children. Specifically, two groups of children had no differences in approximation. Children with dyslexia, however, had significantly lower accuracy in exact addition in both symbolic and non-symbolic tasks than that of typically developing children. Moreover, linguistic performances were selectively associated with exact calculation across individuals. These results suggested that children with dyslexia have a mental arithmetic deficit specifically in the realm of exact calculation, while their approximation ability is relatively intact. Copyright © 2016 Elsevier Ltd. All rights reserved.

Principle of maximum entanglement entropy and local physics of strongly correlated materials.

PubMed

Lanatà, Nicola; Strand, Hugo U R; Yao, Yongxin; Kotliar, Gabriel

2014-07-18

We argue that, because of quantum entanglement, the local physics of strongly correlated materials at zero temperature is described in a very good approximation by a simple generalized Gibbs distribution, which depends on a relatively small number of local quantum thermodynamical potentials. We demonstrate that our statement is exact in certain limits and present numerical calculations of the iron compounds FeSe and FeTe and of the elemental cerium by employing the Gutzwiller approximation that strongly support our theory in general.

The universal function in color dipole model

NASA Astrophysics Data System (ADS)

Jalilian, Z.; Boroun, G. R.

2017-10-01

In this work we review color dipole model and recall properties of the saturation and geometrical scaling in this model. Our primary aim is determining the exact universal function in terms of the introduced scaling variable in different distance than the saturation radius. With inserting the mass in calculation we compute numerically the contribution of heavy productions in small x from the total structure function by the fraction of universal functions and show the geometrical scaling is established due to our scaling variable in this study.

Theory of many-body radiative heat transfer without the constraint of reciprocity

NASA Astrophysics Data System (ADS)

Zhu, Linxiao; Guo, Yu; Fan, Shanhui

2018-03-01

Using a self-consistent scattered field approach based on fluctuational electrodynamics, we develop compact formulas for radiative heat transfer in many-body systems without the constraint of reciprocity. The formulas allow for efficient numerical calculation for a system consisting of a large number of bodies, and are in principle exact. As a demonstration, for a nonreciprocal many-body system, we investigate persistent heat current at thermal equilibrium and directional heat transfer when the system is away from thermal equilibrium.

Engineering topological edge states in two dimensional magnetic photonic crystal

NASA Astrophysics Data System (ADS)

Yang, Bing; Wu, Tong; Zhang, Xiangdong

2017-01-01

Based on a perturbative approach, we propose a simple and efficient method to engineer the topological edge states in two dimensional magnetic photonic crystals. The topological edge states in the microstructures can be constructed and varied by altering the parameters of the microstructure according to the field-energy distributions of the Bloch states at the related Bloch wave vectors. The validity of the proposed method has been demonstrated by exact numerical calculations through three concrete examples. Our method makes the topological edge states "designable."

Nonlinear oscillator with power-form elastic-term: Fourier series expansion of the exact solution

NASA Astrophysics Data System (ADS)

Beléndez, Augusto; Francés, Jorge; Beléndez, Tarsicio; Bleda, Sergio; Pascual, Carolina; Arribas, Enrique

2015-05-01

A family of conservative, truly nonlinear, oscillators with integer or non-integer order nonlinearity is considered. These oscillators have only one odd power-form elastic-term and exact expressions for their period and solution were found in terms of Gamma functions and a cosine-Ateb function, respectively. Only for a few values of the order of nonlinearity, is it possible to obtain the periodic solution in terms of more common functions. However, for this family of conservative truly nonlinear oscillators we show in this paper that it is possible to obtain the Fourier series expansion of the exact solution, even though this exact solution is unknown. The coefficients of the Fourier series expansion of the exact solution are obtained as an integral expression in which a regularized incomplete Beta function appears. These coefficients are a function of the order of nonlinearity only and are computed numerically. One application of this technique is to compare the amplitudes for the different harmonics of the solution obtained using approximate methods with the exact ones computed numerically as shown in this paper. As an example, the approximate amplitudes obtained via a modified Ritz method are compared with the exact ones computed numerically.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bello-Rivas, Juan M.; Elber, Ron; Department of Chemistry, University of Texas at Austin, Austin, Texas 78712

A new theory and an exact computer algorithm for calculating kinetics and thermodynamic properties of a particle system are described. The algorithm avoids trapping in metastable states, which are typical challenges for Molecular Dynamics (MD) simulations on rough energy landscapes. It is based on the division of the full space into Voronoi cells. Prior knowledge or coarse sampling of space points provides the centers of the Voronoi cells. Short time trajectories are computed between the boundaries of the cells that we call milestones and are used to determine fluxes at the milestones. The flux function, an essential component of themore » new theory, provides a complete description of the statistical mechanics of the system at the resolution of the milestones. We illustrate the accuracy and efficiency of the exact Milestoning approach by comparing numerical results obtained on a model system using exact Milestoning with the results of long trajectories and with a solution of the corresponding Fokker-Planck equation. The theory uses an equation that resembles the approximate Milestoning method that was introduced in 2004 [A. K. Faradjian and R. Elber, J. Chem. Phys. 120(23), 10880-10889 (2004)]. However, the current formulation is exact and is still significantly more efficient than straightforward MD simulations on the system studied.« less

Design and Electro-Thermo-Mechanical Behavior Analysis of Au/Si₃N₄ Bimorph Microcantilevers for Static Mode Sensing.

PubMed

Kang, Seok-Won; Fragala, Joe; Kim, Su-Ho; Banerjee, Debjyoti

2017-11-01

This paper presents a design optimization method based on theoretical analysis and numerical calculations, using a commercial multi-physics solver (e.g., ANSYS and ESI CFD-ACE+), for a 3D continuous model, to analyze the bending characteristics of an electrically heated bimorph microcantilever. The results from the theoretical calculation and numerical analysis are compared with those measured using a CCD camera and magnification lenses for a chip level microcantilever array fabricated in this study. The bimorph microcantilevers are thermally actuated by joule heating generated by a 0.4 μm thin-film Au heater deposited on 0.6 μm Si₃N₄ microcantilevers. The initial deflections caused by residual stress resulting from the thermal bonding of two metallic layers with different coefficients of thermal expansion (CTEs) are additionally considered, to find the exact deflected position. The numerically calculated total deflections caused by electrical actuation show differences of 10%, on average, with experimental measurements in the operating current region (i.e., ~25 mA) to prevent deterioration by overheating. Bimorph microcantilevers are promising components for use in various MEMS (Micro-Electro-Mechanical System) sensing applications, and their deflection characteristics in static mode sensing are essential for detecting changes in thermal stress on the surface of microcantilevers.

Design and Electro-Thermo-Mechanical Behavior Analysis of Au/Si3N4 Bimorph Microcantilevers for Static Mode Sensing

PubMed Central

Kim, Su-Ho; Banerjee, Debjyoti

2017-01-01

This paper presents a design optimization method based on theoretical analysis and numerical calculations, using a commercial multi-physics solver (e.g., ANSYS and ESI CFD-ACE+), for a 3D continuous model, to analyze the bending characteristics of an electrically heated bimorph microcantilever. The results from the theoretical calculation and numerical analysis are compared with those measured using a CCD camera and magnification lenses for a chip level microcantilever array fabricated in this study. The bimorph microcantilevers are thermally actuated by joule heating generated by a 0.4 μm thin-film Au heater deposited on 0.6 μm Si3N4 microcantilevers. The initial deflections caused by residual stress resulting from the thermal bonding of two metallic layers with different coefficients of thermal expansion (CTEs) are additionally considered, to find the exact deflected position. The numerically calculated total deflections caused by electrical actuation show differences of 10%, on average, with experimental measurements in the operating current region (i.e., ~25 mA) to prevent deterioration by overheating. Bimorph microcantilevers are promising components for use in various MEMS (Micro-Electro-Mechanical System) sensing applications, and their deflection characteristics in static mode sensing are essential for detecting changes in thermal stress on the surface of microcantilevers. PMID:29104265

Numerical Activities and Information Learned at Home Link to the Exact Numeracy Skills in 5–6 Years-Old Children

PubMed Central

Benavides-Varela, Silvia; Butterworth, Brian; Burgio, Francesca; Arcara, Giorgio; Lucangeli, Daniela; Semenza, Carlo

2016-01-01

It is currently accepted that certain activities within the family environment contribute to develop early numerical skills before schooling. However, it is unknown whether this early experience influences both the exact and the approximate representation of numbers, and if so, which is more important for numerical tasks. In the present study the mathematical performance of 110 children (mean age 5 years 11 months) was evaluated using a battery that included tests of approximate and exact numerical abilities, as well as everyday numerical problems. Moreover, children were assessed on their knowledge of number information learned at home. The parents of the participants provided information regarding daily activities of the children and socio-demographic characteristics of the family. The results showed that the amount of numerical information learned at home was a significant predictor of participants' performance on everyday numerical problems and exact number representations, even after taking account of age, memory span and socio-economic and educational status of the family. We also found that particular activities, such as board games, correlate with the children's counting skills, which are foundational for arithmetic. Crucially, tests relying on approximate representations were not predicted by the numerical knowledge acquired at home. The present research supports claims about the importance and nature of home experiences in the child's acquisition of mathematics. PMID:26903902

Trajectory characteristics and heating of hypervelocity projectiles having large ballistic coefficients

NASA Technical Reports Server (NTRS)

Tauber, Michael E.

1986-01-01

A simple, approximate equation describing the velocity-density relationship (or velocity-altitude) has been derived from the flight of large ballistic coefficient projectiles launched at high speeds. The calculations obtained by using the approximate equation compared well with results for numerical integrations of the exact equations of motion. The flightpath equation was used to parametrically calculate maximum body decelerations and stagnation pressures for initial velocities from 2 to 6 km/s. Expressions were derived for the stagnation-point convective heating rates and total heat loads. The stagnation-point heating was parametrically calculated for a nonablating wall and an ablating carbon surface. Although the heating rates were very high, the pulse decayed quickly. The total nose-region heat shield weight was conservatively estimated to be only about 1 percent of the body mass.

Self-diffusion in a system of interacting Langevin particles

NASA Astrophysics Data System (ADS)

Dean, D. S.; Lefèvre, A.

2004-06-01

The behavior of the self-diffusion constant of Langevin particles interacting via a pairwise interaction is considered. The diffusion constant is calculated approximately within a perturbation theory in the potential strength about the bare diffusion constant. It is shown how this expansion leads to a systematic double expansion in the inverse temperature β and the particle density ρ . The one-loop diagrams in this expansion can be summed exactly and we show that this result is exact in the limit of small β and ρβ constants. The one-loop result can also be resummed using a semiphenomenological renormalization group method which has proved useful in the study of diffusion in random media. In certain cases the renormalization group calculation predicts the existence of a diverging relaxation time signaled by the vanishing of the diffusion constant, possible forms of divergence coming from this approximation are discussed. Finally, at a more quantitative level, the results are compared with numerical simulations, in two dimensions, of particles interacting via a soft potential recently used to model the interaction between coiled polymers.

Tail shortening by discrete hydrodynamics

NASA Astrophysics Data System (ADS)

Kiefer, J.; Visscher, P. B.

1982-02-01

A discrete formulation of hydrodynamics was recently introduced, whose most important feature is that it is exactly renormalizable. Previous numerical work has found that it provides a more efficient and rapidly convergent method for calculating transport coefficients than the usual Green-Kubo method. The latter's convergence difficulties are due to the well-known "long-time tail" of the time correlation function which must be integrated over time. The purpose of the present paper is to present additional evidence that these difficulties are really absent in the discrete equation of motion approach. The "memory" terms in the equation of motion are calculated accurately, and shown to decay much more rapidly with time than the equilibrium time correlations do.

Time-dependent mean-field theory for x-ray near-edge spectroscopy

NASA Astrophysics Data System (ADS)

Bertsch, G. F.; Lee, A. J.

2014-02-01

We derive equations of motion for calculating the near-edge x-ray absorption spectrum in molecules and condensed matter, based on a two-determinant approximation and Dirac's variational principle. The theory provides an exact solution for the linear response when the Hamiltonian or energy functional has only diagonal interactions in some basis. We numerically solve the equations to compare with the Mahan-Nozières-De Dominicis theory of the edge singularity in metallic conductors. Our extracted power-law exponents are similar to those of the analytic theory, but are not in quantitative agreement. The calculational method can be readily generalized to treat Kohn-Sham Hamiltonians with electron-electron interactions derived from correlation-exchange potentials.

Highly parallel demagnetization field calculation using the fast multipole method on tetrahedral meshes with continuous sources

NASA Astrophysics Data System (ADS)

Palmesi, P.; Exl, L.; Bruckner, F.; Abert, C.; Suess, D.

2017-11-01

The long-range magnetic field is the most time-consuming part in micromagnetic simulations. Computational improvements can relieve problems related to this bottleneck. This work presents an efficient implementation of the Fast Multipole Method [FMM] for the magnetic scalar potential as used in micromagnetics. The novelty lies in extending FMM to linearly magnetized tetrahedral sources making it interesting also for other areas of computational physics. We treat the near field directly and in use (exact) numerical integration on the multipole expansion in the far field. This approach tackles important issues like the vectorial and continuous nature of the magnetic field. By using FMM the calculations scale linearly in time and memory.

Full-Dimensional Quantum Calculations of Vibrational Levels of NH4(+) and Isotopomers on An Accurate Ab Initio Potential Energy Surface.

PubMed

Yu, Hua-Gen; Han, Huixian; Guo, Hua

2016-04-14

Vibrational energy levels of the ammonium cation (NH4(+)) and its deuterated isotopomers are calculated using a numerically exact kinetic energy operator on a recently developed nine-dimensional permutation invariant semiglobal potential energy surface fitted to a large number of high-level ab initio points. Like CH4, the vibrational levels of NH4(+) and ND4(+) exhibit a polyad structure, characterized by a collective quantum number P = 2(v1 + v3) + v2 + v4. The low-lying vibrational levels of all isotopomers are assigned and the agreement with available experimental data is better than 1 cm(-1).

Numeric kinetic energy operators for molecules in polyspherical coordinates

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sadri, Keyvan; Meyer, Hans-Dieter; Lauvergnat, David

Generalized curvilinear coordinates, as, e.g., polyspherical coordinates, are in general better adapted to the resolution of the nuclear Schroedinger equation than rectilinear ones like the normal mode coordinates. However, analytical expressions of the kinetic energy operators (KEOs) for molecular systems in polyspherical coordinates may be prohibitively complicated for large systems. In this paper we propose a method to generate a KEO numerically and bring it to a form practicable for dynamical calculations. To examine the new method we calculated vibrational spectra and eigenenergies for nitrous acid (HONO) and compare it with results obtained with an exact analytical KEO derived previouslymore » [F. Richter, P. Rosmus, F. Gatti, and H.-D. Meyer, J. Chem. Phys. 120, 6072 (2004)]. In a second example we calculated {pi}{yields}{pi}* photoabsorption spectrum and eigenenergies of ethene (C{sub 2}H{sub 4}) and compared it with previous work [M. R. Brill, F. Gatti, D. Lauvergnat, and H.-D. Meyer, Chem. Phys. 338, 186 (2007)]. In this ethene study the dimensionality was reduced from 12 to 6 by freezing six internal coordinates. Results for both molecules show that the proposed method for obtaining an approximate KEO is reliable for dynamical calculations. The error in eigenenergies was found to be below 1 cm{sup -1} for most states calculated.« less

An Unconditional Test for Change Point Detection in Binary Sequences with Applications to Clinical Registries.

PubMed

Ellenberger, David; Friede, Tim

2016-08-05

Methods for change point (also sometimes referred to as threshold or breakpoint) detection in binary sequences are not new and were introduced as early as 1955. Much of the research in this area has focussed on asymptotic and exact conditional methods. Here we develop an exact unconditional test. An unconditional exact test is developed which assumes the total number of events as random instead of conditioning on the number of observed events. The new test is shown to be uniformly more powerful than Worsley's exact conditional test and means for its efficient numerical calculations are given. Adaptions of methods by Berger and Boos are made to deal with the issue that the unknown event probability imposes a nuisance parameter. The methods are compared in a Monte Carlo simulation study and applied to a cohort of patients undergoing traumatic orthopaedic surgery involving external fixators where a change in pin site infections is investigated. The unconditional test controls the type I error rate at the nominal level and is uniformly more powerful than (or to be more precise uniformly at least as powerful as) Worsley's exact conditional test which is very conservative for small sample sizes. In the application a beneficial effect associated with the introduction of a new treatment procedure for pin site care could be revealed. We consider the new test an effective and easy to use exact test which is recommended in small sample size change point problems in binary sequences.

A novel method for calculating relative free energy of similar molecules in two environments

NASA Astrophysics Data System (ADS)

Farhi, Asaf; Singh, Bipin

2017-03-01

Calculating relative free energies is a topic of substantial interest and has many applications including solvation and binding free energies, which are used in computational drug discovery. However, there remain the challenges of accuracy, simple implementation, robustness and efficiency, which prevent the calculations from being automated and limit their use. Here we present an exact and complete decoupling analysis in which the partition functions of the compared systems decompose into the partition functions of the common and different subsystems. This decoupling analysis is applicable to submolecules with coupled degrees of freedom such as the methyl group and to any potential function (including the typical dihedral potentials), enabling to remove less terms in the transformation which results in a more efficient calculation. Then we show mathematically, in the context of partition function decoupling, that the two compared systems can be simulated separately, eliminating the need to design a composite system. We demonstrate the decoupling analysis and the separate transformations in a relative free energy calculation using MD simulations for a general force field and compare to another calculation and to experimental results. We present a unified soft-core technique that ensures the monotonicity of the numerically integrated function (analytical proof) which is important for the selection of intermediates. We show mathematically that in this soft-core technique the numerically integrated function can be non-steep only when we transform the systems separately, which can simplify the numerical integration. Finally, we show that when the systems have rugged energy landscape they can be equilibrated without introducing another sampling dimension which can also enable to use the simulation results for other free energy calculations.

Effective transport properties of composites of spheres

NASA Astrophysics Data System (ADS)

Felderhof, B. U.

1994-06-01

The effective linear transport properties of composites of spheres may be studied by the methods of statistical physics. The analysis leads to an exact cluster expansion. The resulting expression for the transport coefficients may be evaluated approximately as the sum of a mean field contribution and correction terms, given by cluster integrals over two-sphere and three-sphere correlation functions. Calculations of this nature have been performed for the effective dielectric constant, as well as the effective elastic constants of composites of spheres. Accurate numerical data for the effective properties may be obtained by computer simulation. An efficient formulation uses multiple expansion in Cartesian coordinates and periodic boundary conditions. Extensive numerical results have been obtained for the effective dielectric constant of a suspension of randomly distributed spheres.

Transverse spin correlation function of the one-dimensional spin- {1}/{2} XY model

NASA Astrophysics Data System (ADS)

Tonegawa, Takashi

1981-12-01

The transverse spin pair correlation function pxn=< SxmSxm+ n>=< SxmSxm+ n> is calculated exactly in the thermodynamic limit of the system described by the one-dimensional, isotropic, spin- {1}/{2}, XY Hamiltonian H=-2J limit∑l=1N(S xlS xl+1+S ylS yl+1) . It is found that at absolute zero temperature ( T = 0), the correlation function ρ xn for n ≥ 0 is given by ρ x2p= {1}/{4}{2}/{π}2plimitΠj=1p-1{4j 2}/{4j 2-1 }2p-2jif n=2p , ρ x2p+1=± {1}/{4}{2}/{π}2p+1limitΠj=1p{4j 2}/{4j 2-1 }2p+2jif n=2p+1 , where the plus sign applies when J is positive and the minus sign applies when J is negative. From these the asymptotic behavior as n → ∞ of |ϱ xn| at T = 0 is derived to be |ρ xn| ˜ {a}/{n} with a = 0.147088⋯. For finite temperatures, ρ xn is calculated numerically. By using the results for ϱ xn, the transverse inverse correlation length and the wavenumber dependent transverse spin pair correlation function are also calculated exactly.

Identification of overlapping communities and their hierarchy by locally calculating community-changing resolution levels

NASA Astrophysics Data System (ADS)

Havemann, Frank; Heinz, Michael; Struck, Alexander; Gläser, Jochen

2011-01-01

We propose a new local, deterministic and parameter-free algorithm that detects fuzzy and crisp overlapping communities in a weighted network and simultaneously reveals their hierarchy. Using a local fitness function, the algorithm greedily expands natural communities of seeds until the whole graph is covered. The hierarchy of communities is obtained analytically by calculating resolution levels at which communities grow rather than numerically by testing different resolution levels. This analytic procedure is not only more exact than its numerical alternatives such as LFM and GCE but also much faster. Critical resolution levels can be identified by searching for intervals in which large changes of the resolution do not lead to growth of communities. We tested our algorithm on benchmark graphs and on a network of 492 papers in information science. Combined with a specific post-processing, the algorithm gives much more precise results on LFR benchmarks with high overlap compared to other algorithms and performs very similarly to GCE.

Transforming high-dimensional potential energy surfaces into sum-of-products form using Monte Carlo methods

NASA Astrophysics Data System (ADS)

Schröder, Markus; Meyer, Hans-Dieter

2017-08-01

We propose a Monte Carlo method, "Monte Carlo Potfit," for transforming high-dimensional potential energy surfaces evaluated on discrete grid points into a sum-of-products form, more precisely into a Tucker form. To this end we use a variational ansatz in which we replace numerically exact integrals with Monte Carlo integrals. This largely reduces the numerical cost by avoiding the evaluation of the potential on all grid points and allows a treatment of surfaces up to 15-18 degrees of freedom. We furthermore show that the error made with this ansatz can be controlled and vanishes in certain limits. We present calculations on the potential of HFCO to demonstrate the features of the algorithm. To demonstrate the power of the method, we transformed a 15D potential of the protonated water dimer (Zundel cation) in a sum-of-products form and calculated the ground and lowest 26 vibrationally excited states of the Zundel cation with the multi-configuration time-dependent Hartree method.

Three friendly walkers

NASA Astrophysics Data System (ADS)

Jensen, Iwan

2017-01-01

More than 15 years ago Guttmann and Vöge (2002 J. Stat. Plan. Inference 101 107), introduced a model of friendly walkers. Since then it has remained unsolved. In this paper we provide the exact solution to a closely allied model which essentially only differs in the boundary conditions. The exact solution is expressed in terms of the reciprocal of the generating function for vicious walkers which is a D-finite function. However, ratios of D-finite functions are inherently not D-finite and in this case we prove that the friendly walkers generating function is the solution to a non-linear differential equation with polynomial coefficients, it is in other words D-algebraic. We find using numerically exact calculations a conjectured expression for the generating function of the original model as a ratio of a D-finite function and the generating function for vicious walkers. We obtain an expression for this D-finite function in terms of a {{}2}{{F}1} hypergeometric function with a rational pullback and its first and second derivatives. Dedicated to Tony Guttmann on the occasion of his 70th birthday.

Resolving power for the diffusion orientation distribution function.

PubMed

Jensen, Jens H; Helpern, Joseph A

2016-08-01

The diffusion orientation distribution function (dODF) is primarily used for white matter fiber tractography. Here the resolving power of the dODF is investigated for a simple diffusion model of two intersecting axonal fiber bundles. The resolving power for the dODF is evaluated using the Sparrow criterion. This is determined for the exact dODF and also for q-space imaging (QSI), q-ball, and kurtosis approximations. Based on theoretical and numerical calculations, the resolving power is found to depend on the eigenvalues of the diffusion model and on the degree of radial weighting for the dODF. The resolving powers of the QSI and q-ball dODFs improve with increased b-value. The kurtosis dODF has a resolving power similar to that of the exact dODF. The dODFs, whether exact or approximate, have finite resolving powers that limit their sensitivity to fiber crossings. The resolving powers for the different dODFs considered here provide convenient benchmarks for assessing and comparing their performance. Magn Reson Med 76:679-688, 2016. © 2015 Wiley Periodicals, Inc. © 2015 Wiley Periodicals, Inc.

Numerical Uncertainty Analysis for Computational Fluid Dynamics using Student T Distribution -- Application of CFD Uncertainty Analysis Compared to Exact Analytical Solution

NASA Technical Reports Server (NTRS)

Groves, Curtis E.; Ilie, marcel; Shallhorn, Paul A.

2014-01-01

Computational Fluid Dynamics (CFD) is the standard numerical tool used by Fluid Dynamists to estimate solutions to many problems in academia, government, and industry. CFD is known to have errors and uncertainties and there is no universally adopted method to estimate such quantities. This paper describes an approach to estimate CFD uncertainties strictly numerically using inputs and the Student-T distribution. The approach is compared to an exact analytical solution of fully developed, laminar flow between infinite, stationary plates. It is shown that treating all CFD input parameters as oscillatory uncertainty terms coupled with the Student-T distribution can encompass the exact solution.

Kuramoto model with uniformly spaced frequencies: Finite-N asymptotics of the locking threshold.

PubMed

Ottino-Löffler, Bertrand; Strogatz, Steven H

2016-06-01

We study phase locking in the Kuramoto model of coupled oscillators in the special case where the number of oscillators, N, is large but finite, and the oscillators' natural frequencies are evenly spaced on a given interval. In this case, stable phase-locked solutions are known to exist if and only if the frequency interval is narrower than a certain critical width, called the locking threshold. For infinite N, the exact value of the locking threshold was calculated 30 years ago; however, the leading corrections to it for finite N have remained unsolved analytically. Here we derive an asymptotic formula for the locking threshold when N≫1. The leading correction to the infinite-N result scales like either N^{-3/2} or N^{-1}, depending on whether the frequencies are evenly spaced according to a midpoint rule or an end-point rule. These scaling laws agree with numerical results obtained by Pazó [D. Pazó, Phys. Rev. E 72, 046211 (2005)PLEEE81539-375510.1103/PhysRevE.72.046211]. Moreover, our analysis yields the exact prefactors in the scaling laws, which also match the numerics.

Worldline approach for numerical computation of electromagnetic Casimir energies: Scalar field coupled to magnetodielectric media

DOE Office of Scientific and Technical Information (OSTI.GOV)

Mackrory, Jonathan B.; Bhattacharya, Tanmoy; Steck, Daniel A.

Here, we present a worldline method for the calculation of Casimir energies for scalar fields coupled to magnetodielectric media. The scalar model we consider may be applied in arbitrary geometries, and it corresponds exactly to one polarization of the electromagnetic field in planar layered media. Starting from the field theory for electromagnetism, we work with the two decoupled polarizations in planar media and develop worldline path integrals, which represent the two polarizations separately, for computing both Casimir and Casimir-Polder potentials. We then show analytically that the path integrals for the transverse-electric polarization coupled to a dielectric medium converge to themore » proper solutions in certain special cases, including the Casimir-Polder potential of an atom near a planar interface, and the Casimir energy due to two planar interfaces. We also evaluate the path integrals numerically via Monte Carlo path-averaging for these cases, studying the convergence and performance of the resulting computational techniques. Lastly, while these scalar methods are only exact in particular geometries, they may serve as an approximation for Casimir energies for the vector electromagnetic field in other geometries.« less

Worldline approach for numerical computation of electromagnetic Casimir energies: Scalar field coupled to magnetodielectric media

DOE PAGES

Mackrory, Jonathan B.; Bhattacharya, Tanmoy; Steck, Daniel A.

2016-10-12

Here, we present a worldline method for the calculation of Casimir energies for scalar fields coupled to magnetodielectric media. The scalar model we consider may be applied in arbitrary geometries, and it corresponds exactly to one polarization of the electromagnetic field in planar layered media. Starting from the field theory for electromagnetism, we work with the two decoupled polarizations in planar media and develop worldline path integrals, which represent the two polarizations separately, for computing both Casimir and Casimir-Polder potentials. We then show analytically that the path integrals for the transverse-electric polarization coupled to a dielectric medium converge to themore » proper solutions in certain special cases, including the Casimir-Polder potential of an atom near a planar interface, and the Casimir energy due to two planar interfaces. We also evaluate the path integrals numerically via Monte Carlo path-averaging for these cases, studying the convergence and performance of the resulting computational techniques. Lastly, while these scalar methods are only exact in particular geometries, they may serve as an approximation for Casimir energies for the vector electromagnetic field in other geometries.« less

Exact solutions for the selection-mutation equilibrium in the Crow-Kimura evolutionary model.

PubMed

Semenov, Yuri S; Novozhilov, Artem S

2015-08-01

We reformulate the eigenvalue problem for the selection-mutation equilibrium distribution in the case of a haploid asexually reproduced population in the form of an equation for an unknown probability generating function of this distribution. The special form of this equation in the infinite sequence limit allows us to obtain analytically the steady state distributions for a number of particular cases of the fitness landscape. The general approach is illustrated by examples; theoretical findings are compared with numerical calculations. Copyright © 2015. Published by Elsevier Inc.

Application of the Kishimoto-Tamura boson expansion theory to a single-j shell model

DOE Office of Scientific and Technical Information (OSTI.GOV)

Li, C.T.; Pedrocchi, V.G.; Tamura, T.

1985-11-01

The boson expansion theory of Kishimoto and Tamura is applied to a single-j shell model. It is shown that this theory is quite accurate, giving results that agree very closely with those of the exact fermion calculations. The fast convergence of the boson expansion is also demonstrated. A critical discussion is then made of an earlier paper by Arima, in which he stated that the Kishimoto-Tamura theory gives rise to very poor numerical results. The source of the trouble encountered by Arima is unmasked.

Space-Time Error Representation and Estimation in Navier-Stokes Calculations

NASA Technical Reports Server (NTRS)

Barth, Timothy J.

2006-01-01

The mathematical framework for a-posteriori error estimation of functionals elucidated by Eriksson et al. [7] and Becker and Rannacher [3] is revisited in a space-time context. Using these theories, a hierarchy of exact and approximate error representation formulas are presented for use in error estimation and mesh adaptivity. Numerical space-time results for simple model problems as well as compressible Navier-Stokes flow at Re = 300 over a 2D circular cylinder are then presented to demonstrate elements of the error representation theory for time-dependent problems.

Pump Spectral Bandwidth, Birefringence, and Entanglement in Type-II Parametric Down Conversion

DOE PAGES

Erenso, Daniel

2009-01-01

The twin photons produced by a type-II spontaneous parametric down conversion are well know as a potential source of photons for quantum teleportation due to the strong entanglement in polarization. This strong entanglement in polarization, however, depends on the spectral composition of the pump photon and the nature of optical isotropy of the crystal. By exact numerical calculation of the concurrence, we have shown that how pump photons spectral width and the birefringence nature of the crystal directly affect the degree of polarization entanglement of the twin photons.

Modelling the phase curve and occultation of WASP-43b with SPIDERMAN

NASA Astrophysics Data System (ADS)

Louden, Tom

2017-06-01

Presenting SPIDERMAN, a fast code for calculating exoplanet phase curves and secondary eclipses with arbitrary two dimensional surface brightness distributions. SPIDERMAN uses an exact geometric algorithm to calculate the area of sub-regions of the planet that are occulted by the star, with no loss in numerical precision. The speed of this calculation makes it possible to run MCMCs to marginalise effectively over the underlying parameters controlling the brightness distribution of exoplanets. The code is fully open source and available over Github. We apply the code to the phase curve of WASP-43b using an analytical surface brightness distribution, and find an excellent fit to the data. We are able to place direct constraints on the physics of heat transport in the atmosphere, such as the ratio between advective and radiative timescales at different altitudes.

Exact thermal density functional theory for a model system: Correlation components and accuracy of the zero-temperature exchange-correlation approximation

DOE PAGES

Smith, J. C.; Pribram-Jones, A.; Burke, K.

2016-06-14

Thermal density functional theory calculations often use the Mermin-Kohn-Sham scheme, but employ ground-state approximations to the exchange-correlation (XC) free energy. In the simplest solvable nontrivial model, an asymmetric Hubbard dimer, we calculate the exact many-body energies and the exact Mermin-Kohn-Sham functionals for this system and extract the exact XC free energy. For moderate temperatures and weak correlation, we find this approximation to be excellent. Here we extract various exact free-energy correlation components and the exact adiabatic connection formula.

Exact thermal density functional theory for a model system: Correlation components and accuracy of the zero-temperature exchange-correlation approximation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Smith, J. C.; Pribram-Jones, A.; Burke, K.

Thermal density functional theory calculations often use the Mermin-Kohn-Sham scheme, but employ ground-state approximations to the exchange-correlation (XC) free energy. In the simplest solvable nontrivial model, an asymmetric Hubbard dimer, we calculate the exact many-body energies and the exact Mermin-Kohn-Sham functionals for this system and extract the exact XC free energy. For moderate temperatures and weak correlation, we find this approximation to be excellent. Here we extract various exact free-energy correlation components and the exact adiabatic connection formula.

Ground-state properties of Na2IrO3 determined from an ab initio Hamiltonian and its extensions containing Kitaev and extended Heisenberg interactions

NASA Astrophysics Data System (ADS)

Okubo, Tsuyoshi; Shinjo, Kazuya; Yamaji, Youhei; Kawashima, Naoki; Sota, Shigetoshi; Tohyama, Takami; Imada, Masatoshi

2017-08-01

We investigate the ground state properties of Na2IrO3 based on numerical calculations of the recently proposed ab initio Hamiltonian represented by Kitaev and extended Heisenberg interactions. To overcome the limitation posed by small tractable system sizes in the exact diagonalization study employed in a previous study [Y. Yamaji et al., Phys. Rev. Lett. 113, 107201 (2014), 10.1103/PhysRevLett.113.107201], we apply a two-dimensional density matrix renormalization group and an infinite-size tensor-network method. By calculating at much larger system sizes, we critically test the validity of the exact diagonalization results. The results consistently indicate that the ground state of Na2IrO3 is a magnetically ordered state with zigzag configuration in agreement with experimental observations and the previous diagonalization study. Applications of the two independent methods in addition to the exact diagonalization study further uncover a consistent and rich phase diagram near the zigzag phase beyond the accessibility of the exact diagonalization. For example, in the parameter space away from the ab initio value of Na2IrO3 controlled by the trigonal distortion, we find three phases: (i) an ordered phase with the magnetic moment aligned mutually in 120 degrees orientation on every third hexagon, (ii) a magnetically ordered phase with a 16-site unit cell, and (iii) an ordered phase with presumably incommensurate periodicity of the moment. It suggests that potentially rich magnetic structures may appear in A2IrO3 compounds for A other than Na. The present results also serve to establish the accuracy of the first-principles approach in reproducing the available experimental results thereby further contributing to finding a route to realize the Kitaev spin liquid.

Full-dimensional quantum calculations of vibrational levels of NH 4 + and isotopomers on an accurate ab initio potential energy surface

DOE PAGES

Hua -Gen Yu; Han, Huixian; Guo, Hua

2016-03-29

Vibrational energy levels of the ammonium cation (NH 4 +) and its deuterated isotopomers are calculated using a numerically exact kinetic energy operator on a recently developed nine-dimensional permutation invariant semiglobal potential energy surface fitted to a large number of high-level ab initio points. Like CH4, the vibrational levels of NH 4 + and ND 4 + exhibit a polyad structure, characterized by a collective quantum number P = 2(v 1 + v 3) + v 2 + v 4. As a result, the low-lying vibrational levels of all isotopomers are assigned and the agreement with available experimental data ismore » better than 1 cm –1.« less

Top++: A program for the calculation of the top-pair cross-section at hadron colliders

NASA Astrophysics Data System (ADS)

Czakon, Michał; Mitov, Alexander

2014-11-01

We present the program Top++ for the numerical evaluation of the total inclusive cross-section for producing top quark pairs at hadron colliders. The program calculates the cross-section in (a) fixed order approach with exact next-to-next-to leading order (NNLO) accuracy and (b) by including soft-gluon resummation for the hadronic cross-section in Mellin space with full next-to-next-to-leading logarithmic (NNLL) accuracy. The program offers the user significant flexibility through the large number (29) of available options. Top++ is written in C++. It has a very simple to use interface that is intuitive and directly reflects the physics. The running of the program requires no programming experience from the user.

Thermal ionization of Cs Rydberg states

NASA Astrophysics Data System (ADS)

Glukhov, I. L.; Ovsiannikov, V. D.

2009-01-01

Rates Pnl of photoionization from Rydberg ns-, np-, nd-states of a valence electron in Cs, induced by black-body radiation, were calculated on the basis of the modified Fues model potential method. The numerical data were approximated with a three-term expression which reproduces in a simple analytical form the dependence of Pnl on the ambient temperature T and on the principal quantum number n. The comparison between approximate and exactly calculated values of the thermal ionization rate demonstrates the applicability of the proposed approximation for highly excited states with n from 20 to 100 in a wide temperature range of T from 100 to 10,000 K. We present coefficients of this approximation for the s-, p- and d-series of Rydberg states.

Angular-momentum couplings in ultra-long-range giant dipole molecules

NASA Astrophysics Data System (ADS)

Stielow, Thomas; Scheel, Stefan; Kurz, Markus

2018-02-01

In this article we extend the theory of ultra-long-range giant dipole molecules, formed by an atom in a giant dipole state and a ground-state alkali-metal atom, by angular-momentum couplings known from recent works on Rydberg molecules. In addition to s -wave scattering, the next higher order of p -wave scattering in the Fermi pseudopotential describing the binding mechanism is considered. Furthermore, the singlet and triplet channels of the scattering interaction as well as angular-momentum couplings such as hyperfine interaction and Zeeman interactions are included. Within the framework of Born-Oppenheimer theory, potential energy surfaces are calculated in both first-order perturbation theory and exact diagonalization. Besides the known pure triplet states, mixed-spin character states are obtained, opening up a whole new landscape of molecular potentials. We determine exact binding energies and wave functions of the nuclear rotational and vibrational motion numerically from the various potential energy surfaces.

Preliminary study of the effects of a reversible chemical reaction on gas bubble dissolution. [for space glass refining

NASA Technical Reports Server (NTRS)

Weinberg, M. C.

1982-01-01

A preliminary investigation is carried out of the effects of a reversible chemical reaction on the dissolution of an isolated, stationary gas bubble in a glass melt. The exact governing equations for the model system are formulated and analyzed. The approximate quasi-steady-state version of these equations is solved analytically, and a calculation is made of bubble dissolution rates. The results are then compared with numerical solutions obtained from the finite difference form of the exact governing equations. It is pointed out that in the microgravity condition of space, the buoyant rise of a gas bubble in a glass melt will be negligible on the time scale of most experiments. For this reason, a determination of the behavior of a stationary gas bubble in a melt is relevant for an understanding of glass refining in space.

Drude weight of the spin-(1)/(2) XXZ chain: Density matrix renormalization group versus exact diagonalization

NASA Astrophysics Data System (ADS)

Karrasch, C.; Hauschild, J.; Langer, S.; Heidrich-Meisner, F.

2013-06-01

We revisit the problem of the spin Drude weight D of the integrable spin-1/2 XXZ chain using two complementary approaches, exact diagonalization (ED) and the time-dependent density-matrix renormalization group (tDMRG). We pursue two main goals. First, we present extensive results for the temperature dependence of D. By exploiting time translation invariance within tDMRG, one can extract D for significantly lower temperatures than in previous tDMRG studies. Second, we discuss the numerical quality of the tDMRG data and elaborate on details of the finite-size scaling of the ED results, comparing calculations carried out in the canonical and grand-canonical ensembles. Furthermore, we analyze the behavior of the Drude weight as the point with SU(2)-symmetric exchange is approached and discuss the relative contribution of the Drude weight to the sum rule as a function of temperature.

A simple extension of Roe's scheme for real gases

DOE Office of Scientific and Technical Information (OSTI.GOV)

Arabi, Sina, E-mail: sina.arabi@polymtl.ca; Trépanier, Jean-Yves; Camarero, Ricardo

The purpose of this paper is to develop a highly accurate numerical algorithm to model real gas flows in local thermodynamic equilibrium (LTE). The Euler equations are solved using a finite volume method based on Roe's flux difference splitting scheme including real gas effects. A novel algorithm is proposed to calculate the Jacobian matrix which satisfies the flux difference splitting exactly in the average state for a general equation of state. This algorithm increases the robustness and accuracy of the method, especially around the contact discontinuities and shock waves where the gas properties jump appreciably. The results are compared withmore » an exact solution of the Riemann problem for the shock tube which considers the real gas effects. In addition, the method is applied to a blunt cone to illustrate the capability of the proposed extension in solving two dimensional flows.« less

Photoproduction of dileptons and photons in p -p collisions at the Large Hadron Collider energies

NASA Astrophysics Data System (ADS)

Ma, Zhi-Lei; Zhu, Jia-Qing

2018-03-01

The production of large pT dileptons and photons originating from photoproduction processes in p-p collisions at Large Hadron Collider energies is calculated. The comparisons between the exact treatment results and the ones of the equivalent photon approximation approach are expressed as the Q2 (the virtuality of photon) and pT distributions. The method developed by Martin and Ryskin is used for avoiding double counting when the coherent and incoherent contributions are considered simultaneously. The numerical results indicate that the equivalent photon approximation is only effective in small Q2 region and can be used for coherent photoproduction processes with proper choice of Qmax2 (the choices Qmax2˜s ^ or ∞ will cause obvious errors), but cannot be used for incoherent photoproduction processes. The exact treatment is needed to deal accurately with the photoproduction of large pT dileptons and photons.

Aberration analysis and calculation in system of Gaussian beam illuminates lenslet array

NASA Astrophysics Data System (ADS)

Zhao, Zhu; Hui, Mei; Zhou, Ping; Su, Tianquan; Feng, Yun; Zhao, Yuejin

2014-09-01

Low order aberration was founded when focused Gaussian beam imaging at Kodak KAI -16000 image detector, which is integrated with lenslet array. Effect of focused Gaussian beam and numerical simulation calculation of the aberration were presented in this paper. First, we set up a model of optical imaging system based on previous experiment. Focused Gaussian beam passed through a pinhole and was received by Kodak KAI -16000 image detector whose microlenses of lenslet array were exactly focused on sensor surface. Then, we illustrated the characteristics of focused Gaussian beam and the effect of relative space position relations between waist of Gaussian beam and front spherical surface of microlenses to the aberration. Finally, we analyzed the main element of low order aberration and calculated the spherical aberration caused by lenslet array according to the results of above two steps. Our theoretical calculations shown that , the numerical simulation had a good agreement with the experimental result. Our research results proved that spherical aberration was the main element and made up about 93.44% of the 48 nm error, which was demonstrated in previous experiment. The spherical aberration is inversely proportional to the value of divergence distance between microlens and waist, and directly proportional to the value of the Gaussian beam waist radius.

Improvement and performance evaluation of the perturbation source method for an exact Monte Carlo perturbation calculation in fixed source problems

NASA Astrophysics Data System (ADS)

Sakamoto, Hiroki; Yamamoto, Toshihiro

2017-09-01

This paper presents improvement and performance evaluation of the "perturbation source method", which is one of the Monte Carlo perturbation techniques. The formerly proposed perturbation source method was first-order accurate, although it is known that the method can be easily extended to an exact perturbation method. A transport equation for calculating an exact flux difference caused by a perturbation is solved. A perturbation particle representing a flux difference is explicitly transported in the perturbed system, instead of in the unperturbed system. The source term of the transport equation is defined by the unperturbed flux and the cross section (or optical parameter) changes. The unperturbed flux is provided by an "on-the-fly" technique during the course of the ordinary fixed source calculation for the unperturbed system. A set of perturbation particle is started at the collision point in the perturbed region and tracked until death. For a perturbation in a smaller portion of the whole domain, the efficiency of the perturbation source method can be improved by using a virtual scattering coefficient or cross section in the perturbed region, forcing collisions. Performance is evaluated by comparing the proposed method to other Monte Carlo perturbation methods. Numerical tests performed for a particle transport in a two-dimensional geometry reveal that the perturbation source method is less effective than the correlated sampling method for a perturbation in a larger portion of the whole domain. However, for a perturbation in a smaller portion, the perturbation source method outperforms the correlated sampling method. The efficiency depends strongly on the adjustment of the new virtual scattering coefficient or cross section.

Exact finite elements for conduction and convection

NASA Technical Reports Server (NTRS)

Thornton, E. A.; Dechaumphai, P.; Tamma, K. K.

1981-01-01

An approach for developing exact one dimensional conduction-convection finite elements is presented. Exact interpolation functions are derived based on solutions to the governing differential equations by employing a nodeless parameter. Exact interpolation functions are presented for combined heat transfer in several solids of different shapes, and for combined heat transfer in a flow passage. Numerical results demonstrate that exact one dimensional elements offer advantages over elements based on approximate interpolation functions.

Numerical evidence of fluctuating stripes in the normal state of high-Tc cuprate superconductors

NASA Astrophysics Data System (ADS)

Huang, Edwin W.; Mendl, Christian B.; Liu, Shenxiu; Johnston, Steve; Jiang, Hong-Chen; Moritz, Brian; Devereaux, Thomas P.

2017-12-01

Upon doping, Mott insulators often exhibit symmetry breaking where charge carriers and their spins organize into patterns known as stripes. For high-transition temperature cuprate superconductors, stripes are widely suspected to exist in a fluctuating form. We used numerically exact determinant quantum Monte Carlo calculations to demonstrate dynamical stripe correlations in the three-band Hubbard model, which represents the local electronic structure of the copper-oxygen plane. Our results, which are robust to varying parameters, cluster size, and boundary conditions, support the interpretation of experimental observations such as the hourglass magnetic dispersion and the Yamada plot of incommensurability versus doping in terms of the physics of fluctuating stripes. These findings provide a different perspective on the intertwined orders emerging from the cuprates’ normal state.

Exact decoupling of the Dirac Hamiltonian. II. The generalized Douglas-Kroll-Hess transformation up to arbitrary order.

PubMed

Reiher, Markus; Wolf, Alexander

2004-12-08

In order to achieve exact decoupling of the Dirac Hamiltonian within a unitary transformation scheme, we have discussed in part I of this series that either a purely numerical iterative technique (the Barysz-Sadlej-Snijders method) or a stepwise analytic approach (the Douglas-Kroll-Hess method) are possible. For the evaluation of Douglas-Kroll-Hess Hamiltonians up to a pre-defined order it was shown that a symbolic scheme has to be employed. In this work, an algorithm for this analytic derivation of Douglas-Kroll-Hess Hamiltonians up to any arbitrary order in the external potential is presented. We discuss how an estimate for the necessary order for exact decoupling (within machine precision) for a given system can be determined from the convergence behavior of the Douglas-Kroll-Hess expansion prior to a quantum chemical calculation. Once this maximum order has been accomplished, the spectrum of the positive-energy part of the decoupled Hamiltonian, e.g., for electronic bound states, cannot be distinguished from the corresponding part of the spectrum of the Dirac operator. An efficient scalar-relativistic implementation of the symbolic operations for the evaluation of the positive-energy part of the block-diagonal Hamiltonian is presented, and its accuracy is tested for ground-state energies of one-electron ions over the whole periodic table. Furthermore, the first many-electron calculations employing sixth up to fourteenth order DKH Hamiltonians are presented. (c) 2004 American Institute of Physics.

Surface calculations with asymptotically long-ranged potentials in the full-potential linearized augmented plane-wave method

NASA Astrophysics Data System (ADS)

Ye, Lin-Hui

2015-09-01

Although the supercell method has been widely used for surface calculations, it only works well with short-ranged potentials, but meets difficulty when the potential decays very slowly into the vacuum. Unfortunately, the exact exchange-correlation potential of the density functional theory is asymptotically long ranged, and therefore is not easily handled by use of supercells. This paper illustrates that the authentic slab geometry, another technique for surface calculations, is not affected by this issue: It works equally well with both short- and long-ranged potentials, with the computational cost and the convergence speed being essentially the same. Using the asymptotically long-ranged Becke-Roussel'89 exchange potential as an example, we have calculated six surfaces of various types. We found that accurate potential values can be obtained even in extremely low density regions of more than 100 Å away from the surface. This high performance allows us to explore the asymptotic region, and prove with clean numerical evidence that the Becke-Roussel'89 potential satisfies the correct asymptotic behavior for slab surfaces, as it does for finite systems. Our finding further implies that the Slater component of the exact exchange optimized effective potential is responsible for the asymptotic behavior, not only for jellium slabs, but for slabs of any type. The Becke-Roussel'89 potential may therefore be used to build asymptotically correct model exchange potentials applicable to both finite systems and slab surfaces.

An Exact Separation of the Spin-Free and Spin-Dependent Terms of the Dirac-Coulomb-Breit Hamiltonian

NASA Technical Reports Server (NTRS)

Dyall, Kenneth G.

1994-01-01

The Dirac Hamiltonian is transformed by extracting the operator (sigma x p)/2mc from the small component of the wave function and applying it to the operators of the original Hamiltonian. The resultant operators contain products of Paull matrices that can be rearranged to give spin-free and spin-dependent operators. These operators are the ones encountered in the Breit-Pauli Hamiltonian, as well as some of higher order in alpha(sup 2). However, since the transformation of the original Dirac Hamiltonian is exact, the new Hamiltonian can be used in variational calculations, with or without the spin-dependent terms. The new small component functions have the same symmetry properties as the large component. Use of only the spin-free terms of the new Hamiltonian permits the same factorization over spin variables as in nonrelativistic theory, and therefore all the post-Self-Consistent Field (SCF) machinery of nonrelativistic calculations can be applied. However, the single-particle functions are two-component orbitals having a large and small component, and the SCF methods must be modified accordingly. Numerical examples are presented, and comparisons are made with the spin-free second-order Douglas-Kroll transformed Hamiltonian of Hess.

Toward Exact Number: Young Children Use One-to-one Correspondence to Measure Set Identity but not Numerical Equality

PubMed Central

Izard, Véronique; Streri, Arlette; Spelke, Elizabeth S.

2014-01-01

Exact integer concepts are fundamental to a wide array of human activities, but their origins are obscure. Some have proposed that children are endowed with a system of natural number concepts, whereas others have argued that children construct these concepts by mastering verbal counting or other numeric symbols. This debate remains unresolved, because it is difficult to test children’s mastery of the logic of integer concepts without using symbols to enumerate large sets, and the symbols themselves could be a source of difficulty for children. Here, we introduce a new method, focusing on large quantities and avoiding the use of words or other symbols for numbers, to study children’s understanding of an essential property underlying integer concepts: the relation of exact numerical equality. Children aged 32-36 months, who possessed no symbols for exact numbers beyond 4, were given one-to-one correspondence cues to help them track a set of puppets, and their enumeration of the set was assessed by a non-verbal manual search task. Children used one-to-one correspondence relations to reconstruct exact quantities in sets of 5 or 6 objects, as long as the elements forming the sets remained the same individuals. In contrast, they failed to track exact quantities when one element was added, removed, or substituted for another. These results suggest an alternative to both nativist and symbol-based constructivist theories of the development of natural number concepts: Before learning symbols for exact numbers, children have a partial understanding of the properties of exact numbers. PMID:24680885

Three-dimensional unsteady lifting surface theory in the subsonic range

NASA Technical Reports Server (NTRS)

Kuessner, H. G.

1985-01-01

The methods of the unsteady lifting surface theory are surveyed. Linearized Euler's equations are simplified by means of a Galileo-Lorentz transformation and a Laplace transformation so that the time and the compressibility of the fluid are limited to two constants. The solutions to this simplified problem are represented as integrals with a differential nucleus; these results in tolerance conditions, for which any exact solution must suffice. It is shown that none of the existing three-dimensional lifting surface theories in subsonic range satisfy these conditions. An oscillating elliptic lifting surface which satisfies the tolerance conditions is calculated through the use of Lame's functions. Numerical examples are calculated for the borderline cases of infinitely stretched elliptic lifting surfaces and of circular lifting surfaces. Out of the harmonic solutions any such temporal changes of the down current are calculated through the use of an inverse Laplace transformation.

Exact finite elements for conduction and convection

NASA Technical Reports Server (NTRS)

Thornton, E. A.; Dechaumphai, P.; Tamma, K. K.

1981-01-01

An appproach for developing exact one dimensional conduction-convection finite elements is presented. Exact interpolation functions are derived based on solutions to the governing differential equations by employing a nodeless parameter. Exact interpolation functions are presented for combined heat transfer in several solids of different shapes, and for combined heat transfer in a flow passage. Numerical results demonstrate that exact one dimensional elements offer advantages over elements based on approximate interpolation functions. Previously announced in STAR as N81-31507

Percolation critical polynomial as a graph invariant

DOE PAGES

Scullard, Christian R.

2012-10-18

Every lattice for which the bond percolation critical probability can be found exactly possesses a critical polynomial, with the root in [0; 1] providing the threshold. Recent work has demonstrated that this polynomial may be generalized through a definition that can be applied on any periodic lattice. The polynomial depends on the lattice and on its decomposition into identical finite subgraphs, but once these are specified, the polynomial is essentially unique. On lattices for which the exact percolation threshold is unknown, the polynomials provide approximations for the critical probability with the estimates appearing to converge to the exact answer withmore » increasing subgraph size. In this paper, I show how the critical polynomial can be viewed as a graph invariant like the Tutte polynomial. In particular, the critical polynomial is computed on a finite graph and may be found using the deletion-contraction algorithm. This allows calculation on a computer, and I present such results for the kagome lattice using subgraphs of up to 36 bonds. For one of these, I find the prediction p c = 0:52440572:::, which differs from the numerical value, p c = 0:52440503(5), by only 6:9 X 10 -7.« less

Iterative solution of the inverse Cauchy problem for an elliptic equation by the conjugate gradient method

NASA Astrophysics Data System (ADS)

Vasil'ev, V. I.; Kardashevsky, A. M.; Popov, V. V.; Prokopev, G. A.

2017-10-01

This article presents results of computational experiment carried out using a finite-difference method for solving the inverse Cauchy problem for a two-dimensional elliptic equation. The computational algorithm involves an iterative determination of the missing boundary condition from the override condition using the conjugate gradient method. The results of calculations are carried out on the examples with exact solutions as well as at specifying an additional condition with random errors are presented. Results showed a high efficiency of the iterative method of conjugate gradients for numerical solution

Quantum phases of dimerized and frustrated Heisenberg spin chains with s = 1/2, 1 and 3/2: an entanglement entropy and fidelity study.

PubMed

Goli, V M L Durga Prasad; Sahoo, Shaon; Ramasesha, S; Sen, Diptiman

2013-03-27

We study here different regions in phase diagrams of the spin-1/2, spin-1 and spin-3/2 one-dimensional antiferromagnetic Heisenberg systems with frustration (next-nearest-neighbor interaction J2) and dimerization (δ). In particular, we analyze the behaviors of the bipartite entanglement entropy and fidelity at the gapless to gapped phase transitions and across the lines separating different phases in the J2-δ plane. All the calculations in this work are based on numerical exact diagonalizations of finite systems.

The Quantum Phase-Dynamical Properties of the Squeezed Vacuum State Intensity-Couple Interacting with the Atom

NASA Technical Reports Server (NTRS)

Fan, An-Fu; Sun, Nian-Chun; Zhou, Xin

1996-01-01

The Phase-dynamical properties of the squeezed vacuum state intensity-couple interacting with the two-level atom in an ideal cavity are studied using the Hermitian phase operator formalism. Exact general expressions for the phase distribution and the associated expectation value and variance of the phase operator have been derived. we have also obtained the analytic results of the phase variance for two special cases-weakly and strongly squeezed vacuum. The results calculated numerically show that squeezing has a significant effect on the phase properties of squeezed vacuum.

Landau-Zener extension of the Tavis-Cummings model: Structure of the solution

DOE PAGES

Sun, Chen; Sinitsyn, Nikolai A.

2016-09-07

We explore the recently discovered solution of the driven Tavis-Cummings model (DTCM). It describes interaction of an arbitrary number of two-level systems with a bosonic mode that has linearly time-dependent frequency. We derive compact and tractable expressions for transition probabilities in terms of the well-known special functions. In this form, our formulas are suitable for fast numerical calculations and analytical approximations. As an application, we obtain the semiclassical limit of the exact solution and compare it to prior approximations. Furthermore, we also reveal connection between DTCM and q-deformed binomial statistics.

Investigating decoherence in a simple system

NASA Technical Reports Server (NTRS)

Albrecht, Andreas

1991-01-01

The results of some simple calculations designed to study quantum decoherence are presented. The physics of quantum decoherence are briefly reviewed, and a very simple 'toy' model is analyzed. Exact solutions are found using numerical techniques. The type of incoherence exhibited by the model can be changed by varying a coupling strength. The author explains why the conventional approach to studying decoherence by checking the diagonality of the density matrix is not always adequate. Two other approaches, the decoherence functional and the Schmidt paths approach, are applied to the toy model and contrasted to each other. Possible problems with each are discussed.

Wigner molecules in carbon-nanotube quantum dots

NASA Astrophysics Data System (ADS)

Secchi, Andrea; Rontani, Massimo

2010-07-01

We demonstrate that electrons in quantum dots defined by electrostatic gates in semiconductor nanotubes freeze orderly in space realizing a “Wigner molecule.” Our exact diagonalization calculations uncover the features of the electron molecule, which may be accessed by tunneling spectroscopy—indeed some of them have already been observed by Deshpande and Bockrath [Nat. Phys. 4, 314 (2008)]10.1038/nphys895. We show that numerical results are satisfactorily reproduced by a simple ansatz vibrational wave function: electrons have localized wave functions, like nuclei in an ordinary molecule, whereas low-energy excitations are collective vibrations of electrons around their equilibrium positions.

Quantum Quenches and Relaxation Dynamics in the Thermodynamic Limit

NASA Astrophysics Data System (ADS)

Mallayya, Krishnanand; Rigol, Marcos

2018-02-01

We implement numerical linked cluster expansions (NLCEs) to study dynamics of lattice systems following quantum quenches, and focus on a hard-core boson model in one-dimensional lattices. We find that, in the nonintegrable regime and within the accessible times, local observables exhibit exponential relaxation. We determine the relaxation rate as one departs from the integrable point and show that it scales quadratically with the strength of the integrability breaking perturbation. We compare the NLCE results with those from exact diagonalization calculations on finite chains with periodic boundary conditions, and show that NLCEs are far more accurate.

Voltage Quench Dynamics of a Kondo System.

PubMed

Antipov, Andrey E; Dong, Qiaoyuan; Gull, Emanuel

2016-01-22

We examine the dynamics of a correlated quantum dot in the mixed valence regime. We perform numerically exact calculations of the current after a quantum quench from equilibrium by rapidly applying a bias voltage in a wide range of initial temperatures. The current exhibits short equilibration times and saturates upon the decrease of temperature at all times, indicating Kondo behavior both in the transient regime and in the steady state. The time-dependent current saturation temperature connects the equilibrium Kondo temperature to a substantially increased value at voltages outside of the linear response. These signatures are directly observable by experiments in the time domain.

Visualization of electronic density

DOE PAGES

Grosso, Bastien; Cooper, Valentino R.; Pine, Polina; ...

2015-04-22

An atom’s volume depends on its electronic density. Although this density can only be evaluated exactly for hydrogen-like atoms, there are many excellent numerical algorithms and packages to calculate it for other materials. 3D visualization of charge density is challenging, especially when several molecular/atomic levels are intertwined in space. We explore several approaches to 3D charge density visualization, including the extension of an anaglyphic stereo visualization application based on the AViz package to larger structures such as nanotubes. We will describe motivations and potential applications of these tools for answering interesting questions about nanotube properties.

Accurate collision-induced line-coupling parameters for the fundamental band of CO in He - Close coupling and coupled states scattering calculations

NASA Technical Reports Server (NTRS)

Green, Sheldon; Boissoles, J.; Boulet, C.

1988-01-01

The first accurate theoretical values for off-diagonal (i.e., line-coupling) pressure-broadening cross sections are presented. Calculations were done for CO perturbed by He at thermal collision energies using an accurate ab initio potential energy surface. Converged close coupling, i.e., numerically exact values, were obtained for coupling to the R(0) and R(2) lines. These were used to test the coupled states (CS) and infinite order sudden (IOS) approximate scattering methods. CS was found to be of quantitative accuracy (a few percent) and has been used to obtain coupling values for lines to R(10). IOS values are less accurate, but, owing to their simplicity, may nonetheless prove useful as has been recently demonstrated.

FDTD subcell graphene model beyond the thin-film approximation

NASA Astrophysics Data System (ADS)

Valuev, Ilya; Belousov, Sergei; Bogdanova, Maria; Kotov, Oleg; Lozovik, Yurii

2017-01-01

A subcell technique for calculation of optical properties of graphene with the finite-difference time-domain (FDTD) method is presented. The technique takes into account the surface conductivity of graphene which allows the correct calculation of its dispersive response for arbitrarily polarized incident waves interacting with the graphene. The developed technique is verified for a planar graphene sheet configuration against the exact analytical solution. Based on the same test case scenario, we also show that the subcell technique demonstrates a superior accuracy and numerical efficiency with respect to the widely used thin-film FDTD approach for modeling graphene. We further apply our technique to the simulations of a graphene metamaterial containing periodically spaced graphene strips (graphene strip-grating) and demonstrate good agreement with the available theoretical results.

Alpha particles diffusion due to charge changes

DOE Office of Scientific and Technical Information (OSTI.GOV)

Clauser, C. F., E-mail: cesar.clauser@ib.edu.ar; Farengo, R.

2015-12-15

Alpha particles diffusion due to charge changes in a magnetized plasma is studied. Analytical calculations and numerical simulations are employed to show that this process can be very important in the pedestal-edge-SOL regions. This is the first study that presents clear evidence of the importance of atomic processes on the diffusion of alpha particles. A simple 1D model that includes inelastic collisions with plasma species, “cold” neutrals, and partially ionized species was employed. The code, which follows the exact particle orbits and includes the effect of inelastic collisions via a Monte Carlo type random process, runs on a graphic processormore » unit (GPU). The analytical and numerical results show excellent agreement when a uniform background (plasma and cold species) is assumed. The simulations also show that the gradients in the density of the plasma and cold species, which are large and opposite in the edge region, produce an inward flux of alpha particles. Calculations of the alpha particles flux reaching the walls or divertor plates should include these processes.« less

Universal corner entanglement of Dirac fermions and gapless bosons from the continuum to the lattice

NASA Astrophysics Data System (ADS)

Helmes, Johannes; Hayward Sierens, Lauren E.; Chandran, Anushya; Witczak-Krempa, William; Melko, Roger G.

2016-09-01

A quantum critical (QC) fluid exhibits universal subleading corrections to the area law of its entanglement entropies. In two dimensions, when the partition involves a corner of angle θ , the subleading term is logarithmic with coefficient aα(θ ) for the α -Rényi entropy. In the smooth limit θ →π ,a1(θ ) yields the central charge of the stress tensor when the QC point is described by a conformal field theory (CFT). For general Rényi indices and angles, aα(θ ) is richer and few general results exist. We study aα(θ ) focusing on two benchmark CFTs, the free Dirac fermion and boson. We perform numerical lattice calculations to obtain high precision results in θ ,α regimes hitherto unexplored. We derive field theory estimates for aα(θ ) , including exact results, and demonstrate an excellent quantitative match with our numerical calculations. We also develop and test strong lower bounds, which apply to both free and interacting QC systems. Finally, we comment on the near collapse of aα(θ ) for various theories, including interacting O (N ) models.

Toward exact number: young children use one-to-one correspondence to measure set identity but not numerical equality.

PubMed

Izard, Véronique; Streri, Arlette; Spelke, Elizabeth S

2014-07-01

Exact integer concepts are fundamental to a wide array of human activities, but their origins are obscure. Some have proposed that children are endowed with a system of natural number concepts, whereas others have argued that children construct these concepts by mastering verbal counting or other numeric symbols. This debate remains unresolved, because it is difficult to test children's mastery of the logic of integer concepts without using symbols to enumerate large sets, and the symbols themselves could be a source of difficulty for children. Here, we introduce a new method, focusing on large quantities and avoiding the use of words or other symbols for numbers, to study children's understanding of an essential property underlying integer concepts: the relation of exact numerical equality. Children aged 32-36 months, who possessed no symbols for exact numbers beyond 4, were given one-to-one correspondence cues to help them track a set of puppets, and their enumeration of the set was assessed by a non-verbal manual search task. Children used one-to-one correspondence relations to reconstruct exact quantities in sets of 5 or 6 objects, as long as the elements forming the sets remained the same individuals. In contrast, they failed to track exact quantities when one element was added, removed, or substituted for another. These results suggest an alternative to both nativist and symbol-based constructivist theories of the development of natural number concepts: Before learning symbols for exact numbers, children have a partial understanding of the properties of exact numbers. Copyright © 2014 The Authors. Published by Elsevier Inc. All rights reserved.

On the efficiency of treating singularities in triatomic variational vibrational computations. The vibrational states of H(+)3 up to dissociation.

PubMed

Szidarovszky, Tamás; Császár, Attila G; Czakó, Gábor

2010-08-01

Several techniques of varying efficiency are investigated, which treat all singularities present in the triatomic vibrational kinetic energy operator given in orthogonal internal coordinates of the two distances-one angle type. The strategies are based on the use of a direct-product basis built from one-dimensional discrete variable representation (DVR) bases corresponding to the two distances and orthogonal Legendre polynomials, or the corresponding Legendre-DVR basis, corresponding to the angle. The use of Legendre functions ensures the efficient treatment of the angular singularity. Matrix elements of the singular radial operators are calculated employing DVRs using the quadrature approximation as well as special DVRs satisfying the boundary conditions and thus allowing for the use of exact DVR expressions. Potential optimized (PO) radial DVRs, based on one-dimensional Hamiltonians with potentials obtained by fixing or relaxing the two non-active coordinates, are also studied. The numerical calculations employed Hermite-DVR, spherical-oscillator-DVR, and Bessel-DVR bases as the primitive radial functions. A new analytical formula is given for the determination of the matrix elements of the singular radial operator using the Bessel-DVR basis. The usually claimed failure of the quadrature approximation in certain singular integrals is revisited in one and three dimensions. It is shown that as long as no potential optimization is carried out the quadrature approximation works almost as well as the exact DVR expressions. If wave functions with finite amplitude at the boundary are to be computed, the basis sets need to meet the required boundary conditions. The present numerical results also confirm that PO-DVRs should be constructed employing relaxed potentials and PO-DVRs can be useful for optimizing quadrature points for calculations applying large coordinate intervals and describing large-amplitude motions. The utility and efficiency of the different algorithms is demonstrated by the computation of converged near-dissociation vibrational energy levels for the H molecular ion.

Numerical evidence of fluctuating stripes in the normal state of high- T c cuprate superconductors

DOE PAGES

Huang, Edwin W.; Mendl, Christian B.; Liu, Shenxiu; ...

2017-12-01

Upon doping, Mott insulators often exhibit symmetry breaking where charge carriers and their spins organize into patterns known as stripes. For high–transition temperature cuprate superconductors, stripes are widely suspected to exist in a fluctuating form. We used numerically exact determinant quantum Monte Carlo calculations to demonstrate dynamical stripe correlations in the three-band Hubbard model, which represents the local electronic structure of the copper-oxygen plane. Our results, which are robust to varying parameters, cluster size, and boundary conditions, support the interpretation of experimental observations such as the hourglass magnetic dispersion and the Yamada plot of incommensurability versus doping in terms ofmore » the physics of fluctuating stripes. Furthermore, these findings provide a different perspective on the intertwined orders emerging from the cuprates’ normal state.« less

Numerical Aspects of Cone Beam Contour Reconstruction

NASA Astrophysics Data System (ADS)

Louis, Alfred K.

2017-12-01

We describe a method for directly calculating the contours of a function from cone beam data. The algorithm is based on a new inversion formula for the gradient of a function presented in Louis (Inverse Probl 32(11):115005, 2016. http://stacks.iop.org/0266-5611/32/i=11/a=115005). The Radon transform of the gradient is found by using a Grangeat type of formula, reducing the inversion problem to the inversion of the Radon transform. In that way the influence of the scanning curve, vital for all exact inversion formulas for complete data, is avoided Numerical results are presented for the circular scanning geometry which neither fulfills the Tuy-Kirillov condition nor the much weaker condition given by the author in Louis (Inverse Probl 32(11):115005, 2016. http://stacks.iop.org/0266-5611/32/i=11/a=115005).

Numerical evidence of fluctuating stripes in the normal state of high- T c cuprate superconductors

DOE Office of Scientific and Technical Information (OSTI.GOV)

Huang, Edwin W.; Mendl, Christian B.; Liu, Shenxiu

Upon doping, Mott insulators often exhibit symmetry breaking where charge carriers and their spins organize into patterns known as stripes. For high–transition temperature cuprate superconductors, stripes are widely suspected to exist in a fluctuating form. We used numerically exact determinant quantum Monte Carlo calculations to demonstrate dynamical stripe correlations in the three-band Hubbard model, which represents the local electronic structure of the copper-oxygen plane. Our results, which are robust to varying parameters, cluster size, and boundary conditions, support the interpretation of experimental observations such as the hourglass magnetic dispersion and the Yamada plot of incommensurability versus doping in terms ofmore » the physics of fluctuating stripes. Furthermore, these findings provide a different perspective on the intertwined orders emerging from the cuprates’ normal state.« less

On the performance of the moment approximation for the numerical computation of fiber stress in turbulent channel flow

NASA Astrophysics Data System (ADS)

Gillissen, J. J. J.; Boersma, B. J.; Mortensen, P. H.; Andersson, H. I.

2007-03-01

Fiber-induced drag reduction can be studied in great detail by means of direct numerical simulation [J. S. Paschkewitz et al., J. Fluid Mech. 518, 281 (2004)]. To account for the effect of the fibers, the Navier-Stokes equations are supplemented by the fiber stress tensor, which depends on the distribution function of fiber orientation angles. We have computed this function in turbulent channel flow, by solving the Fokker-Planck equation numerically. The results are used to validate an approximate method for calculating fiber stress, in which the second moment of the orientation distribution is solved. Since the moment evolution equations contain higher-order moments, a closure relation is required to obtain as many equations as unknowns. We investigate the performance of the eigenvalue-based optimal fitted closure scheme [J. S. Cintra and C. L. Tucker, J. Rheol. 39, 1095 (1995)]. The closure-predicted stress and flow statistics in two-way coupled simulations are within 10% of the "exact" Fokker-Planck solution.

Analysis of Plane-Parallel Electron Beam Propagation in Different Media by Numerical Simulation Methods

NASA Astrophysics Data System (ADS)

Miloichikova, I. A.; Bespalov, V. I.; Krasnykh, A. A.; Stuchebrov, S. G.; Cherepennikov, Yu. M.; Dusaev, R. R.

2018-04-01

Simulation by the Monte Carlo method is widely used to calculate the character of ionizing radiation interaction with substance. A wide variety of programs based on the given method allows users to choose the most suitable package for solving computational problems. In turn, it is important to know exactly restrictions of numerical systems to avoid gross errors. Results of estimation of the feasibility of application of the program PCLab (Computer Laboratory, version 9.9) for numerical simulation of the electron energy distribution absorbed in beryllium, aluminum, gold, and water for industrial, research, and clinical beams are presented. The data obtained using programs ITS and Geant4 being the most popular software packages for solving the given problems and the program PCLab are presented in the graphic form. A comparison and an analysis of the results obtained demonstrate the feasibility of application of the program PCLab for simulation of the absorbed energy distribution and dose of electrons in various materials for energies in the range 1-20 MeV.

Numerical investigation of gapped edge states in fractional quantum Hall-superconductor heterostructures

NASA Astrophysics Data System (ADS)

Repellin, Cécile; Cook, Ashley M.; Neupert, Titus; Regnault, Nicolas

2018-03-01

Fractional quantum Hall-superconductor heterostructures may provide a platform towards non-abelian topological modes beyond Majoranas. However their quantitative theoretical study remains extremely challenging. We propose and implement a numerical setup for studying edge states of fractional quantum Hall droplets with a superconducting instability. The fully gapped edges carry a topological degree of freedom that can encode quantum information protected against local perturbations. We simulate such a system numerically using exact diagonalization by restricting the calculation to the quasihole-subspace of a (time-reversal symmetric) bilayer fractional quantum Hall system of Laughlin ν = 1/3 states. We show that the edge ground states are permuted by spin-dependent flux insertion and demonstrate their fractional 6π Josephson effect, evidencing their topological nature and the Cooper pairing of fractionalized quasiparticles. The versatility and efficiency of our setup make it a well suited method to tackle wider questions of edge phases and phase transitions in fractional quantum Hall systems.

Finite element analysis of wrinkling membranes

NASA Technical Reports Server (NTRS)

Miller, R. K.; Hedgepeth, J. M.; Weingarten, V. I.; Das, P.; Kahyai, S.

1984-01-01

The development of a nonlinear numerical algorithm for the analysis of stresses and displacements in partly wrinkled flat membranes, and its implementation on the SAP VII finite-element code are described. A comparison of numerical results with exact solutions of two benchmark problems reveals excellent agreement, with good convergence of the required iterative procedure. An exact solution of a problem involving axisymmetric deformations of a partly wrinkled shallow curved membrane is also reported.

First-principles calculations of mobility

NASA Astrophysics Data System (ADS)

Krishnaswamy, Karthik

First-principles calculations can be a powerful predictive tool for studying, modeling and understanding the fundamental scattering mechanisms impacting carrier transport in materials. In the past, calculations have provided important qualitative insights, but numerical accuracy has been limited due to computational challenges. In this talk, we will discuss some of the challenges involved in calculating electron-phonon scattering and carrier mobility, and outline approaches to overcome them. Topics will include the limitations of models for electron-phonon interaction, the importance of grid sampling, and the use of Gaussian smearing to replace energy-conserving delta functions. Using prototypical examples of oxides that are of technological importance-SrTiO3, BaSnO3, Ga2O3, and WO3-we will demonstrate computational approaches to overcome these challenges and improve the accuracy. One approach that leads to a distinct improvement in the accuracy is the use of analytic functions for the band dispersion, which allows for an exact solution of the energy-conserving delta function. For select cases, we also discuss direct quantitative comparisons with experimental results. The computational approaches and methodologies discussed in the talk are general and applicable to other materials, and greatly improve the numerical accuracy of the calculated transport properties, such as carrier mobility, conductivity and Seebeck coefficient. This work was performed in collaboration with B. Himmetoglu, Y. Kang, W. Wang, A. Janotti and C. G. Van de Walle, and supported by the LEAST Center, the ONR EXEDE MURI, and NSF.

An Algorithm for the Calculation of Exact Term Discrimination Values.

ERIC Educational Resources Information Center

Willett, Peter

1985-01-01

Reports algorithm for calculation of term discrimination values that is sufficiently fast in operation to permit use of exact values. Evidence is presented to show that relationship between term discrimination and term frequency is crucially dependent upon type of inter-document similarity measure used for calculation of discrimination values. (13…

ADHD and math - The differential effect on calculation and estimation.

PubMed

Ganor-Stern, Dana; Steinhorn, Ofir

2018-05-31

Adults with ADHD were compared to controls when solving multiplication problems exactly and when estimating the results of multidigit multiplication problems relative to reference numbers. The ADHD participants were slower than controls in the exact calculation and in the estimation tasks, but not less accurate. The ADHD participants were similar to controls in showing enhanced accuracy and speed for smaller problem sizes, for trials in which the reference numbers were smaller (vs. larger) than the exact answers and for reference numbers that were far (vs. close) from the exact answer. The two groups similarly used the approximated calculation and the sense of magnitude strategies. They differed however in strategy execution, mainly of the approximated calculation strategy, which requires working memory resources. The increase in reaction time associated with using the approximated calculation strategy was larger for the ADHD compared to the control participants. Thus, ADHD seems to selectively impair calculation processes in estimation tasks that rely on working memory, but it does not hamper estimation skills that are based on sense of magnitude. The educational implications of these findings are discussed. Copyright © 2018. Published by Elsevier B.V.

Exact special twist method for quantum Monte Carlo simulations

NASA Astrophysics Data System (ADS)

Dagrada, Mario; Karakuzu, Seher; Vildosola, Verónica Laura; Casula, Michele; Sorella, Sandro

2016-12-01

We present a systematic investigation of the special twist method introduced by Rajagopal et al. [Phys. Rev. B 51, 10591 (1995), 10.1103/PhysRevB.51.10591] for reducing finite-size effects in correlated calculations of periodic extended systems with Coulomb interactions and Fermi statistics. We propose a procedure for finding special twist values which, at variance with previous applications of this method, reproduce the energy of the mean-field infinite-size limit solution within an adjustable (arbitrarily small) numerical error. This choice of the special twist is shown to be the most accurate single-twist solution for curing one-body finite-size effects in correlated calculations. For these reasons we dubbed our procedure "exact special twist" (EST). EST only needs a fully converged independent-particles or mean-field calculation within the primitive cell and a simple fit to find the special twist along a specific direction in the Brillouin zone. We first assess the performances of EST in a simple correlated model such as the three-dimensional electron gas. Afterwards, we test its efficiency within ab initio quantum Monte Carlo simulations of metallic elements of increasing complexity. We show that EST displays an overall good performance in reducing finite-size errors comparable to the widely used twist average technique but at a much lower computational cost since it involves the evaluation of just one wave function. We also demonstrate that the EST method shows similar performances in the calculation of correlation functions, such as the ionic forces for structural relaxation and the pair radial distribution function in liquid hydrogen. Our conclusions point to the usefulness of EST for correlated supercell calculations; our method will be particularly relevant when the physical problem under consideration requires large periodic cells.

Representation of the exact relativistic electronic Hamiltonian within the regular approximation

NASA Astrophysics Data System (ADS)

Filatov, Michael; Cremer, Dieter

2003-12-01

The exact relativistic Hamiltonian for electronic states is expanded in terms of energy-independent linear operators within the regular approximation. An effective relativistic Hamiltonian has been obtained, which yields in lowest order directly the infinite-order regular approximation (IORA) rather than the zeroth-order regular approximation method. Further perturbational expansion of the exact relativistic electronic energy utilizing the effective Hamiltonian leads to new methods based on ordinary (IORAn) or double [IORAn(2)] perturbation theory (n: order of expansion), which provide improved energies in atomic calculations. Energies calculated with IORA4 and IORA3(2) are accurate up to c-20. Furthermore, IORA is improved by using the IORA wave function to calculate the Rayleigh quotient, which, if minimized, leads to the exact relativistic energy. The outstanding performance of this new IORA method coined scaled IORA is documented in atomic and molecular calculations.

Elementary exact calculations of degree growth and entropy for discrete equations.

PubMed

Halburd, R G

2017-05-01

Second-order discrete equations are studied over the field of rational functions [Formula: see text], where z is a variable not appearing in the equation. The exact degree of each iterate as a function of z can be calculated easily using the standard calculations that arise in singularity confinement analysis, even when the singularities are not confined. This produces elementary yet rigorous entropy calculations.

Quantifying the sensitivity of post-glacial sea level change to laterally varying viscosity

NASA Astrophysics Data System (ADS)

Crawford, Ophelia; Al-Attar, David; Tromp, Jeroen; Mitrovica, Jerry X.; Austermann, Jacqueline; Lau, Harriet C. P.

2018-05-01

We present a method for calculating the derivatives of measurements of glacial isostatic adjustment (GIA) with respect to the viscosity structure of the Earth and the ice sheet history. These derivatives, or kernels, quantify the linearised sensitivity of measurements to the underlying model parameters. The adjoint method is used to enable efficient calculation of theoretically exact sensitivity kernels within laterally heterogeneous earth models that can have a range of linear or non-linear viscoelastic rheologies. We first present a new approach to calculate GIA in the time domain, which, in contrast to the more usual formulation in the Laplace domain, is well suited to continuously varying earth models and to the use of the adjoint method. Benchmarking results show excellent agreement between our formulation and previous methods. We illustrate the potential applications of the kernels calculated in this way through a range of numerical calculations relative to a spherically symmetric background model. The complex spatial patterns of the sensitivities are not intuitive, and this is the first time that such effects are quantified in an efficient and accurate manner.

Dimensional transitions in thermodynamic properties of ideal Maxwell-Boltzmann gases

NASA Astrophysics Data System (ADS)

Aydin, Alhun; Sisman, Altug

2015-04-01

An ideal Maxwell-Boltzmann gas confined in various rectangular nanodomains is considered under quantum size effects. Thermodynamic quantities are calculated from their relations with the partition function, which consists of triple infinite summations over momentum states in each direction. To obtain analytical expressions, summations are converted to integrals for macrosystems by a continuum approximation, which fails at the nanoscale. To avoid both the numerical calculation of summations and the failure of their integral approximations at the nanoscale, a method which gives an analytical expression for a single particle partition function (SPPF) is proposed. It is shown that a dimensional transition in momentum space occurs at a certain magnitude of confinement. Therefore, to represent the SPPF by lower-dimensional analytical expressions becomes possible, rather than numerical calculation of summations. Considering rectangular domains with different aspect ratios, a comparison of the results of derived expressions with those of summation forms of the SPPF is made. It is shown that analytical expressions for the SPPF give very precise results with maximum relative errors of around 1%, 2% and 3% at exactly the transition point for single, double and triple transitions, respectively. Based on dimensional transitions, expressions for free energy, entropy, internal energy, chemical potential, heat capacity and pressure are given analytically valid for any scale.

New numerical approximation of fractional derivative with non-local and non-singular kernel: Application to chaotic models

NASA Astrophysics Data System (ADS)

Toufik, Mekkaoui; Atangana, Abdon

2017-10-01

Recently a new concept of fractional differentiation with non-local and non-singular kernel was introduced in order to extend the limitations of the conventional Riemann-Liouville and Caputo fractional derivatives. A new numerical scheme has been developed, in this paper, for the newly established fractional differentiation. We present in general the error analysis. The new numerical scheme was applied to solve linear and non-linear fractional differential equations. We do not need a predictor-corrector to have an efficient algorithm, in this method. The comparison of approximate and exact solutions leaves no doubt believing that, the new numerical scheme is very efficient and converges toward exact solution very rapidly.

How conservative is Fisher's exact test? A quantitative evaluation of the two-sample comparative binomial trial.

PubMed

Crans, Gerald G; Shuster, Jonathan J

2008-08-15

The debate as to which statistical methodology is most appropriate for the analysis of the two-sample comparative binomial trial has persisted for decades. Practitioners who favor the conditional methods of Fisher, Fisher's exact test (FET), claim that only experimental outcomes containing the same amount of information should be considered when performing analyses. Hence, the total number of successes should be fixed at its observed level in hypothetical repetitions of the experiment. Using conditional methods in clinical settings can pose interpretation difficulties, since results are derived using conditional sample spaces rather than the set of all possible outcomes. Perhaps more importantly from a clinical trial design perspective, this test can be too conservative, resulting in greater resource requirements and more subjects exposed to an experimental treatment. The actual significance level attained by FET (the size of the test) has not been reported in the statistical literature. Berger (J. R. Statist. Soc. D (The Statistician) 2001; 50:79-85) proposed assessing the conservativeness of conditional methods using p-value confidence intervals. In this paper we develop a numerical algorithm that calculates the size of FET for sample sizes, n, up to 125 per group at the two-sided significance level, alpha = 0.05. Additionally, this numerical method is used to define new significance levels alpha(*) = alpha+epsilon, where epsilon is a small positive number, for each n, such that the size of the test is as close as possible to the pre-specified alpha (0.05 for the current work) without exceeding it. Lastly, a sample size and power calculation example are presented, which demonstrates the statistical advantages of implementing the adjustment to FET (using alpha(*) instead of alpha) in the two-sample comparative binomial trial. 2008 John Wiley & Sons, Ltd

Non-equilibrium dynamics from RPMD and CMD.

PubMed

Welsch, Ralph; Song, Kai; Shi, Qiang; Althorpe, Stuart C; Miller, Thomas F

2016-11-28

We investigate the calculation of approximate non-equilibrium quantum time correlation functions (TCFs) using two popular path-integral-based molecular dynamics methods, ring-polymer molecular dynamics (RPMD) and centroid molecular dynamics (CMD). It is shown that for the cases of a sudden vertical excitation and an initial momentum impulse, both RPMD and CMD yield non-equilibrium TCFs for linear operators that are exact for high temperatures, in the t = 0 limit, and for harmonic potentials; the subset of these conditions that are preserved for non-equilibrium TCFs of non-linear operators is also discussed. Furthermore, it is shown that for these non-equilibrium initial conditions, both methods retain the connection to Matsubara dynamics that has previously been established for equilibrium initial conditions. Comparison of non-equilibrium TCFs from RPMD and CMD to Matsubara dynamics at short times reveals the orders in time to which the methods agree. Specifically, for the position-autocorrelation function associated with sudden vertical excitation, RPMD and CMD agree with Matsubara dynamics up to O(t 4 ) and O(t 1 ), respectively; for the position-autocorrelation function associated with an initial momentum impulse, RPMD and CMD agree with Matsubara dynamics up to O(t 5 ) and O(t 2 ), respectively. Numerical tests using model potentials for a wide range of non-equilibrium initial conditions show that RPMD and CMD yield non-equilibrium TCFs with an accuracy that is comparable to that for equilibrium TCFs. RPMD is also used to investigate excited-state proton transfer in a system-bath model, and it is compared to numerically exact calculations performed using a recently developed version of the Liouville space hierarchical equation of motion approach; again, similar accuracy is observed for non-equilibrium and equilibrium initial conditions.

Numerical Solution of the Electron Transport Equation in the Upper Atmosphere

DOE Office of Scientific and Technical Information (OSTI.GOV)

Woods, Mark Christopher; Holmes, Mark; Sailor, William C

A new approach for solving the electron transport equation in the upper atmosphere is derived. The problem is a very stiff boundary value problem, and to obtain an accurate numerical solution, matrix factorizations are used to decouple the fast and slow modes. A stable finite difference method is applied to each mode. This solver is applied to a simplifieed problem for which an exact solution exists using various versions of the boundary conditions that might arise in a natural auroral display. The numerical and exact solutions are found to agree with each other to at least two significant digits.

Continuum theory for cluster morphologies of soft colloids.

PubMed

Kosmrlj, A; Pauschenwein, G J; Kahl, G; Ziherl, P

2011-06-09

We introduce a continuum description of the thermodynamics of colloids with a core-corona architecture. In the case of thick coronas, their overlap can be treated approximately by replacing the exact one-particle density distribution by a suitably shaped step profile, which provides a convenient way of modeling the spherical, columnar, lamellar, and inverted cluster morphologies predicted by numerical simulations and the more involved theories. We use the model to study monodisperse particles with the hard-core/square-shoulder pair interaction as the simplest representatives of the core-corona class. We derive approximate analytical expressions for the enthalpies of the cluster morphologies which offer a clear insight into the mechanisms at work, and we calculate the lattice spacing and the cluster size for all morphologies of the phase sequence as well as the phase-transition pressures. By comparing the results with the exact crystalline minimum-enthalpy configurations, we show that the accuracy of the theory increases with shoulder width. We discuss possible extensions of the theory that could account for the finite-temperature effects.

An improved exceedance theory for combined random stresses

NASA Technical Reports Server (NTRS)

Lester, H. C.

1974-01-01

An extension is presented of Rice's classic solution for the exceedances of a constant level by a single random process to its counterpart for an n-dimensional vector process. An interaction boundary, analogous to the constant level considered by Rice for the one-dimensional case, is assumed in the form of a hypersurface. The theory for the numbers of boundary exceedances is developed by using a joint statistical approach which fully accounts for all cross-correlation effects. An exact expression is derived for the n-dimensional exceedance density function, which is valid for an arbitrary interaction boundary. For application to biaxial states of combined random stress, the general theory is reduced to the two-dimensional case. An elliptical stress interaction boundary is assumed and the exact expression for the density function is presented. The equations are expressed in a format which facilitates calculating the exceedances by numerically evaluating a line integral. The behavior of the density function for the two-dimensional case is briefly discussed.

Lensing in the geodesic light-cone coordinates and its (exact) illustration to an off-center observer in Lemaȋtre-Tolman-Bondi models

DOE Office of Scientific and Technical Information (OSTI.GOV)

Fanizza, G.; Nugier, F., E-mail: giuseppe.fanizza@ba.infn.it, E-mail: fabienjean.nugier@unibo.it

We present in this paper a new application of the geodesic light-cone (GLC) gauge for weak lensing calculations. Using interesting properties of this gauge, we derive an exact expression of the amplification matrix—involving convergence, magnification and shear—and of the deformation matrix—involving the optical scalars. These expressions are simple and non-perturbative as long as no caustics are created on the past light-cone and are, by construction, free from the thin lens approximation. We apply these general expressions on the example of an Lemaȋtre-Tolman-Bondi (LTB) model with an off-center observer and obtain explicit forms for the lensing quantities as a direct consequencemore » of the non-perturbative transformation between GLC and LTB coordinates. We show their evolution in redshift after a numerical integration, for underdense and overdense LTB models, and interpret their respective variations in the simple non-curvature case.« less

Numerical renormalization group calculation of impurity internal energy and specific heat of quantum impurity models

NASA Astrophysics Data System (ADS)

Merker, L.; Costi, T. A.

2012-08-01

We introduce a method to obtain the specific heat of quantum impurity models via a direct calculation of the impurity internal energy requiring only the evaluation of local quantities within a single numerical renormalization group (NRG) calculation for the total system. For the Anderson impurity model we show that the impurity internal energy can be expressed as a sum of purely local static correlation functions and a term that involves also the impurity Green function. The temperature dependence of the latter can be neglected in many cases, thereby allowing the impurity specific heat Cimp to be calculated accurately from local static correlation functions; specifically via Cimp=(∂Eionic)/(∂T)+(1)/(2)(∂Ehyb)/(∂T), where Eionic and Ehyb are the energies of the (embedded) impurity and the hybridization energy, respectively. The term involving the Green function can also be evaluated in cases where its temperature dependence is non-negligible, adding an extra term to Cimp. For the nondegenerate Anderson impurity model, we show by comparison with exact Bethe ansatz calculations that the results recover accurately both the Kondo induced peak in the specific heat at low temperatures as well as the high-temperature peak due to the resonant level. The approach applies to multiorbital and multichannel Anderson impurity models with arbitrary local Coulomb interactions. An application to the Ohmic two-state system and the anisotropic Kondo model is also given, with comparisons to Bethe ansatz calculations. The approach could also be of interest within other impurity solvers, for example, within quantum Monte Carlo techniques.

Fast method to compute scattering by a buried object under a randomly rough surface: PILE combined with FB-SA.

PubMed

Bourlier, Christophe; Kubické, Gildas; Déchamps, Nicolas

2008-04-01

A fast, exact numerical method based on the method of moments (MM) is developed to calculate the scattering from an object below a randomly rough surface. Déchamps et al. [J. Opt. Soc. Am. A23, 359 (2006)] have recently developed the PILE (propagation-inside-layer expansion) method for a stack of two one-dimensional rough interfaces separating homogeneous media. From the inversion of the impedance matrix by block (in which two impedance matrices of each interface and two coupling matrices are involved), this method allows one to calculate separately and exactly the multiple-scattering contributions inside the layer in which the inverses of the impedance matrices of each interface are involved. Our purpose here is to apply this method for an object below a rough surface. In addition, to invert a matrix of large size, the forward-backward spectral acceleration (FB-SA) approach of complexity O(N) (N is the number of unknowns on the interface) proposed by Chou and Johnson [Radio Sci.33, 1277 (1998)] is applied. The new method, PILE combined with FB-SA, is tested on perfectly conducting circular and elliptic cylinders located below a dielectric rough interface obeying a Gaussian process with Gaussian and exponential height autocorrelation functions.

Theoretical treatment of the spin-orbit coupling in the rare gas oxides NeO, ArO, KrO, and XeO

NASA Technical Reports Server (NTRS)

Langhoff, S. R.

1980-01-01

Off-diagonal spin-orbit matrix elements are calculated as a function of internuclear distance for the rare gas oxides NeO, ArO, KrO, and XeO using the full microscopic spin-orbit Hamiltonian, including all one- and two-electron integrals, and POL-CI wave functions comparable to those of Dunning and Hay (1977). A good agreement was found when comparing these results in detail with the calculations of Cohen, Wadt and Hay (1979) that utilize an effective one-electron one-center spin-orbit operator. For the rare gas oxide molecules, it is suggested that the numerical results are a more sensitive test of the wave functions (particularly to the extent of charge transfer) than the exact evaluation of all terms in the full spin-orbit operator.

Visualizing the BEC-BCS crossover in a two-dimensional Fermi gas: Pairing gaps and dynamical response functions from ab initio computations

NASA Astrophysics Data System (ADS)

Vitali, Ettore; Shi, Hao; Qin, Mingpu; Zhang, Shiwei

2017-12-01

Experiments with ultracold atoms provide a highly controllable laboratory setting with many unique opportunities for precision exploration of quantum many-body phenomena. The nature of such systems, with strong interaction and quantum entanglement, makes reliable theoretical calculations challenging. Especially difficult are excitation and dynamical properties, which are often the most directly relevant to experiment. We carry out exact numerical calculations, by Monte Carlo sampling of imaginary-time propagation of Slater determinants, to compute the pairing gap in the two-dimensional Fermi gas from first principles. Applying state-of-the-art analytic continuation techniques, we obtain the spectral function and the density and spin structure factors providing unique tools to visualize the BEC-BCS crossover. These quantities will allow for a direct comparison with experiments.

Capturing nonlocal interaction effects in the Hubbard model: Optimal mappings and limits of applicability

NASA Astrophysics Data System (ADS)

van Loon, E. G. C. P.; Schüler, M.; Katsnelson, M. I.; Wehling, T. O.

2016-10-01

We investigate the Peierls-Feynman-Bogoliubov variational principle to map Hubbard models with nonlocal interactions to effective models with only local interactions. We study the renormalization of the local interaction induced by nearest-neighbor interaction and assess the quality of the effective Hubbard models in reproducing observables of the corresponding extended Hubbard models. We compare the renormalization of the local interactions as obtained from numerically exact determinant quantum Monte Carlo to approximate but more generally applicable calculations using dual boson, dynamical mean field theory, and the random phase approximation. These more approximate approaches are crucial for any application with real materials in mind. Furthermore, we use the dual boson method to calculate observables of the extended Hubbard models directly and benchmark these against determinant quantum Monte Carlo simulations of the effective Hubbard model.

On the Magnetic Squashing Factor and the Lie Transport of Tangents

DOE Office of Scientific and Technical Information (OSTI.GOV)

Scott, Roger B.; Pontin, David I.; Hornig, Gunnar

The squashing factor (or squashing degree) of a vector field is a quantitative measure of the deformation of the field line mapping between two surfaces. In the context of solar magnetic fields, it is often used to identify gradients in the mapping of elementary magnetic flux tubes between various flux domains. Regions where these gradients in the mapping are large are referred to as quasi-separatrix layers (QSLs), and are a continuous extension of separators and separatrix surfaces. These QSLs are observed to be potential sites for the formation of strong electric currents, and are therefore important for the study ofmore » magnetic reconnection in three dimensions. Since the squashing factor, Q , is defined in terms of the Jacobian of the field line mapping, it is most often calculated by first determining the mapping between two surfaces (or some approximation of it) and then numerically differentiating. Tassev and Savcheva have introduced an alternative method, in which they parameterize the change in separation between adjacent field lines, and then integrate along individual field lines to get an estimate of the Jacobian without the need to numerically differentiate the mapping itself. But while their method offers certain computational advantages, it is formulated on a perturbative description of the field line trajectory, and the accuracy of this method is not entirely clear. Here we show, through an alternative derivation, that this integral formulation is, in principle, exact. We then demonstrate the result in the case of a linear, 3D magnetic null, which allows for an exact analytical description and direct comparison to numerical estimates.« less

Numerosity and number signs in deaf Nicaraguan adults

PubMed Central

Flaherty, Molly; Senghas, Ann

2012-01-01

What abilities are entailed in being numerate? Certainly, one is the ability to hold the exact quantity of a set in mind, even as it changes, and even after its members can no longer be perceived. Is counting language necessary to track and reproduce exact quantities? Previous work with speakers of languages that lack number words involved participants only from non-numerate cultures. Deaf Nicaraguan adults all live in a richly numerate culture, but vary in counting ability, allowing us to experimentally differentiate the contribution of these two factors. Thirty deaf and 10 hearing participants performed 11 one-to-one matching and counting tasks. Results suggest that immersion in a numerate culture is not enough to make one fully numerate. A memorized sequence of number symbols is required, though even an unconventional, iconic system is sufficient. Additionally, we find that within a numerate culture, the ability to track precise quantities can be acquired in adulthood. PMID:21899832

Well balancing of the SWE schemes for moving-water steady flows

NASA Astrophysics Data System (ADS)

Caleffi, Valerio; Valiani, Alessandro

2017-08-01

In this work, the exact reproduction of a moving-water steady flow via the numerical solution of the one-dimensional shallow water equations is studied. A new scheme based on a modified version of the HLLEM approximate Riemann solver (Dumbser and Balsara (2016) [18]) that exactly preserves the total head and the discharge in the simulation of smooth steady flows and that correctly dissipates mechanical energy in the presence of hydraulic jumps is presented. This model is compared with a selected set of schemes from the literature, including models that exactly preserve quiescent flows and models that exactly preserve moving-water steady flows. The comparison highlights the strengths and weaknesses of the different approaches. In particular, the results show that the increase in accuracy in the steady state reproduction is counterbalanced by a reduced robustness and numerical efficiency of the models. Some solutions to reduce these drawbacks, at the cost of increased algorithm complexity, are presented.

Accurate Estimate of Some Propagation Characteristics for the First Higher Order Mode in Graded Index Fiber with Simple Analytic Chebyshev Method

NASA Astrophysics Data System (ADS)

Dutta, Ivy; Chowdhury, Anirban Roy; Kumbhakar, Dharmadas

2013-03-01

Using Chebyshev power series approach, accurate description for the first higher order (LP11) mode of graded index fibers having three different profile shape functions are presented in this paper and applied to predict their propagation characteristics. These characteristics include fractional power guided through the core, excitation efficiency and Petermann I and II spot sizes with their approximate analytic formulations. We have shown that where two and three Chebyshev points in LP11 mode approximation present fairly accurate results, the values based on our calculations involving four Chebyshev points match excellently with available exact numerical results.

Two-loop hard-thermal-loop thermodynamics with quarks

NASA Astrophysics Data System (ADS)

Andersen, Jens O.; Petitgirard, Emmanuel; Strickland, Michael

2004-08-01

We calculate the quark contribution to the free energy of a hot quark-gluon plasma to two-loop order using hard-thermal-loop (HTL) perturbation theory. All ultraviolet divergences can be absorbed into renormalizations of the vacuum energy and the HTL quark and gluon mass parameters. The quark and gluon HTL mass parameters are determined self-consistently by a variational prescription. Combining the quark contribution with the two-loop HTL perturbation theory free energy for pure glue we obtain the total two-loop QCD free energy. Comparisons are made with lattice estimates of the free energy for Nf=2 and with exact numerical results obtained in the large-Nf limit.

The Chiral Separation Effect in quenched finite-density QCD

NASA Astrophysics Data System (ADS)

Puhr, Matthias; Buividovich, Pavel

2018-03-01

We present results of a study of the Chiral Separation Effect (CSE) in quenched finite-density QCD. Using a recently developed numerical method we calculate the conserved axial current for exactly chiral overlap fermions at finite density for the first time. We compute the anomalous transport coeffcient for the CSE in the confining and deconfining phase and investigate possible deviations from the universal value. In both phases we find that non-perturbative corrections to the CSE are absent and we reproduce the universal value for the transport coeffcient within small statistical errors. Our results suggest that the CSE can be used to determine the renormalisation factor of the axial current.

Application of the perturbation iteration method to boundary layer type problems.

PubMed

Pakdemirli, Mehmet

2016-01-01

The recently developed perturbation iteration method is applied to boundary layer type singular problems for the first time. As a preliminary work on the topic, the simplest algorithm of PIA(1,1) is employed in the calculations. Linear and nonlinear problems are solved to outline the basic ideas of the new solution technique. The inner and outer solutions are determined with the iteration algorithm and matched to construct a composite expansion valid within all parts of the domain. The solutions are contrasted with the available exact or numerical solutions. It is shown that the perturbation-iteration algorithm can be effectively used for solving boundary layer type problems.

Partition functions of thermally dissociating diatomic molecules and related momentum problem

NASA Astrophysics Data System (ADS)

Buchowiecki, Marcin

2017-11-01

The anharmonicity and ro-vibrational coupling in ro-vibrational partition functions of diatomic molecules are analyzed for the high temperatures of the thermal dissociation regime. The numerically exact partition functions and thermal energies are calculated. At the high temperatures the proper integration of momenta is important if the partition function of the molecule, understood as bounded system, is to be obtained. The problem of proper treatment of momentum is crucial for correctness of high temperature molecular simulations as the decomposition of simulated molecule have to be avoided; the analysis of O2, H2+, and NH3 molecules allows to show importance of βDe value.

Electronic States and Persistent Currents in Nanowire Quantum Ring

NASA Astrophysics Data System (ADS)

Kokurin, I. A.

2018-04-01

The new model of a quantum ring (QR) defined inside a nanowire (NW) is proposed. The one-particle Hamiltonian for electron in [111]-oriented NW QR is constructed taking into account both Rashba and Dresselhaus spin-orbit coupling (SOC). The energy levels as a function of magnetic field are found using the exact numerical diagonalization. The persistent currents (both charge and spin) are calculated. The specificity of SOC and arising anticrossings in energy spectrum lead to unusual features in persistent current behavior. The variation of magnetic field or carrier concentration by means of gate can lead to pure spin persistent current with the charge current being zero.

Towards a feasible implementation of quantum neural networks using quantum dots

DOE Office of Scientific and Technical Information (OSTI.GOV)

Altaisky, Mikhail V., E-mail: altaisky@mx.iki.rssi.ru, E-mail: nzolnik@iki.rssi.ru; Zolnikova, Nadezhda N., E-mail: altaisky@mx.iki.rssi.ru, E-mail: nzolnik@iki.rssi.ru; Kaputkina, Natalia E., E-mail: nataly@misis.ru

2016-03-07

We propose an implementation of quantum neural networks using an array of quantum dots with dipole-dipole interactions. We demonstrate that this implementation is both feasible and versatile by studying it within the framework of GaAs based quantum dot qubits coupled to a reservoir of acoustic phonons. Using numerically exact Feynman integral calculations, we have found that the quantum coherence in our neural networks survive for over a hundred ps even at liquid nitrogen temperatures (77 K), which is three orders of magnitude higher than current implementations, which are based on SQUID-based systems operating at temperatures in the mK range.

Unusual expression of tension of a massless cable with application to the oscillations of a mass suspended to a cable with a variable length

NASA Astrophysics Data System (ADS)

Babaz, Mathieu; Jezequel, Louis; Lamarque, Claude-Henri; Perrard, Patrick

2016-02-01

A new approach of cables' dynamics is presented in this paper. It is based on the exact expression of tension coming from continuum mechanics, while the previous elastic models of cables in open literature consider an approximation of small strain which reduces the cable to a linear spring. The equations of a mass suspended to a massless cable are derived on the basis of this new formulation. The problem is studied and numerically calculated for one and two degrees of freedom. A comparison with the classical approach and a nonlinear analysis are presented.

Joint min-max distribution and Edwards-Anderson's order parameter of the circular 1/f-noise model

NASA Astrophysics Data System (ADS)

Cao, Xiangyu; Le Doussal, Pierre

2016-05-01

We calculate the joint min-max distribution and the Edwards-Anderson's order parameter for the circular model of 1/f-noise. Both quantities, as well as generalisations, are obtained exactly by combining the freezing-duality conjecture and Jack-polynomial techniques. Numerical checks come with significantly improved control of finite-size effects in the glassy phase, and the results convincingly validate the freezing-duality conjecture. Application to diffusive dynamics is discussed. We also provide a formula for the pre-factor ratio of the joint/marginal Carpentier-Le Doussal tail for minimum/maximum which applies to any logarithmic random energy model.

Sparse polynomial space approach to dissipative quantum systems: application to the sub-ohmic spin-boson model.

PubMed

Alvermann, A; Fehske, H

2009-04-17

We propose a general numerical approach to open quantum systems with a coupling to bath degrees of freedom. The technique combines the methodology of polynomial expansions of spectral functions with the sparse grid concept from interpolation theory. Thereby we construct a Hilbert space of moderate dimension to represent the bath degrees of freedom, which allows us to perform highly accurate and efficient calculations of static, spectral, and dynamic quantities using standard exact diagonalization algorithms. The strength of the approach is demonstrated for the phase transition, critical behavior, and dissipative spin dynamics in the spin-boson model.

On the vacuum Einstein equations along curves with a discrete local rotation and reflection symmetry

DOE Office of Scientific and Technical Information (OSTI.GOV)

Korzyński, Mikołaj; Hinder, Ian; Bentivegna, Eloisa, E-mail: korzynski@cft.edu.pl, E-mail: ian.hinder@aei.mpg.de, E-mail: eloisa.bentivegna@ct.infn.it

We discuss the possibility of a dimensional reduction of the Einstein equations in S{sup 3} black-hole lattices. It was reported in previous literature that the evolution of spaces containing curves of local, discrete rotation and reflection symmetry (LDRRS) can be carried out via a system of ODEs along these curves. However, 3+1 Numerical Relativity computations demonstrate that this is not the case, and we show analytically that this is due to the presence of a tensorial quantity which is not suppressed by the symmetry. We calculate the term analytically, and verify numerically for an 8-black-hole lattice that it fully accountsmore » for the anomalous results, and thus quantify its magnitude in this specific case. The presence of this term prevents the exact evolution of these spaces via previously-reported methods which do not involve a full 3+1 integration of Einstein's equation.« less

Lift capability prediction for helicopter rotor blade-numerical evaluation

NASA Astrophysics Data System (ADS)

Rotaru, Constantin; Cîrciu, Ionicǎ; Luculescu, Doru

2016-06-01

The main objective of this paper is to describe the key physical features for modelling the unsteady aerodynamic effects found on helicopter rotor blade operating under nominally attached flow conditions away from stall. The unsteady effects were considered as phase differences between the forcing function and the aerodynamic response, being functions of the reduced frequency, the Mach number and the mode forcing. For a helicopter rotor, the reduced frequency at any blade element can't be exactly calculated but a first order approximation for the reduced frequency gives useful information about the degree of unsteadiness. The sources of unsteady effects were decomposed into perturbations to the local angle of attack and velocity field. The numerical calculus and graphics were made in FLUENT and MAPLE soft environments. This mathematical model is applicable for aerodynamic design of wind turbine rotor blades, hybrid energy systems optimization and aeroelastic analysis.

A matching approach to communicate through the plasma sheath surrounding a hypersonic vehicle

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gao, Xiaotian; Jiang, Binhao, E-mail: jiangbh@hit.edu.cn

2015-06-21

In order to overcome the communication blackout problem suffered by hypersonic vehicles, a matching approach has been proposed for the first time in this paper. It utilizes a double-positive (DPS) material layer surrounding a hypersonic vehicle antenna to match with the plasma sheath enclosing the vehicle. Analytical analysis and numerical results indicate a resonance between the matched layer and the plasma sheath will be formed to mitigate the blackout problem in some conditions. The calculated results present a perfect radiated performance of the antenna, when the match is exactly built between these two layers. The effects of the parameters ofmore » the plasma sheath have been researched by numerical methods. Based on these results, the proposed approach is easier to realize and more flexible to the varying radiated conditions in hypersonic flight comparing with other methods.« less

A Short Research Note on Calculating Exact Distribution Functions and Random Sampling for the 3D NFW Profile

NASA Astrophysics Data System (ADS)

Robotham, A. S. G.; Howlett, Cullan

2018-06-01

In this short note we publish the analytic quantile function for the Navarro, Frenk & White (NFW) profile. All known published and coded methods for sampling from the 3D NFW PDF use either accept-reject, or numeric interpolation (sometimes via a lookup table) for projecting random Uniform samples through the quantile distribution function to produce samples of the radius. This is a common requirement in N-body initial condition (IC), halo occupation distribution (HOD), and semi-analytic modelling (SAM) work for correctly assigning particles or galaxies to positions given an assumed concentration for the NFW profile. Using this analytic description allows for much faster and cleaner code to solve a common numeric problem in modern astronomy. We release R and Python versions of simple code that achieves this sampling, which we note is trivial to reproduce in any modern programming language.

Topological gapped edge states in fractional quantum Hall-superconductor heterostructures

NASA Astrophysics Data System (ADS)

Cook, Ashley; Repellin, Cécile; Regnault, Nicolas; Neupert, Titus

We propose and implement a numerical setup for studying edge states of fractional quantum Hall droplets with a superconducting instability. We focus on a time-reversal symmetric bilayer fractional quantum Hall system of Laughlin ν = 1 / 3 states. The fully gapped edges carry a topological parafermionic degree of freedom that can encode quantum information protected against local perturbations. We numerically simulate such a system using exact diagonalization by restricting the calculation to the Laughlin quasihole subspace. We study the quantization of the total charge on each edge and show that the ground states are permuted by spin flux insertion and the parafermionic Josephson effect, evidencing their topological nature and the Cooper pairing of fractionalized quasiparticles. The full affiliation for Author 3 is: Laboratoire Pierre Aigrain, Ecole Normale Supérieure-PSL Research University, CNRS, Université Pierre et Marie Curie-Sorbonne Universités, Université Paris Diderot-Sorbonne Paris Cité, 24 rue Lhomond, 75231 Paris.

WIND: Computer program for calculation of three dimensional potential compressible flow about wind turbine rotor blades

NASA Technical Reports Server (NTRS)

Dulikravich, D. S.

1980-01-01

A computer program is presented which numerically solves an exact, full potential equation (FPE) for three dimensional, steady, inviscid flow through an isolated wind turbine rotor. The program automatically generates a three dimensional, boundary conforming grid and iteratively solves the FPE while fully accounting for both the rotating cascade and Coriolis effects. The numerical techniques incorporated involve rotated, type dependent finite differencing, a finite volume method, artificial viscosity in conservative form, and a successive line overrelaxation combined with the sequential grid refinement procedure to accelerate the iterative convergence rate. Consequently, the WIND program is capable of accurately analyzing incompressible and compressible flows, including those that are locally transonic and terminated by weak shocks. The program can also be used to analyze the flow around isolated aircraft propellers and helicopter rotors in hover as long as the total relative Mach number of the oncoming flow is subsonic.

Budget of Turbulent Kinetic Energy in a Shock Wave Boundary-Layer Interaction

NASA Technical Reports Server (NTRS)

Vyas, Manan A.; Waindim, Mbu; Gaitonde, Datta V.

2016-01-01

Implicit large-eddy simulation (ILES) of a shock wave/boundary-layer interaction (SBLI) was performed. Quantities present in the exact equation of the turbulent kinetic energy transport were accumulated and used to calculate terms like production, dissipation, molecular diffusion, and turbulent transport. The present results for a turbulent boundary layer were validated by comparison with direct numerical simulation data. It was found that a longer development domain was necessary for the boundary layer to reach an equilibrium state and a finer mesh resolution would improve the predictions. In spite of these findings, trends of the present budget match closely with that of the direct numerical simulation. Budgets for the SBLI region are presented at key axial stations. These budgets showed interesting dynamics as the incoming boundary layer transforms and the terms of the turbulent kinetic energy budget change behavior within the interaction region.

The numeric calculation of eddy current distributions in transcranial magnetic stimulation.

PubMed

Tsuyama, Seichi; Hyodo, Akira; Sekino, Masaki; Hayami, Takehito; Ueno, Shoogo; Iramina, Keiji

2008-01-01

Transcranial magnetic stimulation (TMS) is a method to stimulate neurons in the brain. It is necessary to obtain eddy current distributions and determine parameters such as position, radius and bend-angle of the coil to stimulate target area exactly. In this study, we performed FEM-based numerical simulations of eddy current induced by TMS using three-dimentional human head model with inhomogeneous conductivity. We used double-cone coil and changed the coil radius and bend-angle of coil. The result of computer simulation showed that as coil radius increases, the eddy current became stronger everywhere. And coil with bend-angle of 22.5 degrees induced stronger eddy current than the coil with bendangle of 0 degrees. Meanwhile, when the bend-angle was 45 degrees, eddy current became weaker than these two cases. This simulation allowed us to determine appropriate parameter easier.

Optimised effective potential for ground states, excited states, and time-dependent phenomena

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gross, E.K.U.

1996-12-31

(1) The optimized effective potential method is a variant of the traditional Kohn-Sham scheme. In this variant, the exchange-correlation energy E{sub xc} is an explicit functional of single-particle orbitals. The exchange-correlation potential, given as usual by the functional derivative v{sub xc} = {delta}E{sub xc}/{delta}{rho}, then satisfies as integral equation involving the single-particle orbitals. This integral equation in solved semi-analytically using a scheme recently proposed by Krieger, Li and Iafrate. If the exact (Fock) exchange-energy functional is employed together with the Colle-Salvetti orbital functional for the correlation energy, the mean absolute deviation of the resulting ground-state energies from the exact nonrelativisticmore » values is CT mH for the first-row atoms, as compared to 4.5 mH in a state-of-the-art CI calculation. The proposed scheme is thus significantly more accurate than the conventional Kohn-Sham method while the numerical effort involved is about the same as for an ordinary Hanree-Fock calculation. (2) A time-dependent generalization of the optimized-potential method is presented and applied to the linear-response regime. Since time-dependent density functional theory leads to a formally exact representation of the frequency-dependent linear density response and since the latter, as a function of frequency, has poles at the excitation energies of the fully interacting system, the formalism is suitable for the calculation of excitation energies. A simple additive correction to the Kohn-Sham single-particle excitation energies will be deduced and first results for atomic and molecular singlet and triplet excitation energies will be presented. (3) Beyond the regime of linear response, the time-dependent optimized-potential method is employed to describe atoms in strong emtosecond laser pulses. Ionization yields and harmonic spectra will be presented and compared with experimental data.« less

RT DDA: A hybrid method for predicting the scattering properties by densely packed media

NASA Astrophysics Data System (ADS)

Ramezan Pour, B.; Mackowski, D.

2017-12-01

The most accurate approaches to predicting the scattering properties of particulate media are based on exact solutions of the Maxwell's equations (MEs), such as the T-matrix and discrete dipole methods. Applying these techniques for optically thick targets is challenging problem due to the large-scale computations and are usually substituted by phenomenological radiative transfer (RT) methods. On the other hand, the RT technique is of questionable validity in media with large particle packing densities. In recent works, we used numerically exact ME solvers to examine the effects of particle concentration on the polarized reflection properties of plane parallel random media. The simulations were performed for plane parallel layers of wavelength-sized spherical particles, and results were compared with RT predictions. We have shown that RTE results monotonically converge to the exact solution as the particle volume fraction becomes smaller and one can observe a nearly perfect fit for packing densities of 2%-5%. This study describes the hybrid technique composed of exact and numerical scalar RT methods. The exact methodology in this work is the plane parallel discrete dipole approximation whereas the numerical method is based on the adding and doubling method. This approach not only decreases the computational time owing to the RT method but also includes the interference and multiple scattering effects, so it may be applicable to large particle density conditions.

Improved treatment of exact exchange in Quantum ESPRESSO

DOE PAGES

Barnes, Taylor A.; Kurth, Thorsten; Carrier, Pierre; ...

2017-01-18

Here, we present an algorithm and implementation for the parallel computation of exact exchange in Quantum ESPRESSO (QE) that exhibits greatly improved strong scaling. QE is an open-source software package for electronic structure calculations using plane wave density functional theory, and supports the use of local, semi-local, and hybrid DFT functionals. Wider application of hybrid functionals is desirable for the improved simulation of electronic band energy alignments and thermodynamic properties, but the computational complexity of evaluating the exact exchange potential limits the practical application of hybrid functionals to large systems and requires efficient implementations. We demonstrate that existing implementations ofmore » hybrid DFT that utilize a single data structure for both the local and exact exchange regions of the code are significantly limited in the degree of parallelization achievable. We present a band-pair parallelization approach, in which the calculation of exact exchange is parallelized and evaluated independently from the parallelization of the remainder of the calculation, with the wavefunction data being efficiently transformed on-the-fly into a form that is optimal for each part of the calculation. For a 64 water molecule supercell, our new algorithm reduces the overall time to solution by nearly an order of magnitude.« less

Numerical simulation of KdV equation by finite difference method

NASA Astrophysics Data System (ADS)

Yokus, A.; Bulut, H.

2018-05-01

In this study, the numerical solutions to the KdV equation with dual power nonlinearity by using the finite difference method are obtained. Discretize equation is presented in the form of finite difference operators. The numerical solutions are secured via the analytical solution to the KdV equation with dual power nonlinearity which is present in the literature. Through the Fourier-Von Neumann technique and linear stable, we have seen that the FDM is stable. Accuracy of the method is analyzed via the L2 and L_{∞} norm errors. The numerical, exact approximations and absolute error are presented in tables. We compare the numerical solutions with the exact solutions and this comparison is supported with the graphic plots. Under the choice of suitable values of parameters, the 2D and 3D surfaces for the used analytical solution are plotted.

Numerical method for solving the nonlinear four-point boundary value problems

NASA Astrophysics Data System (ADS)

Lin, Yingzhen; Lin, Jinnan

2010-12-01

In this paper, a new reproducing kernel space is constructed skillfully in order to solve a class of nonlinear four-point boundary value problems. The exact solution of the linear problem can be expressed in the form of series and the approximate solution of the nonlinear problem is given by the iterative formula. Compared with known investigations, the advantages of our method are that the representation of exact solution is obtained in a new reproducing kernel Hilbert space and accuracy of numerical computation is higher. Meanwhile we present the convergent theorem, complexity analysis and error estimation. The performance of the new method is illustrated with several numerical examples.

VAVUQ, Python and Matlab freeware for Verification and Validation, Uncertainty Quantification

NASA Astrophysics Data System (ADS)

Courtney, J. E.; Zamani, K.; Bombardelli, F. A.; Fleenor, W. E.

2015-12-01

A package of scripts is presented for automated Verification and Validation (V&V) and Uncertainty Quantification (UQ) for engineering codes that approximate Partial Differential Equations (PDFs). The code post-processes model results to produce V&V and UQ information. This information can be used to assess model performance. Automated information on code performance can allow for a systematic methodology to assess the quality of model approximations. The software implements common and accepted code verification schemes. The software uses the Method of Manufactured Solutions (MMS), the Method of Exact Solution (MES), Cross-Code Verification, and Richardson Extrapolation (RE) for solution (calculation) verification. It also includes common statistical measures that can be used for model skill assessment. Complete RE can be conducted for complex geometries by implementing high-order non-oscillating numerical interpolation schemes within the software. Model approximation uncertainty is quantified by calculating lower and upper bounds of numerical error from the RE results. The software is also able to calculate the Grid Convergence Index (GCI), and to handle adaptive meshes and models that implement mixed order schemes. Four examples are provided to demonstrate the use of the software for code and solution verification, model validation and uncertainty quantification. The software is used for code verification of a mixed-order compact difference heat transport solver; the solution verification of a 2D shallow-water-wave solver for tidal flow modeling in estuaries; the model validation of a two-phase flow computation in a hydraulic jump compared to experimental data; and numerical uncertainty quantification for 3D CFD modeling of the flow patterns in a Gust erosion chamber.

Revealing Numerical Solutions of a Differential Equation

ERIC Educational Resources Information Center

Glaister, P.

2006-01-01

In this article, the author considers a student exercise that involves determining the exact and numerical solutions of a particular differential equation. He shows how a typical student solution is at variance with a numerical solution, suggesting that the numerical solution is incorrect. However, further investigation shows that this numerical…

Analysis of thin plates with holes by using exact geometrical representation within XFEM.

PubMed

Perumal, Logah; Tso, C P; Leng, Lim Thong

2016-05-01

This paper presents analysis of thin plates with holes within the context of XFEM. New integration techniques are developed for exact geometrical representation of the holes. Numerical and exact integration techniques are presented, with some limitations for the exact integration technique. Simulation results show that the proposed techniques help to reduce the solution error, due to the exact geometrical representation of the holes and utilization of appropriate quadrature rules. Discussion on minimum order of integration order needed to achieve good accuracy and convergence for the techniques presented in this work is also included.

Fully- and weakly-nonlinear biperiodic traveling waves in shallow water

NASA Astrophysics Data System (ADS)

Hirakawa, Tomoaki; Okamura, Makoto

2018-04-01

We directly calculate fully nonlinear traveling waves that are periodic in two independent horizontal directions (biperiodic) in shallow water. Based on the Riemann theta function, we also calculate exact periodic solutions to the Kadomtsev-Petviashvili (KP) equation, which can be obtained by assuming weakly-nonlinear, weakly-dispersive, weakly-two-dimensional waves. To clarify how the accuracy of the biperiodic KP solution is affected when some of the KP approximations are not satisfied, we compare the fully- and weakly-nonlinear periodic traveling waves of various wave amplitudes, wave depths, and interaction angles. As the interaction angle θ decreases, the wave frequency and the maximum wave height of the biperiodic KP solution both increase, and the central peak sharpens and grows beyond the height of the corresponding direct numerical solutions, indicating that the biperiodic KP solution cannot qualitatively model direct numerical solutions for θ ≲ 45^\\circ . To remedy the weak two-dimensionality approximation, we apply the correction of Yeh et al (2010 Eur. Phys. J. Spec. Top. 185 97-111) to the biperiodic KP solution, which substantially improves the solution accuracy and results in wave profiles that are indistinguishable from most other cases.

Exact analytic solution for the spin-up maneuver of an axially symmetric spacecraft

NASA Astrophysics Data System (ADS)

Ventura, Jacopo; Romano, Marcello

2014-11-01

The problem of spinning-up an axially symmetric spacecraft subjected to an external torque constant in magnitude and parallel to the symmetry axis is considered. The existing exact analytic solution for an axially symmetric body is applied for the first time to this problem. The proposed solution is valid for any initial conditions of attitude and angular velocity and for any length of time and rotation amplitude. Furthermore, the proposed solution can be numerically evaluated up to any desired level of accuracy. Numerical experiments and comparison with an existing approximated solution and with the integration of the equations of motion are reported in the paper. Finally, a new approximated solution obtained from the exact one is introduced in this paper.

Rotation relaxation splitting for optimizing parallel RF excitation pulses with T1 - and T2 -relaxations in MRI

NASA Astrophysics Data System (ADS)

Majewski, Kurt

2018-03-01

Exact solutions of the Bloch equations with T1 - and T2 -relaxation terms for piecewise constant magnetic fields are numerically challenging. We therefore investigate an approximation for the achieved magnetization in which rotations and relaxations are split into separate operations. We develop an estimate for its accuracy and explicit first and second order derivatives with respect to the complex excitation radio frequency voltages. In practice, the deviation between an exact solution of the Bloch equations and this rotation relaxation splitting approximation seems negligible. Its computation times are similar to exact solutions without relaxation terms. We apply the developed theory to numerically optimize radio frequency excitation waveforms with T1 - and T2 -relaxations in several examples.

Exact Exchange calculations for periodic systems: a real space approach

NASA Astrophysics Data System (ADS)

Natan, Amir; Marom, Noa; Makmal, Adi; Kronik, Leeor; Kuemmel, Stephan

2011-03-01

We present a real-space method for exact-exchange Kohn-Sham calculations of periodic systems. The method is based on self-consistent solutions of the optimized effective potential (OEP) equation on a three-dimensional non-orthogonal grid, using norm conserving pseudopotentials. These solutions can be either exact, using the S-iteration approach, or approximate, using the Krieger, Li, and Iafrate (KLI) approach. We demonstrate, using a variety of systems, the importance of singularity corrections and use of appropriate pseudopotentials.

Numerical solution of boundary-integral equations for molecular electrostatics.

PubMed

Bardhan, Jaydeep P

2009-03-07

Numerous molecular processes, such as ion permeation through channel proteins, are governed by relatively small changes in energetics. As a result, theoretical investigations of these processes require accurate numerical methods. In the present paper, we evaluate the accuracy of two approaches to simulating boundary-integral equations for continuum models of the electrostatics of solvation. The analysis emphasizes boundary-element method simulations of the integral-equation formulation known as the apparent-surface-charge (ASC) method or polarizable-continuum model (PCM). In many numerical implementations of the ASC/PCM model, one forces the integral equation to be satisfied exactly at a set of discrete points on the boundary. We demonstrate in this paper that this approach to discretization, known as point collocation, is significantly less accurate than an alternative approach known as qualocation. Furthermore, the qualocation method offers this improvement in accuracy without increasing simulation time. Numerical examples demonstrate that electrostatic part of the solvation free energy, when calculated using the collocation and qualocation methods, can differ significantly; for a polypeptide, the answers can differ by as much as 10 kcal/mol (approximately 4% of the total electrostatic contribution to solvation). The applicability of the qualocation discretization to other integral-equation formulations is also discussed, and two equivalences between integral-equation methods are derived.

Interaction and charge transfer between dielectric spheres: Exact and approximate analytical solutions.

PubMed

Lindén, Fredrik; Cederquist, Henrik; Zettergren, Henning

2016-11-21

We present exact analytical solutions for charge transfer reactions between two arbitrarily charged hard dielectric spheres. These solutions, and the corresponding exact ones for sphere-sphere interaction energies, include sums that describe polarization effects to infinite orders in the inverse of the distance between the sphere centers. In addition, we show that these exact solutions may be approximated by much simpler analytical expressions that are useful for many practical applications. This is exemplified through calculations of Langevin type cross sections for forming a compound system of two colliding spheres and through calculations of electron transfer cross sections. We find that it is important to account for dielectric properties and finite sphere sizes in such calculations, which for example may be useful for describing the evolution, growth, and dynamics of nanometer sized dielectric objects such as molecular clusters or dust grains in different environments including astrophysical ones.

No need for external orthogonality in subsystem density-functional theory.

PubMed

Unsleber, Jan P; Neugebauer, Johannes; Jacob, Christoph R

2016-08-03

Recent reports on the necessity of using externally orthogonal orbitals in subsystem density-functional theory (SDFT) [Annu. Rep. Comput. Chem., 8, 2012, 53; J. Phys. Chem. A, 118, 2014, 9182] are re-investigated. We show that in the basis-set limit, supermolecular Kohn-Sham-DFT (KS-DFT) densities can exactly be represented as a sum of subsystem densities, even if the subsystem orbitals are not externally orthogonal. This is illustrated using both an analytical example and in basis-set free numerical calculations for an atomic test case. We further show that even with finite basis sets, SDFT calculations using accurate reconstructed potentials can closely approach the supermolecular KS-DFT density, and that the deviations between SDFT and KS-DFT decrease as the basis-set limit is approached. Our results demonstrate that formally, there is no need to enforce external orthogonality in SDFT, even though this might be a useful strategy when developing projection-based DFT embedding schemes.

Green's Functions from Real-Time Bold-Line Monte Carlo Calculations: Spectral Properties of the Nonequilibrium Anderson Impurity Model

NASA Astrophysics Data System (ADS)

Cohen, Guy; Gull, Emanuel; Reichman, David R.; Millis, Andrew J.

2014-04-01

The nonequilibrium spectral properties of the Anderson impurity model with a chemical potential bias are investigated within a numerically exact real-time quantum Monte Carlo formalism. The two-time correlation function is computed in a form suitable for nonequilibrium dynamical mean field calculations. Additionally, the evolution of the model's spectral properties are simulated in an alternative representation, defined by a hypothetical but experimentally realizable weakly coupled auxiliary lead. The voltage splitting of the Kondo peak is confirmed and the dynamics of its formation after a coupling or gate quench are studied. This representation is shown to contain additional information about the dot's population dynamics. Further, we show that the voltage-dependent differential conductance gives a reasonable qualitative estimate of the equilibrium spectral function, but significant qualitative differences are found including incorrect trends and spurious temperature dependent effects.

Rock climbing: A local-global algorithm to compute minimum energy and minimum free energy pathways.

PubMed

Templeton, Clark; Chen, Szu-Hua; Fathizadeh, Arman; Elber, Ron

2017-10-21

The calculation of minimum energy or minimum free energy paths is an important step in the quantitative and qualitative studies of chemical and physical processes. The computations of these coordinates present a significant challenge and have attracted considerable theoretical and computational interest. Here we present a new local-global approach to study reaction coordinates, based on a gradual optimization of an action. Like other global algorithms, it provides a path between known reactants and products, but it uses a local algorithm to extend the current path in small steps. The local-global approach does not require an initial guess to the path, a major challenge for global pathway finders. Finally, it provides an exact answer (the steepest descent path) at the end of the calculations. Numerical examples are provided for the Mueller potential and for a conformational transition in a solvated ring system.

Incorporation of interfacial roughness into recursion matrix formalism of dynamical X-ray diffraction in multilayers and superlattices.

PubMed

Lobach, Ihar; Benediktovitch, Andrei; Ulyanenkov, Alexander

2017-06-01

Diffraction in multilayers in the presence of interfacial roughness is studied theoretically, the roughness being considered as a transition layer. Exact (within the framework of the two-beam dynamical diffraction theory) differential equations for field amplitudes in a crystalline structure with varying properties along its surface normal are obtained. An iterative scheme for approximate solution of the equations is developed. The presented approach to interfacial roughness is incorporated into the recursion matrix formalism in a way that obviates possible numerical problems. Fitting of the experimental rocking curve is performed in order to test the possibility of reconstructing the roughness value from a diffraction scan. The developed algorithm works substantially faster than the traditional approach to dealing with a transition layer (dividing it into a finite number of thin lamellae). Calculations by the proposed approach are only two to three times longer than calculations for corresponding structures with ideally sharp interfaces.

Language and number: a bilingual training study.

PubMed

Spelke, E S; Tsivkin, S

2001-01-01

Three experiments investigated the role of a specific language in human representations of number. Russian-English bilingual college students were taught new numerical operations (Experiment 1), new arithmetic equations (Experiments 1 and 2), or new geographical or historical facts involving numerical or non-numerical information (Experiment 3). After learning a set of items in each of their two languages, subjects were tested for knowledge of those items, and new items, in both languages. In all the studies, subjects retrieved information about exact numbers more effectively in the language of training, and they solved trained problems more effectively than untrained problems. In contrast, subjects retrieved information about approximate numbers and non-numerical facts with equal efficiency in their two languages, and their training on approximate number facts generalized to new facts of the same type. These findings suggest that a specific, natural language contributes to the representation of large, exact numbers but not to the approximate number representations that humans share with other mammals. Language appears to play a role in learning about exact numbers in a variety of contexts, a finding with implications for practice in bilingual education. The findings prompt more general speculations about the role of language in the development of specifically human cognitive abilities.

Exact image theory for the problem of dielectric/magnetic slab

NASA Technical Reports Server (NTRS)

Lindell, I. V.

1987-01-01

Exact image method, recently introduced for the exact solution of electromagnetic field problems involving homogeneous half spaces and microstrip-like geometries, is developed for the problem of homogeneous slab of dielectric and/or magnetic material in free space. Expressions for image sources, creating the exact reflected and transmitted fields, are given and their numerical evaluation is demonstrated. Nonradiating modes, guided by the slab and responsible for the loss of convergence of the image functions, are considered and extracted. The theory allows, for example, an analysis of finite ground planes in microstrip antenna structures.

The generative basis of natural number concepts.

PubMed

Leslie, Alan M; Gelman, Rochel; Gallistel, C R

2008-06-01

Number concepts must support arithmetic inference. Using this principle, it can be argued that the integer concept of exactly ONE is a necessary part of the psychological foundations of number, as is the notion of the exact equality - that is, perfect substitutability. The inability to support reasoning involving exact equality is a shortcoming in current theories about the development of numerical reasoning. A simple innate basis for the natural number concepts can be proposed that embodies the arithmetic principle, supports exact equality and also enables computational compatibility with real- or rational-valued mental magnitudes.

An exact general remeshing scheme applied to physically conservative voxelization

DOE PAGES

Powell, Devon; Abel, Tom

2015-05-21

We present an exact general remeshing scheme to compute analytic integrals of polynomial functions over the intersections between convex polyhedral cells of old and new meshes. In physics applications this allows one to ensure global mass, momentum, and energy conservation while applying higher-order polynomial interpolation. We elaborate on applications of our algorithm arising in the analysis of cosmological N-body data, computer graphics, and continuum mechanics problems. We focus on the particular case of remeshing tetrahedral cells onto a Cartesian grid such that the volume integral of the polynomial density function given on the input mesh is guaranteed to equal themore » corresponding integral over the output mesh. We refer to this as “physically conservative voxelization.” At the core of our method is an algorithm for intersecting two convex polyhedra by successively clipping one against the faces of the other. This algorithm is an implementation of the ideas presented abstractly by Sugihara [48], who suggests using the planar graph representations of convex polyhedra to ensure topological consistency of the output. This makes our implementation robust to geometric degeneracy in the input. We employ a simplicial decomposition to calculate moment integrals up to quadratic order over the resulting intersection domain. We also address practical issues arising in a software implementation, including numerical stability in geometric calculations, management of cancellation errors, and extension to two dimensions. In a comparison to recent work, we show substantial performance gains. We provide a C implementation intended to be a fast, accurate, and robust tool for geometric calculations on polyhedral mesh elements.« less

Number as a cognitive technology: evidence from Pirahã language and cognition.

PubMed

Frank, Michael C; Everett, Daniel L; Fedorenko, Evelina; Gibson, Edward

2008-09-01

Does speaking a language without number words change the way speakers of that language perceive exact quantities? The Pirahã are an Amazonian tribe who have been previously studied for their limited numerical system [Gordon, P. (2004). Numerical cognition without words: Evidence from Amazonia. Science 306, 496-499]. We show that the Pirahã have no linguistic method whatsoever for expressing exact quantity, not even "one." Despite this lack, when retested on the matching tasks used by Gordon, Pirahã speakers were able to perform exact matches with large numbers of objects perfectly but, as previously reported, they were inaccurate on matching tasks involving memory. These results suggest that language for exact number is a cultural invention rather than a linguistic universal, and that number words do not change our underlying representations of number but instead are a cognitive technology for keeping track of the cardinality of large sets across time, space, and changes in modality.

Path statistics, memory, and coarse-graining of continuous-time random walks on networks

PubMed Central

Kion-Crosby, Willow; Morozov, Alexandre V.

2015-01-01

Continuous-time random walks (CTRWs) on discrete state spaces, ranging from regular lattices to complex networks, are ubiquitous across physics, chemistry, and biology. Models with coarse-grained states (for example, those employed in studies of molecular kinetics) or spatial disorder can give rise to memory and non-exponential distributions of waiting times and first-passage statistics. However, existing methods for analyzing CTRWs on complex energy landscapes do not address these effects. Here we use statistical mechanics of the nonequilibrium path ensemble to characterize first-passage CTRWs on networks with arbitrary connectivity, energy landscape, and waiting time distributions. Our approach can be applied to calculating higher moments (beyond the mean) of path length, time, and action, as well as statistics of any conservative or non-conservative force along a path. For homogeneous networks, we derive exact relations between length and time moments, quantifying the validity of approximating a continuous-time process with its discrete-time projection. For more general models, we obtain recursion relations, reminiscent of transfer matrix and exact enumeration techniques, to efficiently calculate path statistics numerically. We have implemented our algorithm in PathMAN (Path Matrix Algorithm for Networks), a Python script that users can apply to their model of choice. We demonstrate the algorithm on a few representative examples which underscore the importance of non-exponential distributions, memory, and coarse-graining in CTRWs. PMID:26646868

Periodic Anderson model with correlated conduction electrons: Variational and exact diagonalization study

NASA Astrophysics Data System (ADS)

Hagymási, I.; Itai, K.; Sólyom, J.

2012-06-01

We investigate an extended version of the periodic Anderson model (the so-called periodic Anderson-Hubbard model) with the aim to understand the role of interaction between conduction electrons in the formation of the heavy-fermion and mixed-valence states. Two methods are used: (i) variational calculation with the Gutzwiller wave function optimizing numerically the ground-state energy and (ii) exact diagonalization of the Hamiltonian for short chains. The f-level occupancy and the renormalization factor of the quasiparticles are calculated as a function of the energy of the f orbital for a wide range of the interaction parameters. The results obtained by the two methods are in reasonably good agreement for the periodic Anderson model. The agreement is maintained even when the interaction between band electrons, Ud, is taken into account, except for the half-filled case. This discrepancy can be explained by the difference between the physics of the one- and higher-dimensional models. We find that this interaction shifts and widens the energy range of the bare f level, where heavy-fermion behavior can be observed. For large-enough Ud this range may lie even above the bare conduction band. The Gutzwiller method indicates a robust transition from Kondo insulator to Mott insulator in the half-filled model, while Ud enhances the quasiparticle mass when the filling is close to half filling.

Nonadiabatic effects on the charge transfer rate constant: A numerical study of a simple model system

NASA Astrophysics Data System (ADS)

Shin, Seokmin; Metiu, Horia

1995-06-01

We use a minimal model to study the effects of the upper electronic states on the rate of a charge transfer reaction. The model consists of three ions and an electron, all strung on a line. The two ions at the ends of the structure are held fixed, but the middle ion and the electron are allowed to move in one dimension, along the line joining them. The system has two bound states, one in which the electron ties the movable ion to the fixed ion at the left, and the other in which the binding takes place to the fixed ion at the right. The transition between these bound states is a charge transfer reaction. We use the flux-flux correlation function theory to perform two calculations of the rate constant for this reaction. In one we obtain numerically the exact rate constant. In the other we calculate the exact rate constant for the case when the reaction proceeds exclusively on the ground adiabatic state. The difference between these calculations gives the magnitude of the nonadiabatic effects. We find that the nonadiabatic effects are fairly large even when the gap between the ground and the excited adiabatic state substantially exceeds the thermal energy. The rate in the nonadiabatic theory is always smaller than that of the adiabatic one. Both rate constants satisfy the Arrhenius formula. Their activation energies are very close but the nonadiabatic one is always higher. The nonadiabatic preexponential is smaller, due to the fact that the upper electronic state causes an early recrossing of the reactive flux. The description of this reaction in terms of two diabatic states, one for reactants and one for products, is not always adequate. In the limit when nonadiabaticity is small, we need to use a third diabatic state, in which the electron binds to the moving ion as the latter passes through the transition state; this is an atom transfer process. The reaction changes from an atom transfer to an electron transfer, as nonadiabaticity is increased.

Exact method for numerically analyzing a model of local denaturation in superhelically stressed DNA

NASA Astrophysics Data System (ADS)

Fye, Richard M.; Benham, Craig J.

1999-03-01

Local denaturation, the separation at specific sites of the two strands comprising the DNA double helix, is one of the most fundamental processes in biology, required to allow the base sequence to be read both in DNA transcription and in replication. In living organisms this process can be mediated by enzymes which regulate the amount of superhelical stress imposed on the DNA. We present a numerically exact technique for analyzing a model of denaturation in superhelically stressed DNA. This approach is capable of predicting the locations and extents of transition in circular superhelical DNA molecules of kilobase lengths and specified base pair sequences. It can also be used for closed loops of DNA which are typically found in vivo to be kilobases long. The analytic method consists of an integration over the DNA twist degrees of freedom followed by the introduction of auxiliary variables to decouple the remaining degrees of freedom, which allows the use of the transfer matrix method. The algorithm implementing our technique requires O(N2) operations and O(N) memory to analyze a DNA domain containing N base pairs. However, to analyze kilobase length DNA molecules it must be implemented in high precision floating point arithmetic. An accelerated algorithm is constructed by imposing an upper bound M on the number of base pairs that can simultaneously denature in a state. This accelerated algorithm requires O(MN) operations, and has an analytically bounded error. Sample calculations show that it achieves high accuracy (greater than 15 decimal digits) with relatively small values of M (M<0.05N) for kilobase length molecules under physiologically relevant conditions. Calculations are performed on the superhelical pBR322 DNA sequence to test the accuracy of the method. With no free parameters in the model, the locations and extents of local denaturation predicted by this analysis are in quantitatively precise agreement with in vitro experimental measurements. Calculations performed on the fructose-1,6-bisphosphatase gene sequence from yeast show that this approach can also accurately treat in vivo denaturation.

Cumulants of heat transfer across nonlinear quantum systems

NASA Astrophysics Data System (ADS)

Li, Huanan; Agarwalla, Bijay Kumar; Li, Baowen; Wang, Jian-Sheng

2013-12-01

We consider thermal conduction across a general nonlinear phononic junction. Based on two-time observation protocol and the nonequilibrium Green's function method, heat transfer in steady-state regimes is studied, and practical formulas for the calculation of the cumulant generating function are obtained. As an application, the general formalism is used to study anharmonic effects on fluctuation of steady-state heat transfer across a single-site junction with a quartic nonlinear on-site pinning potential. An explicit nonlinear modification to the cumulant generating function exact up to the first order is given, in which the Gallavotti-Cohen fluctuation symmetry is found still valid. Numerically a self-consistent procedure is introduced, which works well for strong nonlinearity.

Generalization of Wilemski-Fixman-Weiss decoupling approximation to the case involving multiple sinks of different sizes, shapes, and reactivities.

PubMed

Uhm, Jesik; Lee, Jinuk; Eun, Changsun; Lee, Sangyoub

2006-08-07

We generalize the Wilemski-Fixman-Weiss decoupling approximation to calculate the transient rate of absorption of point particles into multiple sinks of different sizes, shapes, and reactivities. As an application we consider the case involving two spherical sinks. We obtain a Laplace-transform expression for the transient rate that is in excellent agreement with computer simulations. The long-time steady-state rate has a relatively simple expression, which clearly shows the dependence on the diffusion constant of the particles and on the sizes and reactivities of sinks, and its numerical result is in good agreement with the known exact result that is given in terms of recursion relations.

Exact Solution of Population Redistributions in a Migration Model

NASA Astrophysics Data System (ADS)

Wang, Xue-Wen; Zhang, Li-Jie; Yang, Guo-Hong; Xu, Xin-Jian

2013-10-01

We study a migration model, in which individuals migrate from one community to another. The choices of the source community i and the destination one j are proportional to some power of the population of i (kαi) and j (kβj), respectively. Both analytical calculation and numerical simulation show that the population distribution of communities in stationary states is determined by the parameters α and β. The distribution is widely homogeneous with a characteristic size if α > β. Whereas, for α < β, the distribution is highly heterogeneous with the emergence of condensing phenomenon. Between the two regimes, α = β, the distribution gradually shifts from the nonmonotonous (α < 0) to scale-free (α > 0).

Coulomb interactions in charged fluids.

PubMed

Vernizzi, Graziano; Guerrero-García, Guillermo Iván; de la Cruz, Monica Olvera

2011-07-01

The use of Ewald summation schemes for calculating long-range Coulomb interactions, originally applied to ionic crystalline solids, is a very common practice in molecular simulations of charged fluids at present. Such a choice imposes an artificial periodicity which is generally absent in the liquid state. In this paper we propose a simple analytical O(N(2)) method which is based on Gauss's law for computing exactly the Coulomb interaction between charged particles in a simulation box, when it is averaged over all possible orientations of a surrounding infinite lattice. This method mitigates the periodicity typical of crystalline systems and it is suitable for numerical studies of ionic liquids, charged molecular fluids, and colloidal systems with Monte Carlo and molecular dynamics simulations.

Summing Feynman graphs by Monte Carlo: Planar ϕ3-theory and dynamically triangulated random surfaces

NASA Astrophysics Data System (ADS)

Boulatov, D. V.; Kazakov, V. A.

1988-12-01

New combinatorial identities are suggested relating the ratio of (n - 1)th and nth orders of (planar) perturbation expansion for any quantity to some average over the ensemble of all planar graphs of the nth order. These identities are used for Monte Carlo calculation of critical exponents γstr (string susceptibility) in planar ϕ3-theory and in the dynamically triangulated random surface (DTRS) model near the convergence circle for various dimensions. In the solvable case D = 1 the exact critical properties of the theory are reproduced numerically. After August 3, 1988 the address will be: Cybernetics Council, Academy of Science, ul. Vavilova 40, 117333 Moscow, USSR.

Study of the Effects of Impurities on the Properties of Silicon Materials and Performance of Silicon Solar Cell

NASA Technical Reports Server (NTRS)

Sah, C. T.

1979-01-01

Numerical solutions were obtained from the exact one dimensional transmission line circuit model to study the following effects on the terrestrial performance of silicon solar cells: interband Auger recombination; surface recombination at the contact interfaces; enhanced metallic impurity solubility; diffusion profiles; and defect-impurity recombination centers. Thermal recombination parameters of titanium impurity in silicon were estimated from recent experimental data. Based on those parameters, computer model calculations showed that titanium concentration must be kept below 6x10 to the 12th power Ti/cu cm in order to achieve 16% AM1 efficiency in a silicon solar cell of 250 micrometers thick and 1.5 ohm-cm resistivity.

A new relativistic viscous hydrodynamics code and its application to the Kelvin-Helmholtz instability in high-energy heavy-ion collisions

NASA Astrophysics Data System (ADS)

Okamoto, Kazuhisa; Nonaka, Chiho

2017-06-01

We construct a new relativistic viscous hydrodynamics code optimized in the Milne coordinates. We split the conservation equations into an ideal part and a viscous part, using the Strang spitting method. In the code a Riemann solver based on the two-shock approximation is utilized for the ideal part and the Piecewise Exact Solution (PES) method is applied for the viscous part. We check the validity of our numerical calculations by comparing analytical solutions, the viscous Bjorken's flow and the Israel-Stewart theory in Gubser flow regime. Using the code, we discuss possible development of the Kelvin-Helmholtz instability in high-energy heavy-ion collisions.

An asymptotically exact reduced PDE model for the magnetorotational instability: derivation and numerical simulations

NASA Astrophysics Data System (ADS)

Jamroz, Ben; Julien, Keith; Knobloch, Edgar

2008-12-01

Taking advantage of disparate spatio-temporal scales relevant to astrophysics and laboratory experiments, we derive asymptotically exact reduced partial differential equation models for the magnetorotational instability. These models extend recent single-mode formulations leading to saturation in the presence of weak dissipation, and are characterized by a back-reaction on the imposed shear. Numerical simulations performed for a broad class of initial conditions indicate an initial phase of growth dominated by the optimal (fastest growing) magnetorotational instability fingering mode, followed by a vertical coarsening to a box-filling mode.

A highly accurate finite-difference method with minimum dispersion error for solving the Helmholtz equation

NASA Astrophysics Data System (ADS)

Wu, Zedong; Alkhalifah, Tariq

2018-07-01

Numerical simulation of the acoustic wave equation in either isotropic or anisotropic media is crucial to seismic modeling, imaging and inversion. Actually, it represents the core computation cost of these highly advanced seismic processing methods. However, the conventional finite-difference method suffers from severe numerical dispersion errors and S-wave artifacts when solving the acoustic wave equation for anisotropic media. We propose a method to obtain the finite-difference coefficients by comparing its numerical dispersion with the exact form. We find the optimal finite difference coefficients that share the dispersion characteristics of the exact equation with minimal dispersion error. The method is extended to solve the acoustic wave equation in transversely isotropic (TI) media without S-wave artifacts. Numerical examples show that the method is highly accurate and efficient.

[The relationship between Ridit analysis and rank sum test for one-way ordinal contingency table in medical research].

PubMed

Wang, Ling; Xia, Jie-lai; Yu, Li-li; Li, Chan-juan; Wang, Su-zhen

2008-06-01

To explore several numerical methods of ordinal variable in one-way ordinal contingency table and their interrelationship, and to compare corresponding statistical analysis methods such as Ridit analysis and rank sum test. Formula deduction was based on five simplified grading approaches including rank_r(i), ridit_r(i), ridit_r(ci), ridit_r(mi), and table scores. Practical data set was verified by SAS8.2 in clinical practice (to test the effect of Shiwei solution in treatment for chronic tracheitis). Because of the linear relationship of rank_r(i) = N ridit_r(i) + 1/2 = N ridit_r(ci) = (N + 1) ridit_r(mi), the exact chi2 values in Ridit analysis based on ridit_r(i), ridit_r(ci), and ridit_r(mi), were completely the same, and they were equivalent to the Kruskal-Wallis H test. Traditional Ridit analysis was based on ridit_r(i), and its corresponding chi2 value calculated with an approximate variance (1/12) was conservative. The exact chi2 test of Ridit analysis should be used when comparing multiple groups in the clinical researches because of its special merits such as distribution of mean ridit value on (0,1) and clear graph expression. The exact chi2 test of Ridit analysis can be output directly by proc freq of SAS8.2 with ridit and modridit option (SCORES =). The exact chi2 test of Ridit analysis is equivalent to the Kruskal-Wallis H test, and should be used when comparing multiple groups in the clinical researches.

Mathematical analysis of the boundary-integral based electrostatics estimation approximation for molecular solvation: exact results for spherical inclusions.

PubMed

Bardhan, Jaydeep P; Knepley, Matthew G

2011-09-28

We analyze the mathematically rigorous BIBEE (boundary-integral based electrostatics estimation) approximation of the mixed-dielectric continuum model of molecular electrostatics, using the analytically solvable case of a spherical solute containing an arbitrary charge distribution. Our analysis, which builds on Kirkwood's solution using spherical harmonics, clarifies important aspects of the approximation and its relationship to generalized Born models. First, our results suggest a new perspective for analyzing fast electrostatic models: the separation of variables between material properties (the dielectric constants) and geometry (the solute dielectric boundary and charge distribution). Second, we find that the eigenfunctions of the reaction-potential operator are exactly preserved in the BIBEE model for the sphere, which supports the use of this approximation for analyzing charge-charge interactions in molecular binding. Third, a comparison of BIBEE to the recent GBε theory suggests a modified BIBEE model capable of predicting electrostatic solvation free energies to within 4% of a full numerical Poisson calculation. This modified model leads to a projection-framework understanding of BIBEE and suggests opportunities for future improvements. © 2011 American Institute of Physics

Spike-train spectra and network response functions for non-linear integrate-and-fire neurons.

PubMed

Richardson, Magnus J E

2008-11-01

Reduced models have long been used as a tool for the analysis of the complex activity taking place in neurons and their coupled networks. Recent advances in experimental and theoretical techniques have further demonstrated the usefulness of this approach. Despite the often gross simplification of the underlying biophysical properties, reduced models can still present significant difficulties in their analysis, with the majority of exact and perturbative results available only for the leaky integrate-and-fire model. Here an elementary numerical scheme is demonstrated which can be used to calculate a number of biologically important properties of the general class of non-linear integrate-and-fire models. Exact results for the first-passage-time density and spike-train spectrum are derived, as well as the linear response properties and emergent states of recurrent networks. Given that the exponential integrate-fire model has recently been shown to agree closely with the experimentally measured response of pyramidal cells, the methodology presented here promises to provide a convenient tool to facilitate the analysis of cortical-network dynamics.

Neutrino emission from gamma-ray burst fireballs, revised.

PubMed

Hümmer, Svenja; Baerwald, Philipp; Winter, Walter

2012-06-08

We review the neutrino flux from gamma-ray bursts, which is estimated from gamma-ray observations and used for the interpretation of recent IceCube data, from a particle physics perspective. We numerically calculate the neutrino flux for the same astrophysical assumptions as the analytical fireball neutrino model, including the dominant pion and kaon production modes, flavor mixing, and magnetic field effects on the secondary muons, pions, and kaons. We demonstrate that taking into account the full energy dependencies of all spectra, the normalization of the expected neutrino flux reduces by about one order of magnitude and the spectrum shifts to higher energies, where we can pin down the exact origin of the discrepancies by the recomputation of the analytical models. We also reproduce the IceCube-40 analysis for exactly the same bursts and same assumptions and illustrate the impact of uncertainties. We conclude that the baryonic loading of the fireballs, which is an important control parameter for the emission of cosmic rays, can be constrained significantly with the full-scale experiment after about ten years.

Exact Open Quantum System Dynamics Using the Hierarchy of Pure States (HOPS).

PubMed

Hartmann, Richard; Strunz, Walter T

2017-12-12

We show that the general and numerically exact Hierarchy of Pure States method (HOPS) is very well applicable to calculate the reduced dynamics of an open quantum system. In particular, we focus on environments with a sub-Ohmic spectral density (SD) resulting in an algebraic decay of the bath correlation function (BCF). The universal applicability of HOPS, reaching from weak to strong coupling for zero and nonzero temperature, is demonstrated by solving the spin-boson model for which we find perfect agreement with other methods, each one suitable for a special regime of parameters. The challenges arising in the strong coupling regime are not only reflected in the computational effort needed for the HOPS method to converge but also in the necessity for an importance sampling mechanism, accounted for by the nonlinear variant of HOPS. In order to include nonzero-temperature effects in the strong coupling regime we found that it is highly favorable for the HOPS method to use the zero-temperature BCF and include temperature via a stochastic Hermitian contribution to the system Hamiltonian.

Nonstationary stochastic charge fluctuations of a dust particle in plasmas.

PubMed

Shotorban, B

2011-06-01

Stochastic charge fluctuations of a dust particle that are due to discreteness of electrons and ions in plasmas can be described by a one-step process master equation [T. Matsoukas and M. Russell, J. Appl. Phys. 77, 4285 (1995)] with no exact solution. In the present work, using the system size expansion method of Van Kampen along with the linear noise approximation, a Fokker-Planck equation with an exact Gaussian solution is developed by expanding the master equation. The Gaussian solution has time-dependent mean and variance governed by two ordinary differential equations modeling the nonstationary process of dust particle charging. The model is tested via the comparison of its results to the results obtained by solving the master equation numerically. The electron and ion currents are calculated through the orbital motion limited theory. At various times of the nonstationary process of charging, the model results are in a very good agreement with the master equation results. The deviation is more significant when the standard deviation of the charge is comparable to the mean charge in magnitude.

Exact finite difference schemes for the non-linear unidirectional wave equation

NASA Technical Reports Server (NTRS)

Mickens, R. E.

1985-01-01

Attention is given to the construction of exact finite difference schemes for the nonlinear unidirectional wave equation that describes the nonlinear propagation of a wave motion in the positive x-direction. The schemes constructed for these equations are compared with those obtained by using the usual procedures of numerical analysis. It is noted that the order of the exact finite difference models is equal to the order of the differential equation.

An Astronomical Test of CCD Photometric Precision

NASA Technical Reports Server (NTRS)

Koch, David; Dunham, Edward; Borucki, William; Jenkins, Jon; DeVingenzi, D. (Technical Monitor)

1998-01-01

This article considers a posteriori error estimation of specified functionals for first-order systems of conservation laws discretized using the discontinuous Galerkin (DG) finite element method. Using duality techniques. we derive exact error representation formulas for both linear and nonlinear functionals given an associated bilinear or nonlinear variational form. Weighted residual approximations of the exact error representation formula are then proposed and numerically evaluated for Ringleb flow, an exact solution of the 2-D Euler equations.

Multiple numeric competencies: When a number is not just a number.

PubMed

Peters, Ellen; Bjalkebring, Par

2015-05-01

A growing body of evidence demonstrates the practical and theoretical importance of numeracy in evaluations and choices involving numeric information, an importance that goes beyond simple accuracy in performing mathematical computations. Numeric competency, however, may be multiply determined, but little research has examined potentially separable influences in evaluations and choice. In the present article, we describe 3 numeric competencies and begin to disentangle their effects. Participants (N = 111) completed a series of tasks in 4 1-hr sessions. We first examined relations between objective numeracy, subjective numeracy, and symbolic-number mapping abilities (thought to tap into internal representations of numeric magnitude and the mapping of symbolic numbers onto those representations) using a structural equation model. We then explored their dissociations in numeric and nonnumeric tasks. Higher vs. lower scores in objective numeracy were associated with explicit number operations, including number comparisons and calculations. Those with more vs. less exact mapping had better numeric memory (but not nonnumeric) and produced valuations that were closer to (but did not equal) a risky gamble's expected value, indicating a link with superior number intuitions. Finally, individuals lower vs. higher in subjective numeracy had more negative emotional reactions to numbers and were less motivated and/or confident in numeric tasks. It was less clear whether subjective numeracy might also relate to more general motivations and metacognitions involving nonnumeric information. We conclude that numeric competencies should be used in a more targeted fashion to understand their multiple mechanisms in people's evaluations, choices, and life outcomes. (c) 2015 APA, all rights reserved).

Numerical simulations of strongly correlated electron and spin systems

NASA Astrophysics Data System (ADS)

Changlani, Hitesh Jaiprakash

Developing analytical and numerical tools for strongly correlated systems is a central challenge for the condensed matter physics community. In the absence of exact solutions and controlled analytical approximations, numerical techniques have often contributed to our understanding of these systems. Exact Diagonalization (ED) requires the storage of at least two vectors the size of the Hilbert space under consideration (which grows exponentially with system size) which makes it affordable only for small systems. The Density Matrix Renormalization Group (DMRG) uses an intelligent Hilbert space truncation procedure to significantly reduce this cost, but in its present formulation is limited to quasi-1D systems. Quantum Monte Carlo (QMC) maps the Schrodinger equation to the diffusion equation (in imaginary time) and only samples the eigenvector over time, thereby avoiding the memory limitation. However, the stochasticity involved in the method gives rise to the "sign problem" characteristic of fermion and frustrated spin systems. The first part of this thesis is an effort to make progress in the development of a numerical technique which overcomes the above mentioned problems. We consider novel variational wavefunctions, christened "Correlator Product States" (CPS), that have a general functional form which hopes to capture essential correlations in the ground states of spin and fermion systems in any dimension. We also consider a recent proposal to modify projector (Green's Function) Quantum Monte Carlo to ameliorate the sign problem for realistic and model Hamiltonians (such as the Hubbard model). This exploration led to our own set of improvements, primarily a semistochastic formulation of projector Quantum Monte Carlo. Despite their limitations, existing numerical techniques can yield physical insights into a wide variety of problems. The second part of this thesis considers one such numerical technique - DMRG - and adapts it to study the Heisenberg antiferromagnet on a generic tree graph. Our attention turns to a systematic numerical and semi-analytical study of the effect of local even/odd sublattice imbalance on the low energy spectrum of antiferromagnets on regular Cayley trees. Finally, motivated by previous experiments and theories of randomly diluted antiferromagnets (where an even/odd sublattice imbalance naturally occurs), we present our study of the Heisenberg antiferromagnet on the Cayley tree at the percolation threshold. Our work shows how to detect "emergent" low energy degrees of freedom and compute the effective interactions between them by using data from DMRG calculations.

Conditional spectrum computation incorporating multiple causal earthquakes and ground-motion prediction models

USGS Publications Warehouse

Lin, Ting; Harmsen, Stephen C.; Baker, Jack W.; Luco, Nicolas

2013-01-01

The conditional spectrum (CS) is a target spectrum (with conditional mean and conditional standard deviation) that links seismic hazard information with ground-motion selection for nonlinear dynamic analysis. Probabilistic seismic hazard analysis (PSHA) estimates the ground-motion hazard by incorporating the aleatory uncertainties in all earthquake scenarios and resulting ground motions, as well as the epistemic uncertainties in ground-motion prediction models (GMPMs) and seismic source models. Typical CS calculations to date are produced for a single earthquake scenario using a single GMPM, but more precise use requires consideration of at least multiple causal earthquakes and multiple GMPMs that are often considered in a PSHA computation. This paper presents the mathematics underlying these more precise CS calculations. Despite requiring more effort to compute than approximate calculations using a single causal earthquake and GMPM, the proposed approach produces an exact output that has a theoretical basis. To demonstrate the results of this approach and compare the exact and approximate calculations, several example calculations are performed for real sites in the western United States. The results also provide some insights regarding the circumstances under which approximate results are likely to closely match more exact results. To facilitate these more precise calculations for real applications, the exact CS calculations can now be performed for real sites in the United States using new deaggregation features in the U.S. Geological Survey hazard mapping tools. Details regarding this implementation are discussed in this paper.

Mu- and Tau-Neutrino Spectra Formation in Supernovae

NASA Astrophysics Data System (ADS)

Raffelt, Georg G.

2001-11-01

The μ- and τ-neutrinos emitted from a proto-neutron star are produced by nucleonic bremsstrahlung NN-->NNνν and pair annihilation e+e--->νν, reactions that freeze out at the ``energy sphere.'' Before escaping from there to infinity, the neutrinos diffuse through the ``scattering atmosphere,'' a layer in which their main interaction is elastic scattering on nucleons νN-->Nν. If these collisions are taken to be isoenergetic, as in all numerical supernova simulations, the neutrino flux spectrum escaping to infinity depends only on the medium temperature TES and the thermally averaged optical depth τES at the energy sphere. For τES=10-50, one finds for the spectral flux temperature of the escaping neutrinos Tflux=0.5-0.6TES. Including energy exchange (nucleon recoil) in νN-->Nν can shift Tflux both up and down. ΔTflux depends on τES, on the scattering atmosphere's temperature profile, and on TES. Based on a numerical study, we find that for typical conditions, ΔTflux/Tflux is between -10% and -20% and even for extreme parameter choices does not exceed -30%. The exact value of ΔTflux/Tflux is surprisingly insensitive to the assumed value of the nucleon mass; i.e., the exact efficiency of energy transfer between neutrinos and nucleons is not important as long as it can occur at all. Therefore, calculating the νμ and ντ spectra does not seem to require a precise knowledge of the nuclear medium's dynamical structure functions.

Global Coordinates and Exact Aberration Calculations Applied to Physical Optics Modeling of Complex Optical Systems

NASA Astrophysics Data System (ADS)

Lawrence, G.; Barnard, C.; Viswanathan, V.

1986-11-01

Historically, wave optics computer codes have been paraxial in nature. Folded systems could be modeled by "unfolding" the optical system. Calculation of optical aberrations is, in general, left for the analyst to do with off-line codes. While such paraxial codes were adequate for the simpler systems being studied 10 years ago, current problems such as phased arrays, ring resonators, coupled resonators, and grazing incidence optics require a major advance in analytical capability. This paper describes extension of the physical optics codes GLAD and GLAD V to include a global coordinate system and exact ray aberration calculations. The global coordinate system allows components to be positioned and rotated arbitrarily. Exact aberrations are calculated for components in aligned or misaligned configurations by using ray tracing to compute optical path differences and diffraction propagation. Optical path lengths between components and beam rotations in complex mirror systems are calculated accurately so that coherent interactions in phased arrays and coupled devices may be treated correctly.

A critical comparison of second order closures with direct numerical simulation of homogeneous turbulence

NASA Technical Reports Server (NTRS)

Shih, Tsan-Hsing; Lumley, John L.

1991-01-01

Recently, several second order closure models have been proposed for closing the second moment equations, in which the velocity-pressure gradient (and scalar-pressure gradient) tensor and the dissipation rate tensor are two of the most important terms. In the literature, these correlation tensors are usually decomposed into a so called rapid term and a return-to-isotropy term. Models of these terms have been used in global flow calculations together with other modeled terms. However, their individual behavior in different flows have not been fully examined because they are un-measurable in the laboratory. Recently, the development of direct numerical simulation (DNS) of turbulence has given us the opportunity to do this kind of study. With the direct numerical simulation, we may use the solution to exactly calculate the values of these correlation terms and then directly compare them with the values from their modeled formulations (models). Here, we make direct comparisons of five representative rapid models and eight return-to-isotropy models using the DNS data of forty five homogeneous flows which were done by Rogers et al. (1986) and Lee et al. (1985). The purpose of these direct comparisons is to explore the performance of these models in different flows and identify the ones which give the best performance. The modeling procedure, model constraints, and the various evaluated models are described. The detailed results of the direct comparisons are discussed, and a few concluding remarks on turbulence models are given.

Reproduction of exact solutions of Lipkin model by nonlinear higher random-phase approximation

NASA Astrophysics Data System (ADS)

Terasaki, J.; Smetana, A.; Šimkovic, F.; Krivoruchenko, M. I.

2017-10-01

It is shown that the random-phase approximation (RPA) method with its nonlinear higher generalization, which was previously considered as approximation except for a very limited case, reproduces the exact solutions of the Lipkin model. The nonlinear higher RPA is based on an equation nonlinear on eigenvectors and includes many-particle-many-hole components in the creation operator of the excited states. We demonstrate the exact character of solutions analytically for the particle number N = 2 and numerically for N = 8. This finding indicates that the nonlinear higher RPA is equivalent to the exact Schrödinger equation.

Convergence of high order memory kernels in the Nakajima-Zwanzig generalized master equation and rate constants: Case study of the spin-boson model.

PubMed

Xu, Meng; Yan, Yaming; Liu, Yanying; Shi, Qiang

2018-04-28

The Nakajima-Zwanzig generalized master equation provides a formally exact framework to simulate quantum dynamics in condensed phases. Yet, the exact memory kernel is hard to obtain and calculations based on perturbative expansions are often employed. By using the spin-boson model as an example, we assess the convergence of high order memory kernels in the Nakajima-Zwanzig generalized master equation. The exact memory kernels are calculated by combining the hierarchical equation of motion approach and the Dyson expansion of the exact memory kernel. High order expansions of the memory kernels are obtained by extending our previous work to calculate perturbative expansions of open system quantum dynamics [M. Xu et al., J. Chem. Phys. 146, 064102 (2017)]. It is found that the high order expansions do not necessarily converge in certain parameter regimes where the exact kernel show a long memory time, especially in cases of slow bath, weak system-bath coupling, and low temperature. Effectiveness of the Padé and Landau-Zener resummation approaches is tested, and the convergence of higher order rate constants beyond Fermi's golden rule is investigated.

Convergence of high order memory kernels in the Nakajima-Zwanzig generalized master equation and rate constants: Case study of the spin-boson model

NASA Astrophysics Data System (ADS)

Xu, Meng; Yan, Yaming; Liu, Yanying; Shi, Qiang

2018-04-01

The Nakajima-Zwanzig generalized master equation provides a formally exact framework to simulate quantum dynamics in condensed phases. Yet, the exact memory kernel is hard to obtain and calculations based on perturbative expansions are often employed. By using the spin-boson model as an example, we assess the convergence of high order memory kernels in the Nakajima-Zwanzig generalized master equation. The exact memory kernels are calculated by combining the hierarchical equation of motion approach and the Dyson expansion of the exact memory kernel. High order expansions of the memory kernels are obtained by extending our previous work to calculate perturbative expansions of open system quantum dynamics [M. Xu et al., J. Chem. Phys. 146, 064102 (2017)]. It is found that the high order expansions do not necessarily converge in certain parameter regimes where the exact kernel show a long memory time, especially in cases of slow bath, weak system-bath coupling, and low temperature. Effectiveness of the Padé and Landau-Zener resummation approaches is tested, and the convergence of higher order rate constants beyond Fermi's golden rule is investigated.

Application of the exact exchange potential method for half metallic intermediate band alloy semiconductor.

PubMed

Fernández, J J; Tablero, C; Wahnón, P

2004-06-08

In this paper we present an analysis of the convergence of the band structure properties, particularly the influence on the modification of the bandgap and bandwidth values in half metallic compounds by the use of the exact exchange formalism. This formalism for general solids has been implemented using a localized basis set of numerical functions to represent the exchange density. The implementation has been carried out using a code which uses a linear combination of confined numerical pseudoatomic functions to represent the Kohn-Sham orbitals. The application of this exact exchange scheme to a half-metallic semiconductor compound, in particular to Ga(4)P(3)Ti, a promising material in the field of high efficiency solar cells, confirms the existence of the isolated intermediate band in this compound. (c) 2004 American Institute of Physics.

A Posteriori Error Estimation for Discontinuous Galerkin Approximations of Hyperbolic Systems

NASA Technical Reports Server (NTRS)

Larson, Mats G.; Barth, Timothy J.

1999-01-01

This article considers a posteriori error estimation of specified functionals for first-order systems of conservation laws discretized using the discontinuous Galerkin (DG) finite element method. Using duality techniques, we derive exact error representation formulas for both linear and nonlinear functionals given an associated bilinear or nonlinear variational form. Weighted residual approximations of the exact error representation formula are then proposed and numerically evaluated for Ringleb flow, an exact solution of the 2-D Euler equations.

Modeling of Electromagnetic Scattering by Discrete and Discretely Heterogeneous Random Media by Using Numerically Exact Solutions of the Maxwell Equations

NASA Technical Reports Server (NTRS)

Dlugach, Janna M.; Mishchenko, Michael I.

2017-01-01

In this paper, we discuss some aspects of numerical modeling of electromagnetic scattering by discrete random medium by using numerically exact solutions of the macroscopic Maxwell equations. Typical examples of such media are clouds of interstellar dust, clouds of interplanetary dust in the Solar system, dusty atmospheres of comets, particulate planetary rings, clouds in planetary atmospheres, aerosol particles with numerous inclusions and so on. Our study is based on the results of extensive computations of different characteristics of electromagnetic scattering obtained by using the superposition T-matrix method which represents a direct computer solver of the macroscopic Maxwell equations for an arbitrary multisphere configuration. As a result, in particular, we clarify the range of applicability of the low-density theories of radiative transfer and coherent backscattering as well as of widely used effective-medium approximations.

Numerical solution of the exact cavity equations of motion for an unstable optical resonator.

PubMed

Bowers, M S; Moody, S E

1990-09-20

We solve numerically, we believe for the first time, the exact cavity equations of motion for a realistic unstable resonator with a simple gain saturation model. The cavity equations of motion, first formulated by Siegman ["Exact Cavity Equations for Lasers with Large Output Coupling," Appl. Phys. Lett. 36, 412-414 (1980)], and which we term the dynamic coupled modes (DCM) method of solution, solve for the full 3-D time dependent electric field inside the optical cavity by expanding the field in terms of the actual diffractive transverse eigenmodes of the bare (gain free) cavity with time varying coefficients. The spatially varying gain serves to couple the bare cavity transverse modes and to scatter power from mode to mode. We show that the DCM method numerically converges with respect to the number of eigenmodes in the basis set. The intracavity intensity in the numerical example shown reaches a steady state, and this steady state distribution is compared with that computed from the traditional Fox and Li approach using a fast Fourier transform propagation algorithm. The output wavefronts from both methods are quite similar, and the computed output powers agree to within 10%. The usefulness and advantages of using this method for predicting the output of a laser, especially pulsed lasers used for coherent detection, are discussed.

Approximate Solution Methods for Spectral Radiative Transfer in High Refractive Index Layers

NASA Technical Reports Server (NTRS)

Siegel, R.; Spuckler, C. M.

1994-01-01

Some ceramic materials for high temperature applications are partially transparent for radiative transfer. The refractive indices of these materials can be substantially greater than one which influences internal radiative emission and reflections. Heat transfer behavior of single and laminated layers has been obtained in the literature by numerical solutions of the radiative transfer equations coupled with heat conduction and heating at the boundaries by convection and radiation. Two-flux and diffusion methods are investigated here to obtain approximate solutions using a simpler formulation than required for exact numerical solutions. Isotropic scattering is included. The two-flux method for a single layer yields excellent results for gray and two band spectral calculations. The diffusion method yields a good approximation for spectral behavior in laminated multiple layers if the overall optical thickness is larger than about ten. A hybrid spectral model is developed using the two-flux method in the optically thin bands, and radiative diffusion in bands that are optically thick.

Operational momentum in large-number addition and subtraction by 9-month-olds.

PubMed

McCrink, Koleen; Wynn, Karen

2009-08-01

Recent studies on nonsymbolic arithmetic have illustrated that under conditions that prevent exact calculation, adults display a systematic tendency to overestimate the answers to addition problems and underestimate the answers to subtraction problems. It has been suggested that this operational momentum results from exposure to a culture-specific practice of representing numbers spatially; alternatively, the mind may represent numbers in spatial terms from early in development. In the current study, we asked whether operational momentum is present during infancy, prior to exposure to culture-specific representations of numbers. Infants (9-month-olds) were shown videos of events involving the addition or subtraction of objects with three different types of outcomes: numerically correct, too large, and too small. Infants looked significantly longer only at those incorrect outcomes that violated the momentum of the arithmetic operation (i.e., at too-large outcomes in subtraction events and too-small outcomes in addition events). The presence of operational momentum during infancy indicates developmental continuity in the underlying mechanisms used when operating over numerical representations.

A simple algorithm for beam profile diagnostics using a thermographic camera

DOE Office of Scientific and Technical Information (OSTI.GOV)

Katagiri, Ken; Hojo, Satoru; Honma, Toshihiro

2014-03-15

A new algorithm for digital image processing apparatuses is developed to evaluate profiles of high-intensity DC beams from temperature images of irradiated thin foils. Numerical analyses are performed to examine the reliability of the algorithm. To simulate the temperature images acquired by a thermographic camera, temperature distributions are numerically calculated for 20 MeV proton beams with different parameters. Noise in the temperature images which is added by the camera sensor is also simulated to account for its effect. Using the algorithm, beam profiles are evaluated from the simulated temperature images and compared with exact solutions. We find that niobium ismore » an appropriate material for the thin foil used in the diagnostic system. We also confirm that the algorithm is adaptable over a wide beam current range of 0.11–214 μA, even when employing a general-purpose thermographic camera with rather high noise (ΔT{sub NETD} ≃ 0.3 K; NETD: noise equivalent temperature difference)« less

An assessment of first-order stochastic dispersion theories in porous media

NASA Astrophysics Data System (ADS)

Chin, David A.

1997-12-01

Random realizations of three-dimensional exponentially correlated hydraulic conductivity fields are used in a finite-difference numerical flow model to calculate the mean and covariance of the corresponding Lagrangian-velocity fields. The dispersivity of the porous medium is then determined from the Lagrangian-velocity statistics using the Taylor definition. This estimation procedure is exact, except for numerical errors, and the results are used to assess the accuracy of various first-order dispersion theories in both isotropic and anisotropic porous media. The results show that the Dagan theory is by far the most robust in both isotropic and anisotropic media, producing accurate values of the principal dispersivity components for σy as high as 1.0, In the case of anisotropic media where the flow is at an angle to the principal axis of hydraulic conductivity, it is shown that the dispersivity tensor is rotated away from the flow direction in the non-Fickian phase, but eventually coincides with the flow direction in the Fickian phase.

Do the surface Fermi arcs in Weyl semimetals survive disorder?

NASA Astrophysics Data System (ADS)

Wilson, Justin H.; Pixley, J. H.; Huse, David A.; Refael, Gil; Das Sarma, S.

2018-06-01

We theoretically study the topological robustness of the surface physics induced by Weyl Fermi-arc surface states in the presence of short-ranged quenched disorder and surface-bulk hybridization. This is investigated with numerically exact calculations on a lattice model exhibiting Weyl Fermi arcs. We find that the Fermi-arc surface states, in addition to having a finite lifetime from disorder broadening, hybridize with nonperturbative bulk rare states making them no longer bound to the surface (i.e., they lose their purely surface spectral character). Thus, we provide strong numerical evidence that the Weyl Fermi arcs are not topologically protected from disorder. Nonetheless, the surface chiral velocity is robust and survives in the presence of strong disorder, persisting all the way to the Anderson-localized phase by forming localized current loops that live within the localization length of the surface. Thus, the Weyl semimetal is not topologically robust to the presence of disorder, but the surface chiral velocity is.

Entanglement dynamics of two independent Jaynes-Cummings atoms without the rotating-wave approximation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chen Qinghu; Department of Physics, Zhejiang University, Hangzhou 310027; Yang Yuan

2010-11-15

Entanglement evolution of two independent Jaynes-Cummings atoms without the rotating-wave approximation (RWA) is studied by a numerically exact approach. Previous results based on the RWA are essentially modified in the strong-coupling regime (g{>=}0.1), which has been reached in the recent experiments on the flux qubit coupled to the LC resonator. For the initial Bell state with anticorrelated spins, entanglement sudden death (ESD) is absent in the RWA but does appear in the present numerical calculation without the RWA. Aperiodic entanglement evolution in the strong-coupling regime is observed. The strong atom-cavity coupling facilitates the ESD. The sign of the detuning playsmore » an essential role in the entanglement evolution for strong coupling, which is irrelevant in the RWA. Analytical results based on an unitary transformation are also given, which could not modify the RWA picture essentially. It is suggested that the activation of the photons may be the origin of ESD in this system.« less

Transient well flow in leaky multiple-aquifer systems

NASA Astrophysics Data System (ADS)

Hemker, C. J.

1985-10-01

A previously developed eigenvalue analysis approach to groundwater flow in leaky multiple aquifers is used to derive exact solutions for transient well flow problems in leaky and confined systems comprising any number of aquifers. Equations are presented for the drawdown distribution in systems of infinite extent, caused by wells penetrating one or more of the aquifers completely and discharging each layer at a constant rate. Since the solution obtained may be regarded as a combined analytical-numerical technique, a type of one-dimensional modelling can be applied to find approximate solutions for several complicating conditions. Numerical evaluations are presented as time-drawdown curves and include effects of storage in the aquitard, unconfined conditions, partially penetrating wells and stratified aquifers. The outcome of calculations for relatively simple systems compares very well with published corresponding results. The proposed multilayer solution can be a valuable tool in aquifer test evaluation, as it provides the analytical expression required to enable the application of existing computer methods to the determination of aquifer characteristics.

Static properties of ferromagnetic quantum chains: Numerical results and experimental data on two S=1/2 systems (invited)

NASA Astrophysics Data System (ADS)

Kopinga, K.; Delica, T.; Leschke, H.

1990-05-01

New results of a variant of the numerically exact quantum transfer matrix method have been compared with experimental data on the static properties of [C6H11NH3]CuBr3(CHAB), a ferromagnetic system with about 5% easy-plane anisotropy. Above T=3.5 K, the available data on the zero-field heat capacity, the excess heat capacity ΔC=C(B)-C(B=0), and the magnetization are described with an accuracy comparable to the experimental error. Calculations of the spin-spin correlation functions reveal that the good description of the experimental correlation length in CHAB by a classical spin model is largely accidental. The zero-field susceptibility, which can be deduced from these correlation functions, is in fair agreement with the reported experimental data between 4 and 100 K. The method also seems to yield accurate results for the chlorine isomorph, CHAC, a system with about 2% uniaxial anisotropy.

Application of an NLME-Stochastic Deconvolution Approach to Level A IVIVC Modeling.

PubMed

Kakhi, Maziar; Suarez-Sharp, Sandra; Shepard, Terry; Chittenden, Jason

2017-07-01

Stochastic deconvolution is a parameter estimation method that calculates drug absorption using a nonlinear mixed-effects model in which the random effects associated with absorption represent a Wiener process. The present work compares (1) stochastic deconvolution and (2) numerical deconvolution, using clinical pharmacokinetic (PK) data generated for an in vitro-in vivo correlation (IVIVC) study of extended release (ER) formulations of a Biopharmaceutics Classification System class III drug substance. The preliminary analysis found that numerical and stochastic deconvolution yielded superimposable fraction absorbed (F abs ) versus time profiles when supplied with exactly the same externally determined unit impulse response parameters. In a separate analysis, a full population-PK/stochastic deconvolution was applied to the clinical PK data. Scenarios were considered in which immediate release (IR) data were either retained or excluded to inform parameter estimation. The resulting F abs profiles were then used to model level A IVIVCs. All the considered stochastic deconvolution scenarios, and numerical deconvolution, yielded on average similar results with respect to the IVIVC validation. These results could be achieved with stochastic deconvolution without recourse to IR data. Unlike numerical deconvolution, this also implies that in crossover studies where certain individuals do not receive an IR treatment, their ER data alone can still be included as part of the IVIVC analysis. Published by Elsevier Inc.

Bernstein modes in a non-neutral plasma column

NASA Astrophysics Data System (ADS)

Walsh, Daniel; Dubin, Daniel H. E.

2018-05-01

This paper presents theory and numerical calculations of electrostatic Bernstein modes in an inhomogeneous cylindrical plasma column. These modes rely on finite Larmor radius effects to propagate radially across the column until they are reflected when their frequency matches the upper hybrid frequency. This reflection sets up an internal normal mode on the column and also mode-couples to the electrostatic surface cyclotron wave (which allows the normal mode to be excited and observed using external electrodes). Numerical results predicting the mode spectra, using a novel linear Vlasov code on a cylindrical grid, are presented and compared to an analytical Wentzel Kramers Brillouin (WKB) theory. A previous version of the theory [D. H. E. Dubin, Phys. Plasmas 20(4), 042120 (2013)] expanded the plasma response in powers of 1/B, approximating the local upper hybrid frequency, and consequently, its frequency predictions are spuriously shifted with respect to the numerical results presented here. A new version of the WKB theory avoids this approximation using the exact cold fluid plasma response and does a better job of reproducing the numerical frequency spectrum. The effect of multiple ion species on the mode spectrum is also considered, to make contact with experiments that observe cyclotron modes in a multi-species pure ion plasma [M. Affolter et al., Phys. Plasmas 22(5), 055701 (2015)].

Microstructure based procedure for process parameter control in rolling of aluminum thin foils

NASA Astrophysics Data System (ADS)

Johannes, Kronsteiner; Kabliman, Evgeniya; Klimek, Philipp-Christoph

2018-05-01

In present work, a microstructure based procedure is used for a numerical prediction of strength properties for Al-Mg-Sc thin foils during a hot rolling process. For this purpose, the following techniques were developed and implemented. At first, a toolkit for a numerical analysis of experimental stress-strain curves obtained during a hot compression testing by a deformation dilatometer was developed. The implemented techniques allow for the correction of a temperature increase in samples due to adiabatic heating and for the determination of a yield strength needed for the separation of the elastic and plastic deformation regimes during numerical simulation of multi-pass hot rolling. At the next step, an asymmetric Hot Rolling Simulator (adjustable table inlet/outlet height as well as separate roll infeed) was developed in order to match the exact processing conditions of a semi-industrial rolling procedure. At each element of a finite element mesh the total strength is calculated by in-house Flow Stress Model based on evolution of mean dislocation density. The strength values obtained by numerical modelling were found in a reasonable agreement with results of tensile tests for thin Al-Mg-Sc foils. Thus, the proposed simulation procedure might allow to optimize the processing parameters with respect to the microstructure development.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Barnes, Taylor A.; Kurth, Thorsten; Carrier, Pierre

Here, we present an algorithm and implementation for the parallel computation of exact exchange in Quantum ESPRESSO (QE) that exhibits greatly improved strong scaling. QE is an open-source software package for electronic structure calculations using plane wave density functional theory, and supports the use of local, semi-local, and hybrid DFT functionals. Wider application of hybrid functionals is desirable for the improved simulation of electronic band energy alignments and thermodynamic properties, but the computational complexity of evaluating the exact exchange potential limits the practical application of hybrid functionals to large systems and requires efficient implementations. We demonstrate that existing implementations ofmore » hybrid DFT that utilize a single data structure for both the local and exact exchange regions of the code are significantly limited in the degree of parallelization achievable. We present a band-pair parallelization approach, in which the calculation of exact exchange is parallelized and evaluated independently from the parallelization of the remainder of the calculation, with the wavefunction data being efficiently transformed on-the-fly into a form that is optimal for each part of the calculation. For a 64 water molecule supercell, our new algorithm reduces the overall time to solution by nearly an order of magnitude.« less

An immersed boundary method for simulating vesicle dynamics in three dimensions

NASA Astrophysics Data System (ADS)

Seol, Yunchang; Hu, Wei-Fan; Kim, Yongsam; Lai, Ming-Chih

2016-10-01

We extend our previous immersed boundary (IB) method for 3D axisymmetric inextensible vesicle in Navier-Stokes flows (Hu et al., 2014 [17]) to general three dimensions. Despite a similar spirit in numerical algorithms to the axisymmetric case, the fully 3D numerical implementation is much more complicated and is far from straightforward. A vesicle membrane surface is known to be incompressible and exhibits bending resistance. As in 3D axisymmetric case, instead of keeping the vesicle locally incompressible, we adopt a modified elastic tension energy to make the vesicle surface patch nearly incompressible so that solving the unknown tension (Lagrange multiplier for the incompressible constraint) can be avoided. Nevertheless, the new elastic force derived from the modified tension energy has exactly the same mathematical form as the original one except the different definitions of tension. The vesicle surface is discretized on a triangular mesh where the elastic tension and bending force are calculated on each vertex (Lagrangian marker in the IB method) of the triangulation. A series of numerical tests on the present scheme are conducted to illustrate the robustness and applicability of the method. We perform the convergence study for the immersed boundary forces and the fluid velocity field. We then study the vesicle dynamics in various flows such as quiescent, simple shear, and gravitational flows. Our numerical results show good agreements with those obtained in previous theoretical, experimental and numerical studies.

Continuum calculations of continental deformation in transcurrent environments

NASA Technical Reports Server (NTRS)

Sonder, L. J.; England, P. C.; Houseman, G. A.

1986-01-01

A thin viscous sheet approximation is used to investigate continental deformation near a strike-slip boundary. The vertically averaged velocity field is calculated for a medium characterized by a power law rheology with stress exponent n. Driving stresses include those applied along boundaries of the sheet and those arising from buoyancy forces related to lateral differences in crustal thickness. Exact and approximate analytic solutions for a region with a sinusoidal strike-slip boundary condition are compared with solutions for more geologically relevant boundary conditions obtained using a finite element technique. The across-strike length scale of the deformation is approximately 1/4pi x sq rt n times the dominant wavelength of the imposed strike-slip boundary condition for both the analytic and the numerical solutions; this result is consistent with length scales observed in continental regions of large-scale transcurrent faulting. An approximate, linear relationship between displacement and rotation is found that depends only on the deformation length scale and the rheology. Calculated displacements, finite rotations, and distribution of crustal thicknesses are consistent with those observed in the region of the Pacific-North America plate boundary in California.

Physics of Nonmagnetic Relativistic Thermal Plasmas. Ph.D. Thesis - Calif. Univ., San Diego

NASA Technical Reports Server (NTRS)

Dermer, C. D.

1984-01-01

A detailed treatment of the kinematics of relativistic systems of particles and photons is presented. In the case of a relativistic Maxwell-Boltzmann distribution of particles, the reaction rate and luminosity are written as single integrals over the invariant cross section, and the production spectrum is written as a double integral over the cross section differential in the energy of the produced particles (or photons) in the center-of-momentum system of two colliding particles. The results are applied to the calculation of the annihilation spectrum of a thermal electron-positron plasma, confirming previous numerical and analytic results. Relativistic thermal electron-ion and electron-electron bremsstrahlung are calculated exactly to lowest order, and relativistic thermal electron-positron bremsstrahlung is calculated in an approximate fashion. An approximate treatment of relativistic Comptonization is developed. The question of thermalization of a relativistic plasma is considered. A formula for the energy loss or exchange rate from the interaction of two relativistic Maxwell-Boltzmann plasmas at different temperatures is derived. Application to a stable, uniform, nonmagnetic relativistic thermal plasma is made. Comparison is made with other studies.

Optical gain coefficients of silicon: a theoretical study

NASA Astrophysics Data System (ADS)

Tsai, Chin-Yi

2018-05-01

A theoretical model is presented and an explicit formula is derived for calculating the optical gain coefficients of indirect band-gap semiconductors. This model is based on the second-order time-dependent perturbation theory of quantum mechanics by incorporating all the eight processes of photon/phonon emission and absorption between the band edges of the conduction and valence bands. Numerical calculation results are given for Si. The calculated absorption coefficients agree well with the existing fitting formula of experiment data with two modes of phonons: optical phonons with energy of 57.73 meV and acoustic phonons with energy of 18.27 meV near (but not exactly at) the zone edge of the X-point in the dispersion relation of phonons. These closely match with existing data of 57.5 meV transverse optical (TO) phonons at the X4-point and 18.6 meV transverse acoustic (TA) phonons at the X3-point of the zone edge. The calculated results show that the material optical gain of Si will overcome free-carrier absorption if the energy separation of quasi-Fermi levels between electrons and holes exceeds 1.15 eV.

Stochastic-analytic approach to the calculation of multiply scattered lidar returns

NASA Astrophysics Data System (ADS)

Gillespie, D. T.

1985-08-01

The problem of calculating the nth-order backscattered power of a laser firing short pulses at time zero into an homogeneous cloud with specified scattering and absorption parameters, is discussed. In the problem, backscattered power is measured at any time less than zero by a small receiver colocated with the laser and fitted with a forward looking conical baffle. Theoretical calculations are made on the premise that the laser pulse is composed of propagating photons which are scattered and absorbed by the cloud particles in a probabilistic manner. The effect of polarization was not taken into account in the calculations. An exact formula is derived for backscattered power, based on direct physical arguments together with a rigorous analysis of random variables. It is shown that, for values of n less than or equal to 2, the obtained formula is a well-behaved (3n-4) dimensionless integral. The computational feasibility of the integral formula is demonstrated for a model cloud of isotropically scattering particles. An analytical formula is obtained for a value of n = 2, and a Monte Carlo program was used to obtain numerical results for values of n = 3, . . ., 6.

Precise calculation of quasienergies of a driven two-level atom based on the Guo-Wu-Van Woerkom solution

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wang Yi; Zhang Jingtao; Xu Zhizhan

2010-07-15

The exact algebraic solution recently obtained by Guo, Wu, and Van Woerkom (Phys. Rev. A 73 (2006) 023419) made possible accurate calculations of quasienergies of a driven two-level atom with an arbitrary original energy spacing and laser intensity. Due to the complication of the analytic solutions that involves an infinite number of infinite determinants, many mathematical difficulties must be overcome to obtain precise values of quasienergies. In this paper, with a further developed algebraic method, we show how to solve the computational problem completely and results are presented in a data table. With this table, one can easily obtain allmore » quasienergies of a driven two-level atom with an arbitrary original energy spacing and arbitrary intensity and frequency of the driving laser. The numerical solution technique developed here can be applied to the calculation of Freeman resonances in photoelectron energy spectra. As an example for applications, we show how to use the data table to calculate the peak laser intensity at which a Freeman resonance occurs in the transition between the ground Xe 5p P{sub 3/2} state and the Rydberg state Xe 8p P{sub 3/2}.« less

The effect of rain characteristics on scavenging rate of tritium-oxide from the atmosphere

NASA Astrophysics Data System (ADS)

Piskunov, V. N.; Golubev, A. V.; Balashov, Yu. S.; Mavrin, S. V.; Golubeva, V. N.; Aleinikov, A. Yu.; Kovalenko, V. P.; Solomatin, I. I.

2012-12-01

The results of field experiments, involving HTO scavenging from the atmosphere by precipitation in the vicinity of HT and HTO emission sources, are presented. The experiments were aimed at obtaining direct experimental data on atmospheric HTO scavenging for a variety of rain characteristics (rain intensity and drop spectra).The most reliable are the calculations of the rate of wash-out with precipitation with the use of the method of integration of the constant exchange for a spectrum of drops. The results of such calculations are in good agreement with the experimental data and can serve as a basis for the generalized parameterization dependences. It is shown that the exact calculation can be replaced by a simpler formula using the mean-value theorem.For the known approximations of the spectra of the rain drops, formulas were obtained to give parameterization dependence of the rate of wash-out Λ on the intensity of precipitation p. This approach can be used for rapid assessment, as well as to determine parameters of wash-out of gases with precipitation in the numerical complexes, which are used for the calculation of the transfer and removal of impurities from the atmosphere.

Structural response to discrete and continuous gusts of an airplane having wing bending flexibility and a correlation of calculated and flight results

NASA Technical Reports Server (NTRS)

Houbolt, John C; Kordes, Eldon E

1954-01-01

An analysis is made of the structural response to gusts of an airplane having the degrees of freedom of vertical motion and wing bending flexibility and basic parameters are established. A convenient and accurate numerical solution of the response equations is developed for the case of discrete-gust encounter, an exact solution is made for the simpler case of continuous-sinusoidal-gust encounter, and the procedure is outlined for treating the more realistic condition of continuous random atmospheric turbulence, based on the methods of generalized harmonic analysis. Correlation studies between flight and calculated results are then given to evaluate the influence of wing bending flexibility on the structural response to gusts of two twin-engine transports and one four-engine bomber. It is shown that calculated results obtained by means of a discrete-gust approach reveal the general nature of the flexibility effects and lead to qualitative correlation with flight results. In contrast, calculations by means of the continuous-turbulence approach show good quantitative correlation with flight results and indicate a much greater degree of resolution of the flexibility effects.

Rényi entropies after releasing the Néel state in the XXZ spin-chain

NASA Astrophysics Data System (ADS)

Alba, Vincenzo; Calabrese, Pasquale

2017-11-01

We study the Rényi entropies in the spin-1/2 anisotropic Heisenberg chain after a quantum quench starting from the Néel state. The quench action method allows us to obtain the stationary Rényi entropies for arbitrary values of the index α as generalised free energies evaluated over a calculable thermodynamic macrostate depending on α. We work out this macrostate for several values of α and of the anisotropy Δ by solving the thermodynamic Bethe ansatz equations. By varying α different regions of the Hamiltonian spectrum are accessed. The two extremes are α\\to∞ for which the thermodynamic macrostate is either the ground state or a low-lying excited state (depending on Δ) and α=0 when the macrostate is the infinite temperature state. The Rényi entropies are easily obtained from the macrostate as function of α and a few interesting limits are analytically characterised. We provide robust numerical evidence to confirm our results using exact diagonalisation and a stochastic numerical implementation of Bethe ansatz. Finally, using tDMRG we calculate the time evolution of the Rényi entanglement entropies. For large subsystems and for any α, their density turns out to be compatible with that of the thermodynamic Rényi entropies.

28 CFR 25.7 - Querying records in the system.

Code of Federal Regulations, 2011 CFR

2011-07-01

...) Name; (2) Sex; (3) Race; (4) Complete date of birth; and (5) State of residence. (b) A unique numeric identifier may also be provided to search for additional records based on exact matches by the numeric identifier. Examples of unique numeric identifiers for purposes of this system are: Social Security number...

28 CFR 25.7 - Querying records in the system.

Code of Federal Regulations, 2014 CFR

2014-07-01

...) Name; (2) Sex; (3) Race; (4) Complete date of birth; and (5) State of residence. (b) A unique numeric identifier may also be provided to search for additional records based on exact matches by the numeric identifier. Examples of unique numeric identifiers for purposes of this system are: Social Security number...

28 CFR 25.7 - Querying records in the system.

Code of Federal Regulations, 2013 CFR

2013-07-01

...) Name; (2) Sex; (3) Race; (4) Complete date of birth; and (5) State of residence. (b) A unique numeric identifier may also be provided to search for additional records based on exact matches by the numeric identifier. Examples of unique numeric identifiers for purposes of this system are: Social Security number...

28 CFR 25.7 - Querying records in the system.

Code of Federal Regulations, 2012 CFR

2012-07-01

...) Name; (2) Sex; (3) Race; (4) Complete date of birth; and (5) State of residence. (b) A unique numeric identifier may also be provided to search for additional records based on exact matches by the numeric identifier. Examples of unique numeric identifiers for purposes of this system are: Social Security number...

Quasi-generalized variables

NASA Technical Reports Server (NTRS)

Baumgarten, J.; Ostermeyer, G. P.

1986-01-01

The numerical solution of a system of differential and algebraic equations is difficult, due to the appearance of numerical instabilities. A method is presented here which permits numerical solutions of such a system to be obtained which satisfy the algebraic constraint equations exactly without reducing the order of the differential equations. The method is demonstrated using examples from mechanics.

A new shock-capturing numerical scheme for ideal hydrodynamics

NASA Astrophysics Data System (ADS)

Fecková, Z.; Tomášik, B.

2015-05-01

We present a new algorithm for solving ideal relativistic hydrodynamics based on Godunov method with an exact solution of Riemann problem for an arbitrary equation of state. Standard numerical tests are executed, such as the sound wave propagation and the shock tube problem. Low numerical viscosity and high precision are attained with proper discretization.

Effects of absorption on multiple scattering by random particulate media: exact results.

PubMed

Mishchenko, Michael I; Liu, Li; Hovenier, Joop W

2007-10-01

We employ the numerically exact superposition T-matrix method to perform extensive computations of elec nottromagnetic scattering by a volume of discrete random medium densely filled with increasingly absorbing as well as non-absorbing particles. Our numerical data demonstrate that increasing absorption diminishes and nearly extinguishes certain optical effects such as depolarization and coherent backscattering and increases the angular width of coherent backscattering patterns. This result corroborates the multiple-scattering origin of such effects and further demonstrates the heuristic value of the concept of multiple scattering even in application to densely packed particulate media.

Computer program determines exact two-sided tolerance limits for normal distributions

NASA Technical Reports Server (NTRS)

Friedman, H. A.; Webb, S. R.

1968-01-01

Computer program determines by numerical integration the exact statistical two-sided tolerance limits, when the proportion between the limits is at least a specified number. The program is limited to situations in which the underlying probability distribution for the population sampled is the normal distribution with unknown mean and variance.

Laser-optical and numerical Research of the flow inside the lubricating gap of a journal bearing model

NASA Astrophysics Data System (ADS)

Nobis, M.; Stücke, P.; Schmidt, M.; Riedel, M.

2013-04-01

The laser-optical research of the flow inside the lubricating gap of a journal bearing model is one important task in a larger overall project. The long-term objective is the development of an easy-to-work calculation tool which delivers information about the causes and consequences of cavitation processes in hydrodynamically lubricated journal bearings. Hence, it will be possible to find statements for advantageous and disadvantageous geometrical shapes of the bushings. In conclusion such a calculation tool can provide important insights for the construction and design of future journal bearings. Current design programs are based on a two-dimensional approach for the lubricating gap. The first dimension is the breath of the bearing and the second dimension is the circumferential direction of the bearing. The third dimension, the expansion of the gap in radial direction, will be neglected. Instead of an exact resolution of the flow pattern inside the gap, turbulence models are in use. Past studies on numerical and experimental field have shown that inside the lubricating gap clearly organized and predominantly laminar flow structures can be found. Thus, for a detailed analysis of the reasons and effects of cavitation bubbles, a three-dimensional resolution of the lubricating gap is inevitable. In addition to the qualitative evaluation of the flow with visualization experiments it is possible to perform angle-based velocity measurements inside the gap with the help of a triggered Laser-Doppler- Velocimeter (LDV). The results of these measurements are used to validate three-dimensional CFD flow simulations, and to optimize the numerical mesh structure and the boundary conditions. This paper will present the experimental setup of the bearing model, some exemplary results of the visualization experiments and LDV measurements as well as a comparison between experimental and numerical results.

Least-Squares Spectral Element Solutions to the CAA Workshop Benchmark Problems

NASA Technical Reports Server (NTRS)

Lin, Wen H.; Chan, Daniel C.

1997-01-01

This paper presents computed results for some of the CAA benchmark problems via the acoustic solver developed at Rocketdyne CFD Technology Center under the corporate agreement between Boeing North American, Inc. and NASA for the Aerospace Industry Technology Program. The calculations are considered as benchmark testing of the functionality, accuracy, and performance of the solver. Results of these computations demonstrate that the solver is capable of solving the propagation of aeroacoustic signals. Testing of sound generation and on more realistic problems is now pursued for the industrial applications of this solver. Numerical calculations were performed for the second problem of Category 1 of the current workshop problems for an acoustic pulse scattered from a rigid circular cylinder, and for two of the first CAA workshop problems, i. e., the first problem of Category 1 for the propagation of a linear wave and the first problem of Category 4 for an acoustic pulse reflected from a rigid wall in a uniform flow of Mach 0.5. The aim for including the last two problems in this workshop is to test the effectiveness of some boundary conditions set up in the solver. Numerical results of the last two benchmark problems have been compared with their corresponding exact solutions and the comparisons are excellent. This demonstrates the high fidelity of the solver in handling wave propagation problems. This feature lends the method quite attractive in developing a computational acoustic solver for calculating the aero/hydrodynamic noise in a violent flow environment.

A Numerical Simulation of Scattering from One-Dimensional Inhomogeneous Dielectric Random Surfaces

NASA Technical Reports Server (NTRS)

Sarabandi, Kamal; Oh, Yisok; Ulaby, Fawwaz T.

1996-01-01

In this paper, an efficient numerical solution for the scattering problem of inhomogeneous dielectric rough surfaces is presented. The inhomogeneous dielectric random surface represents a bare soil surface and is considered to be comprised of a large number of randomly positioned dielectric humps of different sizes, shapes, and dielectric constants above an impedance surface. Clods with nonuniform moisture content and rocks are modeled by inhomogeneous dielectric humps and the underlying smooth wet soil surface is modeled by an impedance surface. In this technique, an efficient numerical solution for the constituent dielectric humps over an impedance surface is obtained using Green's function derived by the exact image theory in conjunction with the method of moments. The scattered field from a sample of the rough surface is obtained by summing the scattered fields from all the individual humps of the surface coherently ignoring the effect of multiple scattering between the humps. The statistical behavior of the scattering coefficient sigma(sup 0) is obtained from the calculation of scattered fields of many different realizations of the surface. Numerical results are presented for several different roughnesses and dielectric constants of the random surfaces. The numerical technique is verified by comparing the numerical solution with the solution based on the small perturbation method and the physical optics model for homogeneous rough surfaces. This technique can be used to study the behavior of scattering coefficient and phase difference statistics of rough soil surfaces for which no analytical solution exists.

Sensitivity of inelastic response to numerical integration of strain energy. [for cantilever beam

NASA Technical Reports Server (NTRS)

Kamat, M. P.

1976-01-01

The exact solution to the quasi-static, inelastic response of a cantilever beam of rectangular cross section subjected to a bending moment at the tip is obtained. The material of the beam is assumed to be linearly elastic-linearly strain-hardening. This solution is then compared with three different numerical solutions of the same problem obtained by minimizing the total potential energy using Gaussian quadratures of two different orders and a Newton-Cotes scheme for integrating the strain energy of deformation. Significant differences between the exact dissipative strain energy and its numerical counterpart are emphasized. The consequence of this on the nonlinear transient responses of a beam with solid cross section and that of a thin-walled beam on elastic supports under impulsive loads are examined.

A numerical experiment that provides new results regarding the inception of separation in the flow around a circular cylinder

NASA Astrophysics Data System (ADS)

Malamataris, Nikolaos; Liakos, Anastasios

2015-11-01

The exact value of the Reynolds number regarding the inception of separation in the flow around a circular cylinder is still a matter of research. This work connects the inception of separation with the calculation of a positive pressure gradient around the circumference of the cylinder. The hypothesis is that inception of separation occurs when the pressure gradient becomes positive around the circumference. From the most cited laboratory experiments that have dealt with that subject of inception of separation only Thom has measured the pressure gradient there at very low Reynolds numbers (up to Re=3.5). For this reason, the experimental conditions of his tunnel are simulated in a new numerical experiment. The full Navier Stokes equations in both two and three dimensions are solved with a home made code that utilizes Galerkin finite elements. In the two dimensional numerical experiment, inception of separation is observed at Re=4.3, which is the lowest Reynolds number where inception has been reported computationally. Currently, the three dimensional experiment is under way, in order to compare if there are effects of three dimensional theory of separation in the conditions of Thom's experiments.

Effect of atmospheric turbulence on the bit error probability of a space to ground near infrared laser communications link using binary pulse position modulation and an avalanche photodiode detector

NASA Technical Reports Server (NTRS)

Safren, H. G.

1987-01-01

The effect of atmospheric turbulence on the bit error rate of a space-to-ground near infrared laser communications link is investigated, for a link using binary pulse position modulation and an avalanche photodiode detector. Formulas are presented for the mean and variance of the bit error rate as a function of signal strength. Because these formulas require numerical integration, they are of limited practical use. Approximate formulas are derived which are easy to compute and sufficiently accurate for system feasibility studies, as shown by numerical comparison with the exact formulas. A very simple formula is derived for the bit error rate as a function of signal strength, which requires only the evaluation of an error function. It is shown by numerical calculations that, for realistic values of the system parameters, the increase in the bit error rate due to turbulence does not exceed about thirty percent for signal strengths of four hundred photons per bit or less. The increase in signal strength required to maintain an error rate of one in 10 million is about one or two tenths of a db.

The electrical conductivity of in vivo human uterine fibroids.

PubMed

DeLonzor, Russ; Spero, Richard K; Williams, Joseph J

2011-01-01

The purpose of this study was to determine the value of electrical conductivity that can be used for numerical modelling in vivo radiofrequency ablation (RFA) treatments of human uterine fibroids. No experimental electrical conductivity data have previously been reported for human uterine fibroids. In this study electrical data (voltage) from selected in vivo clinical procedures on human uterine fibroids were used to numerically model the treatments. Measured versus calculated power dissipation profiles were compared to determine uterine fibroid electrical conductivity. Numerical simulations were conducted utilising a wide range of values for tissue thermal conductivity, heat capacity and blood perfusion coefficient. The simulations demonstrated that power dissipation was insensitive to the exact values of these parameters for the simulated geometry, treatment duration, and power level. Consequently, it was possible to determine tissue electrical conductivity without precise knowledge of the values for these parameters. Results of this study showed that an electrical conductivity for uterine fibroids of 0.305 S/m at 37°C and a temperature coefficient of 0.2%/°C can be used for modelling Radio Frequency Ablation of human uterine fibroids at a frequency of 460 kHz for temperatures from 37°C to 100°C.

Finite Element Solution of Unsteady Mixed Convection Flow of Micropolar Fluid over a Porous Shrinking Sheet

PubMed Central

Gupta, Diksha; Singh, Bani

2014-01-01

The objective of this investigation is to analyze the effect of unsteadiness on the mixed convection boundary layer flow of micropolar fluid over a permeable shrinking sheet in the presence of viscous dissipation. At the sheet a variable distribution of suction is assumed. The unsteadiness in the flow and temperature fields is caused by the time dependence of the shrinking velocity and surface temperature. With the aid of similarity transformations, the governing partial differential equations are transformed into a set of nonlinear ordinary differential equations, which are solved numerically, using variational finite element method. The influence of important physical parameters, namely, suction parameter, unsteadiness parameter, buoyancy parameter and Eckert number on the velocity, microrotation, and temperature functions is investigated and analyzed with the help of their graphical representations. Additionally skin friction and the rate of heat transfer have also been computed. Under special conditions, an exact solution for the flow velocity is compared with the numerical results obtained by finite element method. An excellent agreement is observed for the two sets of solutions. Furthermore, to verify the convergence of numerical results, calculations are conducted with increasing number of elements. PMID:24672310

Structure of edge-state inner products in the fractional quantum Hall effect

NASA Astrophysics Data System (ADS)

Fern, R.; Bondesan, R.; Simon, S. H.

2018-04-01

We analyze the inner products of edge state wave functions in the fractional quantum Hall effect, specifically for the Laughlin and Moore-Read states. We use an effective description for these inner products given by a large-N expansion ansatz proposed in a recent work by J. Dubail, N. Read, and E. Rezayi [Phys. Rev. B 86, 245310 (2012), 10.1103/PhysRevB.86.245310]. As noted by these authors, the terms in this ansatz can be constrained using symmetry, a procedure we perform to high orders. We then check this conjecture by calculating the overlaps exactly for small system sizes and compare the numerics with our high-order expansion. We find the effective description to be very accurate.

Dynamical Connections in a Turbulent Fluid: Experiment and Simulation

NASA Astrophysics Data System (ADS)

Kageorge, Logan; Suri, Balachandra; Tithof, Jeff; Grigoriev, Roman; Schatz, Michael

2017-11-01

Embedded in the state space of a turbulent flow there exist invariant solutions to the Navier-Stokes equation called Exact Coherent Structures (ECS). Recent studies have demonstrated that the geometry of the ECS locally describes the evolution of the turbulent flow. Theory suggests that global connections may serve to guide the flow from the neighborhood of one ECS to that of another. We present here a numerical model of a Kolmogorov-like two-dimensional flow in which such connections have been calculated. Moreover, we present an experimental quasi-two-dimensional realization of this flow in which these connections prove dynamically relevant. This work is supported by the National Science Foundation (NSF CMMI 12-34436) and DARPA (HR0011-16-2-0033 subcontract to Georgia Tech).

Spin-state transition in LaCoO3 by variational cluster approximation

NASA Astrophysics Data System (ADS)

Eder, R.

2010-01-01

The variational cluster approximation (VCA) is applied to the calculation of thermodynamical quantities and single-particle spectra of LaCoO3 . Trial self-energies and the numerical value of the Luttinger-Ward functional are obtained by exact diagonalization of a CoO6 cluster. The VCA correctly predicts LaCoO3 as a paramagnetic insulator, and a gradual and relatively smooth increase in the occupation of high-spin Co3+ ions causes the temperature dependence of entropy and magnetic susceptibility. The single-particle spectral function agrees well with experiment; the experimentally observed temperature dependence of photoelectron spectra is reproduced satisfactorily. Remaining discrepancies with experiment highlight the importance of spin-orbit coupling and local lattice relaxation.

Hierarchy of forward-backward stochastic Schrödinger equation

NASA Astrophysics Data System (ADS)

Ke, Yaling; Zhao, Yi

2016-07-01

Driven by the impetus to simulate quantum dynamics in photosynthetic complexes or even larger molecular aggregates, we have established a hierarchy of forward-backward stochastic Schrödinger equation in the light of stochastic unravelling of the symmetric part of the influence functional in the path-integral formalism of reduced density operator. The method is numerically exact and is suited for Debye-Drude spectral density, Ohmic spectral density with an algebraic or exponential cutoff, as well as discrete vibrational modes. The power of this method is verified by performing the calculations of time-dependent population differences in the valuable spin-boson model from zero to high temperatures. By simulating excitation energy transfer dynamics of the realistic full FMO trimer, some important features are revealed.

BLUES function method in computational physics

NASA Astrophysics Data System (ADS)

Indekeu, Joseph O.; Müller-Nedebock, Kristian K.

2018-04-01

We introduce a computational method in physics that goes ‘beyond linear use of equation superposition’ (BLUES). A BLUES function is defined as a solution of a nonlinear differential equation (DE) with a delta source that is at the same time a Green’s function for a related linear DE. For an arbitrary source, the BLUES function can be used to construct an exact solution to the nonlinear DE with a different, but related source. Alternatively, the BLUES function can be used to construct an approximate piecewise analytical solution to the nonlinear DE with an arbitrary source. For this alternative use the related linear DE need not be known. The method is illustrated in a few examples using analytical calculations and numerical computations. Areas for further applications are suggested.

Exact sum rules for inhomogeneous systems containing a zero mode

DOE Office of Scientific and Technical Information (OSTI.GOV)

Amore, Paolo, E-mail: paolo.amore@gmail.com

2014-10-15

We show that the formulas for the sum rules for the eigenvalues of inhomogeneous systems that we have obtained in two recent papers are incomplete when the system contains a zero mode. We prove that there are finite contributions of the zero mode to the sum rules and we explicitly calculate the expressions for the sum rules of order one and two. The previous results for systems that do not contain a zero mode are unaffected. - Highlights: • We discuss the sum rules of the eigenvalues of inhomogeneous systems containing a zero mode. • We derive the explicit expressionsmore » for sum rules of order one and two. • We perform accurate numerical tests of these results for three examples.« less

A new relativistic viscous hydrodynamics code and its application to the Kelvin–Helmholtz instability in high-energy heavy-ion collisions

DOE PAGES

Okamoto, Kazuhisa; Nonaka, Chiho

2017-06-09

Here, we construct a new relativistic viscous hydrodynamics code optimized in the Milne coordinates. We also split the conservation equations into an ideal part and a viscous part, using the Strang spitting method. In the code a Riemann solver based on the two-shock approximation is utilized for the ideal part and the Piecewise Exact Solution (PES) method is applied for the viscous part. Furthemore, we check the validity of our numerical calculations by comparing analytical solutions, the viscous Bjorken’s flow and the Israel–Stewart theory in Gubser flow regime. Using the code, we discuss possible development of the Kelvin–Helmholtz instability inmore » high-energy heavy-ion collisions.« less

Comprehensive T-Matrix Reference Database: A 2012 - 2013 Update

NASA Technical Reports Server (NTRS)

Mishchenko, Michael I.; Videen, Gorden; Khlebtsov, Nikolai G.; Wriedt, Thomas

2013-01-01

The T-matrix method is one of the most versatile, efficient, and accurate theoretical techniques widely used for numerically exact computer calculations of electromagnetic scattering by single and composite particles, discrete random media, and particles imbedded in complex environments. This paper presents the fifth update to the comprehensive database of peer-reviewed T-matrix publications initiated by us in 2004 and includes relevant publications that have appeared since 2012. It also lists several earlier publications not incorporated in the original database, including Peter Waterman's reports from the 1960s illustrating the history of the T-matrix approach and demonstrating that John Fikioris and Peter Waterman were the true pioneers of the multi-sphere method otherwise known as the generalized Lorenz - Mie theory.

Physical models for the normal YORP and diurnal Yarkovsky effects

NASA Astrophysics Data System (ADS)

Golubov, O.; Kravets, Y.; Krugly, Yu. N.; Scheeres, D. J.

2016-06-01

We propose an analytic model for the normal Yarkovsky-O'Keefe-Radzievskii-Paddack (YORP) and diurnal Yarkovsky effects experienced by a convex asteroid. Both the YORP torque and the Yarkovsky force are expressed as integrals of a universal function over the surface of an asteroid. Although in general this function can only be calculated numerically from the solution of the heat conductivity equation, approximate solutions can be obtained in quadratures for important limiting cases. We consider three such simplified models: Rubincam's approximation (zero heat conductivity), low thermal inertia limit (including the next order correction and thus valid for small heat conductivity), and high thermal inertia limit (valid for large heat conductivity). All three simplified models are compared with the exact solution.

One-Shot Decoupling and Page Curves from a Dynamical Model for Black Hole Evaporation.

PubMed

Brádler, Kamil; Adami, Christoph

2016-03-11

One-shot decoupling is a powerful primitive in quantum information theory and was hypothesized to play a role in the black hole information paradox. We study black hole dynamics modeled by a trilinear Hamiltonian whose semiclassical limit gives rise to Hawking radiation. An explicit numerical calculation of the discretized path integral of the S matrix shows that decoupling is exact in the continuous limit, implying that quantum information is perfectly transferred from the black hole to radiation. A striking consequence of decoupling is the emergence of an output radiation entropy profile that follows Page's prediction. We argue that information transfer and the emergence of Page curves is a robust feature of any multilinear interaction Hamiltonian with a bounded spectrum.

Resonant vibrations of a submerged beam

NASA Astrophysics Data System (ADS)

Achenbach, J. D.; Qu, J.

1986-03-01

Forced vibration of a simply supported submerged beam of circular cross section is investigated by the use of two mathematical methods. In the first approach the problem formulation is reduced to a singular integro-differential equation for the transverse deflection. In the second approach the method of matched asymptotic expansions is employed. The integro-differential equation is solved numerically, to yield an exact solution for the frequency response. Subsequent use of a representation integral yields the radiated far field acoustic pressure. The exact results for the beam deflection are compared with approximate results that are available in the literature. Next, a matched asymptotic expansion is worked out by constructing "inner" and "outer" expansions for frequencies near and not near resonance frequencies, respectively. The two expansions are matched in an appropriate manner to yield a uniformly valid solution. The leading term of the matched asymptotic solution is compared with exact numerical results.

Delving Into Dissipative Quantum Dynamics: From Approximate to Numerically Exact Approaches

NASA Astrophysics Data System (ADS)

Chen, Hsing-Ta

In this thesis, I explore dissipative quantum dynamics of several prototypical model systems via various approaches, ranging from approximate to numerically exact schemes. In particular, in the realm of the approximate I explore the accuracy of Pade-resummed master equations and the fewest switches surface hopping (FSSH) algorithm for the spin-boson model, and non-crossing approximations (NCA) for the Anderson-Holstein model. Next, I develop new and exact Monte Carlo approaches and test them on the spin-boson model. I propose well-defined criteria for assessing the accuracy of Pade-resummed quantum master equations, which correctly demarcate the regions of parameter space where the Pade approximation is reliable. I continue the investigation of spin-boson dynamics by benchmark comparisons of the semiclassical FSSH algorithm to exact dynamics over a wide range of parameters. Despite small deviations from golden-rule scaling in the Marcus regime, standard surface hopping algorithm is found to be accurate over a large portion of parameter space. The inclusion of decoherence corrections via the augmented FSSH algorithm improves the accuracy of dynamical behavior compared to exact simulations, but the effects are generally not dramatic for the cases I consider. Next, I introduce new methods for numerically exact real-time simulation based on real-time diagrammatic Quantum Monte Carlo (dQMC) and the inchworm algorithm. These methods optimally recycle Monte Carlo information from earlier times to greatly suppress the dynamical sign problem. In the context of the spin-boson model, I formulate the inchworm expansion in two distinct ways: the first with respect to an expansion in the system-bath coupling and the second as an expansion in the diabatic coupling. In addition, a cumulant version of the inchworm Monte Carlo method is motivated by the latter expansion, which allows for further suppression of the growth of the sign error. I provide a comprehensive comparison of the performance of the inchworm Monte Carlo algorithms to other exact methodologies as well as a discussion of the relative advantages and disadvantages of each. Finally, I investigate the dynamical interplay between the electron-electron interaction and the electron-phonon coupling within the Anderson-Holstein model via two complementary NCAs: the first is constructed around the weak-coupling limit and the second around the polaron limit. The influence of phonons on spectral and transport properties is explored in equilibrium, for non-equilibrium steady state and for transient dynamics after a quench. I find the two NCAs disagree in nontrivial ways, indicating that more reliable approaches to the problem are needed. The complementary frameworks used here pave the way for numerically exact methods based on inchworm dQMC algorithms capable of treating open systems simultaneously coupled to multiple fermionic and bosonic baths.

An exact variational method to calculate rovibrational spectra of polyatomic molecules with large amplitude motion

NASA Astrophysics Data System (ADS)

Yu, Hua-Gen

2016-08-01

We report a new full-dimensional variational algorithm to calculate rovibrational spectra of polyatomic molecules using an exact quantum mechanical Hamiltonian. The rovibrational Hamiltonian of system is derived in a set of orthogonal polyspherical coordinates in the body-fixed frame. It is expressed in an explicitly Hermitian form. The Hamiltonian has a universal formulation regardless of the choice of orthogonal polyspherical coordinates and the number of atoms in molecule, which is suitable for developing a general program to study the spectra of many polyatomic systems. An efficient coupled-state approach is also proposed to solve the eigenvalue problem of the Hamiltonian using a multi-layer Lanczos iterative diagonalization approach via a set of direct product basis set in three coordinate groups: radial coordinates, angular variables, and overall rotational angles. A simple set of symmetric top rotational functions is used for the overall rotation whereas a potential-optimized discrete variable representation method is employed in radial coordinates. A set of contracted vibrationally diabatic basis functions is adopted in internal angular variables. Those diabatic functions are first computed using a neural network iterative diagonalization method based on a reduced-dimension Hamiltonian but only once. The final rovibrational energies are computed using a modified Lanczos method for a given total angular momentum J, which is usually fast. Two numerical applications to CH4 and H2CO are given, together with a comparison with previous results.

Asymptotic radiance and polarization in optically thick media: ocean and clouds.

PubMed

Kattawar, G W; Plass, G N

1976-12-01

Deep in a homogeneous medium that both scatters and absorbs photons, such as a cloud, the ocean, or a thick planetary atmosphere, the radiance decreases exponentially with depth, while the angular dependence of the radiance and polarization is independent of depth. In this diffusion region, the asymptotic radiance and polarization are also independent of the incident distribution of radiation at the upper surface of the medium. An exact expression is derived for the asymptotic radiance and polarization for Rayleigh scattering. The approximate expression for the asymptotic radiance derived from the scalar theory is shown to be in error by as much as 16.4%. An exact expression is also derived for the relation between the diffusion exponent k and the single scattering albedo. A method is developed for the numerical calculation of the asymptotic radiance and polarization for any scattering matrix. Results are given for scattering from the haze L and cloud C3 distributions for a wide range of single scattering albedos. When the absorption is large, the polarization in the diffusion region approaches the values obtained for single scattered photons, while the radiance approaches the value calculated from the expression: phase function divided by (1 + kmicro), where micro is the cosine of the zenith angle. The asymptotic distribution of the radiation is of interest since it depends only on the inherent optical properties of the medium. It is, however, difficult to observe when the absorption is large because of the very low radiance values in the diffusion region.

An exact variational method to calculate rovibrational spectra of polyatomic molecules with large amplitude motion

DOE Office of Scientific and Technical Information (OSTI.GOV)

Yu, Hua-Gen, E-mail: hgy@bnl.gov

We report a new full-dimensional variational algorithm to calculate rovibrational spectra of polyatomic molecules using an exact quantum mechanical Hamiltonian. The rovibrational Hamiltonian of system is derived in a set of orthogonal polyspherical coordinates in the body-fixed frame. It is expressed in an explicitly Hermitian form. The Hamiltonian has a universal formulation regardless of the choice of orthogonal polyspherical coordinates and the number of atoms in molecule, which is suitable for developing a general program to study the spectra of many polyatomic systems. An efficient coupled-state approach is also proposed to solve the eigenvalue problem of the Hamiltonian using amore » multi-layer Lanczos iterative diagonalization approach via a set of direct product basis set in three coordinate groups: radial coordinates, angular variables, and overall rotational angles. A simple set of symmetric top rotational functions is used for the overall rotation whereas a potential-optimized discrete variable representation method is employed in radial coordinates. A set of contracted vibrationally diabatic basis functions is adopted in internal angular variables. Those diabatic functions are first computed using a neural network iterative diagonalization method based on a reduced-dimension Hamiltonian but only once. The final rovibrational energies are computed using a modified Lanczos method for a given total angular momentum J, which is usually fast. Two numerical applications to CH{sub 4} and H{sub 2}CO are given, together with a comparison with previous results.« less

Exact decoupling of the Dirac Hamiltonian. II. The generalized Douglas-Kroll-Hess transformation up to arbitrary order

DOE Office of Scientific and Technical Information (OSTI.GOV)

Reiher, Markus; Wolf, Alexander

In order to achieve exact decoupling of the Dirac Hamiltonian within a unitary transformation scheme, we have discussed in part I of this series that either a purely numerical iterative technique (the Barysz-Sadlej-Snijders method) or a stepwise analytic approach (the Douglas-Kroll-Hess method) are possible. For the evaluation of Douglas-Kroll-Hess Hamiltonians up to a pre-defined order it was shown that a symbolic scheme has to be employed. In this work, an algorithm for this analytic derivation of Douglas-Kroll-Hess Hamiltonians up to any arbitrary order in the external potential is presented. We discuss how an estimate for the necessary order for exactmore » decoupling (within machine precision) for a given system can be determined from the convergence behavior of the Douglas-Kroll-Hess expansion prior to a quantum chemical calculation. Once this maximum order has been accomplished, the spectrum of the positive-energy part of the decoupled Hamiltonian, e.g., for electronic bound states, cannot be distinguished from the corresponding part of the spectrum of the Dirac operator. An efficient scalar-relativistic implementation of the symbolic operations for the evaluation of the positive-energy part of the block-diagonal Hamiltonian is presented, and its accuracy is tested for ground-state energies of one-electron ions over the whole periodic table. Furthermore, the first many-electron calculations employing sixth up to fourteenth order DKH Hamiltonians are presented.« less

Strategic development in exact calculation: group and individual differences in four achievement subtypes.

PubMed

Wylie, Judith; Jordan, Julie-Ann; Mulhern, Gerry

2012-09-01

This longitudinal study sought to identify developmental changes in strategy use between 5 and 7 years of age when solving exact calculation problems. Four mathematics and reading achievement subtypes were examined at four time points. Five strategies were considered: finger counting, verbal counting, delayed retrieval, automatic retrieval, and derived fact retrieval. Results provided unique insights into children's strategic development in exact calculation at this early stage. Group analysis revealed relationships between mathematical and/or reading difficulties and strategy choice, shift, and adaptiveness. Use of derived fact retrieval by 7 years of age distinguished children with mathematical difficulties from other achievement subtypes. Analysis of individual differences revealed marked heterogeneity within all subtypes, suggesting (inter alia) no marked qualitative distinction between our two mathematical difficulty subtypes. Copyright © 2012 Elsevier Inc. All rights reserved.

Isogeometric Divergence-conforming B-splines for the Steady Navier-Stokes Equations

DTIC Science & Technology

2012-04-01

discretizations produce pointwise divergence-free velocity elds and hence exactly satisfy mass conservation. Consequently, discrete variational formulations...cretizations produce pointwise divergence-free velocity fields and hence exactly satisfy mass conservation. Consequently, discrete variational ... variational formulation. Using a combination of an advective for- mulation, SUPG, PSPG, and grad-div stabilization, provably convergent numerical methods

Numerosity and Number Signs in Deaf Nicaraguan Adults

ERIC Educational Resources Information Center

Flaherty, Molly; Senghas, Ann

2011-01-01

What abilities are entailed in being numerate? Certainly, one is the ability to hold the exact quantity of a set in mind, even as it changes, and even after its members can no longer be perceived. Is counting language necessary to track and reproduce exact quantities? Previous work with speakers of languages that lack number words involved…

Effect of exact Coulomb-exchange calculations on band-head spectra of odd-proton nuclei

NASA Astrophysics Data System (ADS)

Koh, Meng-Hock; Nurhafiza, Mohamad Nor

2017-10-01

Previous calculations of band-head energy spectra of odd-mass heavy nuclei in the Hartree-Fock-plus-Bardeen-Cooper-Schrieffer (HF-BCS) framework showed that the agreement with data is better for odd-neutron as compared to odd-proton nuclei. The reason for a poorer agreement with data for the latter have been ascribed to the possible usage of the Slater approximation in calculating the Coulomb-exchange term. In this work, we report the effect of exact Coulomb-exchange calculations on band-head energy spectra of two odd-proton nuclei (namely 237Np and 241Am) as compared to the results obtained using the Slater approximation. We performed self-consistent blocking calculations while taking the breaking of time-reversal symmetry at the mean-field level into account due to the unpaired nucleon. The SkM* and SIII parametrizations of the Skyrme interaction have been employed to approximate the effective nucleon-nucleon interaction while a seniority force is used for the pairing channel. Contrary to what was expected, our preliminary results show no improvement on the band-head spectra as compared to data when the Coulomb-exchange term is calculated exactly.

Identification of penetration path and deposition distribution of radionuclides in houses by experiments and numerical model

NASA Astrophysics Data System (ADS)

Hirouchi, Jun; Takahara, Shogo; Iijima, Masashi; Watanabe, Masatoshi; Munakata, Masahiro

2017-11-01

In order to lift of an evacuation order in evacuation areas and return residents to their homes, human dose assessments are required. However, it is difficult to exactly assess indoor external dose rate because the indoor distribution and infiltration pathways of radionuclides are unclear. This paper describes indoor and outdoor dose rates measured in eight houses in the difficult-to-return area in Fukushima Prefecture and identifies the distribution and main infiltration pathway of radionuclides in houses. In addition, it describes dose rates calculated with a Monte Carlo photon transport code to aid a thorough understanding of the measurements. The measurements and calculations indicate that radionuclides mainly infiltrate through visible openings such as vents, windows, and doors, and then deposit near these visible openings; however, they hardly infiltrate through sockets and air conditioning outlets. The measurements on rough surfaces such as bookshelves implies that radionuclides discharged from the Fukushima-Daiichi nuclear power plant did not deposit locally on rough surfaces.

Unified semiclassical theory for the two-state system: an analytical solution for general nonadiabatic tunneling.

PubMed

Zhu, Chaoyuan; Lin, Sheng Hsien

2006-07-28

Unified semiclasical solution for general nonadiabatic tunneling between two adiabatic potential energy surfaces is established by employing unified semiclassical solution for pure nonadiabatic transition [C. Zhu, J. Chem. Phys. 105, 4159 (1996)] with the certain symmetry transformation. This symmetry comes from a detailed analysis of the reduced scattering matrix for Landau-Zener type of crossing as a special case of nonadiabatic transition and nonadiabatic tunneling. Traditional classification of crossing and noncrossing types of nonadiabatic transition can be quantitatively defined by the rotation angle of adiabatic-to-diabatic transformation, and this rotational angle enters the analytical solution for general nonadiabatic tunneling. The certain two-state exponential potential models are employed for numerical tests, and the calculations from the present general nonadiabatic tunneling formula are demonstrated in very good agreement with the results from exact quantum mechanical calculations. The present general nonadiabatic tunneling formula can be incorporated with various mixed quantum-classical methods for modeling electronically nonadiabatic processes in photochemistry.

Exact Fourier expansion in cylindrical coordinates for the three-dimensional Helmholtz Green function

NASA Astrophysics Data System (ADS)

Conway, John T.; Cohl, Howard S.

2010-06-01

A new method is presented for Fourier decomposition of the Helmholtz Green function in cylindrical coordinates, which is equivalent to obtaining the solution of the Helmholtz equation for a general ring source. The Fourier coefficients of the Green function are split into their half advanced + half retarded and half advanced-half retarded components, and closed form solutions for these components are then obtained in terms of a Horn function and a Kampé de Fériet function respectively. Series solutions for the Fourier coefficients are given in terms of associated Legendre functions, Bessel and Hankel functions and a hypergeometric function. These series are derived either from the closed form 2-dimensional hypergeometric solutions or from an integral representation, or from both. A simple closed form far-field solution for the general Fourier coefficient is derived from the Hankel series. Numerical calculations comparing different methods of calculating the Fourier coefficients are presented. Fourth order ordinary differential equations for the Fourier coefficients are also given and discussed briefly.

Exact solution of mean-field plus an extended T = 1 nuclear pairing Hamiltonian in the seniority-zero symmetric subspace

NASA Astrophysics Data System (ADS)

Pan, Feng; Ding, Xiaoxue; Launey, Kristina D.; Dai, Lianrong; Draayer, Jerry P.

2018-05-01

An extended pairing Hamiltonian that describes multi-pair interactions among isospin T = 1 and angular momentum J = 0 neutron-neutron, proton-proton, and neutron-proton pairs in a spherical mean field, such as the spherical shell model, is proposed based on the standard T = 1 pairing formalism. The advantage of the model lies in the fact that numerical solutions within the seniority-zero symmetric subspace can be obtained more easily and with less computational time than those calculated from the mean-field plus standard T = 1 pairing model. Thus, large-scale calculations within the seniority-zero symmetric subspace of the model is feasible. As an example of the application, the average neutron-proton interaction in even-even N ∼ Z nuclei that can be suitably described in the f5 pg9 shell is estimated in the present model, with a focus on the role of np-pairing correlations.

Hierarchy of stochastic Schrödinger equation towards the calculation of absorption and circular dichroism spectra.

PubMed

Ke, Yaling; Zhao, Yi

2017-05-07

A theoretically solid and numerically exact method is presented for the calculation of absorption and circular dichroism (CD) spectra of molecular aggregates immersed in a harmonic bath constituted as the combination of some prominent quantized vibrational modes and continuous overdamped Brownian oscillators. The feasibility and the validity of newly proposed method are affirmed in the analytical monomer spectra. To go beyond the independent local bath approximation, all the correlations of site energy fluctuations and excitonic coupling fluctuations are included in our strategy, and their influence on the absorption and CD spectra is investigated based on the Frenkel exciton model of homodimer. In the end, a good fit of the absorption and part of CD spectra for the entire B800-B850 ring in the light-harvesting complexes 2 of purple bacteria to the experimental data is given, and the simulation results suggest that the asymmetry in the 800 nm region of CD spectra is actually an indication of B800-B850 inter-ring coupling.

Distribution of genome shared identical by descent by two individuals in grandparent-type relationship.

PubMed Central

Stefanov, V T

2000-01-01

A methodology is introduced for numerical evaluation, with any given accuracy, of the cumulative probabilities of the proportion of genome shared identical by descent (IBD) on chromosome segments by two individuals in a grandparent-type relationship. Programs are provided in the popular software package Maple for rapidly implementing such evaluations in the cases of grandchild-grandparent and great-grandchild-great-grandparent relationships. Our results can be used to identify chromosomal segments that may contain disease genes. Also, exact P values in significance testing for resemblance of either a grandparent with a grandchild or a great-grandparent with a great-grandchild can be calculated. The genomic continuum model, with Haldane's model for the crossover process, is assumed. This is the model that has been used recently in the genetics literature devoted to IBD calculations. Our methodology is based on viewing the model as a special exponential family and elaborating on recent research results for such families. PMID:11063711

Hierarchy of stochastic Schrödinger equation towards the calculation of absorption and circular dichroism spectra

NASA Astrophysics Data System (ADS)

Ke, Yaling; Zhao, Yi

2017-05-01

A theoretically solid and numerically exact method is presented for the calculation of absorption and circular dichroism (CD) spectra of molecular aggregates immersed in a harmonic bath constituted as the combination of some prominent quantized vibrational modes and continuous overdamped Brownian oscillators. The feasibility and the validity of newly proposed method are affirmed in the analytical monomer spectra. To go beyond the independent local bath approximation, all the correlations of site energy fluctuations and excitonic coupling fluctuations are included in our strategy, and their influence on the absorption and CD spectra is investigated based on the Frenkel exciton model of homodimer. In the end, a good fit of the absorption and part of CD spectra for the entire B800-B850 ring in the light-harvesting complexes 2 of purple bacteria to the experimental data is given, and the simulation results suggest that the asymmetry in the 800 nm region of CD spectra is actually an indication of B800-B850 inter-ring coupling.

ANALYZING NUMERICAL ERRORS IN DOMAIN HEAT TRANSPORT MODELS USING THE CVBEM.

USGS Publications Warehouse

Hromadka, T.V.

1987-01-01

Besides providing an exact solution for steady-state heat conduction processes (Laplace-Poisson equations), the CVBEM (complex variable boundary element method) can be used for the numerical error analysis of domain model solutions. For problems where soil-water phase change latent heat effects dominate the thermal regime, heat transport can be approximately modeled as a time-stepped steady-state condition in the thawed and frozen regions, respectively. The CVBEM provides an exact solution of the two-dimensional steady-state heat transport problem, and also provides the error in matching the prescribed boundary conditions by the development of a modeling error distribution or an approximate boundary generation.

Localized solutions of Lugiato-Lefever equations with focused pump.

PubMed

Cardoso, Wesley B; Salasnich, Luca; Malomed, Boris A

2017-12-04

Lugiato-Lefever (LL) equations in one and two dimensions (1D and 2D) accurately describe the dynamics of optical fields in pumped lossy cavities with the intrinsic Kerr nonlinearity. The external pump is usually assumed to be uniform, but it can be made tightly focused too-in particular, for building small pixels. We obtain solutions of the LL equations, with both the focusing and defocusing intrinsic nonlinearity, for 1D and 2D confined modes supported by the localized pump. In the 1D setting, we first develop a simple perturbation theory, based in the sech ansatz, in the case of weak pump and loss. Then, a family of exact analytical solutions for spatially confined modes is produced for the pump focused in the form of a delta-function, with a nonlinear loss (two-photon absorption) added to the LL model. Numerical findings demonstrate that these exact solutions are stable, both dynamically and structurally (the latter means that stable numerical solutions close to the exact ones are found when a specific condition, necessary for the existence of the analytical solution, does not hold). In 2D, vast families of stable confined modes are produced by means of a variational approximation and full numerical simulations.

Fully Nonlinear Modeling and Analysis of Precision Membranes

NASA Technical Reports Server (NTRS)

Pai, P. Frank; Young, Leyland G.

2003-01-01

High precision membranes are used in many current space applications. This paper presents a fully nonlinear membrane theory with forward and inverse analyses of high precision membrane structures. The fully nonlinear membrane theory is derived from Jaumann strains and stresses, exact coordinate transformations, the concept of local relative displacements, and orthogonal virtual rotations. In this theory, energy and Newtonian formulations are fully correlated, and every structural term can be interpreted in terms of vectors. Fully nonlinear ordinary differential equations (ODES) governing the large static deformations of known axisymmetric membranes under known axisymmetric loading (i.e., forward problems) are presented as first-order ODES, and a method for obtaining numerically exact solutions using the multiple shooting procedure is shown. A method for obtaining the undeformed geometry of any axisymmetric membrane with a known inflated geometry and a known internal pressure (i.e., inverse problems) is also derived. Numerical results from forward analysis are verified using results in the literature, and results from inverse analysis are verified using known exact solutions and solutions from the forward analysis. Results show that the membrane theory and the proposed numerical methods for solving nonlinear forward and inverse membrane problems are accurate.

Numerical Calculation of the Peaking Factor of a Water-Cooled W/Cu Monoblock for a Divertor

NASA Astrophysics Data System (ADS)

Han, Le; Chang, Haiping; Zhang, Jingyang; Xu, Tiejun

2015-09-01

In order to accurately predict the incident critical heat flux (ICHF, the heat flux at the heated surface when CHF occurs) of a water-cooled W/Cu monoblock for a divertor, the exact knowledge of its peaking factors (fp) under one-sided heating conditions with different design parameters is a key issue. In this paper, the heat conduction in the solid domain of a water-cooled W/Cu monoblock is calculated numerically by assuming the local heat transfer coefficients (HTC) of the cooling wall to be functions of the local wall temperature, so as to obtain fp. The reliability of the calculation method is validated by an experimental example result, with the maximum error of 2.1% only. The effects of geometric and flow parameters on the fp of a water-cooled W/Cu monoblock are investigated. Within the scope of this study, it is shown that the fp increases with increasing dimensionless W/Cu monoblock width and armour thickness (the shortest distance between the heated surface and Cu layer), and the maximum increases are 43.8% and 22.4% respectively. The dimensionless W/Cu monoblock height and Cu thickness have little effect on fp. The increase of Reynolds number and Jakob number causes the increase of fp, and the maximum increases are 6.8% and 9.6% respectively. Based on the calculated results, an empirical correlation on peaking factor is obtained via regression. These results provide a valuable reference for the thermal-hydraulic design of water-cooled divertors. supported by National Magnetic Confinement Fusion Science Program of China (No. 2010GB104005) and Funding of Jiangsu Innovation Program for Graduate Education, China (CXLX12_0170), the Fundamental Research Funds for the Central Universities of China

Efficient Sample Delay Calculation for 2-D and 3-D Ultrasound Imaging.

PubMed

Ibrahim, Aya; Hager, Pascal A; Bartolini, Andrea; Angiolini, Federico; Arditi, Marcel; Thiran, Jean-Philippe; Benini, Luca; De Micheli, Giovanni

2017-08-01

Ultrasound imaging is a reference medical diagnostic technique, thanks to its blend of versatility, effectiveness, and moderate cost. The core computation of all ultrasound imaging methods is based on simple formulae, except for those required to calculate acoustic propagation delays with high precision and throughput. Unfortunately, advanced three-dimensional (3-D) systems require the calculation or storage of billions of such delay values per frame, which is a challenge. In 2-D systems, this requirement can be four orders of magnitude lower, but efficient computation is still crucial in view of low-power implementations that can be battery-operated, enabling usage in numerous additional scenarios. In this paper, we explore two smart designs of the delay generation function. To quantify their hardware cost, we implement them on FPGA and study their footprint and performance. We evaluate how these architectures scale to different ultrasound applications, from a low-power 2-D system to a next-generation 3-D machine. When using numerical approximations, we demonstrate the ability to generate delay values with sufficient throughput to support 10 000-channel 3-D imaging at up to 30 fps while using 63% of a Virtex 7 FPGA, requiring 24 MB of external memory accessed at about 32 GB/s bandwidth. Alternatively, with similar FPGA occupation, we show an exact calculation method that reaches 24 fps on 1225-channel 3-D imaging and does not require external memory at all. Both designs can be scaled to use a negligible amount of resources for 2-D imaging in low-power applications and for ultrafast 2-D imaging at hundreds of frames per second.

Diagrammatic Monte Carlo approach for diagrammatic extensions of dynamical mean-field theory: Convergence analysis of the dual fermion technique

NASA Astrophysics Data System (ADS)

Gukelberger, Jan; Kozik, Evgeny; Hafermann, Hartmut

2017-07-01

The dual fermion approach provides a formally exact prescription for calculating properties of a correlated electron system in terms of a diagrammatic expansion around dynamical mean-field theory (DMFT). Most practical implementations, however, neglect higher-order interaction vertices beyond two-particle scattering in the dual effective action and further truncate the diagrammatic expansion in the two-particle scattering vertex to a leading-order or ladder-type approximation. In this work, we compute the dual fermion expansion for the two-dimensional Hubbard model including all diagram topologies with two-particle interactions to high orders by means of a stochastic diagrammatic Monte Carlo algorithm. We benchmark the obtained self-energy against numerically exact diagrammatic determinant Monte Carlo simulations to systematically assess convergence of the dual fermion series and the validity of these approximations. We observe that, from high temperatures down to the vicinity of the DMFT Néel transition, the dual fermion series converges very quickly to the exact solution in the whole range of Hubbard interactions considered (4 ≤U /t ≤12 ), implying that contributions from higher-order vertices are small. As the temperature is lowered further, we observe slower series convergence, convergence to incorrect solutions, and ultimately divergence. This happens in a regime where magnetic correlations become significant. We find, however, that the self-consistent particle-hole ladder approximation yields reasonable and often even highly accurate results in this regime.

Reduced Dynamics of the Non-holonomic Whipple Bicycle

NASA Astrophysics Data System (ADS)

Boyer, Frédéric; Porez, Mathieu; Mauny, Johan

2018-06-01

Though the bicycle is a familiar object of everyday life, modeling its full nonlinear three-dimensional dynamics in a closed symbolic form is a difficult issue for classical mechanics. In this article, we address this issue without resorting to the usual simplifications on the bicycle kinematics nor its dynamics. To derive this model, we use a general reduction-based approach in the principal fiber bundle of configurations of the three-dimensional bicycle. This includes a geometrically exact model of the contacts between the wheels and the ground, the explicit calculation of the kernel of constraints, along with the dynamics of the system free of any external forces, and its projection onto the kernel of admissible velocities. The approach takes benefits of the intrinsic formulation of geometric mechanics. Along the path toward the final equations, we show that the exact model of the bicycle dynamics requires to cope with a set of non-symmetric constraints with respect to the structural group of its configuration fiber bundle. The final reduced dynamics are simulated on several examples representative of the bicycle. As expected the constraints imposed by the ground contacts, as well as the energy conservation, are satisfied, while the dynamics can be numerically integrated in real time.

Bubble nuclei within the self-consistent Hartree-Fock mean field plus pairing approach

NASA Astrophysics Data System (ADS)

Phuc, L. Tan; Hung, N. Quang; Dang, N. Dinh

2018-02-01

The depletion of the nuclear density at its center, called the nuclear bubble, is studied within the Skyrme Hartree-Fock mean field consistently incorporating the superfluid pairing. The latter is obtained within the finite-temperature Bardeen-Cooper-Schrieffer theory and within the approach using the exact pairing. The numerical calculations are carried out for 22O and 34Si nuclei, whose bubble structures, caused by a very low occupancy of the 2 s1 /2 level, were previously predicted at T =0 . Among 24 Skyrme interactions under consideration, the MSk3 is the only one which reproduces the experimentally measured occupancy of the 2 s1 /2 proton level as well as the binding energy, and consequently produces the most pronounced bubble structure in 34Si. As compared to the approaches employing the same BSk14 interaction, our approach with exact pairing predicts a pairing effect which is stronger in 22O and weaker in 34Si. The increase in temperature depletes the bubble structure and completely washes it out when the temperature reaches a critical value, at which the factor measuring the depletion of the nucleon density vanishes.

Communication: An exact bound on the bridge function in integral equation theories.

PubMed

Kast, Stefan M; Tomazic, Daniel

2012-11-07

We show that the formal solution of the general closure relation occurring in Ornstein-Zernike-type integral equation theories in terms of the Lambert W function leads to an exact relation between the bridge function and correlation functions, most notably to an inequality that bounds possible bridge values. The analytical results are illustrated on the example of the Lennard-Jones fluid for which the exact bridge function is known from computer simulations under various conditions. The inequality has consequences for the development of bridge function models and rationalizes numerical convergence issues.

Benchmark Problems Used to Assess Computational Aeroacoustics Codes

NASA Technical Reports Server (NTRS)

Dahl, Milo D.; Envia, Edmane

2005-01-01

The field of computational aeroacoustics (CAA) encompasses numerical techniques for calculating all aspects of sound generation and propagation in air directly from fundamental governing equations. Aeroacoustic problems typically involve flow-generated noise, with and without the presence of a solid surface, and the propagation of the sound to a receiver far away from the noise source. It is a challenge to obtain accurate numerical solutions to these problems. The NASA Glenn Research Center has been at the forefront in developing and promoting the development of CAA techniques and methodologies for computing the noise generated by aircraft propulsion systems. To assess the technological advancement of CAA, Glenn, in cooperation with the Ohio Aerospace Institute and the AeroAcoustics Research Consortium, organized and hosted the Fourth CAA Workshop on Benchmark Problems. Participants from industry and academia from both the United States and abroad joined to present and discuss solutions to benchmark problems. These demonstrated technical progress ranging from the basic challenges to accurate CAA calculations to the solution of CAA problems of increasing complexity and difficulty. The results are documented in the proceedings of the workshop. Problems were solved in five categories. In three of the five categories, exact solutions were available for comparison with CAA results. A fourth category of problems representing sound generation from either a single airfoil or a blade row interacting with a gust (i.e., problems relevant to fan noise) had approximate analytical or completely numerical solutions. The fifth category of problems involved sound generation in a viscous flow. In this case, the CAA results were compared with experimental data.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wintermeyer, Niklas; Winters, Andrew R., E-mail: awinters@math.uni-koeln.de; Gassner, Gregor J.

We design an arbitrary high-order accurate nodal discontinuous Galerkin spectral element approximation for the non-linear two dimensional shallow water equations with non-constant, possibly discontinuous, bathymetry on unstructured, possibly curved, quadrilateral meshes. The scheme is derived from an equivalent flux differencing formulation of the split form of the equations. We prove that this discretization exactly preserves the local mass and momentum. Furthermore, combined with a special numerical interface flux function, the method exactly preserves the mathematical entropy, which is the total energy for the shallow water equations. By adding a specific form of interface dissipation to the baseline entropy conserving schememore » we create a provably entropy stable scheme. That is, the numerical scheme discretely satisfies the second law of thermodynamics. Finally, with a particular discretization of the bathymetry source term we prove that the numerical approximation is well-balanced. We provide numerical examples that verify the theoretical findings and furthermore provide an application of the scheme for a partial break of a curved dam test problem.« less

Analytic representations of mK , FK, mη, and Fη in two loop S U (3 ) chiral perturbation theory

NASA Astrophysics Data System (ADS)

Ananthanarayan, B.; Bijnens, Johan; Friot, Samuel; Ghosh, Shayan

2018-06-01

In this work, we consider expressions for the masses and decay constants of the pseudoscalar mesons in S U (3 ) chiral perturbation theory. These involve sunset diagrams and their derivatives evaluated at p2=mP2 (P =π , K , η ). Recalling that there are three mass scales in this theory, mπ, mK and mη, there are instances when the finite part of the sunset diagrams do not admit an expression in terms of elementary functions, and have therefore been evaluated numerically in the past. In a recent publication, an expansion in the external momentum was performed to obtain approximate analytic expressions for mπ and Fπ, the pion mass and decay constant. We provide fully analytic exact expressions for mK and mη, the kaon and eta masses, and FK and Fη, the kaon and eta decay constants. These expressions, calculated using Mellin-Barnes methods, are in the form of double series in terms of two mass ratios. A numerical analysis of the results to evaluate the relative size of contributions coming from loops, chiral logarithms as well as phenomenological low-energy constants is presented. We also present a set of approximate analytic expressions for mK, FK, mη and Fη that facilitate comparisons with lattice results. Finally, we show how exact analytic expressions for mπ and Fπ may be obtained, the latter having been used in conjunction with the results for FK to produce a recently published analytic representation of FK/Fπ.

Classical Control System Design: A non-Graphical Method for Finding the Exact System Parameters

NASA Astrophysics Data System (ADS)

Hussein, Mohammed Tawfik

2008-06-01

The Root Locus method of control system design was developed in the 1940's. It is a set of rules that helps in sketching the path traced by the roots of the closed loop characteristic equation of the system, as a parameter such as a controller gain, k, is varied. The procedure provides approximate sketching guidelines. Designs on control systems using the method are therefore not exact. This paper aims at a non-graphical method for finding the exact system parameters to place a pair of complex conjugate poles on a specified damping ratio line. The overall procedure is based on the exact solution of complex equations on the PC using numerical methods.

Detailed noise statistics for an optically preamplified direct detection receiver

NASA Astrophysics Data System (ADS)

Danielsen, Soeren Lykke; Mikkelsen, Benny; Durhuus, Terji; Joergensen, Carsten; Stubkjaer, Kristian E.

We describe the exact statistics of an optically preamplified direct detection receiver by means of the moment generating function. The theory allows an arbitrary shaped electrical filter in the receiver circuit. The moment generating function (MGF) allows for a precise calculation of the error rate by using the inverse Fast Fourier transform (FFT). The exact results are compared with the usual Gaussian approximation (GA), the saddlepoint approximation (SAP) and the modified Chernoff bound (MCB). This comparison shows that the noise is not Gaussian distributed for all values of the optical amplifier gain. In the region from 20-30 dB gain, calculations shows that the GA underestimates the receiver sensitivity while the SAP is very close to the results of our exact model. Using the MGF derived in the article we then find the optimal bandwidth of the electrical filter in the receiver circuit and calculate the sensitivity degradation due to inter symbol interference (ISI).

A Galleria Boundary Element Method for two-dimensional nonlinear magnetostatics

NASA Astrophysics Data System (ADS)

Brovont, Aaron D.

The Boundary Element Method (BEM) is a numerical technique for solving partial differential equations that is used broadly among the engineering disciplines. The main advantage of this method is that one needs only to mesh the boundary of a solution domain. A key drawback is the myriad of integrals that must be evaluated to populate the full system matrix. To this day these integrals have been evaluated using numerical quadrature. In this research, a Galerkin formulation of the BEM is derived and implemented to solve two-dimensional magnetostatic problems with a focus on accurate, rapid computation. To this end, exact, closed-form solutions have been derived for all the integrals comprising the system matrix as well as those required to compute fields in post-processing; the need for numerical integration has been eliminated. It is shown that calculation of the system matrix elements using analytical solutions is 15-20 times faster than with numerical integration of similar accuracy. Furthermore, through the example analysis of a c-core inductor, it is demonstrated that the present BEM formulation is a competitive alternative to the Finite Element Method (FEM) for linear magnetostatic analysis. Finally, the BEM formulation is extended to analyze nonlinear magnetostatic problems via the Dual Reciprocity Method (DRBEM). It is shown that a coarse, meshless analysis using the DRBEM is able to achieve RMS error of 3-6% compared to a commercial FEM package in lightly saturated conditions.

Ab initio excited states from the in-medium similarity renormalization group

NASA Astrophysics Data System (ADS)

Parzuchowski, N. M.; Morris, T. D.; Bogner, S. K.

2017-04-01

We present two new methods for performing ab initio calculations of excited states for closed-shell systems within the in-medium similarity renormalization group (IMSRG) framework. Both are based on combining the IMSRG with simple many-body methods commonly used to target excited states, such as the Tamm-Dancoff approximation (TDA) and equations-of-motion (EOM) techniques. In the first approach, a two-step sequential IMSRG transformation is used to drive the Hamiltonian to a form where a simple TDA calculation (i.e., diagonalization in the space of 1 p 1 h excitations) becomes exact for a subset of eigenvalues. In the second approach, EOM techniques are applied to the IMSRG ground-state-decoupled Hamiltonian to access excited states. We perform proof-of-principle calculations for parabolic quantum dots in two dimensions and the closed-shell nuclei 16O and 22O. We find that the TDA-IMSRG approach gives better accuracy than the EOM-IMSRG when calculations converge, but it is otherwise lacking the versatility and numerical stability of the latter. Our calculated spectra are in reasonable agreement with analogous EOM-coupled-cluster calculations. This work paves the way for more interesting applications of the EOM-IMSRG approach to calculations of consistently evolved observables such as electromagnetic strength functions and nuclear matrix elements, and extensions to nuclei within one or two nucleons of a closed shell by generalizing the EOM ladder operator to include particle-number nonconserving terms.

Computer-Aided Construction of Chemical Kinetic Models

DOE Office of Scientific and Technical Information (OSTI.GOV)

Green, William H.

2014-12-31

The combustion chemistry of even simple fuels can be extremely complex, involving hundreds or thousands of kinetically significant species. The most reasonable way to deal with this complexity is to use a computer not only to numerically solve the kinetic model, but also to construct the kinetic model in the first place. Because these large models contain so many numerical parameters (e.g. rate coefficients, thermochemistry) one never has sufficient data to uniquely determine them all experimentally. Instead one must work in “predictive” mode, using theoretical rather than experimental values for many of the numbers in the model, and as appropriatemore » refining the most sensitive numbers through experiments. Predictive chemical kinetics is exactly what is needed for computer-aided design of combustion systems based on proposed alternative fuels, particularly for early assessment of the value and viability of proposed new fuels before those fuels are commercially available. This project was aimed at making accurate predictive chemical kinetics practical; this is a challenging goal which requires a range of science advances. The project spanned a wide range from quantum chemical calculations on individual molecules and elementary-step reactions, through the development of improved rate/thermo calculation procedures, the creation of algorithms and software for constructing and solving kinetic simulations, the invention of methods for model-reduction while maintaining error control, and finally comparisons with experiment. Many of the parameters in the models were derived from quantum chemistry calculations, and the models were compared with experimental data measured in our lab or in collaboration with others.« less

Modified Mixed Lagrangian-Eulerian Method Based on Numerical Framework of MT3DMS on Cauchy Boundary.

PubMed

Suk, Heejun

2016-07-01

MT3DMS, a modular three-dimensional multispecies transport model, has long been a popular model in the groundwater field for simulating solute transport in the saturated zone. However, the method of characteristics (MOC), modified MOC (MMOC), and hybrid MOC (HMOC) included in MT3DMS did not treat Cauchy boundary conditions in a straightforward or rigorous manner, from a mathematical point of view. The MOC, MMOC, and HMOC regard the Cauchy boundary as a source condition. For the source, MOC, MMOC, and HMOC calculate the Lagrangian concentration by setting it equal to the cell concentration at an old time level. However, the above calculation is an approximate method because it does not involve backward tracking in MMOC and HMOC or allow performing forward tracking at the source cell in MOC. To circumvent this problem, a new scheme is proposed that avoids direct calculation of the Lagrangian concentration on the Cauchy boundary. The proposed method combines the numerical formulations of two different schemes, the finite element method (FEM) and the Eulerian-Lagrangian method (ELM), into one global matrix equation. This study demonstrates the limitation of all MT3DMS schemes, including MOC, MMOC, HMOC, and a third-order total-variation-diminishing (TVD) scheme under Cauchy boundary conditions. By contrast, the proposed method always shows good agreement with the exact solution, regardless of the flow conditions. Finally, the successful application of the proposed method sheds light on the possible flexibility and capability of the MT3DMS to deal with the mass transport problems of all flow regimes. © 2016, National Ground Water Association.

Gravitational waves and core-collapse supernovae

NASA Astrophysics Data System (ADS)

Bisnovatyi-Kogan, G. S.; Moiseenko, S. G.

2017-11-01

A mechanism of formation of gravitational waves in the Universe is considered for a nonspherical collapse of matter. Nonspherical collapse results are presented for a uniform spheroid of dust and a finite-entropy spheroid. Numerical simulation results on core-collapse supernova explosions are presented for the neutrino and magneto-rotational models. These results are used to estimate the dimensionless amplitude of the gravitational wave with a frequency ν ~ 1300 Hz, radiated during the collapse of the rotating core of a pre-supernova with a mass of 1.2 M⊙ (calculated by the authors in 2D). This estimate agrees well with many other calculations (presented in this paper) that have been done in 2D and 3D settings and which rely on more exact and sophisticated calculations of the gravitational wave amplitude. The formation of the large-scale structure of the Universe in the Zel’dovich pancake model involves the emission of very long-wavelength gravitational waves. The average amplitude of these waves is calculated from the simulation, in the uniform spheroid approximation, of the nonspherical collapse of noncollisional dust matter, which imitates dark matter. It is noted that a gravitational wave radiated during a core-collapse supernova explosion in our Galaxy has a sufficient amplitude to be detected by existing gravitational wave telescopes.

Numerical approach for finite volume three-body interaction

NASA Astrophysics Data System (ADS)

Guo, Peng; Gasparian, Vladimir

2018-01-01

In the present work, we study a numerical approach to one dimensional finite volume three-body interaction, the method is demonstrated by considering a toy model of three spinless particles interacting with pair-wise δ -function potentials. The numerical results are compared with the exact solutions of three spinless bosons interaction when the strength of short-range interactions are set equal for all pairs.

Numerical investigation of sixth order Boussinesq equation

NASA Astrophysics Data System (ADS)

Kolkovska, N.; Vucheva, V.

2017-10-01

We propose a family of conservative finite difference schemes for the Boussinesq equation with sixth order dispersion terms. The schemes are of second order of approximation. The method is conditionally stable with a mild restriction τ = O(h) on the step sizes. Numerical tests are performed for quadratic and cubic nonlinearities. The numerical experiments show second order of convergence of the discrete solution to the exact one.

Numerical evaluation of the bispectrum in multiple field inflation—the transport approach with code

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dias, Mafalda; Frazer, Jonathan; Mulryne, David J.

2016-12-01

We present a complete framework for numerical calculation of the power spectrum and bispectrum in canonical inflation with an arbitrary number of light or heavy fields. Our method includes all relevant effects at tree-level in the loop expansion, including (i) interference between growing and decaying modes near horizon exit; (ii) correlation and coupling between species near horizon exit and on superhorizon scales; (iii) contributions from mass terms; and (iv) all contributions from coupling to gravity. We track the evolution of each correlation function from the vacuum state through horizon exit and the superhorizon regime, with no need to match quantummore » and classical parts of the calculation; when integrated, our approach corresponds exactly with the tree-level Schwinger or 'in-in' formulation of quantum field theory. In this paper we give the equations necessary to evolve all two- and three-point correlation functions together with suitable initial conditions. The final formalism is suitable to compute the amplitude, shape, and scale dependence of the bispectrum in models with | f {sub NL}| of order unity or less, which are a target for future galaxy surveys such as Euclid, DESI and LSST. As an illustration we apply our framework to a number of examples, obtaining quantitatively accurate predictions for their bispectra for the first time. Two accompanying reports describe publicly-available software packages that implement the method.« less

Numerical evaluation of the bispectrum in multiple field inflation—the transport approach with code

NASA Astrophysics Data System (ADS)

Dias, Mafalda; Frazer, Jonathan; Mulryne, David J.; Seery, David

2016-12-01

We present a complete framework for numerical calculation of the power spectrum and bispectrum in canonical inflation with an arbitrary number of light or heavy fields. Our method includes all relevant effects at tree-level in the loop expansion, including (i) interference between growing and decaying modes near horizon exit; (ii) correlation and coupling between species near horizon exit and on superhorizon scales; (iii) contributions from mass terms; and (iv) all contributions from coupling to gravity. We track the evolution of each correlation function from the vacuum state through horizon exit and the superhorizon regime, with no need to match quantum and classical parts of the calculation; when integrated, our approach corresponds exactly with the tree-level Schwinger or `in-in' formulation of quantum field theory. In this paper we give the equations necessary to evolve all two- and three-point correlation functions together with suitable initial conditions. The final formalism is suitable to compute the amplitude, shape, and scale dependence of the bispectrum in models with |fNL| of order unity or less, which are a target for future galaxy surveys such as Euclid, DESI and LSST. As an illustration we apply our framework to a number of examples, obtaining quantitatively accurate predictions for their bispectra for the first time. Two accompanying reports describe publicly-available software packages that implement the method.

Physically consistent data assimilation method based on feedback control for patient-specific blood flow analysis.

PubMed

Ii, Satoshi; Adib, Mohd Azrul Hisham Mohd; Watanabe, Yoshiyuki; Wada, Shigeo

2018-01-01

This paper presents a novel data assimilation method for patient-specific blood flow analysis based on feedback control theory called the physically consistent feedback control-based data assimilation (PFC-DA) method. In the PFC-DA method, the signal, which is the residual error term of the velocity when comparing the numerical and reference measurement data, is cast as a source term in a Poisson equation for the scalar potential field that induces flow in a closed system. The pressure values at the inlet and outlet boundaries are recursively calculated by this scalar potential field. Hence, the flow field is physically consistent because it is driven by the calculated inlet and outlet pressures, without any artificial body forces. As compared with existing variational approaches, although this PFC-DA method does not guarantee the optimal solution, only one additional Poisson equation for the scalar potential field is required, providing a remarkable improvement for such a small additional computational cost at every iteration. Through numerical examples for 2D and 3D exact flow fields, with both noise-free and noisy reference data as well as a blood flow analysis on a cerebral aneurysm using actual patient data, the robustness and accuracy of this approach is shown. Moreover, the feasibility of a patient-specific practical blood flow analysis is demonstrated. Copyright © 2017 John Wiley & Sons, Ltd.

Stability of a dual-spin satellite with two dampers

NASA Technical Reports Server (NTRS)

Alfriend, K. T.; Hubert, C. H.

1974-01-01

The rotational stability of a dual-spin satellite consisting of a main body and a symmetric rotor, both spinning about a common axis, is investigated. The main body is equipped with a spring-mass damper, while a partially filled viscous ring damper is mounted on the rapidly spinning rotor. The effect of fluid motion on the rotational stability of the satellite is calculated, considering the fluid as a single particle moving in a tube with viscous damping. Time constants are obtained by solving approximate equations of motion for the nutation-synchronous and the spin-synchronous modes, and the results are found to agree well with the numerical integrations of the exact equations. A limit cycle may exist for some configurations; the nutation angle tends to increase in such cases.

Magnetocapacitance without magnetism

PubMed Central

Parish, Meera M.

2014-01-01

A substantial magnetodielectric effect is often an indication of coupled magnetic and elastic order, such as is found in the multi-ferroics. However, it has recently been shown that magnetism is not necessary to produce either a magnetoresistance or a magnetocapacitance when the material is inhomogeneous. Here, we will investigate the characteristic magnetic-field-dependent dielectric response of such an inhomogeneous system using exact calculations and numerical simulations of conductor–dielectric composites. In particular, we will show that even simple conductor–dielectric layers exhibit a magneto-capacitance, and thus random bulk inhomogeneities are not a requirement for this effect. Indeed, this work essentially provides a natural generalization of the Maxwell–Wagner effect to finite magnetic field. We will also discuss how this phenomenon has already been observed experimentally in some materials. PMID:24421378

Piecewise linear emulator of the nonlinear Schrödinger equation and the resulting analytic solutions for Bose-Einstein condensates.

PubMed

Theodorakis, Stavros

2003-06-01

We emulate the cubic term Psi(3) in the nonlinear Schrödinger equation by a piecewise linear term, thus reducing the problem to a set of uncoupled linear inhomogeneous differential equations. The resulting analytic expressions constitute an excellent approximation to the exact solutions, as is explicitly shown in the case of the kink, the vortex, and a delta function trap. Such a piecewise linear emulation can be used for any differential equation where the only nonlinearity is a Psi(3) one. In particular, it can be used for the nonlinear Schrödinger equation in the presence of harmonic traps, giving analytic Bose-Einstein condensate solutions that reproduce very accurately the numerically calculated ones in one, two, and three dimensions.

Dissolution of multicomponent bubbles. [gases in glass melts

NASA Technical Reports Server (NTRS)

Weinberg, M. C.; Subramanian, R. S.

1980-01-01

The behavior of an isolated, stationary, multicomponent gas bubble in a glassmelt containing several dissolved gases is considered. The relevant mass-transport equations are formulated and calculations are performed for the case of two diffusing gases using a quasi-stationary model and a numerical solution of the exact mass-transfer equations. The results obtained from these two approaches are compared. The factors which govern the dissolution or growth of a bubble are thermodynamic and kinetic in origin. The tendency of a bubble to grow or shrink at long times is controlled by departure from overall equilibrium, whereas the short-time bubble dynamics may be dominated by kinetic effects. As a result of the existence of these dual influences, maxima and/or minima occur in the functional dependence of the bubble radius on time.

Comment on "Hearing the signal of dark sectors with gravitational wave detectors"

NASA Astrophysics Data System (ADS)

Huang, Da; Lu, Bo-Qiang

2018-03-01

We revisit the calculation of the gravitational wave spectra generated in a classically scale-invariant S U (2 ) gauge sector with a scalar field in the adjoint representation, as discussed by J. Jaeckel, et al. The finite-temperature potential at 1-loop level can induce a strong first-order phase transition, during which gravitational waves can be generated. With the accurate numerical computation of the on-shell Euclidean actions of the nucleation bubbles, we find that the triangle approximation employed by J. Jaeckel et al. strongly distorts the actual potential near its maximum and thus greatly underestimates the action values. As a result, the gravitational wave spectra predicted by J. Jaeckel et al. deviate significantly from the exact ones in peak frequencies and shapes.

Design Tool Using a New Optimization Method Based on a Stochastic Process

NASA Astrophysics Data System (ADS)

Yoshida, Hiroaki; Yamaguchi, Katsuhito; Ishikawa, Yoshio

Conventional optimization methods are based on a deterministic approach since their purpose is to find out an exact solution. However, such methods have initial condition dependence and the risk of falling into local solution. In this paper, we propose a new optimization method based on the concept of path integrals used in quantum mechanics. The method obtains a solution as an expected value (stochastic average) using a stochastic process. The advantages of this method are that it is not affected by initial conditions and does not require techniques based on experiences. We applied the new optimization method to a hang glider design. In this problem, both the hang glider design and its flight trajectory were optimized. The numerical calculation results prove that performance of the method is sufficient for practical use.

An efficient method for solving the steady Euler equations

NASA Technical Reports Server (NTRS)

Liou, M.-S.

1986-01-01

An efficient numerical procedure for solving a set of nonlinear partial differential equations, the steady Euler equations, using Newton's linearization procedure is presented. A theorem indicating quadratic convergence for the case of differential equations is demonstrated. A condition for the domain of quadratic convergence Omega(2) is obtained which indicates that whether an approximation lies in Omega(2) depends on the rate of change and the smoothness of the flow vectors, and hence is problem-dependent. The choice of spatial differencing, of particular importance for the present method, is discussed. The treatment of boundary conditions is addressed, and the system of equations resulting from the foregoing analysis is summarized and solution strategies are discussed. The convergence of calculated solutions is demonstrated by comparing them with exact solutions to one and two-dimensional problems.

Numerical study of the Kitaev-Heisenberg chain

NASA Astrophysics Data System (ADS)

Agrapidis, Cliò Efthimia; van den Brink, Jeroen; Nishimoto, Satoshi

2018-05-01

We study the one-dimensional Kitaev-Heisenberg model as a possible realization of magnetic degrees of freedom of the K-intercalated honeycomb-lattice ruthenium trichloride α-RuCl3, denoted as K0.5RuClm. First, we discuss the possible charge ordering pattern in K0.5RuClm, where half of the j =1/2 spins are replaced by nonmagnetic ions in the honeycomb layer. Next, we investigate the low-energy excitations of the 1D Kitaev-Heisenberg model by calculating the dynamical spin structure factor using the Lanczos exact-diagonalization method. In the vicinity of Kitaev limit, there exist two well-separated dispersions. The bandwidth of each dispersion depends on the Heisenberg and Kitaev terms. This result may be relevant to the low-lying magnetic excitations of K0.5RuClm.

Development of Underwater Laser Scaling Adapter

NASA Astrophysics Data System (ADS)

Bluss, Kaspars

2012-12-01

In this paper the developed laser scaling adapter is presented. The scaling adapter is equipped with a twin laser unit where the two parallel laser beams are projected onto any target giving an exact indication of scale. The body of the laser scaling adapter is made of Teflon, the density of which is approximately two times the water density. The development involved multiple challenges - numerical hydrodynamic calculations for choosing an appropriate shape which would reduce the effects of turbulence, an accurate sealing of the power supply and the laser diodes, and others. The precision is estimated by the partial derivation method. Both experimental and theoretical data conclude the overall precision error to be in the 1% margin. This paper presents the development steps of such an underwater laser scaling adapter for a remotely operated vehicle (ROV).

Vibration-translation energy transfer in anharmonic diatomic molecules. 1: A critical evaluation of the semiclassical approximation

NASA Technical Reports Server (NTRS)

Mckenzie, R. L.

1974-01-01

The semiclassical approximation is applied to anharmonic diatomic oscillators in excited initial states. Multistate numerical solutions giving the vibrational transition probabilities for collinear collisions with an inert atom are compared with equivalent, exact quantum-mechanical calculations. Several symmetrization methods are shown to correlate accurately the predictions of both theories for all initial states, transitions, and molecular types tested, but only if coupling of the oscillator motion and the classical trajectory of the incident particle is considered. In anharmonic heteronuclear molecules, the customary semiclassical method of computing the classical trajectory independently leads to transition probabilities with anomalous low-energy resonances. Proper accounting of the effects of oscillator compression and recoil on the incident particle trajectory removes the anomalies and restores the applicability of the semiclassical approximation.

Effects of the Kelvin-Helmholtz surface instability on supersonic jets

NASA Technical Reports Server (NTRS)

Hardee, P. E.

1982-01-01

An exact numerical calculation is provided for of linear growth and phase velocity of Kelvin-Helmholtz unstable wave modes on a supersonic jet of cylindrical cross section. An expression for the maximally unstable wavenumber of each wave mode is found. Provided a sharp velocity discontinuity exists all wave modes are unstable. A combination of rapid jet expansion and velocity shear across a jet can effectively stabilize all wave modes. The more likely case of slow jet expansion and of velocity shear at the jet surface allows wave modes with maximally unstable wavelength longer than or on the order of the jet radius to grow. The relative energy in different wave modes and effect on the jet is investigated. Energy input into a jet resulting from surface instability is discussed.

Investigation of the Nicole model

DOE Office of Scientific and Technical Information (OSTI.GOV)

Adam, C.; Sanchez-Guillen, J.; Vazquez, R.A.

2006-05-15

We study soliton solutions of the Nicole model - a non-linear four-dimensional field theory consisting of the CP{sup 1} Lagrangian density to the non-integer power (3/2) - using an ansatz within toroidal coordinates, which is indicated by the conformal symmetry of the static equations of motion. We calculate the soliton energies numerically and find that they grow linearly with the topological charge (Hopf index). Further we prove this behavior to hold exactly for the ansatz. On the other hand, for the full three-dimensional system without symmetry reduction we prove a sub-linear upper bound, analogously to the case of the Faddeev-Niemimore » model. It follows that symmetric solitons cannot be true minimizers of the energy for sufficiently large Hopf index, again in analogy to the Faddeev-Niemi model.« less

Ultracold Atoms in a Square Lattice with Spin-Orbit Coupling: Charge Order, Superfluidity, and Topological Signatures

NASA Astrophysics Data System (ADS)

Rosenberg, Peter; Shi, Hao; Zhang, Shiwei

2017-12-01

We present an ab initio, numerically exact study of attractive fermions in square lattices with Rashba spin-orbit coupling. The ground state of this system is a supersolid, with coexisting charge and superfluid order. The superfluid is composed of both singlet and triplet pairs induced by spin-orbit coupling. We perform large-scale calculations using the auxiliary-field quantum Monte Carlo method to provide the first full, quantitative description of the charge, spin, and pairing properties of the system. In addition to characterizing the exotic physics, our results will serve as essential high-accuracy benchmarks for the intense theoretical and especially experimental efforts in ultracold atoms to realize and understand an expanding variety of quantum Hall and topological superconductor systems.

A k-space method for acoustic propagation using coupled first-order equations in three dimensions.

PubMed

Tillett, Jason C; Daoud, Mohammad I; Lacefield, James C; Waag, Robert C

2009-09-01

A previously described two-dimensional k-space method for large-scale calculation of acoustic wave propagation in tissues is extended to three dimensions. The three-dimensional method contains all of the two-dimensional method features that allow accurate and stable calculation of propagation. These features are spectral calculation of spatial derivatives, temporal correction that produces exact propagation in a homogeneous medium, staggered spatial and temporal grids, and a perfectly matched boundary layer. Spectral evaluation of spatial derivatives is accomplished using a fast Fourier transform in three dimensions. This computational bottleneck requires all-to-all communication; execution time in a parallel implementation is therefore sensitive to node interconnect latency and bandwidth. Accuracy of the three-dimensional method is evaluated through comparisons with exact solutions for media having spherical inhomogeneities. Large-scale calculations in three dimensions were performed by distributing the nearly 50 variables per voxel that are used to implement the method over a cluster of computers. Two computer clusters used to evaluate method accuracy are compared. Comparisons of k-space calculations with exact methods including absorption highlight the need to model accurately the medium dispersion relationships, especially in large-scale media. Accurately modeled media allow the k-space method to calculate acoustic propagation in tissues over hundreds of wavelengths.

Brief non-symbolic, approximate number practice enhances subsequent exact symbolic arithmetic in children

PubMed Central

Spelke, Elizabeth S.

2014-01-01

Recent research reveals a link between individual differences in mathematics achievement and performance on tasks that activate the approximate number system (ANS): a primitive cognitive system shared by diverse animal species and by humans of all ages. Here we used a brief experimental paradigm to test one causal hypothesis suggested by this relationship: activation of the ANS may enhance children's performance of symbolic arithmetic. Over 2 experiments, children who briefly practiced tasks that engaged primitive approximate numerical quantities performed better on subsequent exact, symbolic arithmetic problems than did children given other tasks involving comparison and manipulation of non-numerical magnitudes (brightness and length). The practice effect appeared specific to mathematics, as no differences between groups were observed on a comparable sentence completion task. These results move beyond correlational research and provide evidence that the exercise of non-symbolic numerical processes can enhance children's performance of symbolic mathematics. PMID:24462713

Numerical Hydrodynamics in Special Relativity.

PubMed

Martí, José Maria; Müller, Ewald

2003-01-01

This review is concerned with a discussion of numerical methods for the solution of the equations of special relativistic hydrodynamics (SRHD). Particular emphasis is put on a comprehensive review of the application of high-resolution shock-capturing methods in SRHD. Results of a set of demanding test bench simulations obtained with different numerical SRHD methods are compared. Three applications (astrophysical jets, gamma-ray bursts and heavy ion collisions) of relativistic flows are discussed. An evaluation of various SRHD methods is presented, and future developments in SRHD are analyzed involving extension to general relativistic hydrodynamics and relativistic magneto-hydrodynamics. The review further provides FORTRAN programs to compute the exact solution of a 1D relativistic Riemann problem with zero and nonzero tangential velocities, and to simulate 1D relativistic flows in Cartesian Eulerian coordinates using the exact SRHD Riemann solver and PPM reconstruction. Supplementary material is available for this article at 10.12942/lrr-2003-7 and is accessible for authorized users.

Use of multivariable asymptotic expansions in a satellite theory

NASA Technical Reports Server (NTRS)

Dallas, S. S.

1973-01-01

Initial conditions and perturbative force of satellite are restricted to yield motion of equatorial satellite about oblate body. In this manner, exact analytic solution exists and can be used as standard of comparison in numerical accuracy comparisons. Detailed numerical accuracy studies of uniformly valid asymptotic expansions were made.

Eigenstates and dynamics of Hooke's atom: Exact results and path integral simulations

NASA Astrophysics Data System (ADS)

Gholizadehkalkhoran, Hossein; Ruokosenmäki, Ilkka; Rantala, Tapio T.

2018-05-01

The system of two interacting electrons in one-dimensional harmonic potential or Hooke's atom is considered, again. On one hand, it appears as a model for quantum dots in a strong confinement regime, and on the other hand, it provides us with a hard test bench for new methods with the "space splitting" arising from the one-dimensional Coulomb potential. Here, we complete the numerous previous studies of the ground state of Hooke's atom by including the excited states and dynamics, not considered earlier. With the perturbation theory, we reach essentially exact eigenstate energies and wave functions for the strong confinement regime as novel results. We also consider external perturbation induced quantum dynamics in a simple separable case. Finally, we test our novel numerical approach based on real-time path integrals (RTPIs) in reproducing the above. The RTPI turns out to be a straightforward approach with exact account of electronic correlations for solving the eigenstates and dynamics without the conventional restrictions of electronic structure methods.

Distribution of joint local and total size and of extension for avalanches in the Brownian force model

NASA Astrophysics Data System (ADS)

Delorme, Mathieu; Le Doussal, Pierre; Wiese, Kay Jörg

2016-05-01

The Brownian force model is a mean-field model for local velocities during avalanches in elastic interfaces of internal space dimension d , driven in a random medium. It is exactly solvable via a nonlinear differential equation. We study avalanches following a kick, i.e., a step in the driving force. We first recall the calculation of the distributions of the global size (total swept area) and of the local jump size for an arbitrary kick amplitude. We extend this calculation to the joint density of local and global sizes within a single avalanche in the limit of an infinitesimal kick. When the interface is driven by a single point, we find new exponents τ0=5 /3 and τ =7 /4 , depending on whether the force or the displacement is imposed. We show that the extension of a "single avalanche" along one internal direction (i.e., the total length in d =1 ) is finite, and we calculate its distribution following either a local or a global kick. In all cases, it exhibits a divergence P (ℓ ) ˜ℓ-3 at small ℓ . Most of our results are tested in a numerical simulation in dimension d =1 .

Shadow poles in coupled-channel problems calculated with the Berggren basis

NASA Astrophysics Data System (ADS)

Id Betan, R. M.; Kruppa, A. T.; Vertse, T.

2018-02-01

Background: In coupled-channels models the poles of the scattering S matrix are located on different Riemann sheets. Physical observables are affected mainly by poles closest to the physical region but sometimes shadow poles have considerable effect too. Purpose: The purpose of this paper is to show that in coupled-channels problems all poles of the S matrix can be located by an expansion in terms of a properly constructed complex-energy basis. Method: The Berggren basis is used for expanding the coupled-channels solutions. Results: The locations of the poles of the S matrix for the Cox potential, constructed for coupled-channels problems, were numerically calculated and compared with the exact ones. In a nuclear physics application the Jπ=3 /2+ resonant poles of 5He were calculated in a phenomenological two-channel model. The properties of both the normal and shadow resonances agree with previous findings. Conclusions: We have shown that, with an appropriately chosen Berggren basis, all poles of the S matrix including the shadow poles can be determined. We have found that the shadow pole of 5He migrates between Riemann sheets if the coupling strength is varied.

Continuum description of solvent dielectrics in molecular-dynamics simulations of proteins

NASA Astrophysics Data System (ADS)

Egwolf, Bernhard; Tavan, Paul

2003-02-01

We present a continuum approach for efficient and accurate calculation of reaction field forces and energies in classical molecular-dynamics (MD) simulations of proteins in water. The derivation proceeds in two steps. First, we reformulate the electrostatics of an arbitrarily shaped molecular system, which contains partially charged atoms and is embedded in a dielectric continuum representing the water. A so-called fuzzy partition is used to exactly decompose the system into partial atomic volumes. The reaction field is expressed by means of dipole densities localized at the atoms. Since these densities cannot be calculated analytically for general systems, we introduce and carefully analyze a set of approximations in a second step. These approximations allow us to represent the dipole densities by simple dipoles localized at the atoms. We derive a system of linear equations for these dipoles, which can be solved numerically by iteration. After determining the two free parameters of our approximate method we check its quality by comparisons (i) with an analytical solution, which is available for a perfectly spherical system, (ii) with forces obtained from a MD simulation of a soluble protein in water, and (iii) with reaction field energies of small molecules calculated by a finite difference method.

Learn-as-you-go acceleration of cosmological parameter estimates

NASA Astrophysics Data System (ADS)

Aslanyan, Grigor; Easther, Richard; Price, Layne C.

2015-09-01

Cosmological analyses can be accelerated by approximating slow calculations using a training set, which is either precomputed or generated dynamically. However, this approach is only safe if the approximations are well understood and controlled. This paper surveys issues associated with the use of machine-learning based emulation strategies for accelerating cosmological parameter estimation. We describe a learn-as-you-go algorithm that is implemented in the Cosmo++ code and (1) trains the emulator while simultaneously estimating posterior probabilities; (2) identifies unreliable estimates, computing the exact numerical likelihoods if necessary; and (3) progressively learns and updates the error model as the calculation progresses. We explicitly describe and model the emulation error and show how this can be propagated into the posterior probabilities. We apply these techniques to the Planck likelihood and the calculation of ΛCDM posterior probabilities. The computation is significantly accelerated without a pre-defined training set and uncertainties in the posterior probabilities are subdominant to statistical fluctuations. We have obtained a speedup factor of 6.5 for Metropolis-Hastings and 3.5 for nested sampling. Finally, we discuss the general requirements for a credible error model and show how to update them on-the-fly.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Moore, II, Barry; Schrader, Robert L.; Kowalski, Karol

The longest-wavelength π-to-π* electronic excitations of rhodamine-like dyes (RDs) with different group16 heteroatoms (O, S, Se, Te) have been investigated. Time-dependent Kohn–Sham theory (TDKST) calculations were compared with coupled-cluster (CC) and equations-of-motion (EOM) CC results for π-to-π* singlet and triplet excitations. The RDs exhibit characteristics in the TDKST calculations that are very similar to previously investigated cyanine dyes, in the sense that the singlet energies obtained with nonhybrid functionals are too high compared with the CC results at the SD(T) level. The errors became increasingly larger for functionals with increasing amounts of exact exchange. TDKST with all tested functionals ledmore » to severe underestimations of the corresponding triplet excitations and overestimations of the singlet--triplet gaps. Long-range-corrected range-separated exchange and "optimal tuning" of the range separation parameter did not significantly improve the TDKST results. A detailed analysis suggests that the problem is differential electron correlation between the ground and excited states, which is not treated sufficiently by the relatively small integrals over the exchange-correlation response kernel that enters the excitation energy expression. As a result, numerical criteria are suggested that may help identify "cyanine-like" problems in TDKST calculations of excitation spectra.« less

Learn-as-you-go acceleration of cosmological parameter estimates

DOE Office of Scientific and Technical Information (OSTI.GOV)

Aslanyan, Grigor; Easther, Richard; Price, Layne C., E-mail: g.aslanyan@auckland.ac.nz, E-mail: r.easther@auckland.ac.nz, E-mail: lpri691@aucklanduni.ac.nz

2015-09-01

Cosmological analyses can be accelerated by approximating slow calculations using a training set, which is either precomputed or generated dynamically. However, this approach is only safe if the approximations are well understood and controlled. This paper surveys issues associated with the use of machine-learning based emulation strategies for accelerating cosmological parameter estimation. We describe a learn-as-you-go algorithm that is implemented in the Cosmo++ code and (1) trains the emulator while simultaneously estimating posterior probabilities; (2) identifies unreliable estimates, computing the exact numerical likelihoods if necessary; and (3) progressively learns and updates the error model as the calculation progresses. We explicitlymore » describe and model the emulation error and show how this can be propagated into the posterior probabilities. We apply these techniques to the Planck likelihood and the calculation of ΛCDM posterior probabilities. The computation is significantly accelerated without a pre-defined training set and uncertainties in the posterior probabilities are subdominant to statistical fluctuations. We have obtained a speedup factor of 6.5 for Metropolis-Hastings and 3.5 for nested sampling. Finally, we discuss the general requirements for a credible error model and show how to update them on-the-fly.« less

Computer Analysis of 400 HZ Aircraft Electrical Generator Test Data.

DTIC Science & Technology

1980-06-01

Data Acquisition System. ............ 6 3 Voltage Waveform with Data Points. ....... 19 14 Zero Crossover Interpolation. ........ 20 5 Numerical...difference between successive positive-sloped zero crossovers of the waveform. However, the exact time of zero crossover is not known. This is because...data sampling and the generator output are not synchronized. This unsynchronization means that data points which correspond with an exact zero crossover

Phase diagram of q-deformed Yang-Mills theory on S 2 at non-zero θ-angle

NASA Astrophysics Data System (ADS)

Okuyama, Kazumi

2018-04-01

We study the phase diagram of q-deformed Yang-Mills theory on S 2 at non-zero θ-angle using the exact partition function at finite N . By evaluating the exact partition function numerically, we find evidence for the existence of a series of phase transitions at non-zero θ-angle as conjectured in [hep-th/0509004

A Modified Kirchhoff plate theory for Free Vibration analysis of functionally graded material plates using meshfree method

NASA Astrophysics Data System (ADS)

Nguyen Van Do, Vuong

2018-04-01

In this paper, a modified Kirchhoff theory is presented for free vibration analyses of functionally graded material (FGM) plate based on modified radial point interpolation method (RPIM). The shear deformation effects are taken account into modified theory to ignore the locking phenomenon of thin plates. Due to the proposed refined plate theory, the number of independent unknowns reduces one variable and exists with four degrees of freedom per node. The simulated free vibration results employed by the modified RPIM are compared with the other analytical solutions to verify the effectiveness and the accuracy of the developed mesh-free method. Detail parametric studies of the proposed method are then conducted including the effectiveness of thickness ratio, boundary condition and material inhomogeneity on the sample problems of square plates. Results illustrated that the modified mesh-free RPIM can effectively predict the numerical calculation as compared to the exact solutions. The obtained numerical results are indicated that the proposed method are stable and well accurate prediction to evaluate with other published analyses.

Three-dimensional Diffusive Strip Method

NASA Astrophysics Data System (ADS)

Martinez-Ruiz, Daniel; Meunier, Patrice; Duchemin, Laurent; Villermaux, Emmanuel

2016-11-01

The Diffusive Strip Method (DSM) is a near-exact numerical method developed for mixing computations at large Péclet number in two-dimensions. The method consists in following stretched material lines to compute a-posteriori the resulting scalar field is extended here to three-dimensional flows, following surfaces. We describe its 3D peculiarities, and show how it applies to a simple Taylor-Couette configuration with non-rotating boundary conditions at the top end, bottom and outer cylinder. This flow produces an elaborate, although controlled, steady 3D flow which relies on the Ekman pumping arising from the rotation of the inner cylinder is both studied experimentally, and numerically modeled. A recurrent two-cells structure appears formed by stream tubes shaped as nested tori. A scalar blob in the flow experiences a Lagrangian oscillating dynamics with stretchings and compressions, driving the mixing process, and yielding both rapidly-mixed and nearly pure-diffusive regions. A triangulated-surface method is developed to calculate the blob elongation and scalar concentration PDFs through a single variable computation along the advected blob surface, capturing the rich evolution observed in the experiments.

Simulation of Quantum Many-Body Dynamics for Generic Strongly-Interacting Systems

NASA Astrophysics Data System (ADS)

Meyer, Gregory; Machado, Francisco; Yao, Norman

2017-04-01

Recent experimental advances have enabled the bottom-up assembly of complex, strongly interacting quantum many-body systems from individual atoms, ions, molecules and photons. These advances open the door to studying dynamics in isolated quantum systems as well as the possibility of realizing novel out-of-equilibrium phases of matter. Numerical studies provide insight into these systems; however, computational time and memory usage limit common numerical methods such as exact diagonalization to relatively small Hilbert spaces of dimension 215 . Here we present progress toward a new software package for dynamical time evolution of large generic quantum systems on massively parallel computing architectures. By projecting large sparse Hamiltonians into a much smaller Krylov subspace, we are able to compute the evolution of strongly interacting systems with Hilbert space dimension nearing 230. We discuss and benchmark different design implementations, such as matrix-free methods and GPU based calculations, using both pre-thermal time crystals and the Sachdev-Ye-Kitaev model as examples. We also include a simple symbolic language to describe generic Hamiltonians, allowing simulation of diverse quantum systems without any modification of the underlying C and Fortran code.

A boundary integral equation method using auxiliary interior surface approach for acoustic radiation and scattering in two dimensions.

PubMed

Yang, S A

2002-10-01

This paper presents an effective solution method for predicting acoustic radiation and scattering fields in two dimensions. The difficulty of the fictitious characteristic frequency is overcome by incorporating an auxiliary interior surface that satisfies certain boundary condition into the body surface. This process gives rise to a set of uniquely solvable boundary integral equations. Distributing monopoles with unknown strengths over the body and interior surfaces yields the simple source formulation. The modified boundary integral equations are further transformed to ordinary ones that contain nonsingular kernels only. This implementation allows direct application of standard quadrature formulas over the entire integration domain; that is, the collocation points are exactly the positions at which the integration points are located. Selecting the interior surface is an easy task. Moreover, only a few corresponding interior nodal points are sufficient for the computation. Numerical calculations consist of the acoustic radiation and scattering by acoustically hard elliptic and rectangular cylinders. Comparisons with analytical solutions are made. Numerical results demonstrate the efficiency and accuracy of the current solution method.

Nonadiabatic dynamics of photo-induced proton-coupled electron transfer reactions via ring-polymer surface hopping

NASA Astrophysics Data System (ADS)

Shakib, Farnaz; Huo, Pengfei

Photo-induced proton-coupled electron transfer reactions (PCET) are at the heart of energy conversion reactions in photocatalysis. Here, we apply the recently developed ring-polymer surface-hopping (RPSH) approach to simulate the nonadiabatic dynamics of photo-induced PCET. The RPSH method incorporates ring-polymer (RP) quantization of the proton into the fewest-switches surface-hopping (FSSH) approach. Using two diabatic electronic states, corresponding to the electron donor and acceptor states, we model photo-induced PCET with the proton described by a classical isomorphism RP. From the RPSH method, we obtain numerical results that are comparable to those obtained when the proton is treated quantum mechanically. This accuracy stems from incorporating exact quantum statistics, such as proton tunnelling, into approximate quantum dynamics. Additionally, RPSH offers the numerical accuracy along with the computational efficiency. Namely, compared to the FSSH approach in vibronic representation, there is no need to calculate a massive number of vibronic states explicitly. This approach opens up the possibility to accurately and efficiently simulate photo-induced PCET with multiple transferring protons or electrons.

Plasma versus Drude Modeling of the Casimir Force: Beyond the Proximity Force Approximation

NASA Astrophysics Data System (ADS)

Hartmann, Michael; Ingold, Gert-Ludwig; Neto, Paulo A. Maia

2017-07-01

We calculate the Casimir force and its gradient between a spherical and a planar gold surface. Significant numerical improvements allow us to extend the range of accessible parameters into the experimental regime. We compare our numerically exact results with those obtained within the proximity force approximation (PFA) employed in the analysis of all Casimir force experiments reported in the literature so far. Special attention is paid to the difference between the Drude model and the dissipationless plasma model at zero frequency. It is found that the correction to PFA is too small to explain the discrepancy between the experimental data and the PFA result based on the Drude model. However, it turns out that for the plasma model, the corrections to PFA lie well outside the experimental bound obtained by probing the variation of the force gradient with the sphere radius [D. E. Krause et al., Phys. Rev. Lett. 98, 050403 (2007), 10.1103/PhysRevLett.98.050403]. The corresponding corrections based on the Drude model are significantly smaller but still in violation of the experimental bound for small distances between plane and sphere.

Highly accurate symplectic element based on two variational principles

NASA Astrophysics Data System (ADS)

Qing, Guanghui; Tian, Jia

2018-02-01

For the stability requirement of numerical resultants, the mathematical theory of classical mixed methods are relatively complex. However, generalized mixed methods are automatically stable, and their building process is simple and straightforward. In this paper, based on the seminal idea of the generalized mixed methods, a simple, stable, and highly accurate 8-node noncompatible symplectic element (NCSE8) was developed by the combination of the modified Hellinger-Reissner mixed variational principle and the minimum energy principle. To ensure the accuracy of in-plane stress results, a simultaneous equation approach was also suggested. Numerical experimentation shows that the accuracy of stress results of NCSE8 are nearly the same as that of displacement methods, and they are in good agreement with the exact solutions when the mesh is relatively fine. NCSE8 has advantages of the clearing concept, easy calculation by a finite element computer program, higher accuracy and wide applicability for various linear elasticity compressible and nearly incompressible material problems. It is possible that NCSE8 becomes even more advantageous for the fracture problems due to its better accuracy of stresses.

Zeros of Schrödinger's Radial Function Rnl(r) and Kummer's Function 1F1(-a c; z) and Their ``Angle'' Distributions

NASA Astrophysics Data System (ADS)

Tarasov, V. F.

In the present paper exact formulae for the calculation of zeros of Rnl(r) and 1F1(-a c; z), where z = 2 λ r, a = n - l - 1 >= 0 and c = 2l + 2 >= 2 are presented. For a <= 4 the method due to Tartallia and Cardono, and that due to L. Ferrai, L. Euler and J. L. Lagrange are used. In other cases (a > 4) numerical methods are employed to obtain the results (to within 10-15). For greater geometrical obviousness of the irregulary distribution (as a > 3) of zeros xk = zk - (c + a - 1) on the axis y = 0, the circular diagrams with the radius Ra = (a - 1) √ {c + a - 1} are presented for the first time. It is possible to notice some singularities of distribution of these zeros and their images - the points Tk - on the circle. For a = 3 and 4 their exact ``angle'' asymptotics (as c --> ∞) are obtained. It is shown that in the basis of the L. Ferrari, L. Euler and J.-L. Lagrange methods, using for solving the equation 1F1(-4 c; z) = 0, one Common for all these methods. equation is obtained viz., the cubic resolvent equation of FEL-type. Calculating of zeros xk of the Rnl(r) and 1F1(z) functions enable us to show the ``singular'' cases (a, c) = (4, 6), (6, 4), (8, 14), ...

Rate-loss analysis of an efficient quantum repeater architecture

NASA Astrophysics Data System (ADS)

Guha, Saikat; Krovi, Hari; Fuchs, Christopher A.; Dutton, Zachary; Slater, Joshua A.; Simon, Christoph; Tittel, Wolfgang

2015-08-01

We analyze an entanglement-based quantum key distribution (QKD) architecture that uses a linear chain of quantum repeaters employing photon-pair sources, spectral-multiplexing, linear-optic Bell-state measurements, multimode quantum memories, and classical-only error correction. Assuming perfect sources, we find an exact expression for the secret-key rate, and an analytical description of how errors propagate through the repeater chain, as a function of various loss-and-noise parameters of the devices. We show via an explicit analytical calculation, which separately addresses the effects of the principle nonidealities, that this scheme achieves a secret-key rate that surpasses the Takeoka-Guha-Wilde bound—a recently found fundamental limit to the rate-vs-loss scaling achievable by any QKD protocol over a direct optical link—thereby providing one of the first rigorous proofs of the efficacy of a repeater protocol. We explicitly calculate the end-to-end shared noisy quantum state generated by the repeater chain, which could be useful for analyzing the performance of other non-QKD quantum protocols that require establishing long-distance entanglement. We evaluate that shared state's fidelity and the achievable entanglement-distillation rate, as a function of the number of repeater nodes, total range, and various loss-and-noise parameters of the system. We extend our theoretical analysis to encompass sources with nonzero two-pair-emission probability, using an efficient exact numerical evaluation of the quantum state propagation and measurements. We expect our results to spur formal rate-loss analysis of other repeater protocols and also to provide useful abstractions to seed analyses of quantum networks of complex topologies.

Spherical solid model system: Exact evaluation of the van der Waals interaction between a microscopic or submacroscopic spherical solid and a deformable fluid interface

NASA Astrophysics Data System (ADS)

Wang, Y. Z.; Wang, B.; Xiong, X. M.; Zhang, J. X.

2011-03-01

In many previous research work associated with studying the deformation of the fluid interface interacting with a solid, the theoretical calculation of the surface energy density on the deformed fluid interface (or its interaction surface pressure) is often approximately obtained by using the expression for the interaction energy per unit area (or pressure) between two parallel macroscopic plates, e.g. σ(D) = - A / 12 πD2or π(D) = - A / 6 πD3for the van der Waals (vdW) interaction, through invoking the Derjaguin approximation (DA). This approximation however would result in over- or even inaccurate-prediction of the interaction force and the corresponding deformation of the fluid interface due to the invalidation of Derjaguin approximation in cases of microscopic or submacroscopic solids. To circumvent the above limitations existing in the previous DA-based theoretical work, a more accurate and quantitative theoretical model, available for exactly calculating the vdW-induced deformation of a planar fluid interface interacting with a sphere, and the interaction forces taking into account its change, is presented in this paper. The validity and advantage of the new mathematical and physical technique is rigorously verified by comparison with the numerical results on basis of the previous Paraboloid solid (PS) model and the Hamaker's sphere-flat expression (viz. F = - 2 Aa3 / (3 D2( D + 2 a) 2)), as well as its well-known DA-based general form of F / a = - A / 6z p02.

Original electric-vertex formulation of the symmetric eight-vertex model on the square lattice is fully nonuniversal

NASA Astrophysics Data System (ADS)

Krčmár, Roman; Šamaj, Ladislav

2018-01-01

The partition function of the symmetric (zero electric field) eight-vertex model on a square lattice can be formulated either in the original "electric" vertex format or in an equivalent "magnetic" Ising-spin format. In this paper, both electric and magnetic versions of the model are studied numerically by using the corner transfer matrix renormalization-group method which provides reliable data. The emphasis is put on the calculation of four specific critical exponents, related by two scaling relations, and of the central charge. The numerical method is first tested in the magnetic format, the obtained dependencies of critical exponents on the model's parameters agree with Baxter's exact solution, and weak universality is confirmed within the accuracy of the method due to the finite size of the system. In particular, the critical exponents η and δ are constant as required by weak universality. On the other hand, in the electric format, analytic formulas based on the scaling relations are derived for the critical exponents ηe and δe which agree with our numerical data. These exponents depend on the model's parameters which is evidence for the full nonuniversality of the symmetric eight-vertex model in the original electric formulation.

Application of modern radiative transfer tools to model laboratory quartz emissivity

NASA Astrophysics Data System (ADS)

Pitman, Karly M.; Wolff, Michael J.; Clayton, Geoffrey C.

2005-08-01

Planetary remote sensing of regolith surfaces requires use of theoretical models for interpretation of constituent grain physical properties. In this work, we review and critically evaluate past efforts to strengthen numerical radiative transfer (RT) models with comparison to a trusted set of nadir incidence laboratory quartz emissivity spectra. By first establishing a baseline statistical metric to rate successful model-laboratory emissivity spectral fits, we assess the efficacy of hybrid computational solutions (Mie theory + numerically exact RT algorithm) to calculate theoretical emissivity values for micron-sized α-quartz particles in the thermal infrared (2000-200 cm-1) wave number range. We show that Mie theory, a widely used but poor approximation to irregular grain shape, fails to produce the single scattering albedo and asymmetry parameter needed to arrive at the desired laboratory emissivity values. Through simple numerical experiments, we show that corrections to single scattering albedo and asymmetry parameter values generated via Mie theory become more necessary with increasing grain size. We directly compare the performance of diffraction subtraction and static structure factor corrections to the single scattering albedo, asymmetry parameter, and emissivity for dense packing of grains. Through these sensitivity studies, we provide evidence that, assuming RT methods work well given sufficiently well-quantified inputs, assumptions about the scatterer itself constitute the most crucial aspect of modeling emissivity values.

Nonlinear Legendre Spectral Finite Elements for Wind Turbine Blade Dynamics: Preprint

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wang, Q.; Sprague, M. A.; Jonkman, J.

2014-01-01

This paper presents a numerical implementation and examination of new wind turbine blade finite element model based on Geometrically Exact Beam Theory (GEBT) and a high-order spectral finite element method. The displacement-based GEBT is presented, which includes the coupling effects that exist in composite structures and geometric nonlinearity. Legendre spectral finite elements (LSFEs) are high-order finite elements with nodes located at the Gauss-Legendre-Lobatto points. LSFEs can be an order of magnitude more efficient that low-order finite elements for a given accuracy level. Interpolation of the three-dimensional rotation, a major technical barrier in large-deformation simulation, is discussed in the context ofmore » LSFEs. It is shown, by numerical example, that the high-order LSFEs, where weak forms are evaluated with nodal quadrature, do not suffer from a drawback that exists in low-order finite elements where the tangent-stiffness matrix is calculated at the Gauss points. Finally, the new LSFE code is implemented in the new FAST Modularization Framework for dynamic simulation of highly flexible composite-material wind turbine blades. The framework allows for fully interactive simulations of turbine blades in operating conditions. Numerical examples showing validation and LSFE performance will be provided in the final paper.« less

A Highly Accurate Technique for the Treatment of Flow Equations at the Polar Axis in Cylindrical Coordinates using Series Expansions. Appendix A

NASA Technical Reports Server (NTRS)

Constantinescu, George S.; Lele, S. K.

2001-01-01

Numerical methods for solving the flow equations in cylindrical or spherical coordinates should be able to capture the behavior of the exact solution near the regions where the particular form of the governing equations is singular. In this work we focus on the treatment of these numerical singularities for finite-differences methods by reinterpreting the regularity conditions developed in the context of pseudo-spectral methods. A generally applicable numerical method for treating the singularities present at the polar axis, when nonaxisymmetric flows are solved in cylindrical, coordinates using highly accurate finite differences schemes (e.g., Pade schemes) on non-staggered grids, is presented. Governing equations for the flow at the polar axis are derived using series expansions near r=0. The only information needed to calculate the coefficients in these equations are the values of the flow variables and their radial derivatives at the previous iteration (or time) level. These derivatives, which are multi-valued at the polar axis, are calculated without dropping the accuracy of the numerical method using a mapping of the flow domain from (0,R)*(0,2pi) to (-R,R)*(0,pi), where R is the radius of the computational domain. This allows the radial derivatives to be evaluated using high-order differencing schemes (e.g., compact schemes) at points located on the polar axis. The proposed technique is illustrated by results from simulations of laminar-forced jets and turbulent compressible jets using large eddy simulation (LES) methods. In term of the general robustness of the numerical method and smoothness of the solution close to the polar axis, the present results compare very favorably to similar calculations in which the equations are solved in Cartesian coordinates at the polar axis, or in which the singularity is removed by employing a staggered mesh in the radial direction without a mesh point at r=0, following the method proposed recently by Mohseni and Colonius (1). Extension of the method described here for incompressible flows or for any other set of equations that are solved on a non-staggered mesh in cylindrical or spherical coordinates with finite-differences schemes of various level of accuracy is immediate.

Calculating Relativistic Transition Matrix Elements for Hydrogenic Atoms Using Monte Carlo Methods

NASA Astrophysics Data System (ADS)

Alexander, Steven; Coldwell, R. L.

2015-03-01

The nonrelativistic transition matrix elements for hydrogen atoms can be computed exactly and these expressions are given in a number of classic textbooks. The relativistic counterparts of these equations can also be computed exactly but these expressions have been described in only a few places in the literature. In part, this is because the relativistic equations lack the elegant simplicity of the nonrelativistic equations. In this poster I will describe how variational Monte Carlo methods can be used to calculate the energy and properties of relativistic hydrogen atoms and how the wavefunctions for these systems can be used to calculate transition matrix elements.

Large scale exact quantum dynamics calculations: Ten thousand quantum states of acetonitrile

NASA Astrophysics Data System (ADS)

Halverson, Thomas; Poirier, Bill

2015-03-01

'Exact' quantum dynamics (EQD) calculations of the vibrational spectrum of acetonitrile (CH3CN) are performed, using two different methods: (1) phase-space-truncated momentum-symmetrized Gaussian basis and (2) correlated truncated harmonic oscillator basis. In both cases, a simple classical phase space picture is used to optimize the selection of individual basis functions-leading to drastic reductions in basis size, in comparison with existing methods. Massive parallelization is also employed. Together, these tools-implemented into a single, easy-to-use computer code-enable a calculation of tens of thousands of vibrational states of CH3CN to an accuracy of 0.001-10 cm-1.

Efficient exact-exchange time-dependent density-functional theory methods and their relation to time-dependent Hartree-Fock.

PubMed

Hesselmann, Andreas; Görling, Andreas

2011-01-21

A recently introduced time-dependent exact-exchange (TDEXX) method, i.e., a response method based on time-dependent density-functional theory that treats the frequency-dependent exchange kernel exactly, is reformulated. In the reformulated version of the TDEXX method electronic excitation energies can be calculated by solving a linear generalized eigenvalue problem while in the original version of the TDEXX method a laborious frequency iteration is required in the calculation of each excitation energy. The lowest eigenvalues of the new TDEXX eigenvalue equation corresponding to the lowest excitation energies can be efficiently obtained by, e.g., a version of the Davidson algorithm appropriate for generalized eigenvalue problems. Alternatively, with the help of a series expansion of the new TDEXX eigenvalue equation, standard eigensolvers for large regular eigenvalue problems, e.g., the standard Davidson algorithm, can be used to efficiently calculate the lowest excitation energies. With the help of the series expansion as well, the relation between the TDEXX method and time-dependent Hartree-Fock is analyzed. Several ways to take into account correlation in addition to the exact treatment of exchange in the TDEXX method are discussed, e.g., a scaling of the Kohn-Sham eigenvalues, the inclusion of (semi)local approximate correlation potentials, or hybrids of the exact-exchange kernel with kernels within the adiabatic local density approximation. The lowest lying excitations of the molecules ethylene, acetaldehyde, and pyridine are considered as examples.

Numerical Ordering Ability Mediates the Relation between Number-Sense and Arithmetic Competence

ERIC Educational Resources Information Center

Lyons, Ian M.; Beilock, Sian L.

2011-01-01

What predicts human mathematical competence? While detailed models of number representation in the brain have been developed, it remains to be seen exactly how basic number representations link to higher math abilities. We propose that representation of ordinal associations between numerical symbols is one important factor that underpins this…

On the Role of Entailment Patterns and Scalar Implicatures in the Processing of Numerals

ERIC Educational Resources Information Center

Panizza, Daniele; Chierchia, Gennaro; Clifton, Charles, Jr.

2009-01-01

There has been much debate, in both the linguistics and the psycholinguistics literature, concerning numbers and the interpretation of number denoting determiners ("numerals"). Such debate concerns, in particular, the nature and distribution of upper-bounded ("exact") interpretations vs. lower-bounded ("at-least") construals. In the present paper…

An entropy stable nodal discontinuous Galerkin method for the two dimensional shallow water equations on unstructured curvilinear meshes with discontinuous bathymetry

NASA Astrophysics Data System (ADS)

Wintermeyer, Niklas; Winters, Andrew R.; Gassner, Gregor J.; Kopriva, David A.

2017-07-01

We design an arbitrary high-order accurate nodal discontinuous Galerkin spectral element approximation for the non-linear two dimensional shallow water equations with non-constant, possibly discontinuous, bathymetry on unstructured, possibly curved, quadrilateral meshes. The scheme is derived from an equivalent flux differencing formulation of the split form of the equations. We prove that this discretization exactly preserves the local mass and momentum. Furthermore, combined with a special numerical interface flux function, the method exactly preserves the mathematical entropy, which is the total energy for the shallow water equations. By adding a specific form of interface dissipation to the baseline entropy conserving scheme we create a provably entropy stable scheme. That is, the numerical scheme discretely satisfies the second law of thermodynamics. Finally, with a particular discretization of the bathymetry source term we prove that the numerical approximation is well-balanced. We provide numerical examples that verify the theoretical findings and furthermore provide an application of the scheme for a partial break of a curved dam test problem.

Analytic Formulation and Numerical Implementation of an Acoustic Pressure Gradient Prediction

NASA Technical Reports Server (NTRS)

Lee, Seongkyu; Brentner, Kenneth S.; Farassat, F.; Morris, Philip J.

2008-01-01

Two new analytical formulations of the acoustic pressure gradient have been developed and implemented in the PSU-WOPWOP rotor noise prediction code. The pressure gradient can be used to solve the boundary condition for scattering problems and it is a key aspect to solve acoustic scattering problems. The first formulation is derived from the gradient of the Ffowcs Williams-Hawkings (FW-H) equation. This formulation has a form involving the observer time differentiation outside the integrals. In the second formulation, the time differentiation is taken inside the integrals analytically. This formulation avoids the numerical time differentiation with respect to the observer time, which is computationally more efficient. The acoustic pressure gradient predicted by these new formulations is validated through comparison with available exact solutions for a stationary and moving monopole sources. The agreement between the predictions and exact solutions is excellent. The formulations are applied to the rotor noise problems for two model rotors. A purely numerical approach is compared with the analytical formulations. The agreement between the analytical formulations and the numerical method is excellent for both stationary and moving observer cases.

Critical analysis of fragment-orbital DFT schemes for the calculation of electronic coupling values

DOE Office of Scientific and Technical Information (OSTI.GOV)

Schober, Christoph; Reuter, Karsten; Oberhofer, Harald, E-mail: harald.oberhofer@ch.tum.de

2016-02-07

We present a critical analysis of the popular fragment-orbital density-functional theory (FO-DFT) scheme for the calculation of electronic coupling values. We discuss the characteristics of different possible formulations or “flavors” of the scheme which differ by the number of electrons in the calculation of the fragments and the construction of the Hamiltonian. In addition to two previously described variants based on neutral fragments, we present a third version taking a different route to the approximate diabatic state by explicitly considering charged fragments. In applying these FO-DFT flavors to the two molecular test sets HAB7 (electron transfer) and HAB11 (hole transfer),more » we find that our new scheme gives improved electronic couplings for HAB7 (−6.2% decrease in mean relative signed error) and greatly improved electronic couplings for HAB11 (−15.3% decrease in mean relative signed error). A systematic investigation of the influence of exact exchange on the electronic coupling values shows that the use of hybrid functionals in FO-DFT calculations improves the electronic couplings, giving values close to or even better than more sophisticated constrained DFT calculations. Comparing the accuracy and computational cost of each variant, we devise simple rules to choose the best possible flavor depending on the task. For accuracy, our new scheme with charged-fragment calculations performs best, while numerically more efficient at reasonable accuracy is the variant with neutral fragments.« less

iVPIC: A low-­dispersion, energy-­conserving relativistic PIC solver for LPI simulations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chacon, Luis

We have developed a novel low-­dispersion, exactly energy-­conserving PIC algorithm for the relativistic Vlasov-­Maxwell system. The approach features an exact energy conservation theorem while preserving the favorable performance and numerical dispersion properties of explicit PIC. The new algorithm has the potential to enable much longer laser-­plasma-­interaction (LPI) simulations than are currently possible.

An Exactly Solvable Model for the Spread of Disease

ERIC Educational Resources Information Center

Mickens, Ronald E.

2012-01-01

We present a new SIR epidemiological model whose exact analytical solution can be calculated. In this model, unlike previous models, the infective population becomes zero at a finite time. Remarkably, these results can be derived from only an elementary knowledge of differential equations.

Efficient Calculation of Exact Exchange Within the Quantum Espresso Software Package

NASA Astrophysics Data System (ADS)

Barnes, Taylor; Kurth, Thorsten; Carrier, Pierre; Wichmann, Nathan; Prendergast, David; Kent, Paul; Deslippe, Jack

Accurate simulation of condensed matter at the nanoscale requires careful treatment of the exchange interaction between electrons. In the context of plane-wave DFT, these interactions are typically represented through the use of approximate functionals. Greater accuracy can often be obtained through the use of functionals that incorporate some fraction of exact exchange; however, evaluation of the exact exchange potential is often prohibitively expensive. We present an improved algorithm for the parallel computation of exact exchange in Quantum Espresso, an open-source software package for plane-wave DFT simulation. Through the use of aggressive load balancing and on-the-fly transformation of internal data structures, our code exhibits speedups of approximately an order of magnitude for practical calculations. Additional optimizations are presented targeting the many-core Intel Xeon-Phi ``Knights Landing'' architecture, which largely powers NERSC's new Cori system. We demonstrate the successful application of the code to difficult problems, including simulation of water at a platinum interface and computation of the X-ray absorption spectra of transition metal oxides.

INFLUENCES OF RESPONSE RATE AND DISTRIBUTION ON THE CALCULATION OF INTEROBSERVER RELIABILITY SCORES

PubMed Central

Rolider, Natalie U.; Iwata, Brian A.; Bullock, Christopher E.

2012-01-01

We examined the effects of several variations in response rate on the calculation of total, interval, exact-agreement, and proportional reliability indices. Trained observers recorded computer-generated data that appeared on a computer screen. In Study 1, target responses occurred at low, moderate, and high rates during separate sessions so that reliability results based on the four calculations could be compared across a range of values. Total reliability was uniformly high, interval reliability was spuriously high for high-rate responding, proportional reliability was somewhat lower for high-rate responding, and exact-agreement reliability was the lowest of the measures, especially for high-rate responding. In Study 2, we examined the separate effects of response rate per se, bursting, and end-of-interval responding. Response rate and bursting had little effect on reliability scores; however, the distribution of some responses at the end of intervals decreased interval reliability somewhat, proportional reliability noticeably, and exact-agreement reliability markedly. PMID:23322930

Collisionless tearing instability of a bi-Maxwellian neutral sheet - An integrodifferential treatment with exact particle orbits

NASA Technical Reports Server (NTRS)

Burkhart, G. R.; Chen, J.

1989-01-01

The integrodifferential equation describing the linear tearing instability in the bi-Maxwellian neutral sheet is solved without approximating the particle orbits or the eigenfunction psi. Results of this calculation are presented. Comparison between the exact solution and the three-region approximation motivates the piecewise-straight-line approximation, a simplification that allows faster solution of the integrodifferential equation, yet retains the important features of the exact solution.

Optical frequency selective surface design using a GPU accelerated finite element boundary integral method

NASA Astrophysics Data System (ADS)

Ashbach, Jason A.

Periodic metallodielectric frequency selective surface (FSS) designs have historically seen widespread use in the microwave and radio frequency spectra. By scaling the dimensions of an FSS unit cell for use in a nano-fabrication process, these concepts have recently been adapted for use in optical applications as well. While early optical designs have been limited to wellunderstood geometries or optimized pixelated screens, nano-fabrication, lithographic and interconnect technology has progressed to a point where it is possible to fabricate metallic screens of arbitrary geometries featuring curvilinear or even three-dimensional characteristics that are only tens of nanometers wide. In order to design an FSS featuring such characteristics, it is important to have a robust numerical solver that features triangular elements in purely two-dimensional geometries and prismatic or tetrahedral elements in three-dimensional geometries. In this dissertation, a periodic finite element method code has been developed which features prismatic elements whose top and bottom boundaries are truncated by numerical integration of the boundary integral as opposed to an approximate representation found in a perfectly matched layer. However, since no exact solution exists for the calculation of triangular elements in a boundary integral, this process can be time consuming. To address this, these calculations were optimized for parallelization such that they may be done on a graphics processor, which provides a large increase in computational speed. Additionally, a simple geometrical representation using a Bezier surface is presented which provides generality with few variables. With a fast numerical solver coupled with a lowvariable geometric representation, a heuristic optimization algorithm has been used to develop several optical designs such as an absorber, a circular polarization filter, a transparent conductive surface and an enhanced, optical modulator.

Viscous Rayleigh-Taylor instability in spherical geometry

NASA Astrophysics Data System (ADS)

Mikaelian, Karnig O.

2016-02-01

We consider viscous fluids in spherical geometry, a lighter fluid supporting a heavier one. Chandrasekhar [Q. J. Mech. Appl. Math. 8, 1 (1955), 10.1093/qjmam/8.1.1] analyzed this unstable configuration providing the equations needed to find, numerically, the exact growth rates for the ensuing Rayleigh-Taylor instability. He also derived an analytic but approximate solution. We point out a weakness in his approximate dispersion relation (DR) and offer a somewhat improved one. A third DR, based on transforming a planar DR into a spherical one, suffers no unphysical predictions and compares reasonably well with the exact work of Chandrasekhar and a more recent numerical analysis of the problem [Terrones and Carrara, Phys. Fluids 27, 054105 (2015), 10.1063/1.4921648].

On approximating guided waves in plates with thin anisotropic coatings by means of effective boundary conditions

PubMed

Niklasson; Datta; Dunn

2000-09-01

In this paper, effective boundary conditions for elastic wave propagation in plates with thin coatings are derived. These effective boundary conditions are used to obtain an approximate dispersion relation for guided waves in an isotropic plate with thin anisotropic coating layers. The accuracy of the effective boundary conditions is investigated numerically by comparison with exact solutions for two different material systems. The systems considered consist of a metallic core with thin superconducting coatings. It is shown that for wavelengths long compared to the coating thickness there is excellent agreement between the approximate and exact solutions for both systems. Furthermore, numerical results presented might be used to characterize coating properties by ultrasonic techniques.

An Exact, Compressible One-Dimensional Riemann Solver for General, Convex Equations of State

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kamm, James Russell

2015-03-05

This note describes an algorithm with which to compute numerical solutions to the one- dimensional, Cartesian Riemann problem for compressible flow with general, convex equations of state. While high-level descriptions of this approach are to be found in the literature, this note contains most of the necessary details required to write software for this problem. This explanation corresponds to the approach used in the source code that evaluates solutions for the 1D, Cartesian Riemann problem with a JWL equation of state in the ExactPack package [16, 29]. Numerical examples are given with the proposed computational approach for a polytropic equationmore » of state and for the JWL equation of state.« less

The calculating hemispheres: studies of a split-brain patient.

PubMed

Funnell, Margaret G; Colvin, Mary K; Gazzaniga, Michael S

2007-06-11

The purpose of the study was to investigate simple calculation in the two cerebral hemispheres of a split-brain patient. In a series of four experiments, the left hemisphere was superior to the right in simple calculation, confirming the previously reported left hemisphere specialization for calculation. In two different recognition paradigms, right hemisphere performance was at chance for all arithmetic operations, with the exception of subtraction in a two-alternative forced choice paradigm (performance was at chance when the lure differed from the correct answer by a magnitude of 1 but above chance when the magnitude difference was 4). In a recall paradigm, the right hemisphere performed above chance for both addition and subtraction, but performed at chance levels for multiplication and division. The error patterns in that experiment suggested that for subtraction and addition, the right hemisphere does have some capacity for approximating the solution even when it is unable to generate the exact solution. Furthermore, right hemisphere accuracy in addition and subtraction was higher for problems with small operands than with large operands. An additional experiment assessed approximate and exact addition in the two hemispheres for problems with small and large operands. The left hemisphere was equally accurate in both tasks but the right hemisphere was more accurate in approximate addition than in exact addition. In exact addition, right hemisphere accuracy was higher for problems with small operands than large, but the opposite pattern was found for approximate addition.

Bounce universe and black holes from critical Einsteinian cubic gravity

NASA Astrophysics Data System (ADS)

Feng, Xing-Hui; Huang, Hyat; Mai, Zhan-Feng; Lü, Hong

2017-11-01

We show that there exists a critical point for the coupling constants in Einsteinian cubic gravity in which the linearized equations on the maximally symmetric vacuum vanish identically. We construct an exact isotropic bounce universe in the critical theory in four dimensions. The comoving time runs from minus infinity to plus infinity, yielding a smooth universe bouncing between two de Sitter vacua. In five dimensions, we adopt a numerical approach to construct a bounce solution, in which a singularity occurs before the bounce takes place. We then construct exact anisotropic bounces that connect two isotropic de Sitter spacetimes with flat spatial sections. We further construct exact anti-de Sitter black holes in the critical theory in four and five dimensions and obtain an exact anti-de Sitter worm brane in four dimensions.

Nonlinearity Domination in Hassellmann Equation as a Reason for Alternative Framework of its Numerical Simulation

DTIC Science & Technology

2014-09-30

nonlinear Schrodinger equation. It is well known that dark solitons are exact solutions of such equation. In the present paper it has been shown that gray...Reason for Alternative Framework of its Numerical Simulation Vladimir Zakharov, Andrei Pushkarev Waves and Solitons LLC 1719 W. Marlette Ave...situation; study of the implications of modulational instability on solitons , rogue waves and air-surface interaction. APPROACH Numerical methods

A Note on Monotonicity Assumptions for Exact Unconditional Tests in Binary Matched-pairs Designs

PubMed Central

Li, Xiaochun; Liu, Mengling; Goldberg, Judith D.

2011-01-01

Summary Exact unconditional tests have been widely applied to test the difference between two probabilities for 2×2 matched-pairs binary data with small sample size. In this context, Lloyd (2008, Biometrics 64, 716–723) proposed an E + M p-value, that showed better performance than the existing M p-value and C p-value. However, the analytical calculation of the E + M p-value requires that the Barnard convexity condition be satisfied; this can be challenging to prove theoretically. In this paper, by a simple reformulation, we show that a weaker condition, conditional monotonicity, is sufficient to calculate all three p-values (M, C and E + M) and their corresponding exact sizes. Moreover, this conditional monotonicity condition is applicable to non-inferiority tests. PMID:21466507

Exact and approximate aspects of the boson expansion theories

DOE Office of Scientific and Technical Information (OSTI.GOV)

Tamura, T.; Weeks, K.J.; Pedrocchi, V.G.

1981-03-01

It is shown that a boson expansion theory of the Kishimoto-Tamura type not only maps the operators exactly but also the space, and, consequently, the matrix elements of the fermion system onto those of the bosons. Significance of approximations made in calculations is also discussed.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Calero, C.; Knorowski, C.; Travesset, A.

We investigate a general method to calculate the free energy of crystalline solids by considering the harmonic approximation and quasistatically switching the anharmonic contribution. The advantage of this method is that the harmonic approximation provides an already very accurate estimate of the free energy, and therefore the anharmonic term is numerically very small and can be determined to high accuracy. We further show that the anharmonic contribution to the free energy satisfies a number of exact inequalities that place constraints on its magnitude and allows approximate but fast and accurate estimates. The method is implemented into a readily available generalmore » software by combining the code HOODLT (Highly Optimized Object Oriented Dynamic Lattice Theory) for the harmonic part and the molecular dynamics (MD) simulation package HOOMD-blue for the anharmonic part. We use the method to calculate the low temperature phase diagram for Lennard-Jones particles. We demonstrate that hcp is the equilibrium phase at low temperature and pressure and obtain the coexistence curve with the fcc phase, which exhibits reentrant behavior. Furthermore, several implications of the method are discussed.« less

Determination of anharmonic free energy contributions: Low temperature phases of the Lennard-Jones system

DOE PAGES

Calero, C.; Knorowski, C.; Travesset, A.

2016-03-22

We investigate a general method to calculate the free energy of crystalline solids by considering the harmonic approximation and quasistatically switching the anharmonic contribution. The advantage of this method is that the harmonic approximation provides an already very accurate estimate of the free energy, and therefore the anharmonic term is numerically very small and can be determined to high accuracy. We further show that the anharmonic contribution to the free energy satisfies a number of exact inequalities that place constraints on its magnitude and allows approximate but fast and accurate estimates. The method is implemented into a readily available generalmore » software by combining the code HOODLT (Highly Optimized Object Oriented Dynamic Lattice Theory) for the harmonic part and the molecular dynamics (MD) simulation package HOOMD-blue for the anharmonic part. We use the method to calculate the low temperature phase diagram for Lennard-Jones particles. We demonstrate that hcp is the equilibrium phase at low temperature and pressure and obtain the coexistence curve with the fcc phase, which exhibits reentrant behavior. Furthermore, several implications of the method are discussed.« less

Zombie states for description of structure and dynamics of multi-electron systems

NASA Astrophysics Data System (ADS)

Shalashilin, Dmitrii V.

2018-05-01

Canonical Coherent States (CSs) of Harmonic Oscillator have been extensively used as a basis in a number of computational methods of quantum dynamics. However, generalising such techniques for fermionic systems is difficult because Fermionic Coherent States (FCSs) require complicated algebra of Grassmann numbers not well suited for numerical calculations. This paper introduces a coherent antisymmetrised superposition of "dead" and "alive" electronic states called here Zombie State (ZS), which can be used in a manner of FCSs but without Grassmann algebra. Instead, for Zombie States, a very simple sign-changing rule is used in the definition of creation and annihilation operators. Then, calculation of electronic structure Hamiltonian matrix elements between two ZSs becomes very simple and a straightforward technique for time propagation of fermionic wave functions can be developed. By analogy with the existing methods based on Canonical Coherent States of Harmonic Oscillator, fermionic wave functions can be propagated using a set of randomly selected Zombie States as a basis. As a proof of principles, the proposed Coupled Zombie States approach is tested on a simple example showing that the technique is exact.

Finite-temperature time-dependent variation with multiple Davydov states

NASA Astrophysics Data System (ADS)

Wang, Lu; Fujihashi, Yuta; Chen, Lipeng; Zhao, Yang

2017-03-01

The Dirac-Frenkel time-dependent variational approach with Davydov Ansätze is a sophisticated, yet efficient technique to obtain an accurate solution to many-body Schrödinger equations for energy and charge transfer dynamics in molecular aggregates and light-harvesting complexes. We extend this variational approach to finite temperature dynamics of the spin-boson model by adopting a Monte Carlo importance sampling method. In order to demonstrate the applicability of this approach, we compare calculated real-time quantum dynamics of the spin-boson model with that from numerically exact iterative quasiadiabatic propagator path integral (QUAPI) technique. The comparison shows that our variational approach with the single Davydov Ansätze is in excellent agreement with the QUAPI method at high temperatures, while the two differ at low temperatures. Accuracy in dynamics calculations employing a multitude of Davydov trial states is found to improve substantially over the single Davydov Ansatz, especially at low temperatures. At a moderate computational cost, our variational approach with the multiple Davydov Ansatz is shown to provide accurate spin-boson dynamics over a wide range of temperatures and bath spectral densities.

Opening of DNA chain due to force applied on different locations.

PubMed

Singh, Amar; Modi, Tushar; Singh, Navin

2016-09-01

We consider a homogeneous DNA molecule and investigate the effect of random force applied on the unzipping profile of the molecule. How the critical force varies as a function of the chain length or number of base pairs is the objective of this study. In general, the ratio of the critical forces that is applied on the middle of the chain to that which is applied on one of the ends is two. Our study shows that this ratio depends on the length of the chain. This means that the force which is applied to a point can be experienced by a section of the chain. Beyond a length, the base pairs have no information about the applied force. In the case when the chain length is shorter than this length, this ratio may vary. Only in the case when the chain length exceeds a critical length, this ratio is found to be two. Based on the de Gennes formulation, we developed a method to calculate these forces at zero temperature. The exact results at zero temperature match numerical calculations.

Frequency Response Calculations of Input Characteristics of Cavity-Backed Aperture Antennas Using AWE with Hybrid FEM/MoM Technique

NASA Technical Reports Server (NTRS)

Reddy, C. J.; Deshpande, M. D.

1997-01-01

Application of Asymptotic Waveform Evaluation (AWE) is presented in conjunction with a hybrid Finite Element Method (FEM)/Method of Moments (MoM) technique to calculate the input characteristics of cavity-backed aperture antennas over a frequency range. The hybrid FEM/MoM technique is used to form an integro-partial-differential equation to compute the electric field distribution of the cavity-backed aperture antenna. The electric field, thus obtained, is expanded in a Taylor series around the frequency of interest. The coefficients of 'Taylor series (called 'moments') are obtained using the frequency derivatives of the integro-partial-differential Equation formed by the hybrid FEM/MoM technique. Using the moments, the electric field in the cavity is obtained over a frequency range. Using the electric field at different frequencies, the input characteristics of the antenna are obtained over a wide frequency band. Numerical results for an open coaxial line, probe fed cavity, and cavity-backed microstrip patch antennas are presented. Good agreement between AWE and the exact solution over the frequency range is observed.

Semiclassical Path Integral Calculation of Nonlinear Optical Spectroscopy.

PubMed

Provazza, Justin; Segatta, Francesco; Garavelli, Marco; Coker, David F

2018-02-13

Computation of nonlinear optical response functions allows for an in-depth connection between theory and experiment. Experimentally recorded spectra provide a high density of information, but to objectively disentangle overlapping signals and to reach a detailed and reliable understanding of the system dynamics, measurements must be integrated with theoretical approaches. Here, we present a new, highly accurate and efficient trajectory-based semiclassical path integral method for computing higher order nonlinear optical response functions for non-Markovian open quantum systems. The approach is, in principle, applicable to general Hamiltonians and does not require any restrictions on the form of the intrasystem or system-bath couplings. This method is systematically improvable and is shown to be valid in parameter regimes where perturbation theory-based methods qualitatively breakdown. As a test of the methodology presented here, we study a system-bath model for a coupled dimer for which we compare against numerically exact results and standard approximate perturbation theory-based calculations. Additionally, we study a monomer with discrete vibronic states that serves as the starting point for future investigation of vibronic signatures in nonlinear electronic spectroscopy.

Swimming of a linear chain with a cargo in an incompressible viscous fluid with inertia

NASA Astrophysics Data System (ADS)

Felderhof, B. U.

2017-01-01

An approximation to the added mass matrix of an assembly of spheres is constructed on the basis of potential flow theory for situations where one sphere is much larger than the others. In the approximation, the flow potential near a small sphere is assumed to be dipolar, but near the large sphere it involves all higher order multipoles. The analysis is based on an exact result for the potential of a magnetic dipole in the presence of a superconducting sphere. Subsequently, the approximate added mass hydrodynamic interactions are used in a calculation of the swimming velocity and rate of dissipation of linear chain structures consisting of a number of small spheres and a single large one, with account also of frictional hydrodynamic interactions. The results derived for periodic swimming on the basis of a kinematic approach are compared with the bilinear theory, valid for small amplitude of stroke, and with the numerical solution of the approximate equations of motion. The calculations interpolate over the whole range of scale number between the friction-dominated Stokes limit and the inertia-dominated regime.

Efficient numerical technique for calculating the properties of interacting dimers in the Peierls-Hubbard model

NASA Astrophysics Data System (ADS)

Sous, John; Chakraborty, Monodeep; Krems, Roman; Berciu, Mona

2017-04-01

We develop a method to compute the Green's function for two particles in an infinite chain and coupled to phonons by interactions that modulate their hopping as described by the Peierls/Su-Schrieffer-Heeger (SSH) model. The method is based on a variational approximation to the Bogoliubov-Born-Green-Kirkwood-Yvon (BBGKY) hierarchy and is shown to agree with exact digaonalization calculations. We show that the properties of bipolarons arising in such models is qualitatively different from those of the well-studied Holstein bipolarons. In particular, we show that depending on the particle statistics, strongly bound bipolarons may or may not form. In the case of hard-core bosons, we demonstrate novel effects for dimers such as sharp transitions and self-trapping. In the case of soft-core particles/ spinfull fermions, we show that the mediated interactions lead to overscreeing of the bare Hubbard U repulsion resulting in the formation of strongly bound bipolarons. This work was supported by NSERC of Canada and the Stewart Blusson Quantum Matter Institute.

The Symbol Grounding Problem Revisited: A Thorough Evaluation of the ANS Mapping Account and the Proposal of an Alternative Account Based on Symbol–Symbol Associations

PubMed Central

Reynvoet, Bert; Sasanguie, Delphine

2016-01-01

Recently, a lot of studies in the domain of numerical cognition have been published demonstrating a robust association between numerical symbol processing and individual differences in mathematics achievement. Because numerical symbols are so important for mathematics achievement, many researchers want to provide an answer on the ‘symbol grounding problem,’ i.e., how does a symbol acquires its numerical meaning? The most popular account, the approximate number system (ANS) mapping account, assumes that a symbol acquires its numerical meaning by being mapped on a non-verbal and ANS. Here, we critically evaluate four arguments that are supposed to support this account, i.e., (1) there is an evolutionary system for approximate number processing, (2) non-symbolic and symbolic number processing show the same behavioral effects, (3) non-symbolic and symbolic numbers activate the same brain regions which are also involved in more advanced calculation and (4) non-symbolic comparison is related to the performance on symbolic mathematics achievement tasks. Based on this evaluation, we conclude that all of these arguments and consequently also the mapping account are questionable. Next we explored less popular alternative, where small numerical symbols are initially mapped on a precise representation and then, in combination with increasing knowledge of the counting list result in an independent and exact symbolic system based on order relations between symbols. We evaluate this account by reviewing evidence on order judgment tasks following the same four arguments. Although further research is necessary, the available evidence so far suggests that this symbol–symbol association account should be considered as a worthy alternative of how symbols acquire their meaning. PMID:27790179

Exact Riemann solutions of the Ripa model for flat and non-flat bottom topographies

NASA Astrophysics Data System (ADS)

Rehman, Asad; Ali, Ishtiaq; Qamar, Shamsul

2018-03-01

This article is concerned with the derivation of exact Riemann solutions for Ripa model considering flat and non-flat bottom topographies. The Ripa model is a system of shallow water equations accounting for horizontal temperature gradients. In the case of non-flat bottom topography, the mass, momentum and energy conservation principles are utilized to relate the left and right states across the step-type bottom topography. The resulting system of algebraic equations is solved iteratively. Different numerical case studies of physical interest are considered. The solutions obtained from developed exact Riemann solvers are compared with the approximate solutions of central upwind scheme.

Exact relativistic Toda chain eigenfunctions from Separation of Variables and gauge theory

NASA Astrophysics Data System (ADS)

Sciarappa, Antonio

2017-10-01

We provide a proposal, motivated by Separation of Variables and gauge theory arguments, for constructing exact solutions to the quantum Baxter equation associated to the N-particle relativistic Toda chain and test our proposal against numerical results. Quantum Mechanical non-perturbative corrections, essential in order to obtain a sensible solution, are taken into account in our gauge theory approach by considering codimension two defects on curved backgrounds (squashed S 5 and degenerate limits) rather than flat space; this setting also naturally incorporates exact quantization conditions and energy spectrum of the relativistic Toda chain as well as its modular dual structure.

A Numerical Scheme for Ordinary Differential Equations Having Time Varying and Nonlinear Coefficients Based on the State Transition Matrix

NASA Technical Reports Server (NTRS)

Bartels, Robert E.

2002-01-01

A variable order method of integrating initial value ordinary differential equations that is based on the state transition matrix has been developed. The method has been evaluated for linear time variant and nonlinear systems of equations. While it is more complex than most other methods, it produces exact solutions at arbitrary time step size when the time variation of the system can be modeled exactly by a polynomial. Solutions to several nonlinear problems exhibiting chaotic behavior have been computed. Accuracy of the method has been demonstrated by comparison with an exact solution and with solutions obtained by established methods.

Quantum entanglement and criticality of the antiferromagnetic Heisenberg model in an external field.

PubMed

Liu, Guang-Hua; Li, Ruo-Yan; Tian, Guang-Shan

2012-06-27

By Lanczos exact diagonalization and the infinite time-evolving block decimation (iTEBD) technique, the two-site entanglement as well as the bipartite entanglement, the ground state energy, the nearest-neighbor correlations, and the magnetization in the antiferromagnetic Heisenberg (AFH) model under an external field are investigated. With increasing external field, the small size system shows some distinct upward magnetization stairsteps, accompanied synchronously with some downward two-site entanglement stairsteps. In the thermodynamic limit, the two-site entanglement, as well as the bipartite entanglement, the ground state energy, the nearest-neighbor correlations, and the magnetization are calculated, and the critical magnetic field h(c) = 2.0 is determined exactly. Our numerical results show that the quantum entanglement is sensitive to the subtle changing of the ground state, and can be used to describe the magnetization and quantum phase transition. Based on the discontinuous behavior of the first-order derivative of the entanglement entropy and fidelity per site, we think that the quantum phase transition in this model should belong to the second-order category. Furthermore, in the magnon existence region (h < 2.0), a logarithmically divergent behavior of block entanglement which can be described by a free bosonic field theory is observed, and the central charge c is determined to be 1.

Excited state correlations of the finite Heisenberg chain

NASA Astrophysics Data System (ADS)

Pozsgay, Balázs

2017-02-01

We consider short range correlations in excited states of the finite XXZ and XXX Heisenberg spin chains. We conjecture that the known results for the factorized ground state correlations can be applied to the excited states too, if the so-called physical part of the construction is changed appropriately. For the ground state we derive simple algebraic expressions for the physical part; the formulas only use the ground state Bethe roots as an input. We conjecture that the same formulas can be applied to the excited states as well, if the exact Bethe roots of the excited states are used instead. In the XXZ chain the results are expected to be valid for all states (except certain singular cases where regularization is needed), whereas in the XXX case they only apply to singlet states or group invariant operators. Our conjectures are tested against numerical data from exact diagonalization and coordinate Bethe Ansatz calculations, and perfect agreement is found in all cases. In the XXX case we also derive a new result for the nearest-neighbour correlator < σ 1zσ 2z> , which is valid for non-singlet states as well. Our results build a bridge between the known theory of factorized correlations, and the recently conjectured TBA-like description for the building blocks of the construction.

Reconstructing the metric of the local Universe from number counts observations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Vallejo, Sergio Andres; Romano, Antonio Enea, E-mail: antonio.enea.romano@cern.ch

Number counts observations available with new surveys such as the Euclid mission will be an important source of information about the metric of the Universe. We compute the low red-shift expansion for the energy density and the density contrast using an exact spherically symmetric solution in presence of a cosmological constant. At low red-shift the expansion is more precise than linear perturbation theory prediction. We then use the local expansion to reconstruct the metric from the monopole of the density contrast. We test the inversion method using numerical calculations and find a good agreement within the regime of validity ofmore » the red-shift expansion. The method could be applied to observational data to reconstruct the metric of the local Universe with a level of precision higher than the one achievable using perturbation theory.« less

Thermodynamics of pairing in mesoscopic systems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sumaryada, Tony; Volya, Alexander

Using numerical and analytical methods implemented for different models, we conduct a systematic study of the thermodynamic properties of pairing correlations in mesoscopic nuclear systems. Various quantities are calculated and analyzed using the exact solution of pairing. An in-depth comparison of canonical, grand canonical, and microcanonical ensembles is conducted. The nature of the pairing phase transition in a small system is of a particular interest. We discuss the onset of discontinuity in the thermodynamic variables, fluctuations, and evolution of zeros of the canonical and grand canonical partition functions in the complex plane. The behavior of the invariant correlational entropy ismore » also studied in the transitional region of interest. The change in the character of the phase transition due to the presence of a magnetic field is discussed along with studies of superconducting thermodynamics.« less

Analytical model for the density distribution in the Io plasma torus

NASA Technical Reports Server (NTRS)

Mei, YI; Thorne, Richard M.; Bagenal, Fran

1995-01-01

An analytical model is developed for the diffusive equilibrium plasma density distribution in the Io plasma torus. The model has been employed successfully to follow the ray path of plasma waves in the multi-ion Jovian magnetosphere; it would also be valuable for other studies of the Io torus that require a smooth and continuous description of the plasma density and its gradients. Validity of the analytical treatment requires that the temperature of thermal electrons be much lower than the ion temperature and that superthermal electrons be much less abundant than the thermal electrons; these two conditions are satisfied in the warm outer region of the Io torus from L = 6 to L = 10. The analytical solutions agree well with exact numerical calculations for the most dense portion of the Io torus within 30 deg of the equator.

CBR anisotropy from primordial gravitational waves in inflationary cosmologies

NASA Astrophysics Data System (ADS)

Allen, Bruce; Koranda, Scott

1994-09-01

We examine stochastic temperature fluctuations of the cosmic background radiation (CBR) arising via the Sachs-Wolfe effect from gravitational wave perturbations produced in the early Universe. These temperature fluctuations are described by an angular correlation function C(γ). A new (more concise and general) derivation of C(γ) is given, and evaluated for inflationary-universe cosmologies. This yields standard results for angles γ greater than a few degrees, but new results for smaller angles, because we do not make standard long-wavelength approximations to the gravitational wave mode functions. The function C(γ) may be expanded in a series of Legendre polynomials; we use numerical methods to compare the coefficients of the resulting expansion in our exact calculation with standard (approximate) results. We also report some progress towards finding a closed form expression for C(γ).

ANIE: A mathematical algorithm for automated indexing of planar deformation features in quartz grains

NASA Astrophysics Data System (ADS)

Huber, Matthew S.; Ferriãre, Ludovic; Losiak, Anna; Koeberl, Christian

2011-09-01

Abstract- Planar deformation features (PDFs) in quartz, one of the most commonly used diagnostic indicators of shock metamorphism, are planes of amorphous material that follow crystallographic orientations, and can thus be distinguished from non-shock-induced fractures in quartz. The process of indexing data for PDFs from universal-stage measurements has traditionally been performed using a manual graphical method, a time-consuming process in which errors can easily be introduced. A mathematical method and computer algorithm, which we call the Automated Numerical Index Executor (ANIE) program for indexing PDFs, was produced, and is presented here. The ANIE program is more accurate and faster than the manual graphical determination of Miller-Bravais indices, as it allows control of the exact error used in the calculation and removal of human error from the process.

Anti-resonance scattering at defect levels in the quantum conductance of a one-dimensional system

NASA Astrophysics Data System (ADS)

Sun, Z. Z.; Wang, Y. P.; Wang, X. R.

2002-03-01

For the ballistic quantum transport, the conductance of one channel is quantized to a value of 2e^2/h described by the Landauer formula. In the presence of defects, electrons will be scattered by these defects. Thus the conductance will deviate from the values of the quantized conductance. We show that an anti-resonance scattering can occur when an extra defect level is introduced into a conduction band. At the anti-resonance scattering, exact one quantum conductance is destroyed. The conductance takes a non-zero value when the Fermi energy is away from the anti-resonance scattering. The result is consistent with recent numerical calculations given by H. J. Choi et al. (Phys. Rev. Lett. 84, 2917(2000)) and P. L. McEuen et al. (Phys. Rev. Lett. 83, 5098(1999)).

Perturbation theory of a superconducting 0 - π impurity quantum phase transition.

PubMed

Žonda, M; Pokorný, V; Janiš, V; Novotný, T

2015-03-06

A single-level quantum dot with Coulomb repulsion attached to two superconducting leads is studied via the perturbation expansion in the interaction strength. We use the Nambu formalism and the standard many-body diagrammatic representation of the impurity Green functions to formulate the Matsubara self-consistent perturbation expansion. We show that at zero temperature second order of the expansion in its spin-symmetric version yields a nearly perfect agreement with the numerically exact calculations for the position of the 0 - π phase boundary at which the Andreev bound states reach the Fermi energy as well as for the values of single-particle quantities in the 0-phase. We present results for phase diagrams, level occupation, induced local superconducting gap, Josephson current, and energy of the Andreev bound states with the precision surpassing any (semi)analytical approaches employed thus far.

The Tool for Designing Engineering Systems Using a New Optimization Method Based on a Stochastic Process

NASA Astrophysics Data System (ADS)

Yoshida, Hiroaki; Yamaguchi, Katsuhito; Ishikawa, Yoshio

The conventional optimization methods were based on a deterministic approach, since their purpose is to find out an exact solution. However, these methods have initial condition dependence and risk of falling into local solution. In this paper, we propose a new optimization method based on a concept of path integral method used in quantum mechanics. The method obtains a solutions as an expected value (stochastic average) using a stochastic process. The advantages of this method are not to be affected by initial conditions and not to need techniques based on experiences. We applied the new optimization method to a design of the hang glider. In this problem, not only the hang glider design but also its flight trajectory were optimized. The numerical calculation results showed that the method has a sufficient performance.

From Weakly Chaotic Dynamics to Deterministic Subdiffusion via Copula Modeling

NASA Astrophysics Data System (ADS)

Nazé, Pierre

2018-03-01

Copula modeling consists in finding a probabilistic distribution, called copula, whereby its coupling with the marginal distributions of a set of random variables produces their joint distribution. The present work aims to use this technique to connect the statistical distributions of weakly chaotic dynamics and deterministic subdiffusion. More precisely, we decompose the jumps distribution of Geisel-Thomae map into a bivariate one and determine the marginal and copula distributions respectively by infinite ergodic theory and statistical inference techniques. We verify therefore that the characteristic tail distribution of subdiffusion is an extreme value copula coupling Mittag-Leffler distributions. We also present a method to calculate the exact copula and joint distributions in the case where weakly chaotic dynamics and deterministic subdiffusion statistical distributions are already known. Numerical simulations and consistency with the dynamical aspects of the map support our results.

Landau-Zener extension of the Tavis-Cummings model: structure of the solution

NASA Astrophysics Data System (ADS)

Sun, Chen; Sinitsyn, Nikolai

We explore the recently discovered solution of the driven Tavis-Cummings model (DTCM). It describes interaction of arbitrary number of two-level systems with a bosonic mode that has linearly time-dependent frequency. We derive compact and tractable expressions for transition probabilities in terms of the well known special functions. In the new form, our formulas are suitable for fast numerical calculations and analytical approximations. As an application, we obtain the semiclassical limit of the exact solution and compare it to prior approximations. We also reveal connection between DTCM and q-deformed binomial statistics. Under the auspices of the National Nuclear Security Administration of the U.S. Department of Energy at Los Alamos National Laboratory under Contract No. DE-AC52-06NA25396. Authors also thank the support from the LDRD program at LANL.

Light propagation in nanorod arrays

NASA Astrophysics Data System (ADS)

Rahachou, A. I.; Zozoulenko, I. V.

2007-03-01

We study the propagation of TM- and TE-polarized light in two-dimensional arrays of silver nanorods of various diameters in a gelatin background. We calculate the transmittance, reflectance and absorption of arranged and disordered nanorod arrays and compare the exact numerical results with the predictions of the Maxwell-Garnett effective-medium theory. We show that interactions between nanorods, multipole contributions and formations of photonic gaps affect strongly the transmittance spectra that cannot be accounted for in terms of the conventional effective-medium theory. We also demonstrate and explain the degradation of the transmittance in arrays with randomly located rods as well as the weak influence of their fluctuating diameter. For TM modes we outline the importance of the skin effect, which causes the full reflection of the incoming light. We then illustrate the possibility of using periodic arrays of nanorods as high-quality polarizers.

Spin waves in rings of classical magnetic dipoles

NASA Astrophysics Data System (ADS)

Schmidt, Heinz-Jürgen; Schröder, Christian; Luban, Marshall

2017-03-01

We theoretically and numerically investigate spin waves that occur in systems of classical magnetic dipoles that are arranged at the vertices of a regular polygon and interact solely via their magnetic fields. There are certain limiting cases that can be analyzed in detail. One case is that of spin waves as infinitesimal excitations from the system’s ground state, where the dispersion relation can be determined analytically. The frequencies of these infinitesimal spin waves are compared with the peaks of the Fourier transform of the thermal expectation value of the autocorrelation function calculated by Monte Carlo simulations. In the special case of vanishing wave number an exact solution of the equations of motion is possible describing synchronized oscillations with finite amplitudes. Finally, the limiting case of a dipole chain with N\\longrightarrow ∞ is investigated and completely solved.

High-precision calculations in strongly coupled quantum field theory with next-to-leading-order renormalized Hamiltonian Truncation

NASA Astrophysics Data System (ADS)

Elias-Miró, Joan; Rychkov, Slava; Vitale, Lorenzo G.

2017-10-01

Hamiltonian Truncation (a.k.a. Truncated Spectrum Approach) is an efficient numerical technique to solve strongly coupled QFTs in d = 2 spacetime dimensions. Further theoretical developments are needed to increase its accuracy and the range of applicability. With this goal in mind, here we present a new variant of Hamiltonian Truncation which exhibits smaller dependence on the UV cutoff than other existing implementations, and yields more accurate spectra. The key idea for achieving this consists in integrating out exactly a certain class of high energy states, which corresponds to performing renormalization at the cubic order in the interaction strength. We test the new method on the strongly coupled two-dimensional quartic scalar theory. Our work will also be useful for the future goal of extending Hamiltonian Truncation to higher dimensions d ≥ 3.

Role of quantum statistics in multi-particle decay dynamics

NASA Astrophysics Data System (ADS)

Marchewka, Avi; Granot, Er'el

2015-04-01

The role of quantum statistics in the decay dynamics of a multi-particle state, which is suddenly released from a confining potential, is investigated. For an initially confined double particle state, the exact dynamics is presented for both bosons and fermions. The time-evolution of the probability to measure two-particle is evaluated and some counterintuitive features are discussed. For instance, it is shown that although there is a higher chance of finding the two bosons (as oppose to fermions, and even distinguishable particles) at the initial trap region, there is a higher chance (higher than fermions) of finding them on two opposite sides of the trap as if the repulsion between bosons is higher than the repulsion between fermions. The results are demonstrated by numerical simulations and are calculated analytically in the short-time approximation. Furthermore, experimental validation is suggested.

Wave packet and statistical quantum calculations for the He + NeH⁺ → HeH⁺ + Ne reaction on the ground electronic state.

PubMed

Koner, Debasish; Barrios, Lizandra; González-Lezana, Tomás; Panda, Aditya N

2014-09-21

A real wave packet based time-dependent method and a statistical quantum method have been used to study the He + NeH(+) (v, j) reaction with the reactant in various ro-vibrational states, on a recently calculated ab initio ground state potential energy surface. Both the wave packet and statistical quantum calculations were carried out within the centrifugal sudden approximation as well as using the exact Hamiltonian. Quantum reaction probabilities exhibit dense oscillatory pattern for smaller total angular momentum values, which is a signature of resonances in a complex forming mechanism for the title reaction. Significant differences, found between exact and approximate quantum reaction cross sections, highlight the importance of inclusion of Coriolis coupling in the calculations. Statistical results are in fairly good agreement with the exact quantum results, for ground ro-vibrational states of the reactant. Vibrational excitation greatly enhances the reaction cross sections, whereas rotational excitation has relatively small effect on the reaction. The nature of the reaction cross section curves is dependent on the initial vibrational state of the reactant and is typical of a late barrier type potential energy profile.

Multilocus lod scores in large pedigrees: combination of exact and approximate calculations.

PubMed

Tong, Liping; Thompson, Elizabeth

2008-01-01

To detect the positions of disease loci, lod scores are calculated at multiple chromosomal positions given trait and marker data on members of pedigrees. Exact lod score calculations are often impossible when the size of the pedigree and the number of markers are both large. In this case, a Markov Chain Monte Carlo (MCMC) approach provides an approximation. However, to provide accurate results, mixing performance is always a key issue in these MCMC methods. In this paper, we propose two methods to improve MCMC sampling and hence obtain more accurate lod score estimates in shorter computation time. The first improvement generalizes the block-Gibbs meiosis (M) sampler to multiple meiosis (MM) sampler in which multiple meioses are updated jointly, across all loci. The second one divides the computations on a large pedigree into several parts by conditioning on the haplotypes of some 'key' individuals. We perform exact calculations for the descendant parts where more data are often available, and combine this information with sampling of the hidden variables in the ancestral parts. Our approaches are expected to be most useful for data on a large pedigree with a lot of missing data. (c) 2007 S. Karger AG, Basel

Multilocus Lod Scores in Large Pedigrees: Combination of Exact and Approximate Calculations

PubMed Central

Tong, Liping; Thompson, Elizabeth

2007-01-01

To detect the positions of disease loci, lod scores are calculated at multiple chromosomal positions given trait and marker data on members of pedigrees. Exact lod score calculations are often impossible when the size of the pedigree and the number of markers are both large. In this case, a Markov Chain Monte Carlo (MCMC) approach provides an approximation. However, to provide accurate results, mixing performance is always a key issue in these MCMC methods. In this paper, we propose two methods to improve MCMC sampling and hence obtain more accurate lod score estimates in shorter computation time. The first improvement generalizes the block-Gibbs meiosis (M) sampler to multiple meiosis (MM) sampler in which multiple meioses are updated jointly, across all loci. The second one divides the computations on a large pedigree into several parts by conditioning on the haplotypes of some ‘key’ individuals. We perform exact calculations for the descendant parts where more data are often available, and combine this information with sampling of the hidden variables in the ancestral parts. Our approaches are expected to be most useful for data on a large pedigree with a lot of missing data. PMID:17934317

Exact Tests for the Rasch Model via Sequential Importance Sampling

ERIC Educational Resources Information Center

Chen, Yuguo; Small, Dylan

2005-01-01

Rasch proposed an exact conditional inference approach to testing his model but never implemented it because it involves the calculation of a complicated probability. This paper furthers Rasch's approach by (1) providing an efficient Monte Carlo methodology for accurately approximating the required probability and (2) illustrating the usefulness…