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

Filinov, A.V.; Golubnychiy, V.O.; Bonitz, M.

Extending our previous work [A.V. Filinov et al., J. Phys. A 36, 5957 (2003)], we present a detailed discussion of accuracy and practical applications of finite-temperature pseudopotentials for two-component Coulomb systems. Different pseudopotentials are discussed: (i) the diagonal Kelbg potential, (ii) the off-diagonal Kelbg potential, (iii) the improved diagonal Kelbg potential, (iv) an effective potential obtained with the Feynman-Kleinert variational principle, and (v) the 'exact' quantum pair potential derived from the two-particle density matrix. For the improved diagonal Kelbg potential, a simple temperature-dependent fit is derived which accurately reproduces the 'exact' pair potential in the whole temperature range. The derivedmore » pseudopotentials are then used in path integral Monte Carlo and molecular-dynamics (MD) simulations to obtain thermodynamical properties of strongly coupled hydrogen. It is demonstrated that classical MD simulations with spin-dependent interaction potentials for the electrons allow for an accurate description of the internal energy of hydrogen in the difficult regime of partial ionization down to the temperatures of about 60 000 K. Finally, we point out an interesting relationship between the quantum potentials and the effective potentials used in density-functional theory.« less

Notes on the ExactPack Implementation of the DSD Explosive Arc Solver

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

Kaul, Ann; Doebling, Scott William

It has been shown above that the discretization scheme implemented in the ExactPack solver for the DSD Explosive Arc equation is consistent with the Explosive Arc PDE. In addition, a stability analysis has provided a CFL condition for a stable time step. Together, consistency and stability imply convergence of the scheme, which is expected to be close to first-order in time and second-order in space. It is understood that the nonlinearity of the underlying PDE will affect this rate somewhat.

Design of a Variational Multiscale Method for Turbulent Compressible Flows

NASA Technical Reports Server (NTRS)

Diosady, Laslo Tibor; Murman, Scott M.

2013-01-01

A spectral-element framework is presented for the simulation of subsonic compressible high-Reynolds-number flows. The focus of the work is maximizing the efficiency of the computational schemes to enable unsteady simulations with a large number of spatial and temporal degrees of freedom. A collocation scheme is combined with optimized computational kernels to provide a residual evaluation with computational cost independent of order of accuracy up to 16th order. The optimized residual routines are used to develop a low-memory implicit scheme based on a matrix-free Newton-Krylov method. A preconditioner based on the finite-difference diagonalized ADI scheme is developed which maintains the low memory of the matrix-free implicit solver, while providing improved convergence properties. Emphasis on low memory usage throughout the solver development is leveraged to implement a coupled space-time DG solver which may offer further efficiency gains through adaptivity in both space and time.

An Efficient Multicore Implementation of a Novel HSS-Structured Multifrontal Solver Using Randomized Sampling

DOE PAGES

Ghysels, Pieter; Li, Xiaoye S.; Rouet, Francois -Henry; ...

2016-10-27

Here, we present a sparse linear system solver that is based on a multifrontal variant of Gaussian elimination and exploits low-rank approximation of the resulting dense frontal matrices. We use hierarchically semiseparable (HSS) matrices, which have low-rank off-diagonal blocks, to approximate the frontal matrices. For HSS matrix construction, a randomized sampling algorithm is used together with interpolative decompositions. The combination of the randomized compression with a fast ULV HSS factoriz ation leads to a solver with lower computational complexity than the standard multifrontal method for many applications, resulting in speedups up to 7 fold for problems in our test suite.more » The implementation targets many-core systems by using task parallelism with dynamic runtime scheduling. Numerical experiments show performance improvements over state-of-the-art sparse direct solvers. The implementation achieves high performance and good scalability on a range of modern shared memory parallel systems, including the Intel Xeon Phi (MIC). The code is part of a software package called STRUMPACK - STRUctured Matrices PACKage, which also has a distributed memory component for dense rank-structured matrices.« less

Performance of a parallel thermal-hydraulics code TEMPEST

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

Fann, G.I.; Trent, D.S.

The authors describe the parallelization of the Tempest thermal-hydraulics code. The serial version of this code is used for production quality 3-D thermal-hydraulics simulations. Good speedup was obtained with a parallel diagonally preconditioned BiCGStab non-symmetric linear solver, using a spatial domain decomposition approach for the semi-iterative pressure-based and mass-conserved algorithm. The test case used here to illustrate the performance of the BiCGStab solver is a 3-D natural convection problem modeled using finite volume discretization in cylindrical coordinates. The BiCGStab solver replaced the LSOR-ADI method for solving the pressure equation in TEMPEST. BiCGStab also solves the coupled thermal energy equation. Scalingmore » performance of 3 problem sizes (221220 nodes, 358120 nodes, and 701220 nodes) are presented. These problems were run on 2 different parallel machines: IBM-SP and SGI PowerChallenge. The largest problem attains a speedup of 68 on an 128 processor IBM-SP. In real terms, this is over 34 times faster than the fastest serial production time using the LSOR-ADI solver.« less

Non-LTE radiative transfer with lambda-acceleration - Convergence properties using exact full and diagonal lambda-operators

NASA Technical Reports Server (NTRS)

Macfarlane, J. J.

1992-01-01

We investigate the convergence properties of Lambda-acceleration methods for non-LTE radiative transfer problems in planar and spherical geometry. Matrix elements of the 'exact' A-operator are used to accelerate convergence to a solution in which both the radiative transfer and atomic rate equations are simultaneously satisfied. Convergence properties of two-level and multilevel atomic systems are investigated for methods using: (1) the complete Lambda-operator, and (2) the diagonal of the Lambda-operator. We find that the convergence properties for the method utilizing the complete Lambda-operator are significantly better than those of the diagonal Lambda-operator method, often reducing the number of iterations needed for convergence by a factor of between two and seven. However, the overall computational time required for large scale calculations - that is, those with many atomic levels and spatial zones - is typically a factor of a few larger for the complete Lambda-operator method, suggesting that the approach should be best applied to problems in which convergence is especially difficult.

Exact solution of the XXX Gaudin model with generic open boundaries

NASA Astrophysics Data System (ADS)

Hao, Kun; Cao, Junpeng; Yang, Tao; Yang, Wen-Li

2015-03-01

The XXX Gaudin model with generic integrable open boundaries specified by the most general non-diagonal reflecting matrices is studied. Besides the inhomogeneous parameters, the associated Gaudin operators have six free parameters which break the U(1) -symmetry. With the help of the off-diagonal Bethe ansatz, we successfully obtained the eigenvalues of these Gaudin operators and the corresponding Bethe ansatz equations.

Solving Modal Equations of Motion with Initial Conditions Using MSC/NASTRAN DMAP. Part 2; Coupled Versus Uncoupled Integration

NASA Technical Reports Server (NTRS)

Barnett, Alan R.; Ibrahim, Omar M.; Abdallah, Ayman A.; Sullivan, Timothy L.

1993-01-01

By utilizing MSC/NASTRAN DMAP (Direct Matrix Abstraction Program) in an existing NASA Lewis Research Center coupled loads methodology, solving modal equations of motion with initial conditions is possible using either coupled (Newmark-Beta) or uncoupled (exact mode superposition) integration available within module TRD1. Both the coupled and newly developed exact mode superposition methods have been used to perform transient analyses of various space systems. However, experience has shown that in most cases, significant time savings are realized when the equations of motion are integrated using the uncoupled solver instead of the coupled solver. Through the results of a real-world engineering analysis, advantages of using the exact mode superposition methodology are illustrated.

Strong correlation effects in theoretical STM studies of magnetic adatoms

NASA Astrophysics Data System (ADS)

Dang, Hung T.; dos Santos Dias, Manuel; Liebsch, Ansgar; Lounis, Samir

2016-03-01

We present a theoretical study for the scanning tunneling microscopy (STM) spectra of surface-supported magnetic nanostructures, incorporating strong correlation effects. As concrete examples, we study Co and Mn adatoms on the Cu(111) surface, which are expected to represent the opposite limits of Kondo physics and local moment behavior, using a combination of density functional theory and both quantum Monte Carlo and exact diagonalization impurity solvers. We examine in detail the effects of temperature T , correlation strength U , and impurity d electron occupancy Nd on the local density of states. We also study the effective coherence energy scale, i.e., the Kondo temperature TK, which can be extracted from the STM spectra. Theoretical STM spectra are computed as a function of STM tip position relative to each adatom. Because of the multiorbital nature of the adatoms, the STM spectra are shown to consist of a complicated superposition of orbital contributions, with different orbital symmetries, self-energies, and Kondo temperatures. For a Mn adatom, which is close to half-filling, the STM spectra are featureless near the Fermi level. On the other hand, the quasiparticle peak for a Co adatom gives rise to strongly position-dependent Fano line shapes.

Acceleration of Linear Finite-Difference Poisson-Boltzmann Methods on Graphics Processing Units.

PubMed

Qi, Ruxi; Botello-Smith, Wesley M; Luo, Ray

2017-07-11

Electrostatic interactions play crucial roles in biophysical processes such as protein folding and molecular recognition. Poisson-Boltzmann equation (PBE)-based models have emerged as widely used in modeling these important processes. Though great efforts have been put into developing efficient PBE numerical models, challenges still remain due to the high dimensionality of typical biomolecular systems. In this study, we implemented and analyzed commonly used linear PBE solvers for the ever-improving graphics processing units (GPU) for biomolecular simulations, including both standard and preconditioned conjugate gradient (CG) solvers with several alternative preconditioners. Our implementation utilizes the standard Nvidia CUDA libraries cuSPARSE, cuBLAS, and CUSP. Extensive tests show that good numerical accuracy can be achieved given that the single precision is often used for numerical applications on GPU platforms. The optimal GPU performance was observed with the Jacobi-preconditioned CG solver, with a significant speedup over standard CG solver on CPU in our diversified test cases. Our analysis further shows that different matrix storage formats also considerably affect the efficiency of different linear PBE solvers on GPU, with the diagonal format best suited for our standard finite-difference linear systems. Further efficiency may be possible with matrix-free operations and integrated grid stencil setup specifically tailored for the banded matrices in PBE-specific linear systems.

3D Gaussian Beam Modeling

DTIC Science & Technology

2011-09-01

optimized building blocks such as a parallelized tri-diagonal linear solver (used in the “implicit finite differences ” and split-step Pade PE models...and Ding Lee. “A finite - difference treatment of interface conditions for the parabolic wave equation: The horizontal interface.” The Journal of the...Acoustical Society of America, 71(4):855, 1982. 3. Ding Lee and Suzanne T. McDaniel. “A finite - difference treatment of interface conditions for

sdg Interacting boson hamiltonian in the seniority scheme

NASA Astrophysics Data System (ADS)

Yoshinaga, N.

1989-03-01

The sdg interacting boson hamiltonian is derived in the seniority scheme. We use the method of Otsuka, Arima and Iachello in order to derive the boson hamiltonian from the fermion hamiltonian. To examine how good is the boson approximation in the zeroth-order, we carry out the exact shell model calculations in a single j-shell. It is found that almost all low-lying levels are reproduced quite well by diagonalizing the sdg interacting boson hamiltonian in the vibrational case. In the deformed case the introduction of g-bosons improves the reproduction of the spectra and of the binding energies which are obtained by diagonalizing the exact shell model hamiltonian. In particular the sdg interacting boson model reproduces well-developed rotational bands.

Static holes in the geometrically frustrated bow-tie ladder

NASA Astrophysics Data System (ADS)

Martins, George B.; Brenig, Wolfram

2008-10-01

We investigate the doping of a geometrically frustrated spin ladder with static holes by a complementary approach using exact diagonalization and quantum dimers. Results for thermodynamic properties, the singlet density of states, the hole-binding energy and the spin correlations will be presented. For the undoped systems the ground state is non-degenerate, with translationally invariant nearest-neighbor spin correlations. For the doped case, we find that static holes polarize their vicinity through a localization of singlets, reducing the frustration. This polarization induces short range repulsive forces between two holes and an oscillatory behavior of the long range two-hole energy. For most quantities investigated, we find very good agreement between the quantum dimer approach and the results from exact diagonalization.

Anisotropic resonator analysis using the Fourier-Bessel mode solver

NASA Astrophysics Data System (ADS)

Gauthier, Robert C.

2018-03-01

A numerical mode solver for optical structures that conform to cylindrical symmetry using Faraday's and Ampere's laws as starting expressions is developed when electric or magnetic anisotropy is present. The technique builds on the existing Fourier-Bessel mode solver which allows resonator states to be computed exploiting the symmetry properties of the resonator and states to reduce the matrix system. The introduction of anisotropy into the theoretical frame work facilitates the inclusion of PML borders permitting the computation of open ended structures and a better estimation of the resonator state quality factor. Matrix populating expressions are provided that can accommodate any material anisotropy with arbitrary orientation in the computation domain. Several example of electrical anisotropic computations are provided for rationally symmetric structures such as standard optical fibers, axial Bragg-ring fibers and bottle resonators. The anisotropy present in the materials introduces off diagonal matrix elements in the permittivity tensor when expressed in cylindrical coordinates. The effects of the anisotropy of computed states are presented and discussed.

An iterative solver for the 3D Helmholtz equation

NASA Astrophysics Data System (ADS)

Belonosov, Mikhail; Dmitriev, Maxim; Kostin, Victor; Neklyudov, Dmitry; Tcheverda, Vladimir

2017-09-01

We develop a frequency-domain iterative solver for numerical simulation of acoustic waves in 3D heterogeneous media. It is based on the application of a unique preconditioner to the Helmholtz equation that ensures convergence for Krylov subspace iteration methods. Effective inversion of the preconditioner involves the Fast Fourier Transform (FFT) and numerical solution of a series of boundary value problems for ordinary differential equations. Matrix-by-vector multiplication for iterative inversion of the preconditioned matrix involves inversion of the preconditioner and pointwise multiplication of grid functions. Our solver has been verified by benchmarking against exact solutions and a time-domain solver.

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.

Heat Transfer Effects on a Fully Premixed Methane Impinging Flame

DTIC Science & Technology

2014-10-30

Houzeaux et al., 2009). The GM- RES solver is also employed to solve for the enthalpy and species mass fractions. The Gauss - Seidel iterative method is...the system is therefore split to solve the mo- mentum and continuity equations independently. This is achieved by applying an iterative strategy...the momentum equation twice and the continuity equation once. The momentum equation is solved using the GMRES or BICGSTAB method (diagonal and Gauss

A fast direct method for block triangular Toeplitz-like with tri-diagonal block systems from time-fractional partial differential equations

NASA Astrophysics Data System (ADS)

Ke, Rihuan; Ng, Michael K.; Sun, Hai-Wei

2015-12-01

In this paper, we study the block lower triangular Toeplitz-like with tri-diagonal blocks system which arises from the time-fractional partial differential equation. Existing fast numerical solver (e.g., fast approximate inversion method) cannot handle such linear system as the main diagonal blocks are different. The main contribution of this paper is to propose a fast direct method for solving this linear system, and to illustrate that the proposed method is much faster than the classical block forward substitution method for solving this linear system. Our idea is based on the divide-and-conquer strategy and together with the fast Fourier transforms for calculating Toeplitz matrix-vector multiplication. The complexity needs O (MNlog2 ⁡ M) arithmetic operations, where M is the number of blocks (the number of time steps) in the system and N is the size (number of spatial grid points) of each block. Numerical examples from the finite difference discretization of time-fractional partial differential equations are also given to demonstrate the efficiency of the proposed method.

Block Preconditioning to Enable Physics-Compatible Implicit Multifluid Plasma Simulations

NASA Astrophysics Data System (ADS)

Phillips, Edward; Shadid, John; Cyr, Eric; Miller, Sean

2017-10-01

Multifluid plasma simulations involve large systems of partial differential equations in which many time-scales ranging over many orders of magnitude arise. Since the fastest of these time-scales may set a restrictively small time-step limit for explicit methods, the use of implicit or implicit-explicit time integrators can be more tractable for obtaining dynamics at time-scales of interest. Furthermore, to enforce properties such as charge conservation and divergence-free magnetic field, mixed discretizations using volume, nodal, edge-based, and face-based degrees of freedom are often employed in some form. Together with the presence of stiff modes due to integrating over fast time-scales, the mixed discretization makes the required linear solves for implicit methods particularly difficult for black box and monolithic solvers. This work presents a block preconditioning strategy for multifluid plasma systems that segregates the linear system based on discretization type and approximates off-diagonal coupling in block diagonal Schur complement operators. By employing multilevel methods for the block diagonal subsolves, this strategy yields algorithmic and parallel scalability which we demonstrate on a range of problems.

Hubbard physics in the symmetric half-filled periodic anderson-hubbard model

NASA Astrophysics Data System (ADS)

Hagymási, I.; Itai, K.; Sólyom, J.

2013-05-01

Two very different methods — exact diagonalization on finite chains and a variational method — are used to study the possibility of a metal-insulator transition in the symmetric half-filled periodic Anderson-Hubbard model. With this aim we calculate the density of doubly occupied d sites ( gn d ) as a function of various parameters. In the absence of on-site Coulomb interaction ( U f ) between f electrons, the two methods yield similar results. The double occupancy of d levels remains always finite just as in the one-dimensional Hubbard model. Exact diagonalization on finite chains gives the same result for finite U f , while the Gutzwiller method leads to a Brinkman-Rice transition at a critical value ( U {/d c }), which depends on U f and V.

Treatment of geometric singularities in implicit solvent models

NASA Astrophysics Data System (ADS)

Yu, Sining; Geng, Weihua; Wei, G. W.

2007-06-01

Geometric singularities, such as cusps and self-intersecting surfaces, are major obstacles to the accuracy, convergence, and stability of the numerical solution of the Poisson-Boltzmann (PB) equation. In earlier work, an interface technique based PB solver was developed using the matched interface and boundary (MIB) method, which explicitly enforces the flux jump condition at the solvent-solute interfaces and leads to highly accurate biomolecular electrostatics in continuum electric environments. However, such a PB solver, denoted as MIBPB-I, cannot maintain the designed second order convergence whenever there are geometric singularities, such as cusps and self-intersecting surfaces. Moreover, the matrix of the MIBPB-I is not optimally symmetrical, resulting in the convergence difficulty. The present work presents a new interface method based PB solver, denoted as MIBPB-II, to address the aforementioned problems. The present MIBPB-II solver is systematical and robust in treating geometric singularities and delivers second order convergence for arbitrarily complex molecular surfaces of proteins. A new procedure is introduced to make the MIBPB-II matrix optimally symmetrical and diagonally dominant. The MIBPB-II solver is extensively validated by the molecular surfaces of few-atom systems and a set of 24 proteins. Converged electrostatic potentials and solvation free energies are obtained at a coarse grid spacing of 0.5Å and are considerably more accurate than those obtained by the PBEQ and the APBS at finer grid spacings.

QCD dipole model and k T factorization

NASA Astrophysics Data System (ADS)

Bialas, A.; Navelet, H.; Peschanski, R.

2001-01-01

It is shown that the colour dipole approach to hard scattering at high energy is fully compatible with k T factorization at the leading logarithm approximation (in - logx Bj). The relations between the dipole amplitudes and unintegrated diagonal and non-diagonal gluon distributions are given. It is also shown that including the exact gluon kinematics in the k T factorization formula destroys the conservation of transverse position vectors and thus is incompatible with the dipole model for both elastic and diffractive amplitudes.

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

Ghysels, Pieter; Li, Xiaoye S.; Rouet, Francois -Henry

Here, we present a sparse linear system solver that is based on a multifrontal variant of Gaussian elimination and exploits low-rank approximation of the resulting dense frontal matrices. We use hierarchically semiseparable (HSS) matrices, which have low-rank off-diagonal blocks, to approximate the frontal matrices. For HSS matrix construction, a randomized sampling algorithm is used together with interpolative decompositions. The combination of the randomized compression with a fast ULV HSS factoriz ation leads to a solver with lower computational complexity than the standard multifrontal method for many applications, resulting in speedups up to 7 fold for problems in our test suite.more » The implementation targets many-core systems by using task parallelism with dynamic runtime scheduling. Numerical experiments show performance improvements over state-of-the-art sparse direct solvers. The implementation achieves high performance and good scalability on a range of modern shared memory parallel systems, including the Intel Xeon Phi (MIC). The code is part of a software package called STRUMPACK - STRUctured Matrices PACKage, which also has a distributed memory component for dense rank-structured matrices.« less

D4Z - a new renumbering for iterative solution of ground-water flow and solute- transport equations

USGS Publications Warehouse

Kipp, K.L.; Russell, T.F.; Otto, J.S.

1992-01-01

D4 zig-zag (D4Z) is a new renumbering scheme for producing a reduced matrix to be solved by an incomplete LU preconditioned, restarted conjugate-gradient iterative solver. By renumbering alternate diagonals in a zig-zag fashion, a very low sensitivity of convergence rate to renumbering direction is obtained. For two demonstration problems involving groundwater flow and solute transport, iteration counts are related to condition numbers and spectra of the reduced matrices.

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.

Bayesian block-diagonal variable selection and model averaging

PubMed Central

Papaspiliopoulos, O.; Rossell, D.

2018-01-01

Summary We propose a scalable algorithmic framework for exact Bayesian variable selection and model averaging in linear models under the assumption that the Gram matrix is block-diagonal, and as a heuristic for exploring the model space for general designs. In block-diagonal designs our approach returns the most probable model of any given size without resorting to numerical integration. The algorithm also provides a novel and efficient solution to the frequentist best subset selection problem for block-diagonal designs. Posterior probabilities for any number of models are obtained by evaluating a single one-dimensional integral, and other quantities of interest such as variable inclusion probabilities and model-averaged regression estimates are obtained by an adaptive, deterministic one-dimensional numerical integration. The overall computational cost scales linearly with the number of blocks, which can be processed in parallel, and exponentially with the block size, rendering it most adequate in situations where predictors are organized in many moderately-sized blocks. For general designs, we approximate the Gram matrix by a block-diagonal matrix using spectral clustering and propose an iterative algorithm that capitalizes on the block-diagonal algorithms to explore efficiently the model space. All methods proposed in this paper are implemented in the R library mombf. PMID:29861501

Morse oscillator propagator in the high temperature limit I: Theory

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

Toutounji, Mohamad, E-mail: Mtoutounji@uaeu.ac.ae

2017-02-15

In an earlier work of the author the time evolution of Morse oscillator was studied analytically and exactly at low temperatures whereupon optical correlation functions were calculated using Morse oscillator coherent states were employed. Morse oscillator propagator in the high temperature limit is derived and a closed form of its corresponding canonical partition function is obtained. Both diagonal and off-diagonal forms of Morse oscillator propagator are derived in the high temperature limit. Partition functions of diatomic molecules are calculated. - Highlights: • Derives the quantum propagator of Morse oscillator in the high temperature limit. • Uses the resulting diagonal propagatormore » to derive a closed form of Morse oscillator partition function. • Provides a more sophisticated formula of the quantum propagator to test the accuracy of the herein results.« less

Line Interference Effects Using a Refined Robert-Bonamy Formalism: the Test Case of the Isotropic Raman Spectra of Autoperturbed N2

NASA Technical Reports Server (NTRS)

Boulet, Christian; Ma, Qiancheng; Thibault, Franck

2014-01-01

A symmetrized version of the recently developed refined Robert-Bonamy formalism [Q. Ma, C. Boulet, and R. H. Tipping, J. Chem. Phys. 139, 034305 (2013)] is proposed. This model takes into account line coupling effects and hence allows the calculation of the off-diagonal elements of the relaxation matrix, without neglecting the rotational structure of the perturbing molecule. The formalism is applied to the isotropic Raman spectra of autoperturbed N2 for which a benchmark quantum relaxation matrix has recently been proposed. The consequences of the classical path approximation are carefully analyzed. Methods correcting for effects of inelasticity are considered. While in the right direction, these corrections appear to be too crude to provide off diagonal elements which would yield, via the sum rule, diagonal elements in good agreement with the quantum results. In order to overcome this difficulty, a re-normalization procedure is applied, which ensures that the off-diagonal elements do lead to the exact quantum diagonal elements. The agreement between the (re-normalized) semi-classical and quantum relaxation matrices is excellent, at least for the Raman spectra of N2, opening the way to the analysis of more complex molecular systems.

Efficient Parallel Formulations of Hierarchical Methods and Their Applications

NASA Astrophysics Data System (ADS)

Grama, Ananth Y.

1996-01-01

Hierarchical methods such as the Fast Multipole Method (FMM) and Barnes-Hut (BH) are used for rapid evaluation of potential (gravitational, electrostatic) fields in particle systems. They are also used for solving integral equations using boundary element methods. The linear systems arising from these methods are dense and are solved iteratively. Hierarchical methods reduce the complexity of the core matrix-vector product from O(n^2) to O(n log n) and the memory requirement from O(n^2) to O(n). We have developed highly scalable parallel formulations of a hybrid FMM/BH method that are capable of handling arbitrarily irregular distributions. We apply these formulations to astrophysical simulations of Plummer and Gaussian galaxies. We have used our parallel formulations to solve the integral form of the Laplace equation. We show that our parallel hierarchical mat-vecs yield high efficiency and overall performance even on relatively small problems. A problem containing approximately 200K nodes takes under a second to compute on 256 processors and yet yields over 85% efficiency. The efficiency and raw performance is expected to increase for bigger problems. For the 200K node problem, our code delivers about 5 GFLOPS of performance on a 256 processor T3D. This is impressive considering the fact that the problem has floating point divides and roots, and very little locality resulting in poor cache performance. A dense matrix-vector product of the same dimensions would require about 0.5 TeraBytes of memory and about 770 TeraFLOPS of computing speed. Clearly, if the loss in accuracy resulting from the use of hierarchical methods is acceptable, our code yields significant savings in time and memory. We also study the convergence of a GMRES solver built around this mat-vec. We accelerate the convergence of the solver using three preconditioning techniques: diagonal scaling, block-diagonal preconditioning, and inner-outer preconditioning. We study the performance and parallel efficiency of these preconditioned solvers. Using this solver, we solve dense linear systems with hundreds of thousands of unknowns. Solving a 105K unknown problem takes about 10 minutes on a 64 processor T3D. Until very recently, boundary element problems of this magnitude could not even be generated, let alone solved.

A third-order implicit discontinuous Galerkin method based on a Hermite WENO reconstruction for time-accurate solution of the compressible Navier-Stokes equations

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

Xia, Yidong; Liu, Xiaodong; Luo, Hong

2015-06-01

Here, a space and time third-order discontinuous Galerkin method based on a Hermite weighted essentially non-oscillatory reconstruction is presented for the unsteady compressible Euler and Navier–Stokes equations. At each time step, a lower-upper symmetric Gauss–Seidel preconditioned generalized minimal residual solver is used to solve the systems of linear equations arising from an explicit first stage, single diagonal coefficient, diagonally implicit Runge–Kutta time integration scheme. The performance of the developed method is assessed through a variety of unsteady flow problems. Numerical results indicate that this method is able to deliver the designed third-order accuracy of convergence in both space and time,more » while requiring remarkably less storage than the standard third-order discontinous Galerkin methods, and less computing time than the lower-order discontinous Galerkin methods to achieve the same level of temporal accuracy for computing unsteady flow problems.« less

Static Holes in Geometrically Frustrated Bow Tie Ladder

NASA Astrophysics Data System (ADS)

Martins, George; Brenig, Wolfram

2007-03-01

Doping of the geometrically frustrated bow-tie spin ladder with static holes is investigated by a complementary approach using exact diagonalization and hard-core quantum dimers. Results for the thermodynamics in the undoped case, the singlet density of states, the hole-binding energy, and the spin correlations will be presented. We find that the static holes polarize their vicinity by a localization of singlets in order to reduce the frustration. As a consequence the singlet polarization cloud induces short range repulsive forces between the holes with oscillatory longer range behavior. For those systems we have studied, most results for the quantum dimer approach are found to be qualitatively if not quantitatively in agreement with exact diagonalization. The ground state of the undoped system is non-degenerate with translationally invariant nearest-neighbor spin correlations up to a few unit cells, which is consistent with a spin liquid state or a valence bond crystal with very large unit cell. C. Waldtmann, A. Kreutzmann, U. Schollwock, K. Maisinger, and H.-U. Everts, Phys. Rev. B 62, 9472 (2000).

Quantum Entanglement and the Topological Order of Fractional Hall States

NASA Astrophysics Data System (ADS)

Rezayi, Edward

2015-03-01

Fractional quantum Hall states or, more generally, topological phases of matter defy Landau classification based on order parameter and broken symmetry. Instead they have been characterized by their topological order. Quantum information concepts, such as quantum entanglement, appear to provide the most efficient method of detecting topological order solely from the knowledge of the ground state wave function. This talk will focus on real-space bi-partitioning of quantum Hall states and will present both exact diagonalization and quantum Monte Carlo studies of topological entanglement entropy in various geometries. Results on the torus for non-contractible cuts are quite rich and, through the use of minimum entropy states, yield the modular S-matrix and hence uniquely determine the topological order, as shown in recent literature. Concrete examples of minimum entropy states from known quantum Hall wave functions and their corresponding quantum numbers, used in exact diagonalizations, will be given. In collaboration with Clare Abreu and Raul Herrera. Supported by DOE Grant DE-SC0002140.

Polaron dynamics with a multitude of Davydov D{sub 2} trial states

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

Zhou, Nengji; Department of Physics, Hangzhou Normal University, Hangzhou 310046; Huang, Zhongkai

2015-07-07

We propose an extension to the Davydov D{sub 2} Ansatz in the dynamics study of the Holstein molecular crystal model with diagonal and off-diagonal exciton-phonon coupling using the Dirac-Frenkel time-dependent variational principle. The new trial state by the name of the “multi-D{sub 2} Ansatz” is a linear combination of Davydov D{sub 2} trial states, and its validity is carefully examined by quantifying how faithfully it follows the Schrödinger equation. Considerable improvements in accuracy have been demonstrated in comparison with the usual Davydov trial states, i.e., the single D{sub 1} and D{sub 2} Ansätze. With an increase in the number ofmore » the Davydov D{sub 2} trial states in the multi-D{sub 2} Ansatz, deviation from the exact Schrödinger dynamics is gradually diminished, leading to a numerically exact solution to the Schrödinger equation.« less

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.

Line interference effects using a refined Robert-Bonamy formalism: The test case of the isotropic Raman spectra of autoperturbed N{sub 2}

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

Boulet, Christian, E-mail: Christian.boulet@u-psud.fr; Ma, Qiancheng; Thibault, Franck

A symmetrized version of the recently developed refined Robert-Bonamy formalism [Q. Ma, C. Boulet, and R. H. Tipping, J. Chem. Phys. 139, 034305 (2013)] is proposed. This model takes into account line coupling effects and hence allows the calculation of the off-diagonal elements of the relaxation matrix, without neglecting the rotational structure of the perturbing molecule. The formalism is applied to the isotropic Raman spectra of autoperturbed N{sub 2} for which a benchmark quantum relaxation matrix has recently been proposed. The consequences of the classical path approximation are carefully analyzed. Methods correcting for effects of inelasticity are considered. While inmore » the right direction, these corrections appear to be too crude to provide off diagonal elements which would yield, via the sum rule, diagonal elements in good agreement with the quantum results. In order to overcome this difficulty, a re-normalization procedure is applied, which ensures that the off-diagonal elements do lead to the exact quantum diagonal elements. The agreement between the (re-normalized) semi-classical and quantum relaxation matrices is excellent, at least for the Raman spectra of N{sub 2}, opening the way to the analysis of more complex molecular systems.« less

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.

Efficient Broadband Simulation of Fluid-Structure Coupling for Membrane-Type Acoustic Transducer Arrays Using the Multilevel Fast Multipole Algorithm.

PubMed

Shieh, Bernard; Sabra, Karim G; Degertekin, F Levent

2016-11-01

A boundary element model provides great flexibility for the simulation of membrane-type micromachined ultrasonic transducers (MUTs) in terms of membrane shape, actuating mechanism, and array layout. Acoustic crosstalk is accounted for through a mutual impedance matrix that captures the primary crosstalk mechanism of dispersive-guided modes generated at the fluid-solid interface. However, finding the solution to the fully populated boundary element matrix equation using standard techniques requires computation time and memory usage that scales by the cube and by the square of the number of nodes, respectively, limiting simulation to a small number of membranes. We implement a solver with improved speed and efficiency through the application of a multilevel fast multipole algorithm (FMA). By approximating the fields of collections of nodes using multipole expansions of the free-space Green's function, an FMA solver can enable the simulation of hundreds of thousands of nodes while incurring an approximation error that is controllable. Convergence is drastically improved using a problem-specific block-diagonal preconditioner. We demonstrate the solver's capabilities by simulating a 32-element 7-MHz 1-D capacitive MUT (CMUT) phased array with 2880 membranes. The array is simulated using 233280 nodes for a very wide frequency band up to 50 MHz. For a simulation with 15210 nodes, the FMA solver performed ten times faster and used 32 times less memory than a standard solver based on LU decomposition. We investigate the effects of mesh density and phasing on the predicted array response and find that it is necessary to use about seven nodes over the width of the membrane to observe convergence of the solution-even below the first membrane resonance frequency-due to the influence of higher order membrane modes.

Distribution of Off-Diagonal Cross Sections in Quantum Chaotic Scattering: Exact Results and Data Comparison.

PubMed

Kumar, Santosh; Dietz, Barbara; Guhr, Thomas; Richter, Achim

2017-12-15

The recently derived distributions for the scattering-matrix elements in quantum chaotic systems are not accessible in the majority of experiments, whereas the cross sections are. We analytically compute distributions for the off-diagonal cross sections in the Heidelberg approach, which is applicable to a wide range of quantum chaotic systems. Thus, eventually, we fully solve a problem that already arose more than half a century ago in compound-nucleus scattering. We compare our results with data from microwave and compound-nucleus experiments, particularly addressing the transition from isolated resonances towards the Ericson regime of strongly overlapping ones.

Distribution of Off-Diagonal Cross Sections in Quantum Chaotic Scattering: Exact Results and Data Comparison

NASA Astrophysics Data System (ADS)

Kumar, Santosh; Dietz, Barbara; Guhr, Thomas; Richter, Achim

2017-12-01

The recently derived distributions for the scattering-matrix elements in quantum chaotic systems are not accessible in the majority of experiments, whereas the cross sections are. We analytically compute distributions for the off-diagonal cross sections in the Heidelberg approach, which is applicable to a wide range of quantum chaotic systems. Thus, eventually, we fully solve a problem that already arose more than half a century ago in compound-nucleus scattering. We compare our results with data from microwave and compound-nucleus experiments, particularly addressing the transition from isolated resonances towards the Ericson regime of strongly overlapping ones.

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.

On the development of OpenFOAM solvers based on explicit and implicit high-order Runge-Kutta schemes for incompressible flows with heat transfer

NASA Astrophysics Data System (ADS)

D'Alessandro, Valerio; Binci, Lorenzo; Montelpare, Sergio; Ricci, Renato

2018-01-01

Open-source CFD codes provide suitable environments for implementing and testing low-dissipative algorithms typically used to simulate turbulence. In this research work we developed CFD solvers for incompressible flows based on high-order explicit and diagonally implicit Runge-Kutta (RK) schemes for time integration. In particular, an iterated PISO-like procedure based on Rhie-Chow correction was used to handle pressure-velocity coupling within each implicit RK stage. For the explicit approach, a projected scheme was used to avoid the "checker-board" effect. The above-mentioned approaches were also extended to flow problems involving heat transfer. It is worth noting that the numerical technology available in the OpenFOAM library was used for space discretization. In this work, we additionally explore the reliability and effectiveness of the proposed implementations by computing several unsteady flow benchmarks; we also show that the numerical diffusion due to the time integration approach is completely canceled using the solution techniques proposed here.

Large-scale 3-D EM modelling with a Block Low-Rank multifrontal direct solver

NASA Astrophysics Data System (ADS)

Shantsev, Daniil V.; Jaysaval, Piyoosh; de la Kethulle de Ryhove, Sébastien; Amestoy, Patrick R.; Buttari, Alfredo; L'Excellent, Jean-Yves; Mary, Theo

2017-06-01

We put forward the idea of using a Block Low-Rank (BLR) multifrontal direct solver to efficiently solve the linear systems of equations arising from a finite-difference discretization of the frequency-domain Maxwell equations for 3-D electromagnetic (EM) problems. The solver uses a low-rank representation for the off-diagonal blocks of the intermediate dense matrices arising in the multifrontal method to reduce the computational load. A numerical threshold, the so-called BLR threshold, controlling the accuracy of low-rank representations was optimized by balancing errors in the computed EM fields against savings in floating point operations (flops). Simulations were carried out over large-scale 3-D resistivity models representing typical scenarios for marine controlled-source EM surveys, and in particular the SEG SEAM model which contains an irregular salt body. The flop count, size of factor matrices and elapsed run time for matrix factorization are reduced dramatically by using BLR representations and can go down to, respectively, 10, 30 and 40 per cent of their full-rank values for our largest system with N = 20.6 million unknowns. The reductions are almost independent of the number of MPI tasks and threads at least up to 90 × 10 = 900 cores. The BLR savings increase for larger systems, which reduces the factorization flop complexity from O(N2) for the full-rank solver to O(Nm) with m = 1.4-1.6. The BLR savings are significantly larger for deep-water environments that exclude the highly resistive air layer from the computational domain. A study in a scenario where simulations are required at multiple source locations shows that the BLR solver can become competitive in comparison to iterative solvers as an engine for 3-D controlled-source electromagnetic Gauss-Newton inversion that requires forward modelling for a few thousand right-hand sides.

Formal Solutions for Polarized Radiative Transfer. I. The DELO Family

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

Janett, Gioele; Carlin, Edgar S.; Steiner, Oskar

The discussion regarding the numerical integration of the polarized radiative transfer equation is still open and the comparison between the different numerical schemes proposed by different authors in the past is not fully clear. Aiming at facilitating the comprehension of the advantages and drawbacks of the different formal solvers, this work presents a reference paradigm for their characterization based on the concepts of order of accuracy , stability , and computational cost . Special attention is paid to understand the numerical methods belonging to the Diagonal Element Lambda Operator family, in an attempt to highlight their specificities.

A Fast parallel tridiagonal algorithm for a class of CFD applications

NASA Technical Reports Server (NTRS)

Moitra, Stuti; Sun, Xian-He

1996-01-01

The parallel diagonal dominant (PDD) algorithm is an efficient tridiagonal solver. This paper presents for study a variation of the PDD algorithm, the reduced PDD algorithm. The new algorithm maintains the minimum communication provided by the PDD algorithm, but has a reduced operation count. The PDD algorithm also has a smaller operation count than the conventional sequential algorithm for many applications. Accuracy analysis is provided for the reduced PDD algorithm for symmetric Toeplitz tridiagonal (STT) systems. Implementation results on Langley's Intel Paragon and IBM SP2 show that both the PDD and reduced PDD algorithms are efficient and scalable.

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.

Application of NASA General-Purpose Solver to Large-Scale Computations in Aeroacoustics

NASA Technical Reports Server (NTRS)

Watson, Willie R.; Storaasli, Olaf O.

2004-01-01

Of several iterative and direct equation solvers evaluated previously for computations in aeroacoustics, the most promising was the NASA-developed General-Purpose Solver (winner of NASA's 1999 software of the year award). This paper presents detailed, single-processor statistics of the performance of this solver, which has been tailored and optimized for large-scale aeroacoustic computations. The statistics, compiled using an SGI ORIGIN 2000 computer with 12 Gb available memory (RAM) and eight available processors, are the central processing unit time, RAM requirements, and solution error. The equation solver is capable of solving 10 thousand complex unknowns in as little as 0.01 sec using 0.02 Gb RAM, and 8.4 million complex unknowns in slightly less than 3 hours using all 12 Gb. This latter solution is the largest aeroacoustics problem solved to date with this technique. The study was unable to detect any noticeable error in the solution, since noise levels predicted from these solution vectors are in excellent agreement with the noise levels computed from the exact solution. The equation solver provides a means for obtaining numerical solutions to aeroacoustics problems in three dimensions.

Hydrodynamics of suspensions of passive and active rigid particles: a rigid multiblob approach

DOE PAGES

Usabiaga, Florencio Balboa; Kallemov, Bakytzhan; Delmotte, Blaise; ...

2016-01-12

We develop a rigid multiblob method for numerically solving the mobility problem for suspensions of passive and active rigid particles of complex shape in Stokes flow in unconfined, partially confined, and fully confined geometries. As in a number of existing methods, we discretize rigid bodies using a collection of minimally resolved spherical blobs constrained to move as a rigid body, to arrive at a potentially large linear system of equations for the unknown Lagrange multipliers and rigid-body motions. Here we develop a block-diagonal preconditioner for this linear system and show that a standard Krylov solver converges in a modest numbermore » of iterations that is essentially independent of the number of particles. Key to the efficiency of the method is a technique for fast computation of the product of the blob-blob mobility matrix and a vector. For unbounded suspensions, we rely on existing analytical expressions for the Rotne-Prager-Yamakawa tensor combined with a fast multipole method (FMM) to obtain linear scaling in the number of particles. For suspensions sedimented against a single no-slip boundary, we use a direct summation on a graphical processing unit (GPU), which gives quadratic asymptotic scaling with the number of particles. For fully confined domains, such as periodic suspensions or suspensions confined in slit and square channels, we extend a recently developed rigid-body immersed boundary method by B. Kallemov, A. P. S. Bhalla, B. E. Griffith, and A. Donev (Commun. Appl. Math. Comput. Sci. 11 (2016), no. 1, 79-141) to suspensions of freely moving passive or active rigid particles at zero Reynolds number. We demonstrate that the iterative solver for the coupled fluid and rigid-body equations converges in a bounded number of iterations regardless of the system size. In our approach, each iteration only requires a few cycles of a geometric multigrid solver for the Poisson equation, and an application of the block-diagonal preconditioner, leading to linear scaling with the number of particles. We optimize a number of parameters in the iterative solvers and apply our method to a variety of benchmark problems to carefully assess the accuracy of the rigid multiblob approach as a function of the resolution. We also model the dynamics of colloidal particles studied in recent experiments, such as passive boomerangs in a slit channel, as well as a pair of non-Brownian active nanorods sedimented against a wall.« less

Condensates of p-wave pairs are exact solutions for rotating two-component Bose gases.

PubMed

Papenbrock, T; Reimann, S M; Kavoulakis, G M

2012-02-17

We derive exact analytical results for the wave functions and energies of harmonically trapped two-component Bose-Einstein condensates with weakly repulsive interactions under rotation. The isospin symmetric wave functions are universal and do not depend on the matrix elements of the two-body interaction. The comparison with the results from numerical diagonalization shows that the ground state and low-lying excitations consist of condensates of p-wave pairs for repulsive contact interactions, Coulomb interactions, and the repulsive interactions between aligned dipoles.

Challenges in design of Kitaev materials: Magnetic interactions from competing energy scales

NASA Astrophysics Data System (ADS)

Winter, Stephen M.; Li, Ying; Jeschke, Harald O.; Valentí, Roser

2016-06-01

In this study, we reanalyze the magnetic interactions in the Kitaev spin-liquid candidate materials Na2IrO3,α -RuCl3 , and α -Li2IrO3 using nonperturbative exact diagonalization methods. These methods are more appropriate given the relatively itinerant nature of the systems suggested in previous works. We treat all interactions up to third neighbors on equal footing. The computed terms reveal significant long-range coupling, bond anisotropy, and/or off-diagonal couplings which we argue naturally explain the observed ordered phases in these systems. Given these observations, the potential for realizing the spin-liquid state in real materials is analyzed, and synthetic challenges are defined and explained.

Vaidya spacetime in the diagonal coordinates

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

Berezin, V. A., E-mail: berezin@inr.ac.ru; Dokuchaev, V. I., E-mail: dokuchaev@inr.ac.ru; Eroshenko, Yu. N., E-mail: eroshenko@inr.ac.ru

We have analyzed the transformation from initial coordinates (v, r) of the Vaidya metric with light coordinate v to the most physical diagonal coordinates (t, r). An exact solution has been obtained for the corresponding metric tensor in the case of a linear dependence of the mass function of the Vaidya metric on light coordinate v. In the diagonal coordinates, a narrow region (with a width proportional to the mass growth rate of a black hole) has been detected near the visibility horizon of the Vaidya accreting black hole, in which the metric differs qualitatively from the Schwarzschild metric andmore » cannot be represented as a small perturbation. It has been shown that, in this case, a single set of diagonal coordinates (t, r) is insufficient to cover the entire range of initial coordinates (v, r) outside the visibility horizon; at least three sets of diagonal coordinates are required, the domains of which are separated by singular surfaces on which the metric components have singularities (either g{sub 00} = 0 or g{sub 00} = ∞). The energy–momentum tensor diverges on these surfaces; however, the tidal forces turn out to be finite, which follows from an analysis of the deviation equations for geodesics. Therefore, these singular surfaces are exclusively coordinate singularities that can be referred to as false fire-walls because there are no physical singularities on them. We have also considered the transformation from the initial coordinates to other diagonal coordinates (η, y), in which the solution is obtained in explicit form, and there is no energy–momentum tensor divergence.« less

Two Universality Classes for the Many-Body Localization Transition

NASA Astrophysics Data System (ADS)

Khemani, Vedika; Sheng, D. N.; Huse, David A.

2017-08-01

We provide a systematic comparison of the many-body localization (MBL) transition in spin chains with nonrandom quasiperiodic versus random fields. We find evidence suggesting that these belong to two separate universality classes: the first dominated by "intrinsic" intrasample randomness, and the second dominated by external intersample quenched randomness. We show that the effects of intersample quenched randomness are strongly growing, but not yet dominant, at the system sizes probed by exact-diagonalization studies on random models. Thus, the observed finite-size critical scaling collapses in such studies appear to be in a preasymptotic regime near the nonrandom universality class, but showing signs of the initial crossover towards the external-randomness-dominated universality class. Our results provide an explanation for why exact-diagonalization studies on random models see an apparent scaling near the transition while also obtaining finite-size scaling exponents that strongly violate Harris-Chayes bounds that apply to disorder-driven transitions. We also show that the MBL phase is more stable for the quasiperiodic model as compared to the random one, and the transition in the quasiperiodic model suffers less from certain finite-size effects.

Relaxation and thermalization in the one-dimensional Bose-Hubbard model: A case study for the interaction quantum quench from the atomic limit

NASA Astrophysics Data System (ADS)

Heidrich-Meisner, Fabian; Pollet, Lode; Sorg, Stefan; Vidmar, Lev

2015-03-01

We study the relaxation dynamics and thermalization in the one-dimensional Bose-Hubbard model induced by a global interaction quench. Specifically, we start from an initial state that has exactly one boson per site and is the ground state of a system with infinitely strong repulsive interactions at unit filling. The same interaction quench was realized in a recent experiment. Using exact diagonalization and the density-matrix renormalization-group method, we compute the time dependence of such observables as the multiple occupancy and the momentum distribution function. We discuss our numerical results in the framework of the eigenstate thermalization hypothesis and we observe that the microcanonical ensemble describes the time averages of many observables reasonably well for small and intermediate interaction strength. Moreover, the diagonal and the canonical ensembles are practically identical for our initial conditions already on the level of their respective energy distributions for small interaction strengths. Supported by the DFG through FOR 801 and the Alexander von Humboldt foundation.

Parallelized traveling cluster approximation to study numerically spin-fermion models on large lattices

NASA Astrophysics Data System (ADS)

Mukherjee, Anamitra; Patel, Niravkumar D.; Bishop, Chris; Dagotto, Elbio

2015-06-01

Lattice spin-fermion models are important to study correlated systems where quantum dynamics allows for a separation between slow and fast degrees of freedom. The fast degrees of freedom are treated quantum mechanically while the slow variables, generically referred to as the "spins," are treated classically. At present, exact diagonalization coupled with classical Monte Carlo (ED + MC) is extensively used to solve numerically a general class of lattice spin-fermion problems. In this common setup, the classical variables (spins) are treated via the standard MC method while the fermion problem is solved by exact diagonalization. The "traveling cluster approximation" (TCA) is a real space variant of the ED + MC method that allows to solve spin-fermion problems on lattice sizes with up to 103 sites. In this publication, we present a novel reorganization of the TCA algorithm in a manner that can be efficiently parallelized. This allows us to solve generic spin-fermion models easily on 104 lattice sites and with some effort on 105 lattice sites, representing the record lattice sizes studied for this family of models.

Spin-1/2 Heisenberg antiferromagnet on the pyrochlore lattice: An exact diagonalization study

NASA Astrophysics Data System (ADS)

Chandra, V. Ravi; Sahoo, Jyotisman

2018-04-01

We present exact diagonalization calculations for the spin-1/2 nearest-neighbor antiferromagnet on the pyrochlore lattice. We study a section of the lattice in the [111] direction and analyze the Hamiltonian of the breathing pyrochlore system with two coupling constants J1 and J2 for tetrahedra of different orientations and investigate the evolution of the system from the limit of disconnected tetrahedra (J2=0 ) to a correlated state at J1=J2 . We evaluate the low-energy spectrum, two and four spin correlations, and spin chirality correlations for a system size of up to 36 sites. The model shows a fast decay of spin correlations and we confirm the presence of several singlet excitations below the lowest magnetic excitation. We find chirality correlations near J1=J2 to be small at the length scales available at this system size. Evaluation of dimer-dimer correlations and analysis of the nature of the entanglement of the tetrahedral unit shows that the triplet sector of the tetrahedron contributes significantly to the ground-state entanglement at J1=J2 .

Application of Nearly Linear Solvers to Electric Power System Computation

NASA Astrophysics Data System (ADS)

Grant, Lisa L.

To meet the future needs of the electric power system, improvements need to be made in the areas of power system algorithms, simulation, and modeling, specifically to achieve a time frame that is useful to industry. If power system time-domain simulations could run in real-time, then system operators would have situational awareness to implement online control and avoid cascading failures, significantly improving power system reliability. Several power system applications rely on the solution of a very large linear system. As the demands on power systems continue to grow, there is a greater computational complexity involved in solving these large linear systems within reasonable time. This project expands on the current work in fast linear solvers, developed for solving symmetric and diagonally dominant linear systems, in order to produce power system specific methods that can be solved in nearly-linear run times. The work explores a new theoretical method that is based on ideas in graph theory and combinatorics. The technique builds a chain of progressively smaller approximate systems with preconditioners based on the system's low stretch spanning tree. The method is compared to traditional linear solvers and shown to reduce the time and iterations required for an accurate solution, especially as the system size increases. A simulation validation is performed, comparing the solution capabilities of the chain method to LU factorization, which is the standard linear solver for power flow. The chain method was successfully demonstrated to produce accurate solutions for power flow simulation on a number of IEEE test cases, and a discussion on how to further improve the method's speed and accuracy is included.

Fast, exact k-space sample density compensation for trajectories composed of rotationally symmetric segments, and the SNR-optimized image reconstruction from non-Cartesian samples.

PubMed

Mitsouras, Dimitris; Mulkern, Robert V; Rybicki, Frank J

2008-08-01

A recently developed method for exact density compensation of non uniformly arranged samples relies on the analytically known cross-correlations of Fourier basis functions corresponding to the traced k-space trajectory. This method produces a linear system whose solution represents compensated samples that normalize the contribution of each independent element of information that can be expressed by the underlying trajectory. Unfortunately, linear system-based density compensation approaches quickly become computationally demanding with increasing number of samples (i.e., image resolution). Here, it is shown that when a trajectory is composed of rotationally symmetric interleaves, such as spiral and PROPELLER trajectories, this cross-correlations method leads to a highly simplified system of equations. Specifically, it is shown that the system matrix is circulant block-Toeplitz so that the linear system is easily block-diagonalized. The method is described and demonstrated for 32-way interleaved spiral trajectories designed for 256 image matrices; samples are compensated non iteratively in a few seconds by solving the small independent block-diagonalized linear systems in parallel. Because the method is exact and considers all the interactions between all acquired samples, up to a 10% reduction in reconstruction error concurrently with an up to 30% increase in signal to noise ratio are achieved compared to standard density compensation methods. (c) 2008 Wiley-Liss, Inc.

A semi-implicit augmented IIM for Navier–Stokes equations with open, traction, or free boundary conditions

PubMed Central

Li, Zhilin; Xiao, Li; Cai, Qin; Zhao, Hongkai; Luo, Ray

2016-01-01

In this paper, a new Navier–Stokes solver based on a finite difference approximation is proposed to solve incompressible flows on irregular domains with open, traction, and free boundary conditions, which can be applied to simulations of fluid structure interaction, implicit solvent model for biomolecular applications and other free boundary or interface problems. For some problems of this type, the projection method and the augmented immersed interface method (IIM) do not work well or does not work at all. The proposed new Navier–Stokes solver is based on the local pressure boundary method, and a semi-implicit augmented IIM. A fast Poisson solver can be used in our algorithm which gives us the potential for developing fast overall solvers in the future. The time discretization is based on a second order multi-step method. Numerical tests with exact solutions are presented to validate the accuracy of the method. Application to fluid structure interaction between an incompressible fluid and a compressible gas bubble is also presented. PMID:27087702

A semi-implicit augmented IIM for Navier-Stokes equations with open, traction, or free boundary conditions.

PubMed

Li, Zhilin; Xiao, Li; Cai, Qin; Zhao, Hongkai; Luo, Ray

2015-08-15

In this paper, a new Navier-Stokes solver based on a finite difference approximation is proposed to solve incompressible flows on irregular domains with open, traction, and free boundary conditions, which can be applied to simulations of fluid structure interaction, implicit solvent model for biomolecular applications and other free boundary or interface problems. For some problems of this type, the projection method and the augmented immersed interface method (IIM) do not work well or does not work at all. The proposed new Navier-Stokes solver is based on the local pressure boundary method, and a semi-implicit augmented IIM. A fast Poisson solver can be used in our algorithm which gives us the potential for developing fast overall solvers in the future. The time discretization is based on a second order multi-step method. Numerical tests with exact solutions are presented to validate the accuracy of the method. Application to fluid structure interaction between an incompressible fluid and a compressible gas bubble is also presented.

Numerical solution of 3D Navier-Stokes equations with upwind implicit schemes

NASA Technical Reports Server (NTRS)

Marx, Yves P.

1990-01-01

An upwind MUSCL type implicit scheme for the three-dimensional Navier-Stokes equations is presented. Comparison between different approximate Riemann solvers (Roe and Osher) are performed and the influence of the reconstructions schemes on the accuracy of the solution as well as on the convergence of the method is studied. A new limiter is introduced in order to remove the problems usually associated with non-linear upwind schemes. The implementation of a diagonal upwind implicit operator for the three-dimensional Navier-Stokes equations is also discussed. Finally the turbulence modeling is assessed. Good prediction of separated flows are demonstrated if a non-equilibrium turbulence model is used.

Implicit solvers for unstructured meshes

NASA Technical Reports Server (NTRS)

Venkatakrishnan, V.; Mavriplis, Dimitri J.

1991-01-01

Implicit methods for unstructured mesh computations are developed and tested. The approximate system which arises from the Newton-linearization of the nonlinear evolution operator is solved by using the preconditioned generalized minimum residual technique. These different preconditioners are investigated: the incomplete LU factorization (ILU), block diagonal factorization, and the symmetric successive over-relaxation (SSOR). The preconditioners have been optimized to have good vectorization properties. The various methods are compared over a wide range of problems. Ordering of the unknowns, which affects the convergence of these sparse matrix iterative methods, is also investigated. Results are presented for inviscid and turbulent viscous calculations on single and multielement airfoil configurations using globally and adaptively generated meshes.

Gapless spin excitations in the S = 1 / 2 Kagome- and triangular-lattice Heisenberg antiferromagnets

NASA Astrophysics Data System (ADS)

Sakai, Tôru; Nakano, Hiroki

2018-05-01

The S = 1 / 2 kagome- and triangular-lattice Heisenberg antiferromagnets are investigated using the numerical exact diagonalization and the finite-size scaling analysis. The behaviour of the field derivative at zero magnetization is examined for both systems. The present result indicates that the spin excitation is gapless for each system.

Large-scale 3D geoelectromagnetic modeling using parallel adaptive high-order finite element method

DOE PAGES

Grayver, Alexander V.; Kolev, Tzanio V.

2015-11-01

Here, we have investigated the use of the adaptive high-order finite-element method (FEM) for geoelectromagnetic modeling. Because high-order FEM is challenging from the numerical and computational points of view, most published finite-element studies in geoelectromagnetics use the lowest order formulation. Solution of the resulting large system of linear equations poses the main practical challenge. We have developed a fully parallel and distributed robust and scalable linear solver based on the optimal block-diagonal and auxiliary space preconditioners. The solver was found to be efficient for high finite element orders, unstructured and nonconforming locally refined meshes, a wide range of frequencies, largemore » conductivity contrasts, and number of degrees of freedom (DoFs). Furthermore, the presented linear solver is in essence algebraic; i.e., it acts on the matrix-vector level and thus requires no information about the discretization, boundary conditions, or physical source used, making it readily efficient for a wide range of electromagnetic modeling problems. To get accurate solutions at reduced computational cost, we have also implemented goal-oriented adaptive mesh refinement. The numerical tests indicated that if highly accurate modeling results were required, the high-order FEM in combination with the goal-oriented local mesh refinement required less computational time and DoFs than the lowest order adaptive FEM.« less

Large-scale 3D geoelectromagnetic modeling using parallel adaptive high-order finite element method

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

Grayver, Alexander V.; Kolev, Tzanio V.

Here, we have investigated the use of the adaptive high-order finite-element method (FEM) for geoelectromagnetic modeling. Because high-order FEM is challenging from the numerical and computational points of view, most published finite-element studies in geoelectromagnetics use the lowest order formulation. Solution of the resulting large system of linear equations poses the main practical challenge. We have developed a fully parallel and distributed robust and scalable linear solver based on the optimal block-diagonal and auxiliary space preconditioners. The solver was found to be efficient for high finite element orders, unstructured and nonconforming locally refined meshes, a wide range of frequencies, largemore » conductivity contrasts, and number of degrees of freedom (DoFs). Furthermore, the presented linear solver is in essence algebraic; i.e., it acts on the matrix-vector level and thus requires no information about the discretization, boundary conditions, or physical source used, making it readily efficient for a wide range of electromagnetic modeling problems. To get accurate solutions at reduced computational cost, we have also implemented goal-oriented adaptive mesh refinement. The numerical tests indicated that if highly accurate modeling results were required, the high-order FEM in combination with the goal-oriented local mesh refinement required less computational time and DoFs than the lowest order adaptive FEM.« less

High-resolution numerical approximation of traffic flow problems with variable lanes and free-flow velocities.

PubMed

Zhang, Peng; Liu, Ru-Xun; Wong, S C

2005-05-01

This paper develops macroscopic traffic flow models for a highway section with variable lanes and free-flow velocities, that involve spatially varying flux functions. To address this complex physical property, we develop a Riemann solver that derives the exact flux values at the interface of the Riemann problem. Based on this solver, we formulate Godunov-type numerical schemes to solve the traffic flow models. Numerical examples that simulate the traffic flow around a bottleneck that arises from a drop in traffic capacity on the highway section are given to illustrate the efficiency of these schemes.

Transformation matrices between non-linear and linear differential equations

NASA Technical Reports Server (NTRS)

Sartain, R. L.

1983-01-01

In the linearization of systems of non-linear differential equations, those systems which can be exactly transformed into the second order linear differential equation Y"-AY'-BY=0 where Y, Y', and Y" are n x 1 vectors and A and B are constant n x n matrices of real numbers were considered. The 2n x 2n matrix was used to transform the above matrix equation into the first order matrix equation X' = MX. Specially the matrix M and the conditions which will diagonalize or triangularize M were studied. Transformation matrices P and P sub -1 were used to accomplish this diagonalization or triangularization to return to the solution of the second order matrix differential equation system from the first order system.

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.

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.

Deforming black hole and cosmological solutions by quasiperiodic and/or pattern forming structures in modified and Einstein gravity

NASA Astrophysics Data System (ADS)

Bubuianu, Laurenţiu; Vacaru, Sergiu I.

2018-05-01

We elaborate on the anholonomic frame deformation method, AFDM, for constructing exact solutions with quasiperiodic structure in modified gravity theories, MGTs, and general relativity, GR. Such solutions are described by generic off-diagonal metrics, nonlinear and linear connections and (effective) matter sources with coefficients depending on all spacetime coordinates via corresponding classes of generation and integration functions and (effective) matter sources. There are studied effective free energy functionals and nonlinear evolution equations for generating off-diagonal quasiperiodic deformations of black hole and/or homogeneous cosmological metrics. The physical data for such functionals are stated by different values of constants and prescribed symmetries for defining quasiperiodic structures at cosmological scales, or astrophysical objects in nontrivial gravitational backgrounds some similar forms as in condensed matter physics. It is shown how quasiperiodic structures determined by general nonlinear, or additive, functionals for generating functions and (effective) sources may transform black hole like configurations into cosmological metrics and inversely. We speculate on possible implications of quasiperiodic solutions in dark energy and dark matter physics. Finally, it is concluded that geometric methods for constructing exact solutions consist an important alternative tool to numerical relativity for investigating nonlinear effects in astrophysics and cosmology.

Generalized Gibbs state with modified Redfield solution: Exact agreement up to second order

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

Thingna, Juzar; Wang, Jian-Sheng; Haenggi, Peter

A novel scheme for the steady state solution of the standard Redfield quantum master equation is developed which yields agreement with the exact result for the corresponding reduced density matrix up to second order in the system-bath coupling strength. We achieve this objective by use of an analytic continuation of the off-diagonal matrix elements of the Redfield solution towards its diagonal limit. Notably, our scheme does not require the provision of yet higher order relaxation tensors. Testing this modified method for a heat bath consisting of a collection of harmonic oscillators we assess that the system relaxes towards its correctmore » coupling-dependent, generalized quantum Gibbs state in second order. We numerically compare our formulation for a damped quantum harmonic system with the nonequilibrium Green's function formalism: we find good agreement at low temperatures for coupling strengths that are even larger than expected from the very regime of validity of the second-order Redfield quantum master equation. Yet another advantage of our method is that it markedly reduces the numerical complexity of the problem; thus, allowing to study efficiently large-sized system Hilbert spaces.« less

Parallelized traveling cluster approximation to study numerically spin-fermion models on large lattices

DOE PAGES

Mukherjee, Anamitra; Patel, Niravkumar D.; Bishop, Chris; ...

2015-06-08

Lattice spin-fermion models are quite important to study correlated systems where quantum dynamics allows for a separation between slow and fast degrees of freedom. The fast degrees of freedom are treated quantum mechanically while the slow variables, generically referred to as the “spins,” are treated classically. At present, exact diagonalization coupled with classical Monte Carlo (ED + MC) is extensively used to solve numerically a general class of lattice spin-fermion problems. In this common setup, the classical variables (spins) are treated via the standard MC method while the fermion problem is solved by exact diagonalization. The “traveling cluster approximation” (TCA)more » is a real space variant of the ED + MC method that allows to solve spin-fermion problems on lattice sizes with up to 10 3 sites. In this paper, we present a novel reorganization of the TCA algorithm in a manner that can be efficiently parallelized. Finally, this allows us to solve generic spin-fermion models easily on 10 4 lattice sites and with some effort on 10 5 lattice sites, representing the record lattice sizes studied for this family of models.« less

Parallelized traveling cluster approximation to study numerically spin-fermion models on large lattices

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

Mukherjee, Anamitra; Patel, Niravkumar D.; Bishop, Chris

Lattice spin-fermion models are quite important to study correlated systems where quantum dynamics allows for a separation between slow and fast degrees of freedom. The fast degrees of freedom are treated quantum mechanically while the slow variables, generically referred to as the “spins,” are treated classically. At present, exact diagonalization coupled with classical Monte Carlo (ED + MC) is extensively used to solve numerically a general class of lattice spin-fermion problems. In this common setup, the classical variables (spins) are treated via the standard MC method while the fermion problem is solved by exact diagonalization. The “traveling cluster approximation” (TCA)more » is a real space variant of the ED + MC method that allows to solve spin-fermion problems on lattice sizes with up to 10 3 sites. In this paper, we present a novel reorganization of the TCA algorithm in a manner that can be efficiently parallelized. Finally, this allows us to solve generic spin-fermion models easily on 10 4 lattice sites and with some effort on 10 5 lattice sites, representing the record lattice sizes studied for this family of models.« less

Exact Fundamental Limits of the First and Second Hyperpolarizabilities

NASA Astrophysics Data System (ADS)

Lytel, Rick; Mossman, Sean; Crowell, Ethan; Kuzyk, Mark G.

2017-08-01

Nonlinear optical interactions of light with materials originate in the microscopic response of the molecular constituents to excitation by an optical field, and are expressed by the first (β ) and second (γ ) hyperpolarizabilities. Upper bounds to these quantities were derived seventeen years ago using approximate, truncated state models that violated completeness and unitarity, and far exceed those achieved by potential optimization of analytical systems. This Letter determines the fundamental limits of the first and second hyperpolarizability tensors using Monte Carlo sampling of energy spectra and transition moments constrained by the diagonal Thomas-Reiche-Kuhn (TRK) sum rules and filtered by the off-diagonal TRK sum rules. The upper bounds of β and γ are determined from these quantities by applying error-refined extrapolation to perfect compliance with the sum rules. The method yields the largest diagonal component of the hyperpolarizabilities for an arbitrary number of interacting electrons in any number of dimensions. The new method provides design insight to the synthetic chemist and nanophysicist for approaching the limits. This analysis also reveals that the special cases which lead to divergent nonlinearities in the many-state catastrophe are not physically realizable.

A 1D-2D Shallow Water Equations solver for discontinuous porosity field based on a Generalized Riemann Problem

NASA Astrophysics Data System (ADS)

Ferrari, Alessia; Vacondio, Renato; Dazzi, Susanna; Mignosa, Paolo

2017-09-01

A novel augmented Riemann Solver capable of handling porosity discontinuities in 1D and 2D Shallow Water Equation (SWE) models is presented. With the aim of accurately approximating the porosity source term, a Generalized Riemann Problem is derived by adding an additional fictitious equation to the SWEs system and imposing mass and momentum conservation across the porosity discontinuity. The modified Shallow Water Equations are theoretically investigated, and the implementation of an augmented Roe Solver in a 1D Godunov-type finite volume scheme is presented. Robust treatment of transonic flows is ensured by introducing an entropy fix based on the wave pattern of the Generalized Riemann Problem. An Exact Riemann Solver is also derived in order to validate the numerical model. As an extension of the 1D scheme, an analogous 2D numerical model is also derived and validated through test cases with radial symmetry. The capability of the 1D and 2D numerical models to capture different wave patterns is assessed against several Riemann Problems with different wave patterns.

Fingering patterns in magnetic fluids: Perturbative solutions and the stability of exact stationary shapes

NASA Astrophysics Data System (ADS)

Anjos, Pedro H. A.; Lira, Sérgio A.; Miranda, José A.

2018-04-01

We examine the formation of interfacial patterns when a magnetic liquid droplet (ferrofluid, or a magnetorheological fluid), surrounded by a nonmagnetic fluid, is subjected to a radial magnetic field in a Hele-Shaw cell. By using a vortex-sheet formalism, we find exact stationary solutions for the fluid-fluid interface in the form of n -fold polygonal shapes. A weakly nonlinear, mode-coupling method is then utilized to find time-evolving perturbative solutions for the interfacial patterns. The stability of such nonzero surface tension exact solutions is checked and discussed, by trying to systematically approach the exact stationary shapes through perturbative solutions containing an increasingly larger number of participating Fourier modes. Our results indicate that the exact stationary solutions of the problem are stable, and that a good matching between exact and perturbative shape solutions is achieved just by using a few Fourier modes. The stability of such solutions is substantiated by a linearization process close to the stationary shape, where a system of mode-coupling equations is diagonalized, determining the eigenvalues which dictate the stability of a fixed point.

A matrix-form GSM-CFD solver for incompressible fluids and its application to hemodynamics

NASA Astrophysics Data System (ADS)

Yao, Jianyao; Liu, G. R.

2014-10-01

A GSM-CFD solver for incompressible flows is developed based on the gradient smoothing method (GSM). A matrix-form algorithm and corresponding data structure for GSM are devised to efficiently approximate the spatial gradients of field variables using the gradient smoothing operation. The calculated gradient values on various test fields show that the proposed GSM is capable of exactly reproducing linear field and of second order accuracy on all kinds of meshes. It is found that the GSM is much more robust to mesh deformation and therefore more suitable for problems with complicated geometries. Integrated with the artificial compressibility approach, the GSM is extended to solve the incompressible flows. As an example, the flow simulation of carotid bifurcation is carried out to show the effectiveness of the proposed GSM-CFD solver. The blood is modeled as incompressible Newtonian fluid and the vessel is treated as rigid wall in this paper.

A Block Preconditioned Conjugate Gradient-type Iterative Solver for Linear Systems in Thermal Reservoir Simulation

NASA Astrophysics Data System (ADS)

Betté, Srinivas; Diaz, Julio C.; Jines, William R.; Steihaug, Trond

1986-11-01

A preconditioned residual-norm-reducing iterative solver is described. Based on a truncated form of the generalized-conjugate-gradient method for nonsymmetric systems of linear equations, the iterative scheme is very effective for linear systems generated in reservoir simulation of thermal oil recovery processes. As a consequence of employing an adaptive implicit finite-difference scheme to solve the model equations, the number of variables per cell-block varies dynamically over the grid. The data structure allows for 5- and 9-point operators in the areal model, 5-point in the cross-sectional model, and 7- and 11-point operators in the three-dimensional model. Block-diagonal-scaling of the linear system, done prior to iteration, is found to have a significant effect on the rate of convergence. Block-incomplete-LU-decomposition (BILU) and block-symmetric-Gauss-Seidel (BSGS) methods, which result in no fill-in, are used as preconditioning procedures. A full factorization is done on the well terms, and the cells are ordered in a manner which minimizes the fill-in in the well-column due to this factorization. The convergence criterion for the linear (inner) iteration is linked to that of the nonlinear (Newton) iteration, thereby enhancing the efficiency of the computation. The algorithm, with both BILU and BSGS preconditioners, is evaluated in the context of a variety of thermal simulation problems. The solver is robust and can be used with little or no user intervention.

Inelastic Transitions in Slow Collisions of Anti-Hydrogen with Hydrogen Atoms

NASA Astrophysics Data System (ADS)

Harrison, Robert; Krstic, Predrag

2007-06-01

We calculate excited adiabatic states and nonadiabatic coupling matrix elements of a quasimolecular system containing hydrogen and anti-hydrogen atoms, for a range of internuclear distances from 0.2 to 20 Bohrs. High accuracy is achieved by exact diagonalization of the molecular Hamiltionian in a large Gaussian basis. Nonadiabatic dynamics was calculated by solving MOCC equations. Positronium states are included in the consideration.

A Note on Parameters of Random Substitutions by γ-Diagonal Matrices

NASA Astrophysics Data System (ADS)

Kang, Ju-Sung

Random substitutions are very useful and practical method for privacy-preserving schemes. In this paper we obtain the exact relationship between the estimation errors and three parameters used in the random substitutions, namely the privacy assurance metric γ, the total number n of data records, and the size N of transition matrix. We also demonstrate some simulations concerning the theoretical result.

Detailed analysis of the effects of stencil spatial variations with arbitrary high-order finite-difference Maxwell solver

DOE PAGES

Vincenti, H.; Vay, J. -L.

2015-11-22

Due to discretization effects and truncation to finite domains, many electromagnetic simulations present non-physical modifications of Maxwell's equations in space that may generate spurious signals affecting the overall accuracy of the result. Such modifications for instance occur when Perfectly Matched Layers (PMLs) are used at simulation domain boundaries to simulate open media. Another example is the use of arbitrary order Maxwell solver with domain decomposition technique that may under some condition involve stencil truncations at subdomain boundaries, resulting in small spurious errors that do eventually build up. In each case, a careful evaluation of the characteristics and magnitude of themore » errors resulting from these approximations, and their impact at any frequency and angle, requires detailed analytical and numerical studies. To this end, we present a general analytical approach that enables the evaluation of numerical discretization errors of fully three-dimensional arbitrary order finite-difference Maxwell solver, with arbitrary modification of the local stencil in the simulation domain. The analytical model is validated against simulations of domain decomposition technique and PMLs, when these are used with very high-order Maxwell solver, as well as in the infinite order limit of pseudo-spectral solvers. Results confirm that the new analytical approach enables exact predictions in each case. It also confirms that the domain decomposition technique can be used with very high-order Maxwell solver and a reasonably low number of guard cells with negligible effects on the whole accuracy of the simulation.« less

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.

Hidden symmetries for ellipsoid-solitonic deformations of Kerr-Sen black holes and quantum anomalies

NASA Astrophysics Data System (ADS)

Vacaru, Sergiu I.

2013-02-01

We prove the existence of hidden symmetries in the general relativity theory defined by exact solutions with generic off-diagonal metrics, nonholonomic (non-integrable) constraints, and deformations of the frame and linear connection structure. A special role in characterization of such spacetimes is played by the corresponding nonholonomic generalizations of Stackel-Killing and Killing-Yano tensors. There are constructed new classes of black hole solutions and we study hidden symmetries for ellipsoidal and/or solitonic deformations of "prime" Kerr-Sen black holes into "target" off-diagonal metrics. In general, the classical conserved quantities (integrable and not-integrable) do not transfer to the quantized systems and produce quantum gravitational anomalies. We prove that such anomalies can be eliminated via corresponding nonholonomic deformations of fundamental geometric objects (connections and corresponding Riemannian and Ricci tensors) and by frame transforms.

Theoretical study of the dependence of single impurity Anderson model on various parameters within distributional exact diagonalization method

NASA Astrophysics Data System (ADS)

Syaina, L. P.; Majidi, M. A.

2018-04-01

Single impurity Anderson model describes a system consisting of non-interacting conduction electrons coupled with a localized orbital having strongly interacting electrons at a particular site. This model has been proven successful to explain the phenomenon of metal-insulator transition through Anderson localization. Despite the well-understood behaviors of the model, little has been explored theoretically on how the model properties gradually evolve as functions of hybridization parameter, interaction energy, impurity concentration, and temperature. Here, we propose to do a theoretical study on those aspects of a single impurity Anderson model using the distributional exact diagonalization method. We solve the model Hamiltonian by randomly generating sampling distribution of some conducting electron energy levels with various number of occupying electrons. The resulting eigenvalues and eigenstates are then used to define the local single-particle Green function for each sampled electron energy distribution using Lehmann representation. Later, we extract the corresponding self-energy of each distribution, then average over all the distributions and construct the local Green function of the system to calculate the density of states. We repeat this procedure for various values of those controllable parameters, and discuss our results in connection with the criteria of the occurrence of metal-insulator transition in this system.

A simplified analysis of the multigrid V-cycle as a fast elliptic solver

NASA Technical Reports Server (NTRS)

Decker, Naomi H.; Taasan, Shlomo

1988-01-01

For special model problems, Fourier analysis gives exact convergence rates for the two-grid multigrid cycle and, for more general problems, provides estimates of the two-grid convergence rates via local mode analysis. A method is presented for obtaining mutigrid convergence rate estimates for cycles involving more than two grids (using essentially the same analysis as for the two-grid cycle). For the simple cast of the V-cycle used as a fast Laplace solver on the unit square, the k-grid convergence rate bounds obtained by this method are sharper than the bounds predicted by the variational theory. Both theoretical justification and experimental evidence are presented.

A dynamic-solver-consistent minimum action method: With an application to 2D Navier-Stokes equations

NASA Astrophysics Data System (ADS)

Wan, Xiaoliang; Yu, Haijun

2017-02-01

This paper discusses the necessity and strategy to unify the development of a dynamic solver and a minimum action method (MAM) for a spatially extended system when employing the large deviation principle (LDP) to study the effects of small random perturbations. A dynamic solver is used to approximate the unperturbed system, and a minimum action method is used to approximate the LDP, which corresponds to solving an Euler-Lagrange equation related to but more complicated than the unperturbed system. We will clarify possible inconsistencies induced by independent numerical approximations of the unperturbed system and the LDP, based on which we propose to define both the dynamic solver and the MAM on the same approximation space for spatial discretization. The semi-discrete LDP can then be regarded as the exact LDP of the semi-discrete unperturbed system, which is a finite-dimensional ODE system. We achieve this methodology for the two-dimensional Navier-Stokes equations using a divergence-free approximation space. The method developed can be used to study the nonlinear instability of wall-bounded parallel shear flows, and be generalized straightforwardly to three-dimensional cases. Numerical experiments are presented.

Excitonic magnet in external field: Complex order parameter and spin currents

NASA Astrophysics Data System (ADS)

Geffroy, D.; Hariki, A.; Kuneš, J.

2018-04-01

We investigate spin-triplet exciton condensation in the two-orbital Hubbard model close to half-filling by means of dynamical mean-field theory. Employing an impurity solver that handles complex off-diagonal hybridization functions, we study the behavior of excitonic condensate in stoichiometric and doped systems subject to external magnetic field. We find a general tendency of the triplet order parameter to lie perpendicular with the applied field and identify exceptions from this rule. For solutions exhibiting k -odd spin textures, we discuss the Bloch theorem, which, in the absence of spin-orbit coupling, forbids the appearance of spontaneous net spin current. We demonstrate that the Bloch theorem is not obeyed by the dynamical mean-field theory.

Dip and anisotropy effects on flow using a vertically skewed model grid.

PubMed

Hoaglund, John R; Pollard, David

2003-01-01

Darcy flow equations relating vertical and bedding-parallel flow to vertical and bedding-parallel gradient components are derived for a skewed Cartesian grid in a vertical plane, correcting for structural dip given the principal hydraulic conductivities in bedding-parallel and bedding-orthogonal directions. Incorrect-minus-correct flow error results are presented for ranges of structural dip (0 < or = theta < or = 90) and gradient directions (0 < or = phi < or = 360). The equations can be coded into ground water models (e.g., MODFLOW) that can use a skewed Cartesian coordinate system to simulate flow in structural terrain with deformed bedding planes. Models modified with these equations will require input arrays of strike and dip, and a solver that can handle off-diagonal hydraulic conductivity terms.

Implicit solvers for unstructured meshes

NASA Technical Reports Server (NTRS)

Venkatakrishnan, V.; Mavriplis, Dimitri J.

1991-01-01

Implicit methods were developed and tested for unstructured mesh computations. The approximate system which arises from the Newton linearization of the nonlinear evolution operator is solved by using the preconditioned GMRES (Generalized Minimum Residual) technique. Three different preconditioners were studied, namely, the incomplete LU factorization (ILU), block diagonal factorization, and the symmetric successive over relaxation (SSOR). The preconditioners were optimized to have good vectorization properties. SSOR and ILU were also studied as iterative schemes. The various methods are compared over a wide range of problems. Ordering of the unknowns, which affects the convergence of these sparse matrix iterative methods, is also studied. Results are presented for inviscid and turbulent viscous calculations on single and multielement airfoil configurations using globally and adaptively generated meshes.

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

Vincenti, H.; Vay, J. -L.

Due to discretization effects and truncation to finite domains, many electromagnetic simulations present non-physical modifications of Maxwell's equations in space that may generate spurious signals affecting the overall accuracy of the result. Such modifications for instance occur when Perfectly Matched Layers (PMLs) are used at simulation domain boundaries to simulate open media. Another example is the use of arbitrary order Maxwell solver with domain decomposition technique that may under some condition involve stencil truncations at subdomain boundaries, resulting in small spurious errors that do eventually build up. In each case, a careful evaluation of the characteristics and magnitude of themore » errors resulting from these approximations, and their impact at any frequency and angle, requires detailed analytical and numerical studies. To this end, we present a general analytical approach that enables the evaluation of numerical discretization errors of fully three-dimensional arbitrary order finite-difference Maxwell solver, with arbitrary modification of the local stencil in the simulation domain. The analytical model is validated against simulations of domain decomposition technique and PMLs, when these are used with very high-order Maxwell solver, as well as in the infinite order limit of pseudo-spectral solvers. Results confirm that the new analytical approach enables exact predictions in each case. It also confirms that the domain decomposition technique can be used with very high-order Maxwell solver and a reasonably low number of guard cells with negligible effects on the whole accuracy of the simulation.« less

Ground State and Finite Temperature Lanczos Methods

NASA Astrophysics Data System (ADS)

Prelovšek, P.; Bonča, J.

The present review will focus on recent development of exact- diagonalization (ED) methods that use Lanczos algorithm to transform large sparse matrices onto the tridiagonal form. We begin with a review of basic principles of the Lanczos method for computing ground-state static as well as dynamical properties. Next, generalization to finite-temperatures in the form of well established finite-temperature Lanczos method is described. The latter allows for the evaluation of temperatures T>0 static and dynamic quantities within various correlated models. Several extensions and modification of the latter method introduced more recently are analysed. In particular, the low-temperature Lanczos method and the microcanonical Lanczos method, especially applicable within the high-T regime. In order to overcome the problems of exponentially growing Hilbert spaces that prevent ED calculations on larger lattices, different approaches based on Lanczos diagonalization within the reduced basis have been developed. In this context, recently developed method based on ED within a limited functional space is reviewed. Finally, we briefly discuss the real-time evolution of correlated systems far from equilibrium, which can be simulated using the ED and Lanczos-based methods, as well as approaches based on the diagonalization in a reduced basis.

Can nonstandard interactions jeopardize the hierarchy sensitivity of DUNE?

NASA Astrophysics Data System (ADS)

Deepthi, K. N.; Goswami, Srubabati; Nath, Newton

2017-10-01

We study the effect of nonstandard interactions (NSIs) on the propagation of neutrinos through the Earth's matter and how it affects the hierarchy sensitivity of the DUNE experiment. We emphasize the special case when the diagonal NSI parameter ɛe e=-1 , nullifying the standard matter effect. We show that if, in addition, C P violation is maximal then this gives rise to an exact intrinsic hierarchy degeneracy in the appearance channel, irrespective of the baseline and energy. Introduction of the off diagonal NSI parameter, ɛe τ, shifts the position of this degeneracy to a different ɛe e. Moreover the unknown magnitude and phases of the off diagonal NSI parameters can give rise to additional degeneracies. Overall, given the current model independent limits on NSI parameters, the hierarchy sensitivity of DUNE can get seriously impacted. However, a more precise knowledge of the NSI parameters, especially ɛe e, can give rise to an improved sensitivity. Alternatively, if a NSI exists in nature, and still DUNE shows hierarchy sensitivity, certain ranges of the NSI parameters can be excluded. Additionally, we briefly discuss the implications of ɛe e=-1 (in the Earth) on the Mikheyev-Smirnov-Wolfenstein effect in the Sun.

A Riemann solver for RANS

NASA Astrophysics Data System (ADS)

Chuvakhov, P. V.

2014-01-01

An exact expression for a system of both eigenvalues and right/left eigenvectors of a Jacobian matrix for a convective two-equation differential closure RANS operator split along a curvilinear coordinate is derived. It is shown by examples of numerical modeling of supersonic flows over a flat plate and a compression corner with separation that application of the exact system of eigenvalues and eigenvectors to the Roe approach for approximate solution of the Riemann problem gives rise to an increase in the convergence rate, better stability and higher accuracy of a steady-state solution in comparison with those in the case of an approximate system.

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.

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.

An analysis of supersonic flows with low-Reynolds number compressible two-equation turbulence models using LU finite volume implicit numerical techniques

NASA Technical Reports Server (NTRS)

Lee, J.

1994-01-01

A generalized flow solver using an implicit Lower-upper (LU) diagonal decomposition based numerical technique has been coupled with three low-Reynolds number kappa-epsilon models for analysis of problems with engineering applications. The feasibility of using the LU technique to obtain efficient solutions to supersonic problems using the kappa-epsilon model has been demonstrated. The flow solver is then used to explore limitations and convergence characteristics of several popular two equation turbulence models. Several changes to the LU solver have been made to improve the efficiency of turbulent flow predictions. In general, the low-Reynolds number kappa-epsilon models are easier to implement than the models with wall-functions, but require much finer near-wall grid to accurately resolve the physics. The three kappa-epsilon models use different approaches to characterize the near wall regions of the flow. Therefore, the limitations imposed by the near wall characteristics have been carefully resolved. The convergence characteristics of a particular model using a given numerical technique are also an important, but most often overlooked, aspect of turbulence model predictions. It is found that some convergence characteristics could be sacrificed for more accurate near-wall prediction. However, even this gain in accuracy is not sufficient to model the effects of an external pressure gradient imposed by a shock-wave/ boundary-layer interaction. Additional work on turbulence models, especially for compressibility, is required since the solutions obtained with base line turbulence are in only reasonable agreement with the experimental data for the viscous interaction problems.

Experiments in Quantum Coherence and Computation With Single Cooper-Pair Electronics

DTIC Science & Technology

2006-01-22

through the cavity. In the absence of damping, exact diagonalization of the Jaynes - Cumming Hamiltonian yields the excited eigenstates (dressed states...neglecting rapidly oscillating terms and omitting damping for the moment, Eq. (16) reduces to the Jaynes - Cummings Hamiltonian (1) with V=EJ /" and cou...is therefore little entanglement between the field and qubit in this situation and the rotation fidelity is high. To model the effect of the drive on

Graduate Student Support for Quantum Computing With Superconducting Charge States

DTIC Science & Technology

2005-08-31

cavity resonance frequency ωr, the atomic transition frequency Ω, and the strength of the atom- photon coupling g appearing in the Jaynes - Cummings ...the atom through the cavity. In the absence of damping, exact diagonalization of the Jaynes - Cumming Hamiltonian yields the excited eigen- states...cillating terms and omitting damping for the moment, 5 Eq. (16) reduces to the Jaynes - Cummings Hamiltonian (1) with Ω = EJ/~ and the vacuum Rabi frequency

Algebraic multigrid preconditioning within parallel finite-element solvers for 3-D electromagnetic modelling problems in geophysics

NASA Astrophysics Data System (ADS)

Koldan, Jelena; Puzyrev, Vladimir; de la Puente, Josep; Houzeaux, Guillaume; Cela, José María

2014-06-01

We present an elaborate preconditioning scheme for Krylov subspace methods which has been developed to improve the performance and reduce the execution time of parallel node-based finite-element (FE) solvers for 3-D electromagnetic (EM) numerical modelling in exploration geophysics. This new preconditioner is based on algebraic multigrid (AMG) that uses different basic relaxation methods, such as Jacobi, symmetric successive over-relaxation (SSOR) and Gauss-Seidel, as smoothers and the wave front algorithm to create groups, which are used for a coarse-level generation. We have implemented and tested this new preconditioner within our parallel nodal FE solver for 3-D forward problems in EM induction geophysics. We have performed series of experiments for several models with different conductivity structures and characteristics to test the performance of our AMG preconditioning technique when combined with biconjugate gradient stabilized method. The results have shown that, the more challenging the problem is in terms of conductivity contrasts, ratio between the sizes of grid elements and/or frequency, the more benefit is obtained by using this preconditioner. Compared to other preconditioning schemes, such as diagonal, SSOR and truncated approximate inverse, the AMG preconditioner greatly improves the convergence of the iterative solver for all tested models. Also, when it comes to cases in which other preconditioners succeed to converge to a desired precision, AMG is able to considerably reduce the total execution time of the forward-problem code-up to an order of magnitude. Furthermore, the tests have confirmed that our AMG scheme ensures grid-independent rate of convergence, as well as improvement in convergence regardless of how big local mesh refinements are. In addition, AMG is designed to be a black-box preconditioner, which makes it easy to use and combine with different iterative methods. Finally, it has proved to be very practical and efficient in the parallel context.

Reducing Memory Cost of Exact Diagonalization using Singular Value Decomposition

NASA Astrophysics Data System (ADS)

Weinstein, Marvin; Chandra, Ravi; Auerbach, Assa

2012-02-01

We present a modified Lanczos algorithm to diagonalize lattice Hamiltonians with dramatically reduced memory requirements. In contrast to variational approaches and most implementations of DMRG, Lanczos rotations towards the ground state do not involve incremental minimizations, (e.g. sweeping procedures) which may get stuck in false local minima. The lattice of size N is partitioned into two subclusters. At each iteration the rotating Lanczos vector is compressed into two sets of nsvd small subcluster vectors using singular value decomposition. For low entanglement entropy See, (satisfied by short range Hamiltonians), the truncation error is bounded by (-nsvd^1/See). Convergence is tested for the Heisenberg model on Kagom'e clusters of 24, 30 and 36 sites, with no lattice symmetries exploited, using less than 15GB of dynamical memory. Generalization of the Lanczos-SVD algorithm to multiple partitioning is discussed, and comparisons to other techniques are given. Reference: arXiv:1105.0007

Time-dependent generalized Gibbs ensembles in open quantum systems

NASA Astrophysics Data System (ADS)

Lange, Florian; Lenarčič, Zala; Rosch, Achim

2018-04-01

Generalized Gibbs ensembles have been used as powerful tools to describe the steady state of integrable many-particle quantum systems after a sudden change of the Hamiltonian. Here, we demonstrate numerically that they can be used for a much broader class of problems. We consider integrable systems in the presence of weak perturbations which break both integrability and drive the system to a state far from equilibrium. Under these conditions, we show that the steady state and the time evolution on long timescales can be accurately described by a (truncated) generalized Gibbs ensemble with time-dependent Lagrange parameters, determined from simple rate equations. We compare the numerically exact time evolutions of density matrices for small systems with a theory based on block-diagonal density matrices (diagonal ensemble) and a time-dependent generalized Gibbs ensemble containing only a small number of approximately conserved quantities, using the one-dimensional Heisenberg model with perturbations described by Lindblad operators as an example.

The relation between the quantum discord and quantum teleportation: The physical interpretation of the transition point between different quantum discord decay regimes

NASA Astrophysics Data System (ADS)

Roszak, K.; Cywiński, Ł.

2015-10-01

We study quantum teleportation via Bell-diagonal mixed states of two qubits in the context of the intrinsic properties of the quantum discord. We show that when the quantum-correlated state of the two qubits is used for quantum teleportation, the character of the teleportation efficiency changes substantially depending on the Bell-diagonal-state parameters, which can be seen when the worst-case-scenario or best-case-scenario fidelity is studied. Depending on the parameter range, one of two types of single-qubit states is hardest/easiest to teleport. The transition between these two parameter ranges coincides exactly with the transition between the range of classical correlation decay and quantum correlation decay characteristic for the evolution of the quantum discord. The correspondence provides a physical interpretation for the prominent feature of the decay of the quantum discord.

BeamDyn: A High-Fidelity Wind Turbine Blade Solver in the FAST Modular Framework: Preprint

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

Wang, Q.; Sprague, M.; Jonkman, J.

2015-01-01

BeamDyn, a Legendre-spectral-finite-element implementation of geometrically exact beam theory (GEBT), was developed to meet the design challenges associated with highly flexible composite wind turbine blades. In this paper, the governing equations of GEBT are reformulated into a nonlinear state-space form to support its coupling within the modular framework of the FAST wind turbine computer-aided engineering (CAE) tool. Different time integration schemes (implicit and explicit) were implemented and examined for wind turbine analysis. Numerical examples are presented to demonstrate the capability of this new beam solver. An example analysis of a realistic wind turbine blade, the CX-100, is also presented asmore » validation.« less

Well-conditioned fractional collocation methods using fractional Birkhoff interpolation basis

NASA Astrophysics Data System (ADS)

Jiao, Yujian; Wang, Li-Lian; Huang, Can

2016-01-01

The purpose of this paper is twofold. Firstly, we provide explicit and compact formulas for computing both Caputo and (modified) Riemann-Liouville (RL) fractional pseudospectral differentiation matrices (F-PSDMs) of any order at general Jacobi-Gauss-Lobatto (JGL) points. We show that in the Caputo case, it suffices to compute F-PSDM of order μ ∈ (0 , 1) to compute that of any order k + μ with integer k ≥ 0, while in the modified RL case, it is only necessary to evaluate a fractional integral matrix of order μ ∈ (0 , 1). Secondly, we introduce suitable fractional JGL Birkhoff interpolation problems leading to new interpolation polynomial basis functions with remarkable properties: (i) the matrix generated from the new basis yields the exact inverse of F-PSDM at "interior" JGL points; (ii) the matrix of the highest fractional derivative in a collocation scheme under the new basis is diagonal; and (iii) the resulted linear system is well-conditioned in the Caputo case, while in the modified RL case, the eigenvalues of the coefficient matrix are highly concentrated. In both cases, the linear systems of the collocation schemes using the new basis can be solved by an iterative solver within a few iterations. Notably, the inverse can be computed in a very stable manner, so this offers optimal preconditioners for usual fractional collocation methods for fractional differential equations (FDEs). It is also noteworthy that the choice of certain special JGL points with parameters related to the order of the equations can ease the implementation. We highlight that the use of the Bateman's fractional integral formulas and fast transforms between Jacobi polynomials with different parameters, is essential for our algorithm development.

Investigation of the spectral properties and magnetism of BiFeO3 by dynamical mean-field theory

NASA Astrophysics Data System (ADS)

Paul, Souvik; Iuşan, Diana; Thunström, Patrik; Kvashnin, Yaroslav O.; Hellsvik, Johan; Pereiro, Manuel; Delin, Anna; Knut, Ronny; Phuyal, Dibya; Lindblad, Andreas; Karis, Olof; Sanyal, Biplab; Eriksson, Olle

2018-03-01

Using the local density approximation plus dynamical mean-field theory (LDA+DMFT), we have computed the valence-band photoelectron spectra and magnetic excitation spectra of BiFeO3, one of the most studied multiferroics. Within the DMFT approach, the local impurity problem is tackled by the exact diagonalization solver. The solution of the impurity problem within the LDA+DMFT method for the paramagnetic and magnetically ordered phases produces result in agreement with the experimental data on electronic and magnetic structures. For comparison, we also present results obtained by the LDA +U approach which is commonly used to compute the physical properties of this compound. Our LDA+DMFT derived electronic spectra match adequately with the experimental hard x-ray photoelectron spectroscopy and resonant photoelectron spectroscopy for Fe 3 d states, whereas the LDA +U method fails to capture the general features of the measured spectra. This indicates the importance of accurately incorporating the dynamical aspect of electronic correlation among Fe 3 d orbitals to reproduce the experimental excitation spectra. Specifically, the LDA+DMFT derived density of states exhibits a significant amount of Fe 3 d states at the position of Bi lone pairs, implying that the latter are not alone in the spectral scenario. This fact might modify our interpretation about the origin of ferroelectric polarization in this material. Our study demonstrates that the combination of orbital cross sections for the constituent elements and broadening schemes for the spectral functions are crucial to explain the detailed structures of the experimental electronic spectra. Our magnetic excitation spectra computed from the LDA+DMFT result conform well with the inelastic neutron scattering data.

Use of direct and iterative solvers for estimation of SNP effects in genome-wide selection

PubMed Central

2010-01-01

The aim of this study was to compare iterative and direct solvers for estimation of marker effects in genomic selection. One iterative and two direct methods were used: Gauss-Seidel with Residual Update, Cholesky Decomposition and Gentleman-Givens rotations. For resembling different scenarios with respect to number of markers and of genotyped animals, a simulated data set divided into 25 subsets was used. Number of markers ranged from 1,200 to 5,925 and number of animals ranged from 1,200 to 5,865. Methods were also applied to real data comprising 3081 individuals genotyped for 45181 SNPs. Results from simulated data showed that the iterative solver was substantially faster than direct methods for larger numbers of markers. Use of a direct solver may allow for computing (co)variances of SNP effects. When applied to real data, performance of the iterative method varied substantially, depending on the level of ill-conditioning of the coefficient matrix. From results with real data, Gentleman-Givens rotations would be the method of choice in this particular application as it provided an exact solution within a fairly reasonable time frame (less than two hours). It would indeed be the preferred method whenever computer resources allow its use. PMID:21637627

Fluid-structure coupling for wind turbine blade analysis using OpenFOAM

NASA Astrophysics Data System (ADS)

Dose, Bastian; Herraez, Ivan; Peinke, Joachim

2015-11-01

Modern wind turbine rotor blades are designed increasingly large and flexible. This structural flexibility represents a problem for the field of Computational Fluid Dynamics (CFD), which is used for accurate load calculations and detailed investigations of rotor aerodynamics. As the blade geometries within CFD simulations are considered stiff, the effect of blade deformation caused by aerodynamic loads cannot be captured by the common CFD approach. Coupling the flow solver with a structural solver can overcome this restriction and enables the investigation of flexible wind turbine blades. For this purpose, a new Finite Element (FE) solver was implemented into the open source CFD code OpenFOAM. Using a beam element formulation based on the Geometrically Exact Beam Theory (GEBT), the structural model can capture geometric non-linearities such as large deformations. Coupled with CFD solvers of the OpenFOAM package, the new framework represents a powerful tool for aerodynamic investigations. In this work, we investigated the aerodynamic performance of a state of the art wind turbine. For different wind speeds, aerodynamic key parameters are evaluated and compared for both, rigid and flexible blade geometries. The present work is funded within the framework of the joint project Smart Blades (0325601D) by the German Federal Ministry for Economic Affairs and Energy (BMWi) under decision of the German Federal Parliament.

Wave function continuity and the diagonal Born-Oppenheimer correction at conical intersections

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

Meek, Garrett A.; Levine, Benjamin G., E-mail: levine@chemistry.msu.edu

2016-05-14

We demonstrate that though exact in principle, the expansion of the total molecular wave function as a sum over adiabatic Born-Oppenheimer (BO) vibronic states makes inclusion of the second-derivative nonadiabatic energy term near conical intersections practically problematic. In order to construct a well-behaved molecular wave function that has density at a conical intersection, the individual BO vibronic states in the summation must be discontinuous. When the second-derivative nonadiabatic terms are added to the Hamiltonian, singularities in the diagonal BO corrections (DBOCs) of the individual BO states arise from these discontinuities. In contrast to the well-known singularities in the first-derivative couplingsmore » at conical intersections, these singularities are non-integrable, resulting in undefined DBOC matrix elements. Though these singularities suggest that the exact molecular wave function may not have density at the conical intersection point, there is no physical basis for this constraint. Instead, the singularities are artifacts of the chosen basis of discontinuous functions. We also demonstrate that continuity of the total molecular wave function does not require continuity of the individual adiabatic nuclear wave functions. We classify nonadiabatic molecular dynamics methods according to the constraints placed on wave function continuity and analyze their formal properties. Based on our analysis, it is recommended that the DBOC be neglected when employing mixed quantum-classical methods and certain approximate quantum dynamical methods in the adiabatic representation.« less

Wave function continuity and the diagonal Born-Oppenheimer correction at conical intersections

NASA Astrophysics Data System (ADS)

Meek, Garrett A.; Levine, Benjamin G.

2016-05-01

We demonstrate that though exact in principle, the expansion of the total molecular wave function as a sum over adiabatic Born-Oppenheimer (BO) vibronic states makes inclusion of the second-derivative nonadiabatic energy term near conical intersections practically problematic. In order to construct a well-behaved molecular wave function that has density at a conical intersection, the individual BO vibronic states in the summation must be discontinuous. When the second-derivative nonadiabatic terms are added to the Hamiltonian, singularities in the diagonal BO corrections (DBOCs) of the individual BO states arise from these discontinuities. In contrast to the well-known singularities in the first-derivative couplings at conical intersections, these singularities are non-integrable, resulting in undefined DBOC matrix elements. Though these singularities suggest that the exact molecular wave function may not have density at the conical intersection point, there is no physical basis for this constraint. Instead, the singularities are artifacts of the chosen basis of discontinuous functions. We also demonstrate that continuity of the total molecular wave function does not require continuity of the individual adiabatic nuclear wave functions. We classify nonadiabatic molecular dynamics methods according to the constraints placed on wave function continuity and analyze their formal properties. Based on our analysis, it is recommended that the DBOC be neglected when employing mixed quantum-classical methods and certain approximate quantum dynamical methods in the adiabatic representation.

Wave function continuity and the diagonal Born-Oppenheimer correction at conical intersections.

PubMed

Meek, Garrett A; Levine, Benjamin G

2016-05-14

We demonstrate that though exact in principle, the expansion of the total molecular wave function as a sum over adiabatic Born-Oppenheimer (BO) vibronic states makes inclusion of the second-derivative nonadiabatic energy term near conical intersections practically problematic. In order to construct a well-behaved molecular wave function that has density at a conical intersection, the individual BO vibronic states in the summation must be discontinuous. When the second-derivative nonadiabatic terms are added to the Hamiltonian, singularities in the diagonal BO corrections (DBOCs) of the individual BO states arise from these discontinuities. In contrast to the well-known singularities in the first-derivative couplings at conical intersections, these singularities are non-integrable, resulting in undefined DBOC matrix elements. Though these singularities suggest that the exact molecular wave function may not have density at the conical intersection point, there is no physical basis for this constraint. Instead, the singularities are artifacts of the chosen basis of discontinuous functions. We also demonstrate that continuity of the total molecular wave function does not require continuity of the individual adiabatic nuclear wave functions. We classify nonadiabatic molecular dynamics methods according to the constraints placed on wave function continuity and analyze their formal properties. Based on our analysis, it is recommended that the DBOC be neglected when employing mixed quantum-classical methods and certain approximate quantum dynamical methods in the adiabatic representation.

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.

Towards an exact theory of linear absorbance and circular dichroism of pigment-protein complexes: Importance of non-secular contributions

NASA Astrophysics Data System (ADS)

Dinh, Thanh-Chung; Renger, Thomas

2015-01-01

A challenge for the theory of optical spectra of pigment-protein complexes is the equal strength of the pigment-pigment and the pigment-protein couplings. Treating both on an equal footing so far can only be managed by numerically costly approaches. Here, we exploit recent results on a normal mode analysis derived spectral density that revealed the dominance of the diagonal matrix elements of the exciton-vibrational coupling in the exciton state representation. We use a cumulant expansion technique that treats the diagonal parts exactly, includes an infinite summation of the off-diagonal parts in secular and Markov approximations, and provides a systematic perturbative way to include non-secular and non-Markov corrections. The theory is applied to a model dimer and to chlorophyll (Chl) a and Chl b homodimers of the reconstituted water-soluble chlorophyll-binding protein (WSCP) from cauliflower. The model calculations reveal that the non-secular/non-Markov effects redistribute oscillator strength from the strong to the weak exciton transition in absorbance and they diminish the rotational strength of the exciton transitions in circular dichroism. The magnitude of these corrections is in a few percent range of the overall signal, providing a quantitative explanation of the success of time-local convolution-less density matrix theory applied earlier. A close examination of the optical spectra of Chl a and Chl b homodimers in WSCP suggests that the opening angle between Qy transition dipole moments in Chl b homodimers is larger by about 9∘ than for Chl a homodimers for which a crystal structure of a related WSCP complex exists. It remains to be investigated whether this change is due to a different mutual geometry of the pigments or due to the different electronic structures of Chl a and Chl b.

Exchange potential from the common energy denominator approximation for the Kohn-Sham Green's function: Application to (hyper)polarizabilities of molecular chains

NASA Astrophysics Data System (ADS)

Grüning, M.; Gritsenko, O. V.; Baerends, E. J.

2002-04-01

An approximate Kohn-Sham (KS) exchange potential vxσCEDA is developed, based on the common energy denominator approximation (CEDA) for the static orbital Green's function, which preserves the essential structure of the density response function. vxσCEDA is an explicit functional of the occupied KS orbitals, which has the Slater vSσ and response vrespσCEDA potentials as its components. The latter exhibits the characteristic step structure with "diagonal" contributions from the orbital densities |ψiσ|2, as well as "off-diagonal" ones from the occupied-occupied orbital products ψiσψj(≠1)σ*. Comparison of the results of atomic and molecular ground-state CEDA calculations with those of the Krieger-Li-Iafrate (KLI), exact exchange (EXX), and Hartree-Fock (HF) methods show, that both KLI and CEDA potentials can be considered as very good analytical "closure approximations" to the exact KS exchange potential. The total CEDA and KLI energies nearly coincide with the EXX ones and the corresponding orbital energies ɛiσ are rather close to each other for the light atoms and small molecules considered. The CEDA, KLI, EXX-ɛiσ values provide the qualitatively correct order of ionizations and they give an estimate of VIPs comparable to that of the HF Koopmans' theorem. However, the additional off-diagonal orbital structure of vxσCEDA appears to be essential for the calculated response properties of molecular chains. KLI already considerably improves the calculated (hyper)polarizabilities of the prototype hydrogen chains Hn over local density approximation (LDA) and standard generalized gradient approximations (GGAs), while the CEDA results are definitely an improvement over the KLI ones. The reasons of this success are the specific orbital structures of the CEDA and KLI response potentials, which produce in an external field an ultranonlocal field-counteracting exchange potential.

Development and Verification of the Charring Ablating Thermal Protection Implicit System Solver

NASA Technical Reports Server (NTRS)

Amar, Adam J.; Calvert, Nathan D.; Kirk, Benjamin S.

2010-01-01

The development and verification of the Charring Ablating Thermal Protection Implicit System Solver is presented. This work concentrates on the derivation and verification of the stationary grid terms in the equations that govern three-dimensional heat and mass transfer for charring thermal protection systems including pyrolysis gas flow through the porous char layer. The governing equations are discretized according to the Galerkin finite element method with first and second order implicit time integrators. The governing equations are fully coupled and are solved in parallel via Newton's method, while the fully implicit linear system is solved with the Generalized Minimal Residual method. Verification results from exact solutions and the Method of Manufactured Solutions are presented to show spatial and temporal orders of accuracy as well as nonlinear convergence rates.

Cognitive Mechanisms of Insight: The Role of Heuristics and Representational Change in Solving the Eight-Coin Problem

ERIC Educational Resources Information Center

Öllinger, Michael; Jones, Gary; Faber, Amory H.; Knoblich, Günther

2013-01-01

The 8-coin insight problem requires the problem solver to move 2 coins so that each coin touches exactly 3 others. Ormerod, MacGregor, and Chronicle (2002) explained differences in task performance across different versions of the 8-coin problem using the availability of particular moves in a 2-dimensional search space. We explored 2 further…

Efficient Parallel Kernel Solvers for Computational Fluid Dynamics Applications

NASA Technical Reports Server (NTRS)

Sun, Xian-He

1997-01-01

Distributed-memory parallel computers dominate today's parallel computing arena. These machines, such as Intel Paragon, IBM SP2, and Cray Origin2OO, have successfully delivered high performance computing power for solving some of the so-called "grand-challenge" problems. Despite initial success, parallel machines have not been widely accepted in production engineering environments due to the complexity of parallel programming. On a parallel computing system, a task has to be partitioned and distributed appropriately among processors to reduce communication cost and to attain load balance. More importantly, even with careful partitioning and mapping, the performance of an algorithm may still be unsatisfactory, since conventional sequential algorithms may be serial in nature and may not be implemented efficiently on parallel machines. In many cases, new algorithms have to be introduced to increase parallel performance. In order to achieve optimal performance, in addition to partitioning and mapping, a careful performance study should be conducted for a given application to find a good algorithm-machine combination. This process, however, is usually painful and elusive. The goal of this project is to design and develop efficient parallel algorithms for highly accurate Computational Fluid Dynamics (CFD) simulations and other engineering applications. The work plan is 1) developing highly accurate parallel numerical algorithms, 2) conduct preliminary testing to verify the effectiveness and potential of these algorithms, 3) incorporate newly developed algorithms into actual simulation packages. The work plan has well achieved. Two highly accurate, efficient Poisson solvers have been developed and tested based on two different approaches: (1) Adopting a mathematical geometry which has a better capacity to describe the fluid, (2) Using compact scheme to gain high order accuracy in numerical discretization. The previously developed Parallel Diagonal Dominant (PDD) algorithm and Reduced Parallel Diagonal Dominant (RPDD) algorithm have been carefully studied on different parallel platforms for different applications, and a NASA simulation code developed by Man M. Rai and his colleagues has been parallelized and implemented based on data dependency analysis. These achievements are addressed in detail in the paper.

AQUASOL: An efficient solver for the dipolar Poisson–Boltzmann–Langevin equation

PubMed Central

Koehl, Patrice; Delarue, Marc

2010-01-01

The Poisson–Boltzmann (PB) formalism is among the most popular approaches to modeling the solvation of molecules. It assumes a continuum model for water, leading to a dielectric permittivity that only depends on position in space. In contrast, the dipolar Poisson–Boltzmann–Langevin (DPBL) formalism represents the solvent as a collection of orientable dipoles with nonuniform concentration; this leads to a nonlinear permittivity function that depends both on the position and on the local electric field at that position. The differences in the assumptions underlying these two models lead to significant differences in the equations they generate. The PB equation is a second order, elliptic, nonlinear partial differential equation (PDE). Its response coefficients correspond to the dielectric permittivity and are therefore constant within each subdomain of the system considered (i.e., inside and outside of the molecules considered). While the DPBL equation is also a second order, elliptic, nonlinear PDE, its response coefficients are nonlinear functions of the electrostatic potential. Many solvers have been developed for the PB equation; to our knowledge, none of these can be directly applied to the DPBL equation. The methods they use may adapt to the difference; their implementations however are PBE specific. We adapted the PBE solver originally developed by Holst and Saied [J. Comput. Chem. 16, 337 (1995)] to the problem of solving the DPBL equation. This solver uses a truncated Newton method with a multigrid preconditioner. Numerical evidences suggest that it converges for the DPBL equation and that the convergence is superlinear. It is found however to be slow and greedy in memory requirement for problems commonly encountered in computational biology and computational chemistry. To circumvent these problems, we propose two variants, a quasi-Newton solver based on a simplified, inexact Jacobian and an iterative self-consistent solver that is based directly on the PBE solver. While both methods are not guaranteed to converge, numerical evidences suggest that they do and that their convergence is also superlinear. Both variants are significantly faster than the solver based on the exact Jacobian, with a much smaller memory footprint. All three methods have been implemented in a new code named AQUASOL, which is freely available. PMID:20151727

AQUASOL: An efficient solver for the dipolar Poisson-Boltzmann-Langevin equation.

PubMed

Koehl, Patrice; Delarue, Marc

2010-02-14

The Poisson-Boltzmann (PB) formalism is among the most popular approaches to modeling the solvation of molecules. It assumes a continuum model for water, leading to a dielectric permittivity that only depends on position in space. In contrast, the dipolar Poisson-Boltzmann-Langevin (DPBL) formalism represents the solvent as a collection of orientable dipoles with nonuniform concentration; this leads to a nonlinear permittivity function that depends both on the position and on the local electric field at that position. The differences in the assumptions underlying these two models lead to significant differences in the equations they generate. The PB equation is a second order, elliptic, nonlinear partial differential equation (PDE). Its response coefficients correspond to the dielectric permittivity and are therefore constant within each subdomain of the system considered (i.e., inside and outside of the molecules considered). While the DPBL equation is also a second order, elliptic, nonlinear PDE, its response coefficients are nonlinear functions of the electrostatic potential. Many solvers have been developed for the PB equation; to our knowledge, none of these can be directly applied to the DPBL equation. The methods they use may adapt to the difference; their implementations however are PBE specific. We adapted the PBE solver originally developed by Holst and Saied [J. Comput. Chem. 16, 337 (1995)] to the problem of solving the DPBL equation. This solver uses a truncated Newton method with a multigrid preconditioner. Numerical evidences suggest that it converges for the DPBL equation and that the convergence is superlinear. It is found however to be slow and greedy in memory requirement for problems commonly encountered in computational biology and computational chemistry. To circumvent these problems, we propose two variants, a quasi-Newton solver based on a simplified, inexact Jacobian and an iterative self-consistent solver that is based directly on the PBE solver. While both methods are not guaranteed to converge, numerical evidences suggest that they do and that their convergence is also superlinear. Both variants are significantly faster than the solver based on the exact Jacobian, with a much smaller memory footprint. All three methods have been implemented in a new code named AQUASOL, which is freely available.

Bethe states of the trigonometric SU(3) spin chain with generic open boundaries

NASA Astrophysics Data System (ADS)

Sun, Pei; Xin, Zhirong; Qiao, Yi; Wen, Fakai; Hao, Kun; Cao, Junpeng; Li, Guang-Liang; Yang, Tao; Yang, Wen-Li; Shi, Kangjie

2018-06-01

By combining the algebraic Bethe ansatz and the off-diagonal Bethe ansatz, we investigate the trigonometric SU (3) model with generic open boundaries. The eigenvalues of the transfer matrix are given in terms of an inhomogeneous T - Q relation, and the corresponding eigenstates are expressed in terms of nested Bethe-type eigenstates which have well-defined homogeneous limit. This exact solution provides a basis for further analyzing the thermodynamic properties and correlation functions of the anisotropic models associated with higher rank algebras.

Exchange interactions in a dinuclear manganese (II) complex with cyanopyridine-N-oxide bridging ligands

NASA Astrophysics Data System (ADS)

Markosyan, A. S.; Gaidukova, I. Yu.; Ruchkin, A. V.; Anokhin, A. O.; Irkhin, V. Yu.; Ryazanov, M. V.; Kuz'mina, N. P.; Nikiforov, V. N.

2014-01-01

The magnetic properties of dinuclear manganese(II) complex [Mn(hfa)2cpo]2 (where hfa is hexafluoroacetylacetonate anion and cpo is 4-cyanopyridine-N-oxide) are presented. The non-monotonous dependence of magnetic susceptibility is explained in terms of the hierarchy of exchange parameters by using exact diagonalization. The thermodynamic behavior of pure cpo and [Mn(hfa)2(cpo)]2 is simulated numerically by an extrapolation to spin S=5/2. The Mn-Mn exchange integral is evaluated.

Frustrated honeycomb-lattice bilayer quantum antiferromagnet in a magnetic field

NASA Astrophysics Data System (ADS)

Krokhmalskii, Taras; Baliha, Vasyl; Derzhko, Oleg; Schulenburg, Jörg; Richter, Johannes

2018-05-01

Frustrated bilayer quantum magnets have attracted attention as flat-band spin systems with unconventional thermodynamic properties. We study the low-temperature properties of a frustrated honeycomb-lattice bilayer spin-1/2 isotropic (XXX) Heisenberg antiferromagnet in a magnetic field by means of an effective low-energy theory using exact diagonalizations and quantum Monte Carlo simulations. Our main focus is on the magnetization curve and the temperature dependence of the specific heat indicating a finite-temperature phase transition in high magnetic fields.

High-Tc superconductivity: The t-J-V model and its applications

NASA Astrophysics Data System (ADS)

Roy, K.; Pal, P.; Nath, S.; Ghosh, N. K.

2017-05-01

We present numerical results of the t-J-V model in an 8-site tilted square cluster using exact diagonalization (ED) method with periodic boundary conditions. Effective hopping amplitude initially increases with inter-site Coulomb repulsion (V), but decreases at larger V's. The hole-hole correlation decreases with inter-site distances at smaller V. With the increase of Coulomb repulsion, the system becomes ordered. The specific heat curves confirm the non-Fermi liquid behavior of the system under t-J-V model.

Spectral function of few electrons in quantum wires and carbon nanotubes as a signature of Wigner localization

NASA Astrophysics Data System (ADS)

Secchi, Andrea; Rontani, Massimo

2012-03-01

We demonstrate that the profile of the space-resolved spectral function at finite temperature provides a signature of Wigner localization for electrons in quantum wires and semiconducting carbon nanotubes. Our numerical evidence is based on the exact diagonalization of the microscopic Hamiltonian of few particles interacting in gate-defined quantum dots. The minimal temperature required to suppress residual exchange effects in the spectral function image of (nanotubes) quantum wires lies in the (sub)kelvin range.

Nature of Continuous Phase Transitions in Interacting Topological Insulators

DOE PAGES

Zeng, Tian-sheng; Zhu, Wei; Zhu, Jianxin; ...

2017-11-08

Here, we revisit the effects of the Hubbard repulsion on quantum spin Hall effects (QSHE) in two-dimensional quantum lattice models. We present both unbiased exact diagonalization and density-matrix renormalization group simulations with numerical evidence for a continuous quantum phase transition (CQPT) separating QSHE from the topologically trivial antiferromagnetic phase. Our numerical results suggest that the nature of CQPT exhibits distinct finite-size scaling behaviors, which may be consistent with either Ising or XY universality classes for different time-reversal symmetric QSHE systems.

Fractional charge revealed in computer simulations of resonant tunneling in the fractional quantum Hall regime.

PubMed

Tsiper, E V

2006-08-18

The concept of fractional charge is central to the theory of the fractional quantum Hall effect. Here I use exact diagonalization as well as configuration space renormalization to study finite clusters which are large enough to contain two independent edges. I analyze the conditions of resonant tunneling between the two edges. The "computer experiment" reveals a periodic sequence of resonant tunneling events consistent with the experimentally observed fractional quantization of electric charge in units of e/3 and e/5.

Ground state transitions in vertically coupled N-layer single electron quantum dots

NASA Astrophysics Data System (ADS)

Xie, Wenfang; Wang, Anmei

2003-12-01

A method is proposed to exactly diagonalize the Hamiltonian of a N-layer quantum dot containing a single electron in each dot in arbitrary magnetic fields. For N=4, the energy spectra of the dot are calculated as a function of the applied magnetic field. We find discontinuous ground-state energy transitions induced by an external magnetic field in the case of strong coupling. However, in the case of weak coupling, such a transition does not occur and the angular momentum remains zero.

Nature of Continuous Phase Transitions in Interacting Topological Insulators

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

Zeng, Tian-sheng; Zhu, Wei; Zhu, Jianxin

Here, we revisit the effects of the Hubbard repulsion on quantum spin Hall effects (QSHE) in two-dimensional quantum lattice models. We present both unbiased exact diagonalization and density-matrix renormalization group simulations with numerical evidence for a continuous quantum phase transition (CQPT) separating QSHE from the topologically trivial antiferromagnetic phase. Our numerical results suggest that the nature of CQPT exhibits distinct finite-size scaling behaviors, which may be consistent with either Ising or XY universality classes for different time-reversal symmetric QSHE systems.

A closed-form analytical model for predicting 3D boundary layer displacement thickness for the validation of viscous flow solvers

NASA Astrophysics Data System (ADS)

Kumar, V. R. Sanal; Sankar, Vigneshwaran; Chandrasekaran, Nichith; Saravanan, Vignesh; Natarajan, Vishnu; Padmanabhan, Sathyan; Sukumaran, Ajith; Mani, Sivabalan; Rameshkumar, Tharikaa; Nagaraju Doddi, Hema Sai; Vysaprasad, Krithika; Sharan, Sharad; Murugesh, Pavithra; Shankar, S. Ganesh; Nejaamtheen, Mohammed Niyasdeen; Baskaran, Roshan Vignesh; Rahman Mohamed Rafic, Sulthan Ariff; Harisrinivasan, Ukeshkumar; Srinivasan, Vivek

2018-02-01

A closed-form analytical model is developed for estimating the 3D boundary-layer-displacement thickness of an internal flow system at the Sanal flow choking condition for adiabatic flows obeying the physics of compressible viscous fluids. At this unique condition the boundary-layer blockage induced fluid-throat choking and the adiabatic wall-friction persuaded flow choking occur at a single sonic-fluid-throat location. The beauty and novelty of this model is that without missing the flow physics we could predict the exact boundary-layer blockage of both 2D and 3D cases at the sonic-fluid-throat from the known values of the inlet Mach number, the adiabatic index of the gas and the inlet port diameter of the internal flow system. We found that the 3D blockage factor is 47.33 % lower than the 2D blockage factor with air as the working fluid. We concluded that the exact prediction of the boundary-layer-displacement thickness at the sonic-fluid-throat provides a means to correctly pinpoint the causes of errors of the viscous flow solvers. The methodology presented herein with state-of-the-art will play pivotal roles in future physical and biological sciences for a credible verification, calibration and validation of various viscous flow solvers for high-fidelity 2D/3D numerical simulations of real-world flows. Furthermore, our closed-form analytical model will be useful for the solid and hybrid rocket designers for the grain-port-geometry optimization of new generation single-stage-to-orbit dual-thrust-motors with the highest promising propellant loading density within the given envelope without manifestation of the Sanal flow choking leading to possible shock waves causing catastrophic failures.

A finite-volume HLLC-based scheme for compressible interfacial flows with surface tension

NASA Astrophysics Data System (ADS)

Garrick, Daniel P.; Owkes, Mark; Regele, Jonathan D.

2017-06-01

Shock waves are often used in experiments to create a shear flow across liquid droplets to study secondary atomization. Similar behavior occurs inside of supersonic combustors (scramjets) under startup conditions, but it is challenging to study these conditions experimentally. In order to investigate this phenomenon further, a numerical approach is developed to simulate compressible multiphase flows under the effects of surface tension forces. The flow field is solved via the compressible multicomponent Euler equations (i.e., the five equation model) discretized with the finite volume method on a uniform Cartesian grid. The solver utilizes a total variation diminishing (TVD) third-order Runge-Kutta method for time-marching and second order TVD spatial reconstruction. Surface tension is incorporated using the Continuum Surface Force (CSF) model. Fluxes are upwinded with a modified Harten-Lax-van Leer Contact (HLLC) approximate Riemann solver. An interface compression scheme is employed to counter numerical diffusion of the interface. The present work includes modifications to both the HLLC solver and the interface compression scheme to account for capillary force terms and the associated pressure jump across the gas-liquid interface. A simple method for numerically computing the interface curvature is developed and an acoustic scaling of the surface tension coefficient is proposed for the non-dimensionalization of the model. The model captures the surface tension induced pressure jump exactly if the exact curvature is known and is further verified with an oscillating elliptical droplet and Mach 1.47 and 3 shock-droplet interaction problems. The general characteristics of secondary atomization at a range of Weber numbers are also captured in a series of simulations.

A finite-volume HLLC-based scheme for compressible interfacial flows with surface tension

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

Garrick, Daniel P.; Owkes, Mark; Regele, Jonathan D., E-mail: jregele@iastate.edu

Shock waves are often used in experiments to create a shear flow across liquid droplets to study secondary atomization. Similar behavior occurs inside of supersonic combustors (scramjets) under startup conditions, but it is challenging to study these conditions experimentally. In order to investigate this phenomenon further, a numerical approach is developed to simulate compressible multiphase flows under the effects of surface tension forces. The flow field is solved via the compressible multicomponent Euler equations (i.e., the five equation model) discretized with the finite volume method on a uniform Cartesian grid. The solver utilizes a total variation diminishing (TVD) third-order Runge–Kuttamore » method for time-marching and second order TVD spatial reconstruction. Surface tension is incorporated using the Continuum Surface Force (CSF) model. Fluxes are upwinded with a modified Harten–Lax–van Leer Contact (HLLC) approximate Riemann solver. An interface compression scheme is employed to counter numerical diffusion of the interface. The present work includes modifications to both the HLLC solver and the interface compression scheme to account for capillary force terms and the associated pressure jump across the gas–liquid interface. A simple method for numerically computing the interface curvature is developed and an acoustic scaling of the surface tension coefficient is proposed for the non-dimensionalization of the model. The model captures the surface tension induced pressure jump exactly if the exact curvature is known and is further verified with an oscillating elliptical droplet and Mach 1.47 and 3 shock-droplet interaction problems. The general characteristics of secondary atomization at a range of Weber numbers are also captured in a series of simulations.« less

Comparison of νμ->νe Oscillation calculations with matter effects

NASA Astrophysics Data System (ADS)

Gordon, Michael; Toki, Walter

2013-04-01

An introduction to neutrino oscillations in vacuum is presented, followed by a survey of various techniques for obtaining either exact or approximate expressions for νμ->νe oscillations in matter. The method devised by Mann, Kafka, Schneps, and Altinok produces an exact expression for the oscillation by determining explicitely the evolution operator. The method used by Freund yields an approximate oscillation probability by diagonalizing the Hamiltonian, finding the eigenvalues and eigenvectors, and then using those to find modified mixing angles with the matter effect taken into account. The method developed by Arafune, Koike, and Sato uses an alternate method to find an approximation of the evolution operator. These methods are compared to each other using parameters from both the T2K and LBNE experiments.

Exact finite volume expectation values of local operators in excited states

NASA Astrophysics Data System (ADS)

Pozsgay, B.; Szécsényi, I. M.; Takács, G.

2015-04-01

We present a conjecture for the exact expression of finite volume expectation values in excited states in integrable quantum field theories, which is an extension of an earlier conjecture to the case of general diagonal factorized scattering with bound states and a nontrivial bootstrap structure. The conjectured expression is a spectral expansion which uses the exact form factors and the excited state thermodynamic Bethe Ansatz as building blocks. The conjecture is proven for the case of the trace of the energy-moment tensor. Concerning its validity for more general operators, we provide numerical evidence using the truncated conformal space approach. It is found that the expansion fails to be well-defined for small values of the volume in cases when the singularity structure of the TBA equations undergoes a non-trivial rearrangement under some critical value of the volume. Despite these shortcomings, the conjectured expression is expected to be valid for all volumes for most of the excited states, and as an expansion above the critical volume for the rest.

Construction of exact constants of motion and effective models for many-body localized systems

NASA Astrophysics Data System (ADS)

Goihl, M.; Gluza, M.; Krumnow, C.; Eisert, J.

2018-04-01

One of the defining features of many-body localization is the presence of many quasilocal conserved quantities. These constants of motion constitute a cornerstone to an intuitive understanding of much of the phenomenology of many-body localized systems arising from effective Hamiltonians. They may be seen as local magnetization operators smeared out by a quasilocal unitary. However, accurately identifying such constants of motion remains a challenging problem. Current numerical constructions often capture the conserved operators only approximately, thus restricting a conclusive understanding of many-body localization. In this work, we use methods from the theory of quantum many-body systems out of equilibrium to establish an alternative approach for finding a complete set of exact constants of motion which are in addition guaranteed to represent Pauli-z operators. By this we are able to construct and investigate the proposed effective Hamiltonian using exact diagonalization. Hence, our work provides an important tool expected to further boost inquiries into the breakdown of transport due to quenched disorder.

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.

Application of Conjugate Gradient methods to tidal simulation

USGS Publications Warehouse

Barragy, E.; Carey, G.F.; Walters, R.A.

1993-01-01

A harmonic decomposition technique is applied to the shallow water equations to yield a complex, nonsymmetric, nonlinear, Helmholtz type problem for the sea surface and an accompanying complex, nonlinear diagonal problem for the velocities. The equation for the sea surface is linearized using successive approximation and then discretized with linear, triangular finite elements. The study focuses on applying iterative methods to solve the resulting complex linear systems. The comparative evaluation includes both standard iterative methods for the real subsystems and complex versions of the well known Bi-Conjugate Gradient and Bi-Conjugate Gradient Squared methods. Several Incomplete LU type preconditioners are discussed, and the effects of node ordering, rejection strategy, domain geometry and Coriolis parameter (affecting asymmetry) are investigated. Implementation details for the complex case are discussed. Performance studies are presented and comparisons made with a frontal solver. ?? 1993.

Upwind MacCormack Euler solver with non-equilibrium chemistry

NASA Technical Reports Server (NTRS)

Sherer, Scott E.; Scott, James N.

1993-01-01

A computer code, designated UMPIRE, is currently under development to solve the Euler equations in two dimensions with non-equilibrium chemistry. UMPIRE employs an explicit MacCormack algorithm with dissipation introduced via Roe's flux-difference split upwind method. The code also has the capability to employ a point-implicit methodology for flows where stiffness is introduced through the chemical source term. A technique consisting of diagonal sweeps across the computational domain from each corner is presented, which is used to reduce storage and execution requirements. Results depicting one dimensional shock tube flow for both calorically perfect gas and thermally perfect, dissociating nitrogen are presented to verify current capabilities of the program. Also, computational results from a chemical reactor vessel with no fluid dynamic effects are presented to check the chemistry capability and to verify the point implicit strategy.

Multi-processing on supercomputers for computational aerodynamics

NASA Technical Reports Server (NTRS)

Yarrow, Maurice; Mehta, Unmeel B.

1990-01-01

The MIMD concept is applied, through multitasking, with relatively minor modifications to an existing code for a single processor. This approach maps the available memory to multiple processors, exploiting the C-FORTRAN-Unix interface. An existing single processor algorithm is mapped without the need for developing a new algorithm. The procedure of designing a code utilizing this approach is automated with the Unix stream editor. A Multiple Processor Multiple Grid (MPMG) code is developed as a demonstration of this approach. This code solves the three-dimensional, Reynolds-averaged, thin-layer and slender-layer Navier-Stokes equations with an implicit, approximately factored and diagonalized method. This solver is applied to a generic, oblique-wing aircraft problem on a four-processor computer using one process for data management and nonparallel computations and three processes for pseudotime advance on three different grid systems.

Exponential-fitted methods for integrating stiff systems of ordinary differential equations: Applications to homogeneous gas-phase chemical kinetics

NASA Technical Reports Server (NTRS)

Pratt, D. T.

1984-01-01

Conventional algorithms for the numerical integration of ordinary differential equations (ODEs) are based on the use of polynomial functions as interpolants. However, the exact solutions of stiff ODEs behave like decaying exponential functions, which are poorly approximated by polynomials. An obvious choice of interpolant are the exponential functions themselves, or their low-order diagonal Pade (rational function) approximants. A number of explicit, A-stable, integration algorithms were derived from the use of a three-parameter exponential function as interpolant, and their relationship to low-order, polynomial-based and rational-function-based implicit and explicit methods were shown by examining their low-order diagonal Pade approximants. A robust implicit formula was derived by exponential fitting the trapezoidal rule. Application of these algorithms to integration of the ODEs governing homogenous, gas-phase chemical kinetics was demonstrated in a developmental code CREK1D, which compares favorably with the Gear-Hindmarsh code LSODE in spite of the use of a primitive stepsize control strategy.

Focusing of noncircular self-similar shock waves.

PubMed

Betelu, S I; Aronson, D G

2001-08-13

We study the focusing of noncircular shock waves in a perfect gas. We construct an explicit self-similar solution by combining three convergent plane waves with regular shock reflections between them. We then show, with a numerical Riemann solver, that there are initial conditions with smooth shocks whose intermediate asymptotic stage is described by the exact solution. Unlike the focusing of circular shocks, our self-similar shocks have bounded energy density.

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.

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

The High-Resolution Wave-Propagation Method Applied to Meso- and Micro-Scale Flows

NASA Technical Reports Server (NTRS)

Ahmad, Nashat N.; Proctor, Fred H.

2012-01-01

The high-resolution wave-propagation method for computing the nonhydrostatic atmospheric flows on meso- and micro-scales is described. The design and implementation of the Riemann solver used for computing the Godunov fluxes is discussed in detail. The method uses a flux-based wave decomposition in which the flux differences are written directly as the linear combination of the right eigenvectors of the hyperbolic system. The two advantages of the technique are: 1) the need for an explicit definition of the Roe matrix is eliminated and, 2) the inclusion of source term due to gravity does not result in discretization errors. The resulting flow solver is conservative and able to resolve regions of large gradients without introducing dispersion errors. The methodology is validated against exact analytical solutions and benchmark cases for non-hydrostatic atmospheric flows.

An iterative Riemann solver for systems of hyperbolic conservation law s, with application to hyperelastic solid mechanics

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

Miller, Gregory H.

2003-08-06

In this paper we present a general iterative method for the solution of the Riemann problem for hyperbolic systems of PDEs. The method is based on the multiple shooting method for free boundary value problems. We demonstrate the method by solving one-dimensional Riemann problems for hyperelastic solid mechanics. Even for conditions representative of routine laboratory conditions and military ballistics, dramatic differences are seen between the exact and approximate Riemann solution. The greatest discrepancy arises from misallocation of energy between compressional and thermal modes by the approximate solver, resulting in nonphysical entropy and temperature estimates. Several pathological conditions arise in commonmore » practice, and modifications to the method to handle these are discussed. These include points where genuine nonlinearity is lost, degeneracies, and eigenvector deficiencies that occur upon melting.« less

Virtual Petaflop Simulation: Parallel Potential Solvers and New Integrators for Gravitational Systems

NASA Technical Reports Server (NTRS)

Lake, George; Quinn, Thomas; Richardson, Derek C.; Stadel, Joachim

1999-01-01

"The orbit of any one planet depends on the combined motion of all the planets, not to mention the actions of all these on each other. To consider simultaneously all these causes of motion and to define these motions by exact laws allowing of convenient calculation exceeds, unless I am mistaken, the forces of the entire human intellect" -Isaac Newton 1687. Epochal surveys are throwing down the gauntlet for cosmological simulation. We describe three keys to meeting the challenge of N-body simulation: adaptive potential solvers, adaptive integrators and volume renormalization. With these techniques and a dedicated Teraflop facility, simulation can stay even with observation of the Universe. We also describe some problems in the formation and stability of planetary systems. Here, the challenge is to perform accurate integrations that retain Hamiltonian properties for 10(exp 13) timesteps.

Improved Convergence and Robustness of USM3D Solutions on Mixed Element Grids (Invited)

NASA Technical Reports Server (NTRS)

Pandya, Mohagna J.; Diskin, Boris; Thomas, James L.; Frink, Neal T.

2015-01-01

Several improvements to the mixed-element USM3D discretization and defect-correction schemes have been made. A new methodology for nonlinear iterations, called the Hierarchical Adaptive Nonlinear Iteration Scheme (HANIS), has been developed and implemented. It provides two additional hierarchies around a simple and approximate preconditioner of USM3D. The hierarchies are a matrix-free linear solver for the exact linearization of Reynolds-averaged Navier Stokes (RANS) equations and a nonlinear control of the solution update. Two variants of the new methodology are assessed on four benchmark cases, namely, a zero-pressure gradient flat plate, a bump-in-channel configuration, the NACA 0012 airfoil, and a NASA Common Research Model configuration. The new methodology provides a convergence acceleration factor of 1.4 to 13 over the baseline solver technology.

Studying relaxation phenomena via effective master equations

NASA Astrophysics Data System (ADS)

Chan, David; Wan, Jones T. K.; Chu, L. L.; Yu, K. W.

2000-04-01

The real-time dynamics of various relaxation phenomena can be conveniently formulated by a master equation with the enumeration of transition rates between given classes of conformations. To study the relaxation time towards equilibrium, it suffices to solve for the second largest eigenvalue of the resulting eigenvalue equation. Generally speaking, there is no analytic solution for the dynamic equation. Mean-field approaches generally yield misleading results while the presumably exact Monte-Carlo methods require prohibitive time steps in most real systems. In this work, we propose an exact decimation procedure for reducing the number of conformations significantly, while there is no loss of information, i.e., the reduced (or effective) equation is an exact transformed version of the original one. However, we have to pay the price: the initial Markovianity of the evolution equation is lost and the reduced equation contains memory terms in the transition rates. Since the transformed equation has significantly reduced number of degrees of freedom, the systems can readily be diagonalized by iterative means, to obtain the exact second largest eigenvalue and hence the relaxation time. The decimation method has been applied to various relaxation equations with generally desirable results. The advantages and limitations of the method will be discussed.

On the consistency of the Oppenheimer-Snyder solution for a dust star. Reply to Marshall's criticism

NASA Astrophysics Data System (ADS)

Zakir, Zahid

2018-02-01

The recent alternative to the Oppenheimer-Snyder (OS) solution for a dust star proposed by Marshall in the paper "Gravitational collapse without black holes" (Astrophys. Space Sci. 342:329, 2012) is analyzed. It is shown that this proposal leads to a non-diagonal metric, with which the Einstein equations become practically unsolvable. Any ansatz proposed as their exact solution turns out to be arbitrary and may be unlimited number of the such solutions. This is due to the fact that an auxiliary function y(R,r), introduced by OS as t=M(y), is unambiguously fixed by the diagonality condition and the matching on the surface, and thus in the non-diagonal case it remains arbitrary. It is also shown that the OS solution, as a description in terms of the Schwarzschild coordinates, leads to a frozen star (or frozar) picture not only for the surface, asymptotically freezing outside the gravitational radius, but for interior layers too which also freeze near their own asymptotes. At most of the inner region these asymptotes are located almost equidistantly and only for layers initially close to the surface they become denser. The reason for the such densifying is not "a gravitational repulsion", but their later freezing and higher spatial contractions, while they remain be uniform and free falling in the comoving frames.

Unveiling magnetic interactions of ruthenium trichloride via constraining direction of orbital moments: Potential routes to realize a quantum spin liquid

NASA Astrophysics Data System (ADS)

Hou, Y. S.; Xiang, H. J.; Gong, X. G.

2017-08-01

Recent experiments reveal that the honeycomb ruthenium trichloride α -RuC l3 is a prime candidate of the Kitaev quantum spin liquid (QSL). However, there is no theoretical model which can properly describe its experimental dynamical response due to the lack of a full understanding of its magnetic interactions. Here, we propose a general scheme to calculate the magnetic interactions in systems (e.g., α -RuC l3 ) with nonnegligible orbital moments by constraining the directions of orbital moments. With this scheme, we put forward a minimal J1-K1-Γ1-J3-K3 model for α -RuC l3 and find that: (I) The third nearest neighbor (NN) antiferromagnetic Heisenberg interaction J3 stabilizes the zigzag antiferromagnetic order; (II) The NN symmetric off-diagonal exchange Γ1 plays a pivotal role in determining the preferred direction of magnetic moments and generating the spin wave gap. An exact diagonalization study on this model shows that the Kitaev QSL can be realized by suppressing the NN symmetric off-diagonal exchange Γ1 and the third NN Heisenberg interaction J3. Thus, we not only propose a powerful general scheme for investigating the intriguing magnetism of Jeff=1 /2 magnets, but also point out future directions for realizing the Kitaev QSL in the honeycomb ruthenium trichloride α -RuC l3 .

Overlaps with arbitrary two-site states in the XXZ spin chain

NASA Astrophysics Data System (ADS)

Pozsgay, B.

2018-05-01

We present a conjectured exact formula for overlaps between the Bethe states of the spin-1/2 XXZ chain and generic two-site states. The result takes the same form as in the previously known cases: it involves the same ratio of two Gaudin-like determinants, and a product of single-particle overlap functions, which can be fixed using a combination of the quench action and quantum transfer matrix methods. Our conjecture is confirmed by numerical data from exact diagonalization. For one-site states, the formula is found to be correct even in chains with odd length. It is also pointed out that the ratio of the Gaudin-like determinants plays a crucial role in the overlap sum rule: it guarantees that in the thermodynamic limit there remains no term in the quench action.

Trial wave functions for a composite Fermi liquid on a torus

NASA Astrophysics Data System (ADS)

Fremling, M.; Moran, N.; Slingerland, J. K.; Simon, S. H.

2018-01-01

We study the two-dimensional electron gas in a magnetic field at filling fraction ν =1/2 . At this filling the system is in a gapless state which can be interpreted as a Fermi liquid of composite fermions. We construct trial wave functions for the system on a torus, based on this idea, and numerically compare these to exact wave functions for small systems found by exact diagonalization. We find that the trial wave functions give an excellent description of the ground state of the system, as well as its charged excitations, in all momentum sectors. We analyze the dispersion of the composite fermions and the Berry phase associated with dragging a single fermion around the Fermi surface and comment on the implications of our results for the current debate on whether composite fermions are Dirac fermions.

An Initial Investigation of the Effects of Turbulence Models on the Convergence of the RK/Implicit Scheme

NASA Technical Reports Server (NTRS)

Swanson, R. C.; Rossow, C.-C.

2008-01-01

A three-stage Runge-Kutta (RK) scheme with multigrid and an implicit preconditioner has been shown to be an effective solver for the fluid dynamic equations. This scheme has been applied to both the compressible and essentially incompressible Reynolds-averaged Navier-Stokes (RANS) equations using the algebraic turbulence model of Baldwin and Lomax (BL). In this paper we focus on the convergence of the RK/implicit scheme when the effects of turbulence are represented by either the Spalart-Allmaras model or the Wilcox k-! model, which are frequently used models in practical fluid dynamic applications. Convergence behavior of the scheme with these turbulence models and the BL model are directly compared. For this initial investigation we solve the flow equations and the partial differential equations of the turbulence models indirectly coupled. With this approach we examine the convergence behavior of each system. Both point and line symmetric Gauss-Seidel are considered for approximating the inverse of the implicit operator of the flow solver. To solve the turbulence equations we use a diagonally dominant alternating direction implicit (DDADI) scheme. Computational results are presented for three airfoil flow cases and comparisons are made with experimental data. We demonstrate that the two-dimensional RANS equations and transport-type equations for turbulence modeling can be efficiently solved with an indirectly coupled algorithm that uses the RK/implicit scheme for the flow equations.

Isovector and isoscalar tensor charges of the nucleon from lattice QCD

DOE PAGES

Bhattacharya, Tanmoy; Cirigliano, Vincenzo; Cohen, Saul D.; ...

2015-11-01

Here, we present results for the isovector and flavor diagonal tensor charges g u–d T, g u T, g d T, and g s T needed to probe novel tensor interactions at the TeV scale in neutron and nuclear β-decays and the contribution of the quark electric dipole moment (EDM) to the neutron EDM. The lattice QCD calculations were done using nine ensembles of gauge configurations generated by the MILC collaboration using the HISQ action with 2+1+1 dynamical flavors. These ensembles span three lattice spacings a ≈ 0.06, 0.09 and 0.12 fm and three quark masses corresponding to the pionmore » masses M π ≈ 130, 220 and 310 MeV. Using estimates from these ensembles, we quantify all systematic uncertainties and perform a simultaneous extrapolation in the lattice spacing, volume and light quark masses for the connected contributions. The final estimates of the connected nucleon (proton) tensor charge for the isovector combination is g u–d T = 1.020(76) in the MS¯ scheme at 2 GeV. The additional disconnected quark loop contributions needed for the flavor-diagonal matrix elements are calculated using a stochastic estimator employing the truncated solver method with the all-mode-averaging technique. We find that the size of the disconnected contribution is smaller than the statistical error in the connected contribution. This allows us to bound the disconnected contribution and include it as an additional uncertainty in the flavor-diagonal charges. After a continuum extrapolation, we find g u T = 0.774(66), g d T = –0.233(28) and g u+d T = 0.541(67). The strangeness tensor charge, that can make a significant contribution to the neutron EDM due to the large ratio m s/m u,d, is g s T = 0.008(9) in the continuum limit.« less

IETI – Isogeometric Tearing and Interconnecting

PubMed Central

Kleiss, Stefan K.; Pechstein, Clemens; Jüttler, Bert; Tomar, Satyendra

2012-01-01

Finite Element Tearing and Interconnecting (FETI) methods are a powerful approach to designing solvers for large-scale problems in computational mechanics. The numerical simulation problem is subdivided into a number of independent sub-problems, which are then coupled in appropriate ways. NURBS- (Non-Uniform Rational B-spline) based isogeometric analysis (IGA) applied to complex geometries requires to represent the computational domain as a collection of several NURBS geometries. Since there is a natural decomposition of the computational domain into several subdomains, NURBS-based IGA is particularly well suited for using FETI methods. This paper proposes the new IsogEometric Tearing and Interconnecting (IETI) method, which combines the advanced solver design of FETI with the exact geometry representation of IGA. We describe the IETI framework for two classes of simple model problems (Poisson and linearized elasticity) and discuss the coupling of the subdomains along interfaces (both for matching interfaces and for interfaces with T-joints, i.e. hanging nodes). Special attention is paid to the construction of a suitable preconditioner for the iterative linear solver used for the interface problem. We report several computational experiments to demonstrate the performance of the proposed IETI method. PMID:24511167

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

Calculated momentum dependence of Zhang-Rice states in transition metal oxides.

PubMed

Yin, Quan; Gordienko, Alexey; Wan, Xiangang; Savrasov, Sergey Y

2008-02-15

Using a combination of local density functional theory and cluster exact diagonalization based dynamical mean field theory, we calculate many-body electronic structures of several Mott insulating oxides including undoped high T(c) materials. The dispersions of the lowest occupied electronic states are associated with the Zhang-Rice singlets in cuprates and with doublets, triplets, quadruplets, and quintets in more general cases. Our results agree with angle resolved photoemission experiments including the decrease of the spectral weight of the Zhang-Rice band as it approaches k=0.

Discrete disorder models for many-body localization

NASA Astrophysics Data System (ADS)

Janarek, Jakub; Delande, Dominique; Zakrzewski, Jakub

2018-04-01

Using exact diagonalization technique, we investigate the many-body localization phenomenon in the 1D Heisenberg chain comparing several disorder models. In particular we consider a family of discrete distributions of disorder strengths and compare the results with the standard uniform distribution. Both statistical properties of energy levels and the long time nonergodic behavior are discussed. The results for different discrete distributions are essentially identical to those obtained for the continuous distribution, provided the disorder strength is rescaled by the standard deviation of the random distribution. Only for the binary distribution significant deviations are observed.

Quantum dimer model for the pseudogap metal

PubMed Central

Punk, Matthias; Allais, Andrea; Sachdev, Subir

2015-01-01

We propose a quantum dimer model for the metallic state of the hole-doped cuprates at low hole density, p. The Hilbert space is spanned by spinless, neutral, bosonic dimers and spin S=1/2, charge +e fermionic dimers. The model realizes a “fractionalized Fermi liquid” with no symmetry breaking and small hole pocket Fermi surfaces enclosing a total area determined by p. Exact diagonalization, on lattices of sizes up to 8×8, shows anisotropic quasiparticle residue around the pocket Fermi surfaces. We discuss the relationship to experiments. PMID:26195771

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

High speed corner and gap-seal computations using an LU-SGS scheme

NASA Technical Reports Server (NTRS)

Coirier, William J.

1989-01-01

The hybrid Lower-Upper Symmetric Gauss-Seidel (LU-SGS) algorithm was added to a widely used series of 2D/3D Euler/Navier-Stokes solvers and was demonstrated for a particular class of high-speed flows. A limited study was conducted to compare the hybrid LU-SGS for approximate Newton iteration and diagonalized Beam-Warming (DBW) schemes on a work and convergence history basis. The hybrid LU-SGS algorithm is more efficient and easier to implement than the DBW scheme originally present in the code for the cases considered. The code was validated for the hypersonic flow through two mutually perpendicular flat plates and then used to investigate the flow field in and around a simplified scramjet module gap seal configuration. Due to the similarities, the gap seal flow was compared to hypersonic corner flow at the same freestream conditions and Reynolds number.

The DANTE Boltzmann transport solver: An unstructured mesh, 3-D, spherical harmonics algorithm compatible with parallel computer architectures

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

McGhee, J.M.; Roberts, R.M.; Morel, J.E.

1997-06-01

A spherical harmonics research code (DANTE) has been developed which is compatible with parallel computer architectures. DANTE provides 3-D, multi-material, deterministic, transport capabilities using an arbitrary finite element mesh. The linearized Boltzmann transport equation is solved in a second order self-adjoint form utilizing a Galerkin finite element spatial differencing scheme. The core solver utilizes a preconditioned conjugate gradient algorithm. Other distinguishing features of the code include options for discrete-ordinates and simplified spherical harmonics angular differencing, an exact Marshak boundary treatment for arbitrarily oriented boundary faces, in-line matrix construction techniques to minimize memory consumption, and an effective diffusion based preconditioner formore » scattering dominated problems. Algorithm efficiency is demonstrated for a massively parallel SIMD architecture (CM-5), and compatibility with MPP multiprocessor platforms or workstation clusters is anticipated.« less

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.

Improved Convergence and Robustness of USM3D Solutions on Mixed-Element Grids

NASA Technical Reports Server (NTRS)

Pandya, Mohagna J.; Diskin, Boris; Thomas, James L.; Frink, Neal T.

2016-01-01

Several improvements to the mixed-element USM3D discretization and defect-correction schemes have been made. A new methodology for nonlinear iterations, called the Hierarchical Adaptive Nonlinear Iteration Method, has been developed and implemented. The Hierarchical Adaptive Nonlinear Iteration Method provides two additional hierarchies around a simple and approximate preconditioner of USM3D. The hierarchies are a matrix-free linear solver for the exact linearization of Reynolds-averaged Navier-Stokes equations and a nonlinear control of the solution update. Two variants of the Hierarchical Adaptive Nonlinear Iteration Method are assessed on four benchmark cases, namely, a zero-pressure-gradient flat plate, a bump-in-channel configuration, the NACA 0012 airfoil, and a NASA Common Research Model configuration. The new methodology provides a convergence acceleration factor of 1.4 to 13 over the preconditioner-alone method representing the baseline solver technology.

Improved Convergence and Robustness of USM3D Solutions on Mixed-Element Grids

NASA Technical Reports Server (NTRS)

Pandya, Mohagna J.; Diskin, Boris; Thomas, James L.; Frinks, Neal T.

2016-01-01

Several improvements to the mixed-elementUSM3Ddiscretization and defect-correction schemes have been made. A new methodology for nonlinear iterations, called the Hierarchical Adaptive Nonlinear Iteration Method, has been developed and implemented. The Hierarchical Adaptive Nonlinear Iteration Method provides two additional hierarchies around a simple and approximate preconditioner of USM3D. The hierarchies are a matrix-free linear solver for the exact linearization of Reynolds-averaged Navier-Stokes equations and a nonlinear control of the solution update. Two variants of the Hierarchical Adaptive Nonlinear Iteration Method are assessed on four benchmark cases, namely, a zero-pressure-gradient flat plate, a bump-in-channel configuration, the NACA 0012 airfoil, and a NASA Common Research Model configuration. The new methodology provides a convergence acceleration factor of 1.4 to 13 over the preconditioner-alone method representing the baseline solver technology.

Log-Linear Modeling of Agreement among Expert Exposure Assessors

PubMed Central

Hunt, Phillip R.; Friesen, Melissa C.; Sama, Susan; Ryan, Louise; Milton, Donald

2015-01-01

Background: Evaluation of expert assessment of exposure depends, in the absence of a validation measurement, upon measures of agreement among the expert raters. Agreement is typically measured using Cohen’s Kappa statistic, however, there are some well-known limitations to this approach. We demonstrate an alternate method that uses log-linear models designed to model agreement. These models contain parameters that distinguish between exact agreement (diagonals of agreement matrix) and non-exact associations (off-diagonals). In addition, they can incorporate covariates to examine whether agreement differs across strata. Methods: We applied these models to evaluate agreement among expert ratings of exposure to sensitizers (none, likely, high) in a study of occupational asthma. Results: Traditional analyses using weighted kappa suggested potential differences in agreement by blue/white collar jobs and office/non-office jobs, but not case/control status. However, the evaluation of the covariates and their interaction terms in log-linear models found no differences in agreement with these covariates and provided evidence that the differences observed using kappa were the result of marginal differences in the distribution of ratings rather than differences in agreement. Differences in agreement were predicted across the exposure scale, with the likely moderately exposed category more difficult for the experts to differentiate from the highly exposed category than from the unexposed category. Conclusions: The log-linear models provided valuable information about patterns of agreement and the structure of the data that were not revealed in analyses using kappa. The models’ lack of dependence on marginal distributions and the ease of evaluating covariates allow reliable detection of observational bias in exposure data. PMID:25748517

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.

Matrix-Product-State Algorithm for Finite Fractional Quantum Hall Systems

NASA Astrophysics Data System (ADS)

Liu, Zhao; Bhatt, R. N.

2015-09-01

Exact diagonalization is a powerful tool to study fractional quantum Hall (FQH) systems. However, its capability is limited by the exponentially increasing computational cost. In order to overcome this difficulty, density-matrix-renormalization-group (DMRG) algorithms were developed for much larger system sizes. Very recently, it was realized that some model FQH states have exact matrix-product-state (MPS) representation. Motivated by this, here we report a MPS code, which is closely related to, but different from traditional DMRG language, for finite FQH systems on the cylinder geometry. By representing the many-body Hamiltonian as a matrix-product-operator (MPO) and using single-site update and density matrix correction, we show that our code can efficiently search the ground state of various FQH systems. We also compare the performance of our code with traditional DMRG. The possible generalization of our code to infinite FQH systems and other physical systems is also discussed.

(p,q) deformations and (p,q)-vector coherent states of the Jaynes-Cummings model in the rotating wave approximation

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

Ben Geloun, Joseph; Govaerts, Jan; Hounkonnou, M. Norbert

2007-03-15

Classes of (p,q) deformations of the Jaynes-Cummings model in the rotating wave approximation are considered. Diagonalization of the Hamiltonian is performed exactly, leading to useful spectral decompositions of a series of relevant operators. The latter include ladder operators acting between adjacent energy eigenstates within two separate infinite discrete towers, except for a singleton state. These ladder operators allow for the construction of (p,q)-deformed vector coherent states. Using (p,q) arithmetics, explicit and exact solutions to the associated moment problem are displayed, providing new classes of coherent states for such models. Finally, in the limit of decoupled spin sectors, our analysis translatesmore » into (p,q) deformations of the supersymmetric harmonic oscillator, such that the two supersymmetric sectors get intertwined through the action of the ladder operators as well as in the associated coherent states.« less

The difference between two random mixed quantum states: exact and asymptotic spectral analysis

NASA Astrophysics Data System (ADS)

Mejía, José; Zapata, Camilo; Botero, Alonso

2017-01-01

We investigate the spectral statistics of the difference of two density matrices, each of which is independently obtained by partially tracing a random bipartite pure quantum state. We first show how a closed-form expression for the exact joint eigenvalue probability density function for arbitrary dimensions can be obtained from the joint probability density function of the diagonal elements of the difference matrix, which is straightforward to compute. Subsequently, we use standard results from free probability theory to derive a relatively simple analytic expression for the asymptotic eigenvalue density (AED) of the difference matrix ensemble, and using Carlson’s theorem, we obtain an expression for its absolute moments. These results allow us to quantify the typical asymptotic distance between the two random mixed states using various distance measures; in particular, we obtain the almost sure asymptotic behavior of the operator norm distance and the trace distance.

Spatial correlations in driven-dissipative photonic lattices

NASA Astrophysics Data System (ADS)

Biondi, Matteo; Lienhard, Saskia; Blatter, Gianni; Türeci, Hakan E.; Schmidt, Sebastian

2017-12-01

We study the nonequilibrium steady-state of interacting photons in cavity arrays as described by the driven-dissipative Bose–Hubbard and spin-1/2 XY model. For this purpose, we develop a self-consistent expansion in the inverse coordination number of the array (∼ 1/z) to solve the Lindblad master equation of these systems beyond the mean-field approximation. Our formalism is compared and benchmarked with exact numerical methods for small systems based on an exact diagonalization of the Liouvillian and a recently developed corner-space renormalization technique. We then apply this method to obtain insights beyond mean-field in two particular settings: (i) we show that the gas–liquid transition in the driven-dissipative Bose–Hubbard model is characterized by large density fluctuations and bunched photon statistics. (ii) We study the antibunching–bunching transition of the nearest-neighbor correlator in the driven-dissipative spin-1/2 XY model and provide a simple explanation of this phenomenon.

Corner-corrected diagonal-norm summation-by-parts operators for the first derivative with increased order of accuracy

NASA Astrophysics Data System (ADS)

Del Rey Fernández, David C.; Boom, Pieter D.; Zingg, David W.

2017-02-01

Combined with simultaneous approximation terms, summation-by-parts (SBP) operators offer a versatile and efficient methodology that leads to consistent, conservative, and provably stable discretizations. However, diagonal-norm operators with a repeating interior-point operator that have thus far been constructed suffer from a loss of accuracy. While on the interior, these operators are of degree 2p, at a number of nodes near the boundaries, they are of degree p, and therefore of global degree p - meaning the highest degree monomial for which the operators are exact at all nodes. This implies that for hyperbolic problems and operators of degree greater than unity they lead to solutions with a global order of accuracy lower than the degree of the interior-point operator. In this paper, we develop a procedure to construct diagonal-norm first-derivative SBP operators that are of degree 2p at all nodes and therefore can lead to solutions of hyperbolic problems of order 2 p + 1. This is accomplished by adding nonzero entries in the upper-right and lower-left corners of SBP operator matrices with a repeating interior-point operator. This modification necessitates treating these new operators as elements, where mesh refinement is accomplished by increasing the number of elements in the mesh rather than increasing the number of nodes. The significant improvements in accuracy of this new family, for the same repeating interior-point operator, are demonstrated in the context of the linear convection equation.

Matrix-product-state method with local basis optimization for nonequilibrium electron-phonon systems

NASA Astrophysics Data System (ADS)

Heidrich-Meisner, Fabian; Brockt, Christoph; Dorfner, Florian; Vidmar, Lev; Jeckelmann, Eric

We present a method for simulating the time evolution of quasi-one-dimensional correlated systems with strongly fluctuating bosonic degrees of freedom (e.g., phonons) using matrix product states. For this purpose we combine the time-evolving block decimation (TEBD) algorithm with a local basis optimization (LBO) approach. We discuss the performance of our approach in comparison to TEBD with a bare boson basis, exact diagonalization, and diagonalization in a limited functional space. TEBD with LBO can reduce the computational cost by orders of magnitude when boson fluctuations are large and thus it allows one to investigate problems that are out of reach of other approaches. First, we test our method on the non-equilibrium dynamics of a Holstein polaron and show that it allows us to study the regime of strong electron-phonon coupling. Second, the method is applied to the scattering of an electronic wave packet off a region with electron-phonon coupling. Our study reveals a rich physics including transient self-trapping and dissipation. Supported by Deutsche Forschungsgemeinschaft (DFG) via FOR 1807.

Coherent optical excitations in superconducting qubit chain

NASA Astrophysics Data System (ADS)

Ian, Hou; Liu, Yu-Xi

2012-06-01

In the recent years, the theories of quantum optics have been borrowed to study the flows of electron pairs and their interactions with the circuit photon in the superconducting qubit circuits. These studies bring about new theories of quantum optics, such as the tunable electromagnetically induced transparency effect, peculiar to the Cooper pairs in circuits. In this talk, we focus on a special type of superconducting qubit circuits: superconducting qubit chain (SQC), which comprises dozens of qubits linearly placed along a stripline resonator. Since the dimensions of the qubits and the stripline have made their interactions inhomogeneous, the SQC cannot be diagonalized using the usual Dicke model. We present a new theoretical method, the deformation-projection method, for the exact diagonalization of the collective excitations of the qubits. This method allows us to predict that these excitations emulate the behaviors of Wannier and Frenckel excitons in the solid-state systems. The spontaneous emissions from the individual qubits in SQC are relayed to their neighbors, eventually arriving at a coherent emission, known as superradiance. We present a quantum relay model, which is crucial to quantum information processing, based on this finding.

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

Volkas, R. R.; Foot, R.; He, X.

The universal QCD color theory is extended to an SU(3)/sub 1//direct product/SU(3)/sub 2//direct product/SU(3)/sub 3/ gauge theory, where quarks of the /ital i/th generation transform as triplets under SU(3)/sub /ital i// and singlets under the other two factors. The usual color group is then identified with the diagonal subgroup, which remains exact after symmetry breaking. The gauge bosons associated with the 16 broken generators then form two massive octets under ordinary color. The interactions between quarks and these heavy gluonlike particles are explicitly nonuniversal and thus an exploration of their physical implications allows us to shed light on the fundamentalmore » issue of strong-interaction universality. Nonuniversality and weak flavor mixing are shown to generate heavy-gluon-induced flavor-changing neutral currents. The phenomenology of these processes is studied, as they provide the major experimental constraint on the extended theory. Three symmetry-breaking scenarios are presented. The first has color breaking occurring at the weak scale, while the second and third divorce the two scales. The third model has the interesting feature of radiatively induced off-diagonal Kobayashi-Maskawa matrix elements.« less

Anelastic sensitivity kernels with parsimonious storage for adjoint tomography and full waveform inversion

NASA Astrophysics Data System (ADS)

Komatitsch, Dimitri; Xie, Zhinan; Bozdaǧ, Ebru; Sales de Andrade, Elliott; Peter, Daniel; Liu, Qinya; Tromp, Jeroen

2016-09-01

We introduce a technique to compute exact anelastic sensitivity kernels in the time domain using parsimonious disk storage. The method is based on a reordering of the time loop of time-domain forward/adjoint wave propagation solvers combined with the use of a memory buffer. It avoids instabilities that occur when time-reversing dissipative wave propagation simulations. The total number of required time steps is unchanged compared to usual acoustic or elastic approaches. The cost is reduced by a factor of 4/3 compared to the case in which anelasticity is partially accounted for by accommodating the effects of physical dispersion. We validate our technique by performing a test in which we compare the Kα sensitivity kernel to the exact kernel obtained by saving the entire forward calculation. This benchmark confirms that our approach is also exact. We illustrate the importance of including full attenuation in the calculation of sensitivity kernels by showing significant differences with physical-dispersion-only kernels.

Toward an optimal solver for time-spectral fluid-dynamic and aeroelastic solutions on unstructured meshes

NASA Astrophysics Data System (ADS)

Mundis, Nathan L.; Mavriplis, Dimitri J.

2017-09-01

The time-spectral method applied to the Euler and coupled aeroelastic equations theoretically offers significant computational savings for purely periodic problems when compared to standard time-implicit methods. However, attaining superior efficiency with time-spectral methods over traditional time-implicit methods hinges on the ability rapidly to solve the large non-linear system resulting from time-spectral discretizations which become larger and stiffer as more time instances are employed or the period of the flow becomes especially short (i.e. the maximum resolvable wave-number increases). In order to increase the efficiency of these solvers, and to improve robustness, particularly for large numbers of time instances, the Generalized Minimal Residual Method (GMRES) is used to solve the implicit linear system over all coupled time instances. The use of GMRES as the linear solver makes time-spectral methods more robust, allows them to be applied to a far greater subset of time-accurate problems, including those with a broad range of harmonic content, and vastly improves the efficiency of time-spectral methods. In previous work, a wave-number independent preconditioner that mitigates the increased stiffness of the time-spectral method when applied to problems with large resolvable wave numbers has been developed. This preconditioner, however, directly inverts a large matrix whose size increases in proportion to the number of time instances. As a result, the computational time of this method scales as the cube of the number of time instances. In the present work, this preconditioner has been reworked to take advantage of an approximate-factorization approach that effectively decouples the spatial and temporal systems. Once decoupled, the time-spectral matrix can be inverted in frequency space, where it has entries only on the main diagonal and therefore can be inverted quite efficiently. This new GMRES/preconditioner combination is shown to be over an order of magnitude more efficient than the previous wave-number independent preconditioner for problems with large numbers of time instances and/or large reduced frequencies.

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.

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.

Semiclassical description of resonance-assisted tunneling in one-dimensional integrable models

NASA Astrophysics Data System (ADS)

Le Deunff, Jérémy; Mouchet, Amaury; Schlagheck, Peter

2013-10-01

Resonance-assisted tunneling is investigated within the framework of one-dimensional integrable systems. We present a systematic recipe, based on Hamiltonian normal forms, to construct one-dimensional integrable models that exhibit resonance island chain structures with accurately controlled sizes and positions of the islands. Using complex classical trajectories that evolve along suitably defined paths in the complex time domain, we construct a semiclassical theory of the resonance-assisted tunneling process. This semiclassical approach yields a compact analytical expression for tunnelling-induced level splittings which is found to be in very good agreement with the exact splittings obtained through numerical diagonalization.

Finite-size effects in Anderson localization of one-dimensional Bose-Einstein condensates

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

Cestari, J. C. C.; Foerster, A.; Gusmao, M. A.

We investigate the disorder-induced localization transition in Bose-Einstein condensates for the Anderson and Aubry-Andre models in the noninteracting limit using exact diagonalization. We show that, in addition to the standard superfluid fraction, other tools such as the entanglement and fidelity can provide clear signatures of the transition. Interestingly, the fidelity exhibits good sensitivity even for small lattices. Effects of the system size on these quantities are analyzed in detail, including the determination of a finite-size-scaling law for the critical disorder strength in the case of the Anderson model.

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.

Bound States in Dimerized and Frustrated Heisenberg Chains

NASA Astrophysics Data System (ADS)

Bouzerar, G.; Sil, S.

Using the Bond-Operator Technique (BOT), we have studied the low energy excitation spectrum of a frustrated dimerized antiferromagnetic Heisenberg chain. In particular, we have compared our analytical results with previous Exact Diagonalization (ED) data. Qualitatively, the BOT results are in good agreement with the ED data. And even a very good quantitative agreement is obtained in some parameter region. It is clearly shown that there is only one elementary excitation branch (lowest triplet branch) and that the two other well defined excitations which appear below the continuum, one singlet and one triplet, are bound states of two elementary triplets.

A SEMI-LAGRANGIAN TWO-LEVEL PRECONDITIONED NEWTON-KRYLOV SOLVER FOR CONSTRAINED DIFFEOMORPHIC IMAGE REGISTRATION.

PubMed

Mang, Andreas; Biros, George

2017-01-01

We propose an efficient numerical algorithm for the solution of diffeomorphic image registration problems. We use a variational formulation constrained by a partial differential equation (PDE), where the constraints are a scalar transport equation. We use a pseudospectral discretization in space and second-order accurate semi-Lagrangian time stepping scheme for the transport equations. We solve for a stationary velocity field using a preconditioned, globalized, matrix-free Newton-Krylov scheme. We propose and test a two-level Hessian preconditioner. We consider two strategies for inverting the preconditioner on the coarse grid: a nested preconditioned conjugate gradient method (exact solve) and a nested Chebyshev iterative method (inexact solve) with a fixed number of iterations. We test the performance of our solver in different synthetic and real-world two-dimensional application scenarios. We study grid convergence and computational efficiency of our new scheme. We compare the performance of our solver against our initial implementation that uses the same spatial discretization but a standard, explicit, second-order Runge-Kutta scheme for the numerical time integration of the transport equations and a single-level preconditioner. Our improved scheme delivers significant speedups over our original implementation. As a highlight, we observe a 20 × speedup for a two dimensional, real world multi-subject medical image registration problem.

An application of a two-equation model of turbulence to three-dimensional chemically reacting flows

NASA Technical Reports Server (NTRS)

Lee, J.

1994-01-01

A numerical study of three dimensional chemically reacting and non-reacting flowfields is conducted using a two-equation model of turbulence. A generalized flow solver using an implicit Lower-Upper (LU) diagonal decomposition numerical technique and finite-rate chemistry has been coupled with a low-Reynolds number two-equation model of turbulence. This flow solver is then used to study chemically reacting turbulent supersonic flows inside combustors with synergetic fuel injectors. The reacting and non-reacting turbulent combustor solutions obtained are compared with zero-equation turbulence model solutions and with available experimental data. The hydrogen-air chemistry is modeled using a nine-species/eighteen reaction model. A low-Reynolds number k-epsilon model was used to model the effect of turbulence because, in general, the low-Reynolds number k-epsilon models are easier to implement numerically and are far more general than algebraic models. However, low-Reynolds number k-epsilon models require a much finer near-wall grid resolution than high-Reynolds number models to resolve accurately the near-wall physics. This is especially true in complex flowfields, where the stiff nature of the near-wall turbulence must be resolved. Therefore, the limitations imposed by the near-wall characteristics and compressible model corrections need to be evaluated further. The gradient-diffusion hypothesis is used to model the effects of turbulence on the mass diffusion process. The influence of this low-Reynolds number turbulence model on the reacting flowfield predictions was studied parametrically.

A mixed fluid-kinetic solver for the Vlasov-Poisson equations

NASA Astrophysics Data System (ADS)

Cheng, Yongtao

Plasmas are ionized gases that appear in a wide range of applications including astrophysics and space physics, as well as in laboratory settings such as in magnetically confined fusion. There are two prevailing types of modeling strategies to describe a plasma system: kinetic models and fluid models. Kinetic models evolve particle probability density distributions (PDFs) in phase space, which are accurate but computationally expensive. Fluid models evolve a small number of moments of the distribution function and reduce the dimension of the solution. However, some approximation is necessary to close the system, and finding an accurate moment closure that correctly captures the dynamics away from thermodynamic equilibrium is a difficult and still open problem. The main contributions of the present work can be divided into two main parts: (1) a new class of moment closures, based on a modification of existing quadrature-based moment-closure methods, is developed using bi-B-spline and bi-bubble representations; and (2) a novel mixed solver that combines a fluid and a kinetic solver is proposed, which uses the new class of moment-closure methods described in the first part. For the newly developed quadrature-based moment-closure based on bi-B-spline and bi-bubble representation, the explicit form of flux terms and the moment-realizability conditions are given. It is shown that while the bi-delta system is weakly hyperbolic, the newly proposed fluid models are strongly hyperbolic. Using a high-order Runge-Kutta discontinuous Galerkin method together with Strang operator splitting, the resulting models are applied to the Vlasov-Poisson-Fokker-Planck system in the high field limit. In the second part of this work, results from kinetic solver are used to provide a corrected closure to the fluid model. This correction keeps the fluid model hyperbolic and gives fluid results that match the moments as computed from the kinetic solution. Furthermore, a prolongation operation based on the bi-bubble moment-closure is used to make the first few moments of the kinetic and fluid solvers match. This results in a kinetic solver that exactly conserves mass and total energy. This mixed fluid-kinetic solver is applied to standard test problems for the Vlasov-Poisson system, including two-stream-instability problem and Landau damping.

Generalized approximate spin projection calculations of effective exchange integrals of the CaMn4O5 cluster in the S1 and S3 states of the oxygen evolving complex of photosystem II.

PubMed

Isobe, H; Shoji, M; Yamanaka, S; Mino, H; Umena, Y; Kawakami, K; Kamiya, N; Shen, J-R; Yamaguchi, K

2014-06-28

Full geometry optimizations followed by the vibrational analysis were performed for eight spin configurations of the CaMn4O4X(H2O)3Y (X = O, OH; Y = H2O, OH) cluster in the S1 and S3 states of the oxygen evolution complex (OEC) of photosystem II (PSII). The energy gaps among these configurations obtained by vertical, adiabatic and adiabatic plus zero-point-energy (ZPE) correction procedures have been used for computation of the effective exchange integrals (J) in the spin Hamiltonian model. The J values are calculated by the (1) analytical method and the (2) generalized approximate spin projection (AP) method that eliminates the spin contamination errors of UB3LYP solutions. Using J values derived from these methods, exact diagonalization of the spin Hamiltonian matrix was carried out, yielding excitation energies and spin densities of the ground and lower-excited states of the cluster. The obtained results for the right (R)- and left (L)-opened structures in the S1 and S3 states are found to be consistent with available optical and magnetic experimental results. Implications of the computational results are discussed in relation to (a) the necessity of the exact diagonalization for computations of reliable energy levels, (b) magneto-structural correlations in the CaMn4O5 cluster of the OEC of PSII, (c) structural symmetry breaking in the S1 and S3 states, and (d) the right- and left-handed scenarios for the O-O bond formation for water oxidation.

Local error estimates for adaptive simulation of the Reaction–Diffusion Master Equation via operator splitting

PubMed Central

Hellander, Andreas; Lawson, Michael J; Drawert, Brian; Petzold, Linda

2015-01-01

The efficiency of exact simulation methods for the reaction-diffusion master equation (RDME) is severely limited by the large number of diffusion events if the mesh is fine or if diffusion constants are large. Furthermore, inherent properties of exact kinetic-Monte Carlo simulation methods limit the efficiency of parallel implementations. Several approximate and hybrid methods have appeared that enable more efficient simulation of the RDME. A common feature to most of them is that they rely on splitting the system into its reaction and diffusion parts and updating them sequentially over a discrete timestep. This use of operator splitting enables more efficient simulation but it comes at the price of a temporal discretization error that depends on the size of the timestep. So far, existing methods have not attempted to estimate or control this error in a systematic manner. This makes the solvers hard to use for practitioners since they must guess an appropriate timestep. It also makes the solvers potentially less efficient than if the timesteps are adapted to control the error. Here, we derive estimates of the local error and propose a strategy to adaptively select the timestep when the RDME is simulated via a first order operator splitting. While the strategy is general and applicable to a wide range of approximate and hybrid methods, we exemplify it here by extending a previously published approximate method, the Diffusive Finite-State Projection (DFSP) method, to incorporate temporal adaptivity. PMID:26865735

CHOLLA: A New Massively Parallel Hydrodynamics Code for Astrophysical Simulation

NASA Astrophysics Data System (ADS)

Schneider, Evan E.; Robertson, Brant E.

2015-04-01

We present Computational Hydrodynamics On ParaLLel Architectures (Cholla ), a new three-dimensional hydrodynamics code that harnesses the power of graphics processing units (GPUs) to accelerate astrophysical simulations. Cholla models the Euler equations on a static mesh using state-of-the-art techniques, including the unsplit Corner Transport Upwind algorithm, a variety of exact and approximate Riemann solvers, and multiple spatial reconstruction techniques including the piecewise parabolic method (PPM). Using GPUs, Cholla evolves the fluid properties of thousands of cells simultaneously and can update over 10 million cells per GPU-second while using an exact Riemann solver and PPM reconstruction. Owing to the massively parallel architecture of GPUs and the design of the Cholla code, astrophysical simulations with physically interesting grid resolutions (≳2563) can easily be computed on a single device. We use the Message Passing Interface library to extend calculations onto multiple devices and demonstrate nearly ideal scaling beyond 64 GPUs. A suite of test problems highlights the physical accuracy of our modeling and provides a useful comparison to other codes. We then use Cholla to simulate the interaction of a shock wave with a gas cloud in the interstellar medium, showing that the evolution of the cloud is highly dependent on its density structure. We reconcile the computed mixing time of a turbulent cloud with a realistic density distribution destroyed by a strong shock with the existing analytic theory for spherical cloud destruction by describing the system in terms of its median gas density.

Local error estimates for adaptive simulation of the Reaction-Diffusion Master Equation via operator splitting.

PubMed

Hellander, Andreas; Lawson, Michael J; Drawert, Brian; Petzold, Linda

2014-06-01

The efficiency of exact simulation methods for the reaction-diffusion master equation (RDME) is severely limited by the large number of diffusion events if the mesh is fine or if diffusion constants are large. Furthermore, inherent properties of exact kinetic-Monte Carlo simulation methods limit the efficiency of parallel implementations. Several approximate and hybrid methods have appeared that enable more efficient simulation of the RDME. A common feature to most of them is that they rely on splitting the system into its reaction and diffusion parts and updating them sequentially over a discrete timestep. This use of operator splitting enables more efficient simulation but it comes at the price of a temporal discretization error that depends on the size of the timestep. So far, existing methods have not attempted to estimate or control this error in a systematic manner. This makes the solvers hard to use for practitioners since they must guess an appropriate timestep. It also makes the solvers potentially less efficient than if the timesteps are adapted to control the error. Here, we derive estimates of the local error and propose a strategy to adaptively select the timestep when the RDME is simulated via a first order operator splitting. While the strategy is general and applicable to a wide range of approximate and hybrid methods, we exemplify it here by extending a previously published approximate method, the Diffusive Finite-State Projection (DFSP) method, to incorporate temporal adaptivity.

Improving Transportation Services for the University of the Thai Chamber of Commerce: A Case Study on Solving the Mixed-Fleet Vehicle Routing Problem with Split Deliveries

NASA Astrophysics Data System (ADS)

Suthikarnnarunai, N.; Olinick, E.

2009-01-01

We present a case study on the application of techniques for solving the Vehicle Routing Problem (VRP) to improve the transportation service provided by the University of The Thai Chamber of Commerce to its staff. The problem is modeled as VRP with time windows, split deliveries, and a mixed fleet. An exact algorithm and a heuristic solution procedure are developed to solve the problem and implemented in the AMPL modeling language and CPLEX Integer Programming solver. Empirical results indicate that the heuristic can find relatively good solutions in a small fraction of the time required by the exact method. We also perform sensitivity analysis and find that a savings in outsourcing cost can be achieved with a small increase in vehicle capacity.

Reliable and efficient solution of genome-scale models of Metabolism and macromolecular Expression

DOE PAGES

Ma, Ding; Yang, Laurence; Fleming, Ronan M. T.; ...

2017-01-18

Currently, Constraint-Based Reconstruction and Analysis (COBRA) is the only methodology that permits integrated modeling of Metabolism and macromolecular Expression (ME) at genome-scale. Linear optimization computes steady-state flux solutions to ME models, but flux values are spread over many orders of magnitude. Data values also have greatly varying magnitudes. Furthermore, standard double-precision solvers may return inaccurate solutions or report that no solution exists. Exact simplex solvers based on rational arithmetic require a near-optimal warm start to be practical on large problems (current ME models have 70,000 constraints and variables and will grow larger). We also developed a quadrupleprecision version of ourmore » linear and nonlinear optimizer MINOS, and a solution procedure (DQQ) involving Double and Quad MINOS that achieves reliability and efficiency for ME models and other challenging problems tested here. DQQ will enable extensive use of large linear and nonlinear models in systems biology and other applications involving multiscale data.« less

Reliable and efficient solution of genome-scale models of Metabolism and macromolecular Expression

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

Ma, Ding; Yang, Laurence; Fleming, Ronan M. T.

Currently, Constraint-Based Reconstruction and Analysis (COBRA) is the only methodology that permits integrated modeling of Metabolism and macromolecular Expression (ME) at genome-scale. Linear optimization computes steady-state flux solutions to ME models, but flux values are spread over many orders of magnitude. Data values also have greatly varying magnitudes. Furthermore, standard double-precision solvers may return inaccurate solutions or report that no solution exists. Exact simplex solvers based on rational arithmetic require a near-optimal warm start to be practical on large problems (current ME models have 70,000 constraints and variables and will grow larger). We also developed a quadrupleprecision version of ourmore » linear and nonlinear optimizer MINOS, and a solution procedure (DQQ) involving Double and Quad MINOS that achieves reliability and efficiency for ME models and other challenging problems tested here. DQQ will enable extensive use of large linear and nonlinear models in systems biology and other applications involving multiscale data.« less

Many-body Green’s function theory for electron-phonon interactions: Ground state properties of the Holstein dimer

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

Säkkinen, Niko; Leeuwen, Robert van; Peng, Yang

2015-12-21

We study ground-state properties of a two-site, two-electron Holstein model describing two molecules coupled indirectly via electron-phonon interaction by using both exact diagonalization and self-consistent diagrammatic many-body perturbation theory. The Hartree and self-consistent Born approximations used in the present work are studied at different levels of self-consistency. The governing equations are shown to exhibit multiple solutions when the electron-phonon interaction is sufficiently strong, whereas at smaller interactions, only a single solution is found. The additional solutions at larger electron-phonon couplings correspond to symmetry-broken states with inhomogeneous electron densities. A comparison to exact results indicates that this symmetry breaking is stronglymore » correlated with the formation of a bipolaron state in which the two electrons prefer to reside on the same molecule. The results further show that the Hartree and partially self-consistent Born solutions obtained by enforcing symmetry do not compare well with exact energetics, while the fully self-consistent Born approximation improves the qualitative and quantitative agreement with exact results in the same symmetric case. This together with a presented natural occupation number analysis supports the conclusion that the fully self-consistent approximation describes partially the bipolaron crossover. These results contribute to better understanding how these approximations cope with the strong localizing effect of the electron-phonon interaction.« 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.

AFMPB: An adaptive fast multipole Poisson-Boltzmann solver for calculating electrostatics in biomolecular systems

NASA Astrophysics Data System (ADS)

Lu, Benzhuo; Cheng, Xiaolin; Huang, Jingfang; McCammon, J. Andrew

2010-06-01

A Fortran program package is introduced for rapid evaluation of the electrostatic potentials and forces in biomolecular systems modeled by the linearized Poisson-Boltzmann equation. The numerical solver utilizes a well-conditioned boundary integral equation (BIE) formulation, a node-patch discretization scheme, a Krylov subspace iterative solver package with reverse communication protocols, and an adaptive new version of fast multipole method in which the exponential expansions are used to diagonalize the multipole-to-local translations. The program and its full description, as well as several closely related libraries and utility tools are available at http://lsec.cc.ac.cn/~lubz/afmpb.html and a mirror site at http://mccammon.ucsd.edu/. This paper is a brief summary of the program: the algorithms, the implementation and the usage. Program summaryProgram title: AFMPB: Adaptive fast multipole Poisson-Boltzmann solver Catalogue identifier: AEGB_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEGB_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: GPL 2.0 No. of lines in distributed program, including test data, etc.: 453 649 No. of bytes in distributed program, including test data, etc.: 8 764 754 Distribution format: tar.gz Programming language: Fortran Computer: Any Operating system: Any RAM: Depends on the size of the discretized biomolecular system Classification: 3 External routines: Pre- and post-processing tools are required for generating the boundary elements and for visualization. Users can use MSMS ( http://www.scripps.edu/~sanner/html/msms_home.html) for pre-processing, and VMD ( http://www.ks.uiuc.edu/Research/vmd/) for visualization. Sub-programs included: An iterative Krylov subspace solvers package from SPARSKIT by Yousef Saad ( http://www-users.cs.umn.edu/~saad/software/SPARSKIT/sparskit.html), and the fast multipole methods subroutines from FMMSuite ( http://www.fastmultipole.org/). Nature of problem: Numerical solution of the linearized Poisson-Boltzmann equation that describes electrostatic interactions of molecular systems in ionic solutions. Solution method: A novel node-patch scheme is used to discretize the well-conditioned boundary integral equation formulation of the linearized Poisson-Boltzmann equation. Various Krylov subspace solvers can be subsequently applied to solve the resulting linear system, with a bounded number of iterations independent of the number of discretized unknowns. The matrix-vector multiplication at each iteration is accelerated by the adaptive new versions of fast multipole methods. The AFMPB solver requires other stand-alone pre-processing tools for boundary mesh generation, post-processing tools for data analysis and visualization, and can be conveniently coupled with different time stepping methods for dynamics simulation. Restrictions: Only three or six significant digits options are provided in this version. Unusual features: Most of the codes are in Fortran77 style. Memory allocation functions from Fortran90 and above are used in a few subroutines. Additional comments: The current version of the codes is designed and written for single core/processor desktop machines. Check http://lsec.cc.ac.cn/~lubz/afmpb.html and http://mccammon.ucsd.edu/ for updates and changes. Running time: The running time varies with the number of discretized elements ( N) in the system and their distributions. In most cases, it scales linearly as a function of N.

Yet another family of diagonal metrics for de Sitter and anti-de Sitter spacetimes

NASA Astrophysics Data System (ADS)

Podolský, Jiří; Hruška, Ondřej

2017-06-01

In this work we present and analyze a new class of coordinate representations of de Sitter and anti-de Sitter spacetimes for which the metrics are diagonal and (typically) static and axially symmetric. Contrary to the well-known forms of these fundamental geometries, that usually correspond to a 1 +3 foliation with the 3-space of a constant spatial curvature, the new metrics are adapted to a 2 +2 foliation, and are warped products of two 2-spaces of constant curvature. This new class of (anti-)de Sitter metrics depends on the value of cosmological constant Λ and two discrete parameters +1 ,0 ,-1 related to the curvature of the 2-spaces. The class admits 3 distinct subcases for Λ >0 and 8 subcases for Λ <0 . We systematically study all these possibilities. In particular, we explicitly present the corresponding parametrizations of the (anti-)de Sitter hyperboloid, visualize the coordinate lines and surfaces within the global conformal cylinder, investigate their mutual relations, present some closely related forms of the metrics, and give transformations to standard de Sitter and anti-de Sitter metrics. Using these results, we also provide a physical interpretation of B -metrics as exact gravitational fields of a tachyon.

A new family of high-order compact upwind difference schemes with good spectral resolution

NASA Astrophysics Data System (ADS)

Zhou, Qiang; Yao, Zhaohui; He, Feng; Shen, M. Y.

2007-12-01

This paper presents a new family of high-order compact upwind difference schemes. Unknowns included in the proposed schemes are not only the values of the function but also those of its first and higher derivatives. Derivative terms in the schemes appear only on the upwind side of the stencil. One can calculate all the first derivatives exactly as one solves explicit schemes when the boundary conditions of the problem are non-periodic. When the proposed schemes are applied to periodic problems, only periodic bi-diagonal matrix inversions or periodic block-bi-diagonal matrix inversions are required. Resolution optimization is used to enhance the spectral representation of the first derivative, and this produces a scheme with the highest spectral accuracy among all known compact schemes. For non-periodic boundary conditions, boundary schemes constructed in virtue of the assistant scheme make the schemes not only possess stability for any selective length scale on every point in the computational domain but also satisfy the principle of optimal resolution. Also, an improved shock-capturing method is developed. Finally, both the effectiveness of the new hybrid method and the accuracy of the proposed schemes are verified by executing four benchmark test cases.

Quantum critical spin-2 chain with emergent SU(3) symmetry.

PubMed

Chen, Pochung; Xue, Zhi-Long; McCulloch, I P; Chung, Ming-Chiang; Huang, Chao-Chun; Yip, S-K

2015-04-10

We study the quantum critical phase of an SU(2) symmetric spin-2 chain obtained from spin-2 bosons in a one-dimensional lattice. We obtain the scaling of the finite-size energies and entanglement entropy by exact diagonalization and density-matrix renormalization group methods. From the numerical results of the energy spectra, central charge, and scaling dimension we identify the conformal field theory describing the whole critical phase to be the SU(3)_{1} Wess-Zumino-Witten model. We find that, while the Hamiltonian is only SU(2) invariant, in this critical phase there is an emergent SU(3) symmetry in the thermodynamic limit.

Experimental observation of the 1/3 magnetization plateau in the diamond-chain compound Cu3(CO3)2(OH)2.

PubMed

Kikuchi, H; Fujii, Y; Chiba, M; Mitsudo, S; Idehara, T; Tonegawa, T; Okamoto, K; Sakai, T; Kuwai, T; Ohta, H

2005-06-10

The magnetic susceptibility, high field magnetization, and specific heat measurements of Cu3(CO3)2(OH)2, which is a model substance for the frustrating diamond spin chain model, have been performed using single crystals. Two broad peaks are observed at around 20 and 5 K in both magnetic susceptibility and specific heat results. The magnetization curve has a clear plateau at one third of the saturation magnetization. The experimental results are examined in terms of theoretical expectations based on exact diagonalization and density matrix renormalization group methods. An origin of magnetic anisotropy is also discussed.

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.

Duality-mediated critical amplitude ratios for the (2 + 1)-dimensional S = 1XY model

NASA Astrophysics Data System (ADS)

Nishiyama, Yoshihiro

2017-09-01

The phase transition for the (2 + 1)-dimensional spin-S = 1XY model was investigated numerically. Because of the boson-vortex duality, the spin stiffness ρs in the ordered phase and the vortex-condensate stiffness ρv in the disordered phase should have a close relationship. We employed the exact diagonalization method, which yields the excitation gap directly. As a result, we estimate the amplitude ratios ρs,v/Δ (Δ: Mott insulator gap) by means of the scaling analyses for the finite-size cluster with N ≤ 22 spins. The ratio ρs/ρv admits a quantitative measure of deviation from selfduality.

Interband excitations in the 1D limit of two-band fractional Chern insulators

NASA Astrophysics Data System (ADS)

Jaworowski, Błażej; Kaczmarkiewicz, Piotr; Potasz, Paweł; Wójs, Arkadiusz

2018-05-01

We investigate the stability of the one-dimensional limit of ν = 1 / 3 Laughlin-like fractional Chern insulator with respect to the interband interaction. We propose a construction for the excitations in the infinite-interaction case and show that the energy gap remains finite in the thermodynamic limit. Next, by means of exact diagonalization and Density Matrix Renormalization Group approaches, we consider deviations from ideal dimerization and show that they reduce the stability of the FCI-like states. Finally, to show that our approach is not restricted to one model, we identify the dimer structure behind the thin-torus limit of other system - the checkerboard lattice.

Fidelity Study of Superconductivity in Extended Hubbard Models

NASA Astrophysics Data System (ADS)

Plonka, Nachum; Jia, Chunjing; Moritz, Brian; Wang, Yao; Devereaux, Thomas

2015-03-01

The role of strong electronic correlations on unconventional superconductivity remains an important open question. Here, we explore the influence of long-range Coulomb interactions, present in real material systems, through nearest and next-nearest neighbor extended Hubbard interactions in addition to the usual on-site terms. Utilizing large scale, numerical exact diagonalization, we analyze the signatures of superconductivity in the ground states through the fidelity metric of quantum information theory. We find that these extended interactions enhance charge fluctuations with various wave vectors. These suppress superconductivity in general, but in certain parameter regimes superconductivity is sustained. This has implications for tuning extended interactions in real materials.

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.

A wideband FMBEM for 2D acoustic design sensitivity analysis based on direct differentiation method

NASA Astrophysics Data System (ADS)

Chen, Leilei; Zheng, Changjun; Chen, Haibo

2013-09-01

This paper presents a wideband fast multipole boundary element method (FMBEM) for two dimensional acoustic design sensitivity analysis based on the direct differentiation method. The wideband fast multipole method (FMM) formed by combining the original FMM and the diagonal form FMM is used to accelerate the matrix-vector products in the boundary element analysis. The Burton-Miller formulation is used to overcome the fictitious frequency problem when using a single Helmholtz boundary integral equation for exterior boundary-value problems. The strongly singular and hypersingular integrals in the sensitivity equations can be evaluated explicitly and directly by using the piecewise constant discretization. The iterative solver GMRES is applied to accelerate the solution of the linear system of equations. A set of optimal parameters for the wideband FMBEM design sensitivity analysis are obtained by observing the performances of the wideband FMM algorithm in terms of computing time and memory usage. Numerical examples are presented to demonstrate the efficiency and validity of the proposed algorithm.

Development of advanced Navier-Stokes solver

NASA Technical Reports Server (NTRS)

Yoon, Seokkwan

1994-01-01

The objective of research was to develop and validate new computational algorithms for solving the steady and unsteady Euler and Navier-Stokes equations. The end-products are new three-dimensional Euler and Navier-Stokes codes that are faster, more reliable, more accurate, and easier to use. The three-dimensional Euler and full/thin-layer Reynolds-averaged Navier-Stokes equations for compressible/incompressible flows are solved on structured hexahedral grids. The Baldwin-Lomax algebraic turbulence model is used for closure. The space discretization is based on a cell-centered finite-volume method augmented by a variety of numerical dissipation models with optional total variation diminishing limiters. The governing equations are integrated in time by an implicit method based on lower-upper factorization and symmetric Gauss-Seidel relaxation. The algorithm is vectorized on diagonal planes of sweep using two-dimensional indices in three dimensions. Convergence rates and the robustness of the codes are enhanced by the use of an implicit full approximation storage multigrid method.

Kinetics of the electric double layer formation modelled by the finite difference method

NASA Astrophysics Data System (ADS)

Valent, Ivan

2017-11-01

Dynamics of the elctric double layer formation in 100 mM NaCl solution for sudden potentail steps of 10 and 20 mV was simulated using the Poisson-Nernst-Planck theory and VLUGR2 solver for partial differential equations. The used approach was verified by comparing the obtained steady-state solution with the available exact solution. The simulations allowed for detailed analysis of the relaxation processes of the individual ions and the electric potential. Some computational aspects of the problem were discussed.

Connected and disconnected contributions to nucleon axial form factors using Nf = 2 twisted mass fermions at the physical point

NASA Astrophysics Data System (ADS)

Alexandrou, Constantia; Constantinou, Martha; Hadjiyiannakou, Kyriakos; Jansen, Karl; Kallidonis, Christos; Koutsou, Giannis; Vaquero Avilés-Casco, Alejandro

2018-03-01

We present results on the isovector and isoscalar nucleon axial form factors including disconnected contributions, using an ensemble of Nf = 2 twisted mass cloverimproved Wilson fermions simulated with approximately the physical value of the pion mass. The light disconnected quark loops are computed using exact deflation, while the strange and the charm quark loops are evaluated using the truncated solver method. Techniques such as the summation and the two-state fits have been employed to access ground-state dominance.

Lagrangian solution of supersonic real gas flows

NASA Technical Reports Server (NTRS)

Loh, Ching-Yuen; Liou, Meng-Sing

1993-01-01

The present extention of a Lagrangian approach of the Riemann solution procedure, which was originally proposed for perfect gases, to real gases, is nontrivial and requires the development of an exact real-gas Riemann solver for the Lagrangian form of the conservation laws. Calculations including complex wave interactions of various types were conducted to test the accuracy and robustness of the approach. Attention is given to the case of 2D oblique waves' capture, where a slip line is clearly in evidence; the real gas effect is demonstrated in the case of a generic engine nozzle.

Ignition of detonation in accreted helium envelopes

NASA Astrophysics Data System (ADS)

Glasner, S. Ami; Livne, E.; Steinberg, E.; Yalinewich, A.; Truran, James W.

2018-05-01

Sub-Chandrasekhar CO white dwarfs accreting helium have been considered as candidates for Type Ia supernova (SNIa) progenitors since the early 1980s (helium shell mass >0.1 M⊙). These models, once detonated, did not fit the observed spectra and light curve of typical SNIa observations. New theoretical work examined detonations on much less massive (<0.05 M⊙) envelopes. They find stable detonations that lead to light curves, spectra, and abundances that compare relatively well with the observational data. The exact mechanism leading to the ignition of helium detonation is a key issue, since it is a mandatory first step for the whole scenario. As the flow of the accreted envelope is unstable to convection long before any hydrodynamic phenomena develops, a multidimensional approach is needed in order to study the ignition process. The complex convective reactive flow is challenging to any hydrodynamical solver. To the best of our knowledge, all previous 2D studies ignited the detonation artificially. We present here, for the first time, fully consistent results from two hydrodynamical 2D solvers that adopt two independent accurate schemes. For both solvers, an effort was made to overcome the problematics raised by the finite resolution and numerical diffusion by the advective terms. Our best models lead to the ignition of a detonation in a convective cell. Our results are robust and the agreement between the two different numerical approaches is very good.

FWT2D: A massively parallel program for frequency-domain full-waveform tomography of wide-aperture seismic data—Part 1: Algorithm

NASA Astrophysics Data System (ADS)

Sourbier, Florent; Operto, Stéphane; Virieux, Jean; Amestoy, Patrick; L'Excellent, Jean-Yves

2009-03-01

This is the first paper in a two-part series that describes a massively parallel code that performs 2D frequency-domain full-waveform inversion of wide-aperture seismic data for imaging complex structures. Full-waveform inversion methods, namely quantitative seismic imaging methods based on the resolution of the full wave equation, are computationally expensive. Therefore, designing efficient algorithms which take advantage of parallel computing facilities is critical for the appraisal of these approaches when applied to representative case studies and for further improvements. Full-waveform modelling requires the resolution of a large sparse system of linear equations which is performed with the massively parallel direct solver MUMPS for efficient multiple-shot simulations. Efficiency of the multiple-shot solution phase (forward/backward substitutions) is improved by using the BLAS3 library. The inverse problem relies on a classic local optimization approach implemented with a gradient method. The direct solver returns the multiple-shot wavefield solutions distributed over the processors according to a domain decomposition driven by the distribution of the LU factors. The domain decomposition of the wavefield solutions is used to compute in parallel the gradient of the objective function and the diagonal Hessian, this latter providing a suitable scaling of the gradient. The algorithm allows one to test different strategies for multiscale frequency inversion ranging from successive mono-frequency inversion to simultaneous multifrequency inversion. These different inversion strategies will be illustrated in the following companion paper. The parallel efficiency and the scalability of the code will also be quantified.

An Adaptively-Refined, Cartesian, Cell-Based Scheme for the Euler and Navier-Stokes Equations. Ph.D. Thesis - Michigan Univ.

NASA Technical Reports Server (NTRS)

Coirier, William John

1994-01-01

A Cartesian, cell-based scheme for solving the Euler and Navier-Stokes equations in two dimensions is developed and tested. Grids about geometrically complicated bodies are generated automatically, by recursive subdivision of a single Cartesian cell encompassing the entire flow domain. Where the resulting cells intersect bodies, polygonal 'cut' cells are created. The geometry of the cut cells is computed using polygon-clipping algorithms. The grid is stored in a binary-tree data structure which provides a natural means of obtaining cell-to-cell connectivity and of carrying out solution-adaptive refinement. The Euler and Navier-Stokes equations are solved on the resulting grids using a finite-volume formulation. The convective terms are upwinded, with a limited linear reconstruction of the primitive variables used to provide input states to an approximate Riemann solver for computing the fluxes between neighboring cells. A multi-stage time-stepping scheme is used to reach a steady-state solution. Validation of the Euler solver with benchmark numerical and exact solutions is presented. An assessment of the accuracy of the approach is made by uniform and adaptive grid refinements for a steady, transonic, exact solution to the Euler equations. The error of the approach is directly compared to a structured solver formulation. A non smooth flow is also assessed for grid convergence, comparing uniform and adaptively refined results. Several formulations of the viscous terms are assessed analytically, both for accuracy and positivity. The two best formulations are used to compute adaptively refined solutions of the Navier-Stokes equations. These solutions are compared to each other, to experimental results and/or theory for a series of low and moderate Reynolds numbers flow fields. The most suitable viscous discretization is demonstrated for geometrically-complicated internal flows. For flows at high Reynolds numbers, both an altered grid-generation procedure and a different formulation of the viscous terms are shown to be necessary. A hybrid Cartesian/body-fitted grid generation approach is demonstrated. In addition, a grid-generation procedure based on body-aligned cell cutting coupled with a viscous stensil-construction procedure based on quadratic programming is presented.

Uni-directional optical pulses, temporal propagation, and spatial and temporal dispersion

NASA Astrophysics Data System (ADS)

Kinsler, P.

2018-02-01

I derive a temporally propagated uni-directional optical pulse equation valid in the few cycle limit. Temporal propagation is advantageous because it naturally preserves causality, unlike the competing spatially propagated models. The exact coupled bi-directional equations that this approach generates can be efficiently approximated down to a uni-directional form in cases where an optical pulse changes little over one optical cycle. They also permit a direct term-to-term comparison of the exact bi-directional theory with its corresponding approximate uni-directional theory. Notably, temporal propagation handles dispersion in a different way, and this difference serves to highlight existing approximations inherent in spatially propagated treatments of dispersion. Accordingly, I emphasise the need for future work in clarifying the limitations of the dispersion conversion required by these types of approaches; since the only alternative in the few cycle limit may be to resort to the much more computationally intensive full Maxwell equation solvers.

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.

Patch planting of hard spin-glass problems: Getting ready for the next generation of optimization approaches

NASA Astrophysics Data System (ADS)

Wang, Wenlong; Mandrà, Salvatore; Katzgraber, Helmut

We propose a patch planting heuristic that allows us to create arbitrarily-large Ising spin-glass instances on any topology and with any type of disorder, and where the exact ground-state energy of the problem is known by construction. By breaking up the problem into patches that can be treated either with exact or heuristic solvers, we can reconstruct the optimum of the original, considerably larger, problem. The scaling of the computational complexity of these instances with various patch numbers and sizes is investigated and compared with random instances using population annealing Monte Carlo and quantum annealing on the D-Wave 2X quantum annealer. The method can be useful for benchmarking of novel computing technologies and algorithms. NSF-DMR-1208046 and the Office of the Director of National Intelligence (ODNI), Intelligence Advanced Research Projects Activity (IARPA), via MIT Lincoln Laboratory Air Force Contract No. FA8721-05-C-0002.

Efficient steady-state solver for hierarchical quantum master equations

NASA Astrophysics Data System (ADS)

Zhang, Hou-Dao; Qiao, Qin; Xu, Rui-Xue; Zheng, Xiao; Yan, YiJing

2017-07-01

Steady states play pivotal roles in many equilibrium and non-equilibrium open system studies. Their accurate evaluations call for exact theories with rigorous treatment of system-bath interactions. Therein, the hierarchical equations-of-motion (HEOM) formalism is a nonperturbative and non-Markovian quantum dissipation theory, which can faithfully describe the dissipative dynamics and nonlinear response of open systems. Nevertheless, solving the steady states of open quantum systems via HEOM is often a challenging task, due to the vast number of dynamical quantities involved. In this work, we propose a self-consistent iteration approach that quickly solves the HEOM steady states. We demonstrate its high efficiency with accurate and fast evaluations of low-temperature thermal equilibrium of a model Fenna-Matthews-Olson pigment-protein complex. Numerically exact evaluation of thermal equilibrium Rényi entropies and stationary emission line shapes is presented with detailed discussion.

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.

THOR: an open-source exo-GCM

NASA Astrophysics Data System (ADS)

Grosheintz, Luc; Mendonça, João; Käppeli, Roger; Lukas Grimm, Simon; Mishra, Siddhartha; Heng, Kevin

2015-12-01

In this talk, I will present THOR, the first fully conservative, GPU-accelerated exo-GCM (general circulation model) on a nearly uniform, global grid that treats shocks and is non-hydrostatic. THOR will be freely available to the community as a standard tool.Unlike most GCMs THOR solves the full, non-hydrostatic Euler equations instead of the primitive equations. The equations are solved on a global three-dimensional icosahedral grid by a second order Finite Volume Method (FVM). Icosahedral grids are nearly uniform refinements of an icosahedron. We've implemented three different versions of this grid. FVM conserves the prognostic variables (density, momentum and energy) exactly and doesn't require a diffusion term (artificial viscosity) in the Euler equations to stabilize our solver. Historically FVM was designed to treat discontinuities correctly. Hence it excels at resolving shocks, including those present in hot exoplanetary atmospheres.Atmospheres are generally in near hydrostatic equilibrium. We therefore implement a well-balancing technique recently developed at the ETH Zurich. This well-balancing ensures that our FVM maintains hydrostatic equilibrium to machine precision. Better yet, it is able to resolve pressure perturbations from this equilibrium as small as one part in 100'000. It is important to realize that these perturbations are significantly smaller than the truncation error of the same scheme without well-balancing. If during the course of the simulation (due to forcing) the atmosphere becomes non-hydrostatic, our solver continues to function correctly.THOR just passed an important mile stone. We've implemented the explicit part of the solver. The explicit solver is useful to study instabilities or local problems on relatively short time scales. I'll show some nice properties of the explicit THOR. An explicit solver is not appropriate for climate study because the time step is limited by the sound speed. Therefore, we are working on the first fully implicit GCM. By ESS3, I hope to present results for the advection equation.THOR is part of the Exoclimes Simulation Platform (ESP), a set of open-source community codes for simulating and understanding the atmospheres of exoplanets. The ESP also includes tools for radiative transfer and retrieval (HELIOS), an opacity calculator (HELIOS-K), and a chemical kinetics solver (VULCAN). We expect to publicly release an initial version of THOR in 2016 on www.exoclime.org.

Spectral modeling of radiation in combustion systems

NASA Astrophysics Data System (ADS)

Pal, Gopalendu

Radiation calculations are important in combustion due to the high temperatures encountered but has not been studied in sufficient detail in the case of turbulent flames. Radiation calculations for such problems require accurate, robust, and computationally efficient models for the solution of radiative transfer equation (RTE), and spectral properties of radiation. One more layer of complexity is added in predicting the overall heat transfer in turbulent combustion systems due to nonlinear interactions between turbulent fluctuations and radiation. The present work is aimed at the development of finite volume-based high-accuracy thermal radiation modeling, including spectral radiation properties in order to accurately capture turbulence-radiation interactions (TRI) and predict heat transfer in turbulent combustion systems correctly and efficiently. The turbulent fluctuations of temperature and chemical species concentrations have strong effects on spectral radiative intensities, and TRI create a closure problem when the governing partial differential equations are averaged. Recently, several approaches have been proposed to take TRI into account. Among these attempts the most promising approaches are the probability density function (PDF) methods, which can treat nonlinear coupling between turbulence and radiative emission exactly, i.e., "emission TRI". The basic idea of the PDF method is to treat physical variables as random variables and to solve the PDF transport equation stochastically. The actual reacting flow field is represented by a large number of discrete stochastic particles each carrying their own random variable values and evolving with time. The mean value of any function of those random variables, such as the chemical source term, can be evaluated exactly by taking the ensemble average of particles. The local emission term belongs to this class and thus, can be evaluated directly and exactly from particle ensembles. However, the local absorption term involves interactions between the local particle and energy emitted by all other particles and, hence, cannot be obtained from particle ensembles directly. To close the nonlinear coupling between turbulence and absorption, i.e., "absorption TRI", an optically thin fluctuation approximation can be applied to virtually all combustion problems and obtain acceptable accuracy. In the present study a composition-PDF method is applied, in which only the temperature and the species concentrations are treated as random variables. A closely coupled hybrid finite-volume/Monte Carlo scheme is adopted, in which the Monte Carlo method is used to solve the composition-PDF for chemical reactions and the finite volume method is used to solve for the flow field and radiation. Spherical harmonics method-based finite volume solvers (P-1 and P-3) are developed using the data structures of the high fidelity open-source code flow software OpenFOAM. Spectral radiative properties of the participating medium are modeled using full-spectrum k-distribution methods. Advancements of basic k-distribution methods are performed for nongray nonhomogeneous gas- and particulate-phase (soot, fuel droplets, ash, etc.) participating media using multi-scale and multi-group based approaches. These methods achieve close-to benchmark line-by-line (LBL) accuracy in strongly inhomogeneous media at a tiny fraction of LBL's computational cost. A portable spectral module is developed, which includes all the basic to advanced k-distribution methods along with the precompiled accurate and compact k-distribution databases. The P-1 /P-3 RTE solver coupled with the spectral module is used in conjunction with the combined Reynolds-averaged Navier-Stokes (RANS) and composition-PDF-based turbulence-chemistry solver to investigate TRI in multiphase turbulent combustion systems. The combustion solvers developed in this study is employed to simulate several turbulent jet flames, such as Sandia Flame D, and artificial nonsooting and sooting flames derived from Flame D. The effects of combustion chemistry, radiation and TRI on total heat transfer and pollutant (such as NO x) generation are studied for the above flames. The accuracy of the overall combustion solver is assessed by comparing it with the experimental data for Flame D. Comparison of the accuracy and the computational cost among various spectral models and RTE solvers is extensively done on the artificial flames derived from Flame D to demonstrate the necessity of accurate modeling of radiation in combustion problems.

Electrophoresis for genotyping: microtiter array diagonal gel electrophoresis on horizontal polyacrylamide gels, hydrolink, or agarose.

PubMed

Day, I N; Humphries, S E

1994-11-01

Electrophoresis of DNA has been performed traditionally in either an agarose or acrylamide gel matrix. Considerable effort has been directed to improved quality agaroses capable of high resolution, but for small fragments, such as those from polymerase chain reaction (PCR) and post-PCR digests, acrylamide still offers the highest resolution. Although agarose gels can easily be prepared in an open-faced format to gain the conveniences of horizontal electrophoresis, acrylamide does not polymerize in the presence of air and the usual configurations for gel preparation lead to electrophoresis in the vertical dimension. We describe here a very simple device and method to prepare and manipulate horizontal polyacrylamide gels (H-PAGE). In addition, the open-faced horizontal arrangement enables loading of arrays of wells. Since many procedures are undertaken in standard 96-well microtiter plates, we have also designed a device which preserves the exact configuration of the 8 x 12 array and enables electrophoresis in tracks following a 71.6 degrees diagonal between wells (MADGE, microtiter array diagonal gel electrophoresis), using either acrylamide or agarose. This eliminates almost all of the staff time taken in setup, loading, and recordkeeping and offers high resolution for genotyping pattern recognition. The nature and size of the gels allow direct stacking of gels in one tank, so that a tank used typically to analyze 30-60 samples can readily be used to analyze 1000-2000 samples. The gels would also enable robotic loading. Electrophoresis allows analysis of size and charge, parameters inaccessible to liquid-phase methods: thus, genotyping size patterns, variable length repeats, and haplotypes is possible, as well as adaptability to typing of point variations using protocols which create a difference detectable by electrophoresis.

Robust parallel iterative solvers for linear and least-squares problems, Final Technical Report

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

Saad, Yousef

2014-01-16

The primary goal of this project is to study and develop robust iterative methods for solving linear systems of equations and least squares systems. The focus of the Minnesota team is on algorithms development, robustness issues, and on tests and validation of the methods on realistic problems. 1. The project begun with an investigation on how to practically update a preconditioner obtained from an ILU-type factorization, when the coefficient matrix changes. 2. We investigated strategies to improve robustness in parallel preconditioners in a specific case of a PDE with discontinuous coefficients. 3. We explored ways to adapt standard preconditioners formore » solving linear systems arising from the Helmholtz equation. These are often difficult linear systems to solve by iterative methods. 4. We have also worked on purely theoretical issues related to the analysis of Krylov subspace methods for linear systems. 5. We developed an effective strategy for performing ILU factorizations for the case when the matrix is highly indefinite. The strategy uses shifting in some optimal way. The method was extended to the solution of Helmholtz equations by using complex shifts, yielding very good results in many cases. 6. We addressed the difficult problem of preconditioning sparse systems of equations on GPUs. 7. A by-product of the above work is a software package consisting of an iterative solver library for GPUs based on CUDA. This was made publicly available. It was the first such library that offers complete iterative solvers for GPUs. 8. We considered another form of ILU which blends coarsening techniques from Multigrid with algebraic multilevel methods. 9. We have released a new version on our parallel solver - called pARMS [new version is version 3]. As part of this we have tested the code in complex settings - including the solution of Maxwell and Helmholtz equations and for a problem of crystal growth.10. As an application of polynomial preconditioning we considered the problem of evaluating f(A)v which arises in statistical sampling. 11. As an application to the methods we developed, we tackled the problem of computing the diagonal of the inverse of a matrix. This arises in statistical applications as well as in many applications in physics. We explored probing methods as well as domain-decomposition type methods. 12. A collaboration with researchers from Toulouse, France, considered the important problem of computing the Schur complement in a domain-decomposition approach. 13. We explored new ways of preconditioning linear systems, based on low-rank approximations.« less

Use of the preconditioned conjugate gradient algorithm as a generic solver for mixed-model equations in animal breeding applications.

PubMed

Tsuruta, S; Misztal, I; Strandén, I

2001-05-01

Utility of the preconditioned conjugate gradient algorithm with a diagonal preconditioner for solving mixed-model equations in animal breeding applications was evaluated with 16 test problems. The problems included single- and multiple-trait analyses, with data on beef, dairy, and swine ranging from small examples to national data sets. Multiple-trait models considered low and high genetic correlations. Convergence was based on relative differences between left- and right-hand sides. The ordering of equations was fixed effects followed by random effects, with no special ordering within random effects. The preconditioned conjugate gradient program implemented with double precision converged for all models. However, when implemented in single precision, the preconditioned conjugate gradient algorithm did not converge for seven large models. The preconditioned conjugate gradient and successive overrelaxation algorithms were subsequently compared for 13 of the test problems. The preconditioned conjugate gradient algorithm was easy to implement with the iteration on data for general models. However, successive overrelaxation requires specific programming for each set of models. On average, the preconditioned conjugate gradient algorithm converged in three times fewer rounds of iteration than successive overrelaxation. With straightforward implementations, programs using the preconditioned conjugate gradient algorithm may be two or more times faster than those using successive overrelaxation. However, programs using the preconditioned conjugate gradient algorithm would use more memory than would comparable implementations using successive overrelaxation. Extensive optimization of either algorithm can influence rankings. The preconditioned conjugate gradient implemented with iteration on data, a diagonal preconditioner, and in double precision may be the algorithm of choice for solving mixed-model equations when sufficient memory is available and ease of implementation is essential.

Fast iterative solution of the Bethe-Salpeter eigenvalue problem using low-rank and QTT tensor approximation

NASA Astrophysics Data System (ADS)

Benner, Peter; Dolgov, Sergey; Khoromskaia, Venera; Khoromskij, Boris N.

2017-04-01

In this paper, we propose and study two approaches to approximate the solution of the Bethe-Salpeter equation (BSE) by using structured iterative eigenvalue solvers. Both approaches are based on the reduced basis method and low-rank factorizations of the generating matrices. We also propose to represent the static screen interaction part in the BSE matrix by a small active sub-block, with a size balancing the storage for rank-structured representations of other matrix blocks. We demonstrate by various numerical tests that the combination of the diagonal plus low-rank plus reduced-block approximation exhibits higher precision with low numerical cost, providing as well a distinct two-sided error estimate for the smallest eigenvalues of the Bethe-Salpeter operator. The complexity is reduced to O (Nb2) in the size of the atomic orbitals basis set, Nb, instead of the practically intractable O (Nb6) scaling for the direct diagonalization. In the second approach, we apply the quantized-TT (QTT) tensor representation to both, the long eigenvectors and the column vectors in the rank-structured BSE matrix blocks, and combine this with the ALS-type iteration in block QTT format. The QTT-rank of the matrix entities possesses almost the same magnitude as the number of occupied orbitals in the molecular systems, No

Algorithms for parallel flow solvers on message passing architectures

NASA Technical Reports Server (NTRS)

Vanderwijngaart, Rob F.

1995-01-01

The purpose of this project has been to identify and test suitable technologies for implementation of fluid flow solvers -- possibly coupled with structures and heat equation solvers -- on MIMD parallel computers. In the course of this investigation much attention has been paid to efficient domain decomposition strategies for ADI-type algorithms. Multi-partitioning derives its efficiency from the assignment of several blocks of grid points to each processor in the parallel computer. A coarse-grain parallelism is obtained, and a near-perfect load balance results. In uni-partitioning every processor receives responsibility for exactly one block of grid points instead of several. This necessitates fine-grain pipelined program execution in order to obtain a reasonable load balance. Although fine-grain parallelism is less desirable on many systems, especially high-latency networks of workstations, uni-partition methods are still in wide use in production codes for flow problems. Consequently, it remains important to achieve good efficiency with this technique that has essentially been superseded by multi-partitioning for parallel ADI-type algorithms. Another reason for the concentration on improving the performance of pipeline methods is their applicability in other types of flow solver kernels with stronger implied data dependence. Analytical expressions can be derived for the size of the dynamic load imbalance incurred in traditional pipelines. From these it can be determined what is the optimal first-processor retardation that leads to the shortest total completion time for the pipeline process. Theoretical predictions of pipeline performance with and without optimization match experimental observations on the iPSC/860 very well. Analysis of pipeline performance also highlights the effect of uncareful grid partitioning in flow solvers that employ pipeline algorithms. If grid blocks at boundaries are not at least as large in the wall-normal direction as those immediately adjacent to them, then the first processor in the pipeline will receive a computational load that is less than that of subsequent processors, magnifying the pipeline slowdown effect. Extra compensation is needed for grid boundary effects, even if all grid blocks are equally sized.

Almost conserved operators in nearly many-body localized systems

NASA Astrophysics Data System (ADS)

Pancotti, Nicola; Knap, Michael; Huse, David A.; Cirac, J. Ignacio; Bañuls, Mari Carmen

2018-03-01

We construct almost conserved local operators, that possess a minimal commutator with the Hamiltonian of the system, near the many-body localization transition of a one-dimensional disordered spin chain. We collect statistics of these slow operators for different support sizes and disorder strengths, both using exact diagonalization and tensor networks. Our results show that the scaling of the average of the smallest commutators with the support size is sensitive to Griffiths effects in the thermal phase and the onset of many-body localization. Furthermore, we demonstrate that the probability distributions of the commutators can be analyzed using extreme value theory and that their tails reveal the difference between diffusive and subdiffusive dynamics in the thermal phase.

Is the ground state of 5d4 double-perovskite Iridate Ba2YIrO6 magnetic or nonmagnetic?

NASA Astrophysics Data System (ADS)

Gong, Hoshin; Kim, Kyoo; Kim, Beom Hyun; Kim, Bongjae; Kim, Junwon; Min, B. I.

2018-05-01

We have investigated electronic structures and magnetic properties of double perovskite Iridate Ba2YIrO6 with 5d4 configuration, employing the exact diagonalization method for multi-site clusters. We have considered a many-body Hamiltonian for all d states (eg and t2g) including all relevant physical parameters such as the Coulomb correlation, spin-orbit coupling, crystal-field effect, and Hund coupling. We have found that the ground state of Ba2YIrO6 is nonmagnetic and that the Hund coupling plays an important role in the magnetic properties of the 5d4 systems, unlike the well-studied 5d5 systems.

Hole pairing and thermodynamic properties of the two dimensional frustrated t-J model

NASA Astrophysics Data System (ADS)

Roy, K.; Pal, P.; Nath, S.; Ghosh, N. K.

2018-04-01

The frustrated t-J model is investigated by using the exact-diagonalization (ED) method on an 8-site cluster. The effect on next-nearest-neighbor (NNN) exchange interaction J' (frustration) on the hole pairing and the thermodynamic properties of the system is considered. Two holes initially remain unbound at smaller value of J'/t, but tend to bind at larger value. The maximum possibility of pair formation has been observed to be at NNN sites. Entropy calculation shows that the system goes to more disordered state with J'. The specific heat curves show a single peak structure. A decrease in effective exchange energy is observed due to the frustration.

Stress Response of Granular Systems

NASA Astrophysics Data System (ADS)

Ramola, Kabir; Chakraborty, Bulbul

2017-10-01

We develop a framework for stress response in two dimensional granular media, with and without friction, that respects vector force balance at the microscopic level. We introduce local gauge degrees of freedom that determine the response of contact forces between constituent grains on a given, disordered, contact network, to external perturbations. By mapping this response to the spectral properties of the graph Laplacian corresponding to the underlying contact network, we show that this naturally leads to spatial localization of forces. We present numerical evidence for localization using exact diagonalization studies of network Laplacians of soft disk packings. Finally, we discuss the role of other constraints, such as torque balance, in determining the stability of a granular packing to external perturbations.

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.

Relativistic energy-dispersion relations of 2D rectangular lattices

NASA Astrophysics Data System (ADS)

Ata, Engin; Demirhan, Doğan; Büyükkılıç, Fevzi

2017-04-01

An exactly solvable relativistic approach based on inseparable periodic well potentials is developed to obtain energy-dispersion relations of spin states of a single-electron in two-dimensional (2D) rectangular lattices. Commutation of axes transfer matrices is exploited to find energy dependencies of the wave vector components. From the trace of the lattice transfer matrix, energy-dispersion relations of conductance and valence states are obtained in transcendental form. Graphical solutions of relativistic and nonrelativistic transcendental energy-dispersion relations are plotted to compare how lattice parameters V0, core and interstitial size of the rectangular lattice affects to the energy-band structures in a situation core and interstitial diagonals are of equal slope.

Phase transition in one Josephson junction with a side-coupled magnetic impurity

NASA Astrophysics Data System (ADS)

Zhi, Li-Ming; Wang, Xiao-Qi; Jiang, Cui; Yi, Guang-Yu; Gong, Wei-Jiang

2018-04-01

This work focuses on one Josephson junction with a side-coupled magnetic impurity. And then, the Josephson phase transition is theoretically investigated, with the help of the exact diagonalization approach. It is found that even in the absence of intradot Coulomb interaction, the magnetic impurity can efficiently induce the phenomenon of Josephson phase transition, which is tightly related to the spin correlation manners (i.e., ferromagnetic or antiferromagnetic) between the impurity and the junction. Moreover, the impurity plays different roles when it couples to the dot and superconductor, respectively. This work can be helpful in describing the influence of one magnetic impurity on the supercurrent through the Josephson junction.

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.

Optical coefficients in a semiconductor quantum ring: Electric field and donor impurity effects

NASA Astrophysics Data System (ADS)

Duque, C. M.; Acosta, Ruben E.; Morales, A. L.; Mora-Ramos, M. E.; Restrepo, R. L.; Ojeda, J. H.; Kasapoglu, E.; Duque, C. A.

2016-10-01

The electron states in a two-dimensional quantum dot ring are calculated in the presence of a donor impurity atom under the effective mass and parabolic band approximations. The effect of an externally applied electric field is also taken into account. The wavefunctions are obtained via the exact diagonalization of the problem Hamiltonian using a 2D expansion within the adiabatic approximation. The impurity-related optical response is analyzed via the optical absorption, relative refractive index change and the second harmonics generation. The dependencies of the electron states and these optical coefficients with the changes in the configuration of the quantum ring system are discussed in detail.

Fidelity study of superconductivity in extended Hubbard models

NASA Astrophysics Data System (ADS)

Plonka, N.; Jia, C. J.; Wang, Y.; Moritz, B.; Devereaux, T. P.

2015-07-01

The Hubbard model with local on-site repulsion is generally thought to possess a superconducting ground state for appropriate parameters, but the effects of more realistic long-range Coulomb interactions have not been studied extensively. We study the influence of these interactions on superconductivity by including nearest- and next-nearest-neighbor extended Hubbard interactions in addition to the usual on-site terms. Utilizing numerical exact diagonalization, we analyze the signatures of superconductivity in the ground states through the fidelity metric of quantum information theory. We find that nearest and next-nearest neighbor interactions have thresholds above which they destabilize superconductivity regardless of whether they are attractive or repulsive, seemingly due to competing charge fluctuations.

Analysis of the aerodynamic performance of the multi-rotor concept

NASA Astrophysics Data System (ADS)

Chasapogiannis, Petros; Prospathopoulos, John M.; Voutsinas, Spyros G.; Chaviaropoulos, Takis K.

2014-06-01

The concept of a large (~20MW) multi-rotor wind turbine intended for offshore installations is analysed with respect to its aerodynamic performance. The effect of closely clustering rotors on a single actuator disk is estimated using two different modelling approaches: a CFD solver in which the rotors are simulated as distinct actuator disks and a vortex based solver in which the blade geometry is exactly considered. In the present work, a system of 7 rotors is simulated with a centre to centre spacing of 1.05D. At nominal conditions (tip speed ratio=9) both models predict an increase in power of ~3% alongside with an increase in thrust of ~1.5%. The analysis of the flow field indicates that in the 7 rotor system the individual wakes merge into one wake at ~2D and that flow recovery starts at approximately the same downstream distance as in the single rotor case. As regards the dynamic implications of the close spacing of the rotors it was found that there is an increase in the loading amplitude ranging from 0.30-2.13% at blade level in rated conditions.

FUN3D Manual: 12.9

NASA Technical Reports Server (NTRS)

Biedron, Robert T.; Carlson, Jan-Renee; Derlaga, Joseph M.; Gnoffo, Peter A.; Hammond, Dana P.; Jones, William T.; Kleb, Bil; Lee-Rausch, Elizabeth M.; Nielsen, Eric J.; Park, Michael A.;

FUN3D Manual: 13.2

NASA Technical Reports Server (NTRS)

Biedron, Robert T.; Carlson, Jan-Renee; Derlaga, Joseph M.; Gnoffo, Peter A.; Hammond, Dana P.; Jones, William T.; Kleb, William L.; Lee-Rausch, Elizabeth M.; Nielsen, Eric J.; Park, Michael A.;

FUN3D Manual: 12.6

NASA Technical Reports Server (NTRS)

Biedron, Robert T.; Derlaga, Joseph M.; Gnoffo, Peter A.; Hammond, Dana P.; Jones, William T.; Kleb, William L.; Lee-Rausch, Elizabeth M.; Nielsen, Eric J.; Park, Michael A.; Rumsey, Christopher L.;

FUN3D Manual: 12.7

NASA Technical Reports Server (NTRS)

Biedron, Robert T.; Carlson, Jan-Renee; Derlaga, Joseph M.; Gnoffo, Peter A.; Hammond, Dana P.; Jones, William T.; Kleb, Bil; Lee-Rausch, Elizabeth M.; Nielsen, Eric J.; Park, Michael A.;

FUN3D Manual: 12.5

NASA Technical Reports Server (NTRS)

Biedron, Robert T.; Derlaga, Joseph M.; Gnoffo, Peter A.; Hammond, Dana P.; Jones, William T.; Kleb, William L.; Lee-Rausch, Elizabeth M.; Nielsen, Eric J.; Park, Michael A.; Rumsey, Christopher L.;

FUN3D Manual: 12.8

NASA Technical Reports Server (NTRS)

Biedron, Robert T.; Carlson, Jan-Renee; Derlaga, Joseph M.; Gnoffo, Peter A.; Hammond, Dana P.; Jones, William T.; Kleb, Bil; Lee-Rausch, Elizabeth M.; Nielsen, Eric J.; Park, Michael A.;

FUN3D Manual: 12.4

NASA Technical Reports Server (NTRS)

Biedron, Robert T.; Derlaga, Joseph M.; Gnoffo, Peter A.; Hammond, Dana P.; Jones, William T.; Kleb, Bil; Lee-Rausch, Elizabeth M.; Nielsen, Eric J.; Park, Michael A.; Rumsey, Christopher L.;

FUN3D Manual: 13.1

NASA Technical Reports Server (NTRS)

Biedron, Robert T.; Carlson, Jan-Renee; Derlaga, Joseph M.; Gnoffo, Peter A.; Hammond, Dana P.; Jones, William T.; Kleb, Bil; Lee-Rausch, Elizabeth M.; Nielsen, Eric J.; Park, Michael A.;

FUN3D Manual: 13.0

NASA Technical Reports Server (NTRS)

Biedron, Robert T.; Carlson, Jan-Renee; Derlaga, Joseph M.; Gnoffo, Peter A.; Hammond, Dana P.; Jones, William T.; Kleb, Bill; Lee-Rausch, Elizabeth M.; Nielsen, Eric J.; Park, Michael A.;

FUN3D Manual: 13.3

NASA Technical Reports Server (NTRS)

Biedron, Robert T.; Carlson, Jan-Renee; Derlaga, Joseph M.; Gnoffo, Peter A.; Hammond, Dana P.; Jones, William T.; Kleb, Bil; Lee-Rausch, Elizabeth M.; Nielsen, Eric J.; Park, Michael A.;

A parallel algorithm for 2D visco-acoustic frequency-domain full-waveform inversion: application to a dense OBS data set

NASA Astrophysics Data System (ADS)

Sourbier, F.; Operto, S.; Virieux, J.

2006-12-01

We present a distributed-memory parallel algorithm for 2D visco-acoustic full-waveform inversion of wide-angle seismic data. Our code is written in fortran90 and use MPI for parallelism. The algorithm was applied to real wide-angle data set recorded by 100 OBSs with a 1-km spacing in the eastern-Nankai trough (Japan) to image the deep structure of the subduction zone. Full-waveform inversion is applied sequentially to discrete frequencies by proceeding from the low to the high frequencies. The inverse problem is solved with a classic gradient method. Full-waveform modeling is performed with a frequency-domain finite-difference method. In the frequency-domain, solving the wave equation requires resolution of a large unsymmetric system of linear equations. We use the massively parallel direct solver MUMPS (http://www.enseeiht.fr/irit/apo/MUMPS) for distributed-memory computer to solve this system. The MUMPS solver is based on a multifrontal method for the parallel factorization. The MUMPS algorithm is subdivided in 3 main steps: a symbolic analysis step that performs re-ordering of the matrix coefficients to minimize the fill-in of the matrix during the subsequent factorization and an estimation of the assembly tree of the matrix. Second, the factorization is performed with dynamic scheduling to accomodate numerical pivoting and provides the LU factors distributed over all the processors. Third, the resolution is performed for multiple sources. To compute the gradient of the cost function, 2 simulations per shot are required (one to compute the forward wavefield and one to back-propagate residuals). The multi-source resolutions can be performed in parallel with MUMPS. In the end, each processor stores in core a sub-domain of all the solutions. These distributed solutions can be exploited to compute in parallel the gradient of the cost function. Since the gradient of the cost function is a weighted stack of the shot and residual solutions of MUMPS, each processor computes the corresponding sub-domain of the gradient. In the end, the gradient is centralized on the master processor using a collective communation. The gradient is scaled by the diagonal elements of the Hessian matrix. This scaling is computed only once per frequency before the first iteration of the inversion. Estimation of the diagonal terms of the Hessian requires performing one simulation per non redondant shot and receiver position. The same strategy that the one used for the gradient is used to compute the diagonal Hessian in parallel. This algorithm was applied to a dense wide-angle data set recorded by 100 OBSs in the eastern Nankai trough, offshore Japan. Thirteen frequencies ranging from 3 and 15 Hz were inverted. Tweny iterations per frequency were computed leading to 260 tomographic velocity models of increasing resolution. The velocity model dimensions are 105 km x 25 km corresponding to a finite-difference grid of 4201 x 1001 grid with a 25-m grid interval. The number of shot was 1005 and the number of inverted OBS gathers was 93. The inversion requires 20 days on 6 32-bits bi-processor nodes with 4 Gbytes of RAM memory per node when only the LU factorization is performed in parallel. Preliminary estimations of the time required to perform the inversion with the fully-parallelized code is 6 and 4 days using 20 and 50 processors respectively.

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

Mazzarella, G.; Toigo, F.; Salasnich, L.

We consider a bosonic Josephson junction made of N ultracold and dilute atoms confined by a quasi-one-dimensional double-well potential within the two-site Bose-Hubbard model framework. The behavior of the system is investigated at zero temperature by varying the interatomic interaction from the strongly attractive regime to the repulsive one. We show that the ground state exhibits a crossover from a macroscopic Schroedinger-cat state to a separable Fock state through an atomic coherent regime. By diagonalizing the Bose-Hubbard Hamiltonian we characterize the emergence of the macroscopic cat states by calculating the Fisher information F, the coherence by means of the visibilitymore » {alpha} of the interference fringes in the momentum distribution, and the quantum correlations by using the entanglement entropy S. Both Fisher information and visibility are shown to be related to the ground-state energy by employing the Hellmann-Feynman theorem. This result, together with a perturbative calculation of the ground-state energy, allows simple analytical formulas for F and {alpha} to be obtained over a range of interactions, in excellent agreement with the exact diagonalization of the Bose-Hubbard Hamiltonian. In the attractive regime the entanglement entropy attains values very close to its upper limit for a specific interaction strength lying in the region where coherence is lost and self-trapping sets in.« less

A simple molecular mechanics integrator in mixed rigid body and dihedral angle space

PubMed Central

Vitalis, Andreas; Pappu, Rohit V.

2014-01-01

We propose a numerical scheme to integrate equations of motion in a mixed space of rigid-body and dihedral angle coordinates. The focus of the presentation is biomolecular systems and the framework is applicable to polymers with tree-like topology. By approximating the effective mass matrix as diagonal and lumping all bias torques into the time dependencies of the diagonal elements, we take advantage of the formal decoupling of individual equations of motion. We impose energy conservation independently for every degree of freedom and this is used to derive a numerical integration scheme. The cost of all auxiliary operations is linear in the number of atoms. By coupling the scheme to one of two popular thermostats, we extend the method to sample constant temperature ensembles. We demonstrate that the integrator of choice yields satisfactory stability and is free of mass-metric tensor artifacts, which is expected by construction of the algorithm. Two fundamentally different systems, viz., liquid water and an α-helical peptide in a continuum solvent are used to establish the applicability of our method to a wide range of problems. The resultant constant temperature ensembles are shown to be thermodynamically accurate. The latter relies on detailed, quantitative comparisons to data from reference sampling schemes operating on exactly the same sets of degrees of freedom. PMID:25053299

Exact solutions to model surface and volume charge distributions

NASA Astrophysics Data System (ADS)

Mukhopadhyay, S.; Majumdar, N.; Bhattacharya, P.; Jash, A.; Bhattacharya, D. S.

2016-10-01

Many important problems in several branches of science and technology deal with charges distributed along a line, over a surface and within a volume. Recently, we have made use of new exact analytic solutions of surface charge distributions to develop the nearly exact Boundary Element Method (neBEM) toolkit. This 3D solver has been successful in removing some of the major drawbacks of the otherwise elegant Green's function approach and has been found to be very accurate throughout the computational domain, including near- and far-field regions. Use of truly distributed singularities (in contrast to nodally concentrated ones) on rectangular and right-triangular elements used for discretizing any three-dimensional geometry has essentially removed many of the numerical and physical singularities associated with the conventional BEM. In this work, we will present this toolkit and the development of several numerical models of space charge based on exact closed-form expressions. In one of the models, Particles on Surface (ParSur), the space charge inside a small elemental volume of any arbitrary shape is represented as being smeared on several surfaces representing the volume. From the studies, it can be concluded that the ParSur model is successful in getting the estimates close to those obtained using the first-principles, especially close to and within the cell. In the paper, we will show initial applications of ParSur and other models in problems related to high energy physics.

A Spectral Element Discretisation on Unstructured Triangle / Tetrahedral Meshes for Elastodynamics

NASA Astrophysics Data System (ADS)

May, Dave A.; Gabriel, Alice-A.

2017-04-01

The spectral element method (SEM) defined over quadrilateral and hexahedral element geometries has proven to be a fast, accurate and scalable approach to study wave propagation phenomena. In the context of regional scale seismology and or simulations incorporating finite earthquake sources, the geometric restrictions associated with hexahedral elements can limit the applicability of the classical quad./hex. SEM. Here we describe a continuous Galerkin spectral element discretisation defined over unstructured meshes composed of triangles (2D), or tetrahedra (3D). The method uses a stable, nodal basis constructed from PKD polynomials and thus retains the spectral accuracy and low dispersive properties of the classical SEM, in addition to the geometric versatility provided by unstructured simplex meshes. For the particular basis and quadrature rule we have adopted, the discretisation results in a mass matrix which is not diagonal, thereby mandating linear solvers be utilised. To that end, we have developed efficient solvers and preconditioners which are robust with respect to the polynomial order (p), and possess high arithmetic intensity. Furthermore, we also consider using implicit time integrators, together with a p-multigrid preconditioner to circumvent the CFL condition. Implicit time integrators become particularly relevant when considering solving problems on poor quality meshes, or meshes containing elements with a widely varying range of length scales - both of which frequently arise when meshing non-trivial geometries. We demonstrate the applicability of the new method by examining a number of two- and three-dimensional wave propagation scenarios. These scenarios serve to characterise the accuracy and cost of the new method. Lastly, we will assess the potential benefits of using implicit time integrators for regional scale wave propagation simulations.

Scaling of the polarization amplitude in quantum many-body systems in one dimension

NASA Astrophysics Data System (ADS)

Kobayashi, Ryohei; Nakagawa, Yuya O.; Fukusumi, Yoshiki; Oshikawa, Masaki

2018-04-01

Resta proposed a definition of the electric polarization in one-dimensional systems in terms of the ground-state expectation value of the large gauge transformation operator. Vanishing of the expectation value in the thermodynamic limit implies that the system is a conductor. We study Resta's polarization amplitude (expectation value) in the S =1 /2 XXZ chain and its several generalizations, in the gapless conducting Tomonaga-Luttinger liquid phase. We obtain an analytical expression in the lowest-order perturbation theory about the free fermion point (XY chain) and an exact result for the Haldane-Shastry model with long-range interactions. We also obtain numerical results, mostly using the exact diagonalization method. We find that the amplitude exhibits a power-law scaling in the system size (chain length) and vanishes in the thermodynamic limit. On the other hand, the exponent depends on the model even when the low-energy limit is described by the Tomonaga-Luttinger liquid with the same Luttinger parameter. We find that a change in the exponent occurs when the Umklapp term(s) are eliminated, suggesting the importance of the Umklapp terms.

Confined One Dimensional Harmonic Oscillator as a Two-Mode System

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

Gueorguiev, V G; Rau, A P; Draayer, J P

2005-07-11

The one-dimensional harmonic oscillator in a box problem is possibly the simplest example of a two-mode system. This system has two exactly solvable limits, the harmonic oscillator and a particle in a (one-dimensional) box. Each of the two limits has a characteristic spectral structure describing the two different excitation modes of the system. Near each of these limits, one can use perturbation theory to achieve an accurate description of the eigenstates. Away from the exact limits, however, one has to carry out a matrix diagonalization because the basis-state mixing that occurs is typically too large to be reproduced in anymore » other way. An alternative to casting the problem in terms of one or the other basis set consists of using an ''oblique'' basis that uses both sets. Through a study of this alternative in this one-dimensional problem, we are able to illustrate practical solutions and infer the applicability of the concept for more complex systems, such as in the study of complex nuclei where oblique-basis calculations have been successful.« less

Rashba quantum wire: exact solution and ballistic transport.

PubMed

Perroni, C A; Bercioux, D; Ramaglia, V Marigliano; Cataudella, V

2007-05-08

The effect of Rashba spin-orbit interaction in quantum wires with hard-wall boundaries is discussed. The exact wavefunction and eigenvalue equation are worked out, pointing out the mixing between the spin and spatial parts. The spectral properties are also studied within perturbation theory with respect to the strength of the spin-orbit interaction and diagonalization procedure. A comparison is made with the results of a simple model, the two-band model, that takes account only of the first two sub-bands of the wire. Finally, the transport properties within the ballistic regime are analytically calculated for the two-band model and through a tight-binding Green function for the entire system. Single and double interfaces separating regions with different strengths of spin-orbit interaction are analysed by injecting carriers into the first and the second sub-band. It is shown that in the case of a single interface the spin polarization in the Rashba region is different from zero, and in the case of two interfaces the spin polarization shows oscillations due to spin-selective bound states.

Efficient implementation of one- and two-component analytical energy gradients in exact two-component theory

NASA Astrophysics Data System (ADS)

Franzke, Yannick J.; Middendorf, Nils; Weigend, Florian

2018-03-01

We present an efficient algorithm for one- and two-component analytical energy gradients with respect to nuclear displacements in the exact two-component decoupling approach to the one-electron Dirac equation (X2C). Our approach is a generalization of the spin-free ansatz by Cheng and Gauss [J. Chem. Phys. 135, 084114 (2011)], where the perturbed one-electron Hamiltonian is calculated by solving a first-order response equation. Computational costs are drastically reduced by applying the diagonal local approximation to the unitary decoupling transformation (DLU) [D. Peng and M. Reiher, J. Chem. Phys. 136, 244108 (2012)] to the X2C Hamiltonian. The introduced error is found to be almost negligible as the mean absolute error of the optimized structures amounts to only 0.01 pm. Our implementation in TURBOMOLE is also available within the finite nucleus model based on a Gaussian charge distribution. For a X2C/DLU gradient calculation, computational effort scales cubically with the molecular size, while storage increases quadratically. The efficiency is demonstrated in calculations of large silver clusters and organometallic iridium complexes.

Three-Dimensional Simulations of Electron Beams Focused by Periodic Permanent Magnets

NASA Technical Reports Server (NTRS)

Kory, Carol L.

1999-01-01

A fully three-dimensional (3D) model of an electron beam focused by a periodic permanent magnet (PPM) stack has been developed. First, the simulation code MAFIA was used to model a PPM stack using the magnetostatic solver. The exact geometry of the magnetic focusing structure was modeled; thus, no approximations were made regarding the off-axis fields. The fields from the static solver were loaded into the 3D particle-in-cell (PIC) solver of MAFIA where fully 3D behavior of the beam was simulated in the magnetic focusing field. The PIC solver computes the time-integration of electromagnetic fields simultaneously with the time integration of the equations of motion of charged particles that move under the influence of those fields. Fields caused by those moving charges are also taken into account; thus, effects like space charge and magnetic forces between particles are fully simulated. The electron beam is simulated by a number of macro-particles. These macro-particles represent a given charge Q amounting to that of several million electrons in order to conserve computational time and memory. Particle motion is unrestricted, so particle trajectories can cross paths and move in three dimensions under the influence of 3D electric and magnetic fields. Correspondingly, there is no limit on the initial current density distribution of the electron beam, nor its density distribution at any time during the simulation. Simulation results including beam current density, percent ripple and percent transmission will be presented, and the effects current, magnetic focusing strength and thermal velocities have on beam behavior will be demonstrated using 3D movies showing the evolution of beam characteristics in time and space. Unlike typical beam optics models, this 3D model allows simulation of asymmetric designs such as non- circularly symmetric electrostatic or magnetic focusing as well as the inclusion of input/output couplers.

Impact ionization processes in the steady state of a driven Mott-insulating layer coupled to metallic leads

NASA Astrophysics Data System (ADS)

Sorantin, Max E.; Dorda, Antonius; Held, Karsten; Arrigoni, Enrico

2018-03-01

We study a simple model of photovoltaic energy harvesting across a Mott-insulating gap consisting of a correlated layer connected to two metallic leads held at different chemical potentials. We address, in particular, the issue of impact ionization, whereby a particle photoexcited to the high-energy part of the upper Hubbard band uses its extra energy to produce a second particle-hole excitation. We find a drastic increase of the photocurrent upon entering the frequency regime where impact ionization is possible. At large values of the Mott gap, where impact ionization is energetically not allowed, we observe a suppression of the current and a piling up of charge in the high-energy part of the upper Hubbard band. Our study is based on a Floquet dynamical mean-field theory treatment of the steady state with the so-called auxiliary master equation approach as impurity solver. We verify that an additional approximation, taking the self-energy diagonal in the Floquet indices, is appropriate for the parameter range we are considering.

Spectral-based propagation schemes for time-dependent quantum systems with application to carbon nanotubes

NASA Astrophysics Data System (ADS)

Chen, Zuojing; Polizzi, Eric

2010-11-01

Effective modeling and numerical spectral-based propagation schemes are proposed for addressing the challenges in time-dependent quantum simulations of systems ranging from atoms, molecules, and nanostructures to emerging nanoelectronic devices. While time-dependent Hamiltonian problems can be formally solved by propagating the solutions along tiny simulation time steps, a direct numerical treatment is often considered too computationally demanding. In this paper, however, we propose to go beyond these limitations by introducing high-performance numerical propagation schemes to compute the solution of the time-ordered evolution operator. In addition to the direct Hamiltonian diagonalizations that can be efficiently performed using the new eigenvalue solver FEAST, we have designed a Gaussian propagation scheme and a basis-transformed propagation scheme (BTPS) which allow to reduce considerably the simulation times needed by time intervals. It is outlined that BTPS offers the best computational efficiency allowing new perspectives in time-dependent simulations. Finally, these numerical schemes are applied to study the ac response of a (5,5) carbon nanotube within a three-dimensional real-space mesh framework.

Applications of automatic differentiation in computational fluid dynamics

NASA Technical Reports Server (NTRS)

Green, Lawrence L.; Carle, A.; Bischof, C.; Haigler, Kara J.; Newman, Perry A.

1994-01-01

Automatic differentiation (AD) is a powerful computational method that provides for computing exact sensitivity derivatives (SD) from existing computer programs for multidisciplinary design optimization (MDO) or in sensitivity analysis. A pre-compiler AD tool for FORTRAN programs called ADIFOR has been developed. The ADIFOR tool has been easily and quickly applied by NASA Langley researchers to assess the feasibility and computational impact of AD in MDO with several different FORTRAN programs. These include a state-of-the-art three dimensional multigrid Navier-Stokes flow solver for wings or aircraft configurations in transonic turbulent flow. With ADIFOR the user specifies sets of independent and dependent variables with an existing computer code. ADIFOR then traces the dependency path throughout the code, applies the chain rule to formulate derivative expressions, and generates new code to compute the required SD matrix. The resulting codes have been verified to compute exact non-geometric and geometric SD for a variety of cases. in less time than is required to compute the SD matrix using centered divided differences.

BeamDyn: a high-fidelity wind turbine blade solver in the FAST modular framework

DOE PAGES

Wang, Qi; Sprague, Michael A.; Jonkman, Jason; ...

2017-03-14

Here, this paper presents a numerical implementation of the geometrically exact beam theory based on the Legendre-spectral-finite-element (LSFE) method. The displacement-based geometrically exact beam theory is presented, and the special treatment of three-dimensional rotation parameters is reviewed. An LSFE is a high-order finite element with nodes located at the Gauss-Legendre-Lobatto points. These elements can be an order of magnitude more computationally efficient than low-order finite elements for a given accuracy level. The new module, BeamDyn, is implemented in the FAST modularization framework for dynamic simulation of highly flexible composite-material wind turbine blades within the FAST aeroelastic engineering model. The frameworkmore » allows for fully interactive simulations of turbine blades in operating conditions. Numerical examples are provided to validate BeamDyn and examine the LSFE performance as well as the coupling algorithm in the FAST modularization framework. BeamDyn can also be used as a stand-alone high-fidelity beam tool.« less

Compressible, multiphase semi-implicit method with moment of fluid interface representation

DOE PAGES

Jemison, Matthew; Sussman, Mark; Arienti, Marco

2014-09-16

A unified method for simulating multiphase flows using an exactly mass, momentum, and energy conserving Cell-Integrated Semi-Lagrangian advection algorithm is presented. The deforming material boundaries are represented using the moment-of-fluid method. Our new algorithm uses a semi-implicit pressure update scheme that asymptotically preserves the standard incompressible pressure projection method in the limit of infinite sound speed. The asymptotically preserving attribute makes the new method applicable to compressible and incompressible flows including stiff materials; enabling large time steps characteristic of incompressible flow algorithms rather than the small time steps required by explicit methods. Moreover, shocks are captured and material discontinuities aremore » tracked, without the aid of any approximate or exact Riemann solvers. As a result, wimulations of underwater explosions and fluid jetting in one, two, and three dimensions are presented which illustrate the effectiveness of the new algorithm at efficiently computing multiphase flows containing shock waves and material discontinuities with large “impedance mismatch.”« less

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.

BeamDyn: a high-fidelity wind turbine blade solver in the FAST modular framework

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

Wang, Qi; Sprague, Michael A.; Jonkman, Jason

Here, this paper presents a numerical implementation of the geometrically exact beam theory based on the Legendre-spectral-finite-element (LSFE) method. The displacement-based geometrically exact beam theory is presented, and the special treatment of three-dimensional rotation parameters is reviewed. An LSFE is a high-order finite element with nodes located at the Gauss-Legendre-Lobatto points. These elements can be an order of magnitude more computationally efficient than low-order finite elements for a given accuracy level. The new module, BeamDyn, is implemented in the FAST modularization framework for dynamic simulation of highly flexible composite-material wind turbine blades within the FAST aeroelastic engineering model. The frameworkmore » allows for fully interactive simulations of turbine blades in operating conditions. Numerical examples are provided to validate BeamDyn and examine the LSFE performance as well as the coupling algorithm in the FAST modularization framework. BeamDyn can also be used as a stand-alone high-fidelity beam tool.« less

State Counting for Excited Bands of the Fractional Quantum Hall Effect: Exclusion Rules for Bound Excitons

NASA Astrophysics Data System (ADS)

Coimbatore Balram, Ajit; Wójs, Arkadiusz; Jain, Jainendra

2014-03-01

Exact diagonalization studies have revealed that the energy spectrum of interacting electrons in the lowest Landau level splits, non-perturbatively, into bands. The theory of nearly free composite fermions (CFs) has been shown to be valid for the lowest band, and thus to capture the low temperature physics, but it over-predicts the number of states for the excited bands. We explain the state counting of higher bands in terms of composite fermions with an infinitely strong short range interaction between a CF particle and a CF hole. This interaction, the form of which we derive from the microscopic CF theory, eliminates configurations containing certain tightly bound CF excitons. With this modification, the CF theory reproduces, for all well-defined excited bands, an exact counting for ν > 1 / 3 , and an almost exact counting for ν <= 1 / 3 . The resulting insight clarifies that the corrections to the nearly free CF theory are not thermodynamically significant at sufficiently low temperatures, thus providing a microscopic explanation for why it has proved successful for the analysis of the various properties of the CF Fermi sea. NSF grants DMR-1005536 and DMR-0820404, Polish NCN grant 2011/01/B/ST3/04504 and EU Marie Curie Grant PCIG09-GA-2011-294186, Research Computing and Cyberinfrastructure, PSU and Wroclaw Centre for Networking and Supercomputing

Fractional charge and emergent mass hierarchy in diagonal two-leg t – J cylinders

DOE PAGES

Jiang, Yi-Fan; Jiang, Hong-Chen; Yao, Hong; ...

2017-06-06

Here, we define a class of “diagonal” tmore » $-$ J ladders rotated by π / 4 relative to the canonical lattice directions of the square lattice, and study it using density matrix renormalization group. Here, we focus on the two-leg cylinder with a doped hole concentration near x = $$\\frac{1}{4}$$ . At exactly x = $$\\frac{1}{4}$$, the system forms a period 4 charge density wave and exhibits spin-charge separation. Slightly away from $$\\frac{1}{4}$$ doping, we observe several topologically distinct types of solitons with well-defined fractionalized quantum numbers. Remarkably, given the absence of any obvious small parameter, the effective masses of the emergent solitons differ by several orders of magnitude.« less

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

Ma, Xiaoyao; Hall, Randall W.; Löffler, Frank

The Sign Learning Kink (SiLK) based Quantum Monte Carlo (QMC) method is used to calculate the ab initio ground state energies for multiple geometries of the H2O, N2, and F2 molecules. The method is based on Feynman’s path integral formulation of quantum mechanics and has two stages. The first stage is called the learning stage and reduces the well-known QMC minus sign problem by optimizing the linear combinations of Slater determinants which are used in the second stage, a conventional QMC simulation. The method is tested using different vector spaces and compared to the results of other quantum chemical methodsmore » and to exact diagonalization. Our findings demonstrate that the SiLK method is accurate and reduces or eliminates the minus sign problem.« less

Dynamics of a Dirac oscillator coupled to an external field: a new class of solvable problems

NASA Astrophysics Data System (ADS)

Sadurní, E.; Torres, J. M.; Seligman, T. H.

2010-07-01

The Dirac oscillator coupled to an external two-component field can retain its solvability, if couplings are appropriately chosen. This provides a new class of integrable systems. A simplified way of a solution is given by recasting the known solution of the Dirac oscillator into matrix form; there one notes that a block-diagonal form arises in a Hamiltonian formulation. The blocks are two dimensional. Choosing couplings that do not affect the block structure, these blow up the 2 × 2 matrices to 4 × 4 matrices, thus conserving solvability. The result can be cast again in covariant form. By way of an example we apply this exact solution to calculate the evolution of entanglement.

Light-Enhanced Spin Fluctuations and d -Wave Superconductivity at a Phase Boundary

NASA Astrophysics Data System (ADS)

Wang, Yao; Chen, Cheng-Chien; Moritz, B.; Devereaux, T. P.

2018-06-01

Time-domain techniques have shown the potential of photomanipulating existing orders and inducing new states of matter in strongly correlated materials. Using time-resolved exact diagonalization, we perform numerical studies of pump dynamics in a Mott-Peierls system with competing charge and spin density waves. A light-enhanced d -wave superconductivity is observed when the system resides near a quantum phase boundary. By examining the evolution of spin, charge, and superconducting susceptibilities, we show that a subdominant state in equilibrium can be stabilized by photomanipulating the charge order to allow superconductivity to appear and dominate. This work provides an interpretation of light-induced superconductivity from the perspective of order competition and offers a promising approach for designing novel emergent states out of equilibrium.

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.

Ground-state energies of the nonlinear sigma model and the Heisenberg spin chains

NASA Technical Reports Server (NTRS)

Zhang, Shoucheng; Schulz, H. J.; Ziman, Timothy

1989-01-01

A theorem on the O(3) nonlinear sigma model with the topological theta term is proved, which states that the ground-state energy at theta = pi is always higher than the ground-state energy at theta = 0, for the same value of the coupling constant g. Provided that the nonlinear sigma model gives the correct description for the Heisenberg spin chains in the large-s limit, this theorem makes a definite prediction relating the ground-state energies of the half-integer and the integer spin chains. The ground-state energies obtained from the exact Bethe ansatz solution for the spin-1/2 chain and the numerical diagonalization on the spin-1, spin-3/2, and spin-2 chains support this prediction.

Hubbard pair cluster in the external fields. Studies of the magnetic properties

NASA Astrophysics Data System (ADS)

Balcerzak, T.; Szałowski, K.

2018-06-01

The magnetic properties of the two-site Hubbard cluster (dimer or pair), embedded in the external electric and magnetic fields and treated as the open system, are studied by means of the exact diagonalization of the Hamiltonian. The formalism of the grand canonical ensemble is adopted. The phase diagrams, on-site magnetizations, spin-spin correlations, mean occupation numbers and hopping energy are investigated and illustrated in figures. An influence of temperature, mean electron concentration, Coulomb U parameter and external fields on the quantities of interest is presented and discussed. In particular, the anomalous behaviour of the magnetization and correlation function vs. temperature near the critical magnetic field is found. Also, the effect of magnetization switching by the external fields is demonstrated.

Competing orders in the Hofstadter t -J model

NASA Astrophysics Data System (ADS)

Tu, Wei-Lin; Schindler, Frank; Neupert, Titus; Poilblanc, Didier

2018-01-01

The Hofstadter model describes noninteracting fermions on a lattice in the presence of an external magnetic field. Motivated by the plethora of solid-state phases emerging from electron interactions, we consider an interacting version of the Hofstadter model, including a Hubbard repulsion U . We investigate this model in the large-U limit corresponding to a t -J Hamiltonian with an external (orbital) magnetic field. By using renormalized mean-field theory supplemented by exact diagonalization calculations of small clusters, we find evidence for competing symmetry-breaking phases, exhibiting (possibly coexisting) charge, bond, and superconducting orders. Topological properties of the states are also investigated, and some of our results are compared to related experiments involving ultracold atoms loaded on optical lattices in the presence of a synthetic gauge field.

Fidelity study of superconductivity in extended Hubbard models

DOE PAGES

Plonka, N.; Jia, C. J.; Wang, Y.; ...

2015-07-08

The Hubbard model with local on-site repulsion is generally thought to possess a superconducting ground state for appropriate parameters, but the effects of more realistic long-range Coulomb interactions have not been studied extensively. We study the influence of these interactions on superconductivity by including nearest- and next-nearest-neighbor extended Hubbard interactions in addition to the usual on-site terms. Utilizing numerical exact diagonalization, we analyze the signatures of superconductivity in the ground states through the fidelity metric of quantum information theory. Finally, we find that nearest and next-nearest neighbor interactions have thresholds above which they destabilize superconductivity regardless of whether they aremore » attractive or repulsive, seemingly due to competing charge fluctuations.« less

Strong spin-orbit effects in transition metal oxides with tetrahedral coordination

NASA Astrophysics Data System (ADS)

Forte, Filomena; Guerra, Delia; Autieri, Carmine; Romano, Alfonso; Noce, Canio; Avella, Adolfo

2018-05-01

To prove that spin-orbit coupling can play a relevant role in determining the magnetic structure of transition metal oxides with tetrahedral coordination, we investigate the d1 Mott insulator KOsO4, combining density functional theory calculations and the exact diagonalization approach. We find that the interplay between crystal field, strong spin-orbit coupling, electronic correlations and structural distortions brings the system towards an antiferromagnetic phase, characterized by a non-vanishing orbital angular momentum and anisotropy among the in-plane and the out-of-plane antiferromagnetic correlations. We also show that, due to the peculiar interplay between spin-orbit coupling, Hund's coupling and hopping connectivity the system is on the verge of developing short range ferromagnetic correlations marked by strong directionality.

Exact diagonalization of quantum lattice models on coprocessors

NASA Astrophysics Data System (ADS)

Siro, T.; Harju, A.

2016-10-01

We implement the Lanczos algorithm on an Intel Xeon Phi coprocessor and compare its performance to a multi-core Intel Xeon CPU and an NVIDIA graphics processor. The Xeon and the Xeon Phi are parallelized with OpenMP and the graphics processor is programmed with CUDA. The performance is evaluated by measuring the execution time of a single step in the Lanczos algorithm. We study two quantum lattice models with different particle numbers, and conclude that for small systems, the multi-core CPU is the fastest platform, while for large systems, the graphics processor is the clear winner, reaching speedups of up to 7.6 compared to the CPU. The Xeon Phi outperforms the CPU with sufficiently large particle number, reaching a speedup of 2.5.

Novel half-magnetization plateau and nematiclike transition in the S =1 skew chain Ni2V2O7

NASA Astrophysics Data System (ADS)

Ouyang, Z. W.; Sun, Y. C.; Wang, J. F.; Yue, X. Y.; Chen, R.; Wang, Z. X.; He, Z. Z.; Xia, Z. C.; Liu, Y.; Rao, G. H.

2018-04-01

A quantized magnetization plateau is usually not expected when a classic spin-flop transition occurs in a low-dimensional antiferromagnet. Here, we report an experimental observation of a spin-flop transition followed by a wide half-magnetization plateau in the S =1 skew-chain system Ni2V2O7 . This plateau, which is stabilized in fields of 8-30 T, is realized through an exotic nematiclike phase transition for magnetic fields applied along all three crystallographic axes, resulting in rich anisotropic phase diagrams. We discuss a possible mechanism whereby the magnetic frustration and interchain interactions may cause this half-magnetization plateau, which is in agreement with our exact diagonalization result.

Quantum phases of spinful Fermi gases in optical cavities

NASA Astrophysics Data System (ADS)

Colella, E.; Citro, R.; Barsanti, M.; Rossini, D.; Chiofalo, M.-L.

2018-04-01

We explore the quantum phases emerging from the interplay between spin and motional degrees of freedom of a one-dimensional quantum fluid of spinful fermionic atoms, effectively interacting via a photon-mediating mechanism with tunable sign and strength g , as it can be realized in present-day experiments with optical cavities. We find the emergence, in the very same system, of spin- and atomic-density wave ordering, accompanied by the occurrence of superfluidity for g >0 , while cavity photons are seen to drive strong correlations at all g values, with fermionic character for g >0 , and bosonic character for g <0 . Due to the long-range nature of interactions, to infer these results we combine mean-field and exact-diagonalization methods supported by bosonization analysis.

Current collapse in tunneling transport through benzene.

PubMed

Hettler, M H; Wenzel, W; Wegewijs, M R; Schoeller, H

2003-02-21

We investigate the electrical transport through a system of benzene coupled to metal electrodes by electron tunneling. Using electronic structure calculations, a semiquantitative model for the pi electrons of the benzene is derived that includes general two-body interactions. After exact diagonalization of the benzene model the transport is computed using perturbation theory for weak electrode-benzene coupling (golden rule approximation). We include the effect of an applied electric field on the molecular states, as well as radiative relaxation. We predict a current collapse and strong negative differential conductance due to a "blocking" state when the electrode is coupled to the para-position of benzene. In contrast, for coupling to the meta-position, a series of steps in the I-V curve is found.

Multiparticle instability in a spin-imbalanced Fermi gas

NASA Astrophysics Data System (ADS)

Whitehead, T. M.; Conduit, G. J.

2018-01-01

Weak attractive interactions in a spin-imbalanced Fermi gas induce a multiparticle instability, binding multiple fermions together. The maximum binding energy per particle is achieved when the ratio of the number of up- and down-spin particles in the instability is equal to the ratio of the up- and down-spin densities of states in momentum at the Fermi surfaces, to utilize the variational freedom of all available momentum states. We derive this result using an analytical approach, and verify it using exact diagonalization. The multiparticle instability extends the Cooper pairing instability of balanced Fermi gases to the imbalanced case, and could form the basis of a many-body state, analogously to the construction of the Bardeen-Cooper-Schrieffer theory of superconductivity out of Cooper pairs.

Many-body localization in a long range XXZ model with random-field

NASA Astrophysics Data System (ADS)

Li, Bo

2016-12-01

Many-body localization (MBL) in a long range interaction XXZ model with random field are investigated. Using the exact diagonal method, the MBL phase diagram with different tuning parameters and interaction range is obtained. It is found that the phase diagram of finite size results supplies strong evidence to confirm that the threshold interaction exponent α = 2. The tuning parameter Δ can efficiently change the MBL edge in high energy density stats, thus the system can be controlled to transfer from thermal phase to MBL phase by changing Δ. The energy level statistics data are consistent with result of the MBL phase diagram. However energy level statistics data cannot detect the thermal phase correctly in extreme long range case.

Landau problem with time dependent mass in time dependent electric and harmonic background fields

NASA Astrophysics Data System (ADS)

Lawson, Latévi M.; Avossevou, Gabriel Y. H.

2018-04-01

The spectrum of a Hamiltonian describing the dynamics of a Landau particle with time-dependent mass and frequency undergoing the influence of a uniform time-dependent electric field is obtained. The configuration space wave function of the model is expressed in terms of the generalised Laguerre polynomials. To diagonalize the time-dependent Hamiltonian, we employ the Lewis-Riesenfeld method of invariants. To this end, we introduce a unitary transformation in the framework of the algebraic formalism to construct the invariant operator of the system and then to obtain the exact solution of the Hamiltonian. We recover the solutions of the ordinary Landau problem in the absence of the electric and harmonic fields for a constant particle mass.

Electron spin resonance modes in a strong-leg ladder in the Tomonaga-Luttinger liquid phase

NASA Astrophysics Data System (ADS)

Ozerov, M.; Maksymenko, M.; Wosnitza, J.; Honecker, A.; Landee, C. P.; Turnbull, M. M.; Furuya, S. C.; Giamarchi, T.; Zvyagin, S. A.

2015-12-01

Magnetic excitations in the strong-leg quantum spin ladder compound (C7H10N) 2CuBr4 (known as DIMPY) in the field-induced Tomonaga-Luttinger spin-liquid phase are studied by means of high-field electron spin resonance (ESR) spectroscopy. The presence of a gapped ESR mode with unusual nonlinear frequency-field dependence is revealed experimentally. Using a combination of analytic and exact-diagonalization methods, we compute the dynamical structure factor and identify this mode with longitudinal excitations in the antisymmetric channel. We argue that these excitations constitute a fingerprint of the spin dynamics in a strong-leg spin-1/2 Heisenberg antiferromagnetic ladder and owe their ESR observability to the uniform Dzyaloshinskii-Moriya interaction.

Comprehensive Thematic T-Matrix Reference Database: A 2015-2017 Update

NASA Technical Reports Server (NTRS)

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

2017-01-01

The T-matrix method pioneered by Peter C. Waterman is one of the most versatile and efficient numerically exact computer solvers of the time-harmonic macroscopic Maxwell equations. It is widely used for the computation of electromagnetic scattering by single and composite particles, discrete random media, periodic structures (including metamaterials), and particles in the vicinity of plane or rough interfaces separating media with different refractive indices. This paper is the eighth update to the comprehensive thematic database of peer-reviewed T-matrix publications initiated in 2004 and lists relevant publications that have appeared since 2015. It also references a small number of earlier publications overlooked previously.

Comprehensive thematic T-matrix reference database: A 2015-2017 update

NASA Astrophysics Data System (ADS)

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

2017-11-01

The T-matrix method pioneered by Peter C. Waterman is one of the most versatile and efficient numerically exact computer solvers of the time-harmonic macroscopic Maxwell equations. It is widely used for the computation of electromagnetic scattering by single and composite particles, discrete random media, periodic structures (including metamaterials), and particles in the vicinity of plane or rough interfaces separating media with different refractive indices. This paper is the eighth update to the comprehensive thematic database of peer-reviewed T-matrix publications initiated in 2004 and lists relevant publications that have appeared since 2015. It also references a small number of earlier publications overlooked previously.

A Fast MoM Solver (GIFFT) for Large Arrays of Microstrip and Cavity-Backed Antennas

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

Fasenfest, B J; Capolino, F; Wilton, D

2005-02-02

A straightforward numerical analysis of large arrays of arbitrary contour (and possibly missing elements) requires large memory storage and long computation times. Several techniques are currently under development to reduce this cost. One such technique is the GIFFT (Green's function interpolation and FFT) method discussed here that belongs to the class of fast solvers for large structures. This method uses a modification of the standard AIM approach [1] that takes into account the reusability properties of matrices that arise from identical array elements. If the array consists of planar conducting bodies, the array elements are meshed using standard subdomain basismore » functions, such as the RWG basis. The Green's function is then projected onto a sparse regular grid of separable interpolating polynomials. This grid can then be used in a 2D or 3D FFT to accelerate the matrix-vector product used in an iterative solver [2]. The method has been proven to greatly reduce solve time by speeding up the matrix-vector product computation. The GIFFT approach also reduces fill time and memory requirements, since only the near element interactions need to be calculated exactly. The present work extends GIFFT to layered material Green's functions and multiregion interactions via slots in ground planes. In addition, a preconditioner is implemented to greatly reduce the number of iterations required for a solution. The general scheme of the GIFFT method is reported in [2]; this contribution is limited to presenting new results for array antennas made of slot-excited patches and cavity-backed patch antennas.« less

High-Order Hyperbolic Residual-Distribution Schemes on Arbitrary Triangular Grids

NASA Technical Reports Server (NTRS)

Mazaheri, Alireza; Nishikawa, Hiroaki

2015-01-01

In this paper, we construct high-order hyperbolic residual-distribution schemes for general advection-diffusion problems on arbitrary triangular grids. We demonstrate that the second-order accuracy of the hyperbolic schemes can be greatly improved by requiring the scheme to preserve exact quadratic solutions. We also show that the improved second-order scheme can be easily extended to third-order by further requiring the exactness for cubic solutions. We construct these schemes based on the LDA and the SUPG methodology formulated in the framework of the residual-distribution method. For both second- and third-order-schemes, we construct a fully implicit solver by the exact residual Jacobian of the second-order scheme, and demonstrate rapid convergence of 10-15 iterations to reduce the residuals by 10 orders of magnitude. We demonstrate also that these schemes can be constructed based on a separate treatment of the advective and diffusive terms, which paves the way for the construction of hyperbolic residual-distribution schemes for the compressible Navier-Stokes equations. Numerical results show that these schemes produce exceptionally accurate and smooth solution gradients on highly skewed and anisotropic triangular grids, including curved boundary problems, using linear elements. We also present Fourier analysis performed on the constructed linear system and show that an under-relaxation parameter is needed for stabilization of Gauss-Seidel relaxation.

A simple molecular mechanics integrator in mixed rigid body and dihedral angle space

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

Vitalis, Andreas, E-mail: a.vitalis@bioc.uzh.ch; Pappu, Rohit V.

2014-07-21

We propose a numerical scheme to integrate equations of motion in a mixed space of rigid-body and dihedral angle coordinates. The focus of the presentation is biomolecular systems and the framework is applicable to polymers with tree-like topology. By approximating the effective mass matrix as diagonal and lumping all bias torques into the time dependencies of the diagonal elements, we take advantage of the formal decoupling of individual equations of motion. We impose energy conservation independently for every degree of freedom and this is used to derive a numerical integration scheme. The cost of all auxiliary operations is linear inmore » the number of atoms. By coupling the scheme to one of two popular thermostats, we extend the method to sample constant temperature ensembles. We demonstrate that the integrator of choice yields satisfactory stability and is free of mass-metric tensor artifacts, which is expected by construction of the algorithm. Two fundamentally different systems, viz., liquid water and an α-helical peptide in a continuum solvent are used to establish the applicability of our method to a wide range of problems. The resultant constant temperature ensembles are shown to be thermodynamically accurate. The latter relies on detailed, quantitative comparisons to data from reference sampling schemes operating on exactly the same sets of degrees of freedom.« less

Obtaining highly excited eigenstates of the localized XX chain via DMRG-X.

PubMed

Devakul, Trithep; Khemani, Vedika; Pollmann, Frank; Huse, David A; Sondhi, S L

2017-12-13

We benchmark a variant of the recently introduced density matrix renormalization group (DMRG)-X algorithm against exact results for the localized random field XX chain. We find that the eigenstates obtained via DMRG-X exhibit a highly accurate l-bit description for system sizes much bigger than the direct, many-body, exact diagonalization in the spin variables is able to access. We take advantage of the underlying free fermion description of the XX model to accurately test the strengths and limitations of this algorithm for large system sizes. We discuss the theoretical constraints on the performance of the algorithm from the entanglement properties of the eigenstates, and its actual performance at different values of disorder. A small but significant improvement to the algorithm is also presented, which helps significantly with convergence. We find that, at high entanglement, DMRG-X shows a bias towards eigenstates with low entanglement, but can be improved with increased bond dimension. This result suggests that one must be careful when applying the algorithm for interacting many-body localized spin models near a transition.This article is part of the themed issue 'Breakdown of ergodicity in quantum systems: from solids to synthetic matter'. © 2017 The Author(s).

Obtaining highly excited eigenstates of the localized XX chain via DMRG-X

NASA Astrophysics Data System (ADS)

Devakul, Trithep; Khemani, Vedika; Pollmann, Frank; Huse, David A.; Sondhi, S. L.

2017-10-01

We benchmark a variant of the recently introduced density matrix renormalization group (DMRG)-X algorithm against exact results for the localized random field XX chain. We find that the eigenstates obtained via DMRG-X exhibit a highly accurate l-bit description for system sizes much bigger than the direct, many-body, exact diagonalization in the spin variables is able to access. We take advantage of the underlying free fermion description of the XX model to accurately test the strengths and limitations of this algorithm for large system sizes. We discuss the theoretical constraints on the performance of the algorithm from the entanglement properties of the eigenstates, and its actual performance at different values of disorder. A small but significant improvement to the algorithm is also presented, which helps significantly with convergence. We find that, at high entanglement, DMRG-X shows a bias towards eigenstates with low entanglement, but can be improved with increased bond dimension. This result suggests that one must be careful when applying the algorithm for interacting many-body localized spin models near a transition. This article is part of the themed issue 'Breakdown of ergodicity in quantum systems: from solids to synthetic matter'.

Density-Functional Theory description of transport in the single-electron transistor

NASA Astrophysics Data System (ADS)

Zawadzki, Krissia; Oliveira, Luiz N.

The Kondo effect governs the low-temperature transport properties of the single electron transistor (SET), a quantum dot bridging two electron gases. In the weak coupling limit, for odd dot occupation, the gate-potential profile of the conductance approaches a step, known as the Kondo plateau. The plateau and other SET properties being well understood on the basis of the Anderson model, more realistic (i. e., DFT) descriptions of the device are now desired. This poses a challenge, since the SET is strongly correlated. DFT computations that reproduce the conductance plateau have been reported, e. g., by, which rely on the exact functional provided by the Bethe-Ansatz solution for the Anderson model. Here, sticking to DFT tradition, we employ a functional derived from a homogeneous system: the parametrization of the Lieb-Wu solution for the Hubbard model due to. Our computations reproduce the plateau and yield other results in accurate agreement with the exact diagonalization of the Anderson Hamiltonian. The prospects for extensions to realistic descriptions of two-dimensional nanostructured devices will be discussed. Luiz N. Oliveira thanks CNPq (312658/2013-3) and Krissia Zawadzki thanks CNPq (140703/2014-4) for financial support.

Time-dependent Gutzwiller theory of magnetic excitations in the Hubbard model

NASA Astrophysics Data System (ADS)

Seibold, G.; Becca, F.; Rubin, P.; Lorenzana, J.

2004-04-01

We use a spin-rotational invariant Gutzwiller energy functional to compute random-phase-approximation-like (RPA) fluctuations on top of the Gutzwiller approximation (GA). The method can be viewed as an extension of the previously developed GA+RPA approach for the charge sector [G. Seibold and J. Lorenzana, Phys. Rev. Lett. 86, 2605 (2001)] with respect to the inclusion of the magnetic excitations. Unlike the charge case, no assumptions about the time evolution of the double occupancy are needed in this case. Interestingly, in a spin-rotational invariant system, we find the correct degeneracy between triplet excitations, showing the consistency of both computations. Since no restrictions are imposed on the symmetry of the underlying saddle-point solution, our approach is suitable for the evaluation of the magnetic susceptibility and dynamical structure factor in strongly correlated inhomogeneous systems. We present a detailed study of the quality of our approach by comparing with exact diagonalization results and show its much higher accuracy compared to the conventional Hartree-Fock+RPA theory. In infinite dimensions, where the GA becomes exact for the Gutzwiller variational energy, we evaluate ferromagnetic and antiferromagnetic instabilities from the transverse magnetic susceptibility. The resulting phase diagram is in complete agreement with previous variational computations.

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

Ma, Xiaoyao; Hall, Randall W.; Department of Chemistry, Louisiana State University, Baton Rouge, Louisiana 70803

The Sign Learning Kink (SiLK) based Quantum Monte Carlo (QMC) method is used to calculate the ab initio ground state energies for multiple geometries of the H{sub 2}O, N{sub 2}, and F{sub 2} molecules. The method is based on Feynman’s path integral formulation of quantum mechanics and has two stages. The first stage is called the learning stage and reduces the well-known QMC minus sign problem by optimizing the linear combinations of Slater determinants which are used in the second stage, a conventional QMC simulation. The method is tested using different vector spaces and compared to the results of othermore » quantum chemical methods and to exact diagonalization. Our findings demonstrate that the SiLK method is accurate and reduces or eliminates the minus sign problem.« less

Infrared singularities of scattering amplitudes in perturbative QCD

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

Becher, Thomas; Neubert, Matthias

2013-11-01

An exact formula is derived for the infrared singularities of dimensionally regularized scattering amplitudes in massless QCD with an arbitrary number of legs, valid at any number of loops. It is based on the conjecture that the anomalous-dimension matrix of n-jet operators in soft-collinear effective theory contains only a single non-trivial color structure, whose coefficient is the cusp anomalous dimension of Wilson loops with light-like segments. Its color-diagonal part is characterized by two anomalous dimensions, which are extracted to three-loop order from known perturbative results for the quark and gluon form factors. This allows us to predict the three-loop coefficientsmore » of all 1/epsilon^k poles for an arbitrary n-parton scattering amplitudes, generalizing existing two-loop results.« less

High-Power Collective Charging of a Solid-State Quantum Battery

NASA Astrophysics Data System (ADS)

Ferraro, Dario; Campisi, Michele; Andolina, Gian Marcello; Pellegrini, Vittorio; Polini, Marco

2018-03-01

Quantum information theorems state that it is possible to exploit collective quantum resources to greatly enhance the charging power of quantum batteries (QBs) made of many identical elementary units. We here present and solve a model of a QB that can be engineered in solid-state architectures. It consists of N two-level systems coupled to a single photonic mode in a cavity. We contrast this collective model ("Dicke QB"), whereby entanglement is genuinely created by the common photonic mode, to the one in which each two-level system is coupled to its own separate cavity mode ("Rabi QB"). By employing exact diagonalization, we demonstrate the emergence of a quantum advantage in the charging power of Dicke QBs, which scales like √{N } for N ≫1 .

Perfect Diode in Quantum Spin Chains

NASA Astrophysics Data System (ADS)

Balachandran, Vinitha; Benenti, Giuliano; Pereira, Emmanuel; Casati, Giulio; Poletti, Dario

2018-05-01

We study the rectification of the spin current in X X Z chains segmented in two parts, each with a different anisotropy parameter. Using exact diagonalization and a matrix product state algorithm, we find that a large rectification (of the order of 1 04) is attainable even using a short chain of N =8 spins, when one-half of the chain is gapless while the other has a large enough anisotropy. We present evidence of diffusive transport when the current is driven in one direction and of a transition to an insulating behavior of the system when driven in the opposite direction, leading to a perfect diode in the thermodynamic limit. The above results are explained in terms of matching of the spectrum of magnon excitations between the two halves of the chain.

Anisotropy-driven transition from the Moore-Read state to quantum Hall stripes

NASA Astrophysics Data System (ADS)

Zhu, Zheng; Sodemann, Inti; Sheng, D. N.; Fu, Liang

2017-05-01

We investigate the nature of the quantum Hall liquid in a half-filled second Landau level (n =1 ) as a function of band mass anisotropy using numerical exact diagonalization and density matrix renormalization group methods. We find increasing the mass anisotropy induces a quantum phase transition from the Moore-Read state to a charge density wave state. By analyzing the energy spectrum, guiding center structure factors, and by adding weak pinning potentials, we show that this charge density wave is a unidirectional quantum Hall stripe, which has a periodicity of a few magnetic lengths and survives in the thermodynamic limit. We find smooth profiles for the guiding center occupation function that reveal the strong coupling nature of the array of chiral Luttinger liquids residing at the stripe edges.

Formation of helical domain walls in the fractional quantum Hall regime as a step toward realization of high-order non-Abelian excitations

NASA Astrophysics Data System (ADS)

Wu, Tailung; Wan, Zhong; Kazakov, Aleksandr; Wang, Ying; Simion, George; Liang, Jingcheng; West, Kenneth W.; Baldwin, Kirk; Pfeiffer, Loren N.; Lyanda-Geller, Yuli; Rokhinson, Leonid P.

2018-06-01

We propose an experimentally feasible platform to realize parafermions (high-order non-Abelian excitations) based on spin transitions in the fractional quantum Hall effect regime. As a proof of concept we demonstrate a local control of the spin transition at a filling factor 2/3 and formation of a conducting fractional helical domain wall (fhDW) along a gate boundary. Coupled to an s -wave superconductor these fhDWs are expected to support parafermionic excitations. We present exact diagonalization numerical studies of fhDWs and show that they indeed possess electronic and magnetic structures needed for the formation of parafermions. A reconfigurable network of fhDWs will allow manipulation and braiding of parafermionic excitations in multigate devices.

Emergent Fermi Sea in A System of Interacting Bosons

NASA Astrophysics Data System (ADS)

Wu, Yinghai; Jain, Jainendra

2015-03-01

An understanding of the possible ways in which interactions can produce fundamentally new emergent many-body states is a central problem of condensed matter physics. We ask if a Fermi sea can arise in a system of bosons subject to contact interaction. Based on exact diagonalization studies and variational wave functions, we predict that such a state is likely to occur when a system of two-component bosons in two dimensions, interacting via a species independent contact interaction, is exposed to a synthetic magnetic field of strength that corresponds to a filling factor of unity. The bosons each bind a single vortex as a result of the repulsive interaction, and these fermionic bound states, namely composite fermions, form a spin-singlet Fermi sea. Financial support from the DOE under Grant No. DE-SC0005042.

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.

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.

Crossover between few and many fermions in a harmonic trap

NASA Astrophysics Data System (ADS)

Grining, Tomasz; Tomza, Michał; Lesiuk, Michał; Przybytek, Michał; Musiał, Monika; Moszynski, Robert; Lewenstein, Maciej; Massignan, Pietro

2015-12-01

The properties of a balanced two-component Fermi gas in a one-dimensional harmonic trap are studied by means of the coupled-cluster method. For few fermions we recover the results of exact diagonalization, yet with this method we are able to study much larger systems. We compute the energy, the chemical potential, the pairing gap, and the density profile of the trapped clouds, smoothly mapping the crossover between the few-body and many-body limits. The energy is found to converge surprisingly rapidly to the many-body result for every value of the interaction strength. Many more particles are instead needed to give rise to the nonanalytic behavior of the pairing gap, and to smoothen the pronounced even-odd oscillations of the chemical potential induced by the shell structure of the trap.

Simplicity and efficiency of integrate-and-fire neuron models.

PubMed

Plesser, Hans E; Diesmann, Markus

2009-02-01

Lovelace and Cios (2008) recently proposed a very simple spiking neuron (VSSN) model for simulations of large neuronal networks as an efficient replacement for the integrate-and-fire neuron model. We argue that the VSSN model falls behind key advances in neuronal network modeling over the past 20 years, in particular, techniques that permit simulators to compute the state of the neuron without repeated summation over the history of input spikes and to integrate the subthreshold dynamics exactly. State-of-the-art solvers for networks of integrate-and-fire model neurons are substantially more efficient than the VSSN simulator and allow routine simulations of networks of some 10(5) neurons and 10(9) connections on moderate computer clusters.

Gas Evolution Dynamics in Godunov-Type Schemes and Analysis of Numerical Shock Instability

NASA Technical Reports Server (NTRS)

Xu, Kun

1999-01-01

In this paper we are going to study the gas evolution dynamics of the exact and approximate Riemann solvers, e.g., the Flux Vector Splitting (FVS) and the Flux Difference Splitting (FDS) schemes. Since the FVS scheme and the Kinetic Flux Vector Splitting (KFVS) scheme have the same physical mechanism and similar flux function, based on the analysis of the discretized KFVS scheme the weakness and advantage of the FVS scheme are closely observed. The subtle dissipative mechanism of the Godunov method in the 2D case is also analyzed, and the physical reason for shock instability, i.e., carbuncle phenomena and odd-even decoupling, is presented.

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.

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.

Distilling perfect GHZ states from two copies of non-GHZ-diagonal mixed states

NASA Astrophysics Data System (ADS)

Wang, Xin-Wen; Tang, Shi-Qing; Yuan, Ji-Bing; Zhang, Deng-Yu

2017-06-01

It has been shown that a nearly pure Greenberger-Horne-Zeilinger (GHZ) state could be distilled from a large (even infinite) number of GHZ-diagonal states that can be obtained by depolarizing general multipartite mixed states (non-GHZ-diagonal states) through sequences of (probabilistic) local operations and classical communications. We here demonstrate that perfect GHZ states can be extracted, with certain probabilities, from two copies of non-GHZ-diagonal mixed states when some conditions are satisfied. This result implies that it is not necessary to depolarize these entangled mixed states to the GHZ-diagonal type, and that they are better than GHZ-diagonal states for distillation of pure GHZ states. We find a wide class of multipartite entangled mixed states that fulfill the requirements. Moreover, we display that the obtained result can be applied to practical noisy environments, e.g., amplitude-damping channels. Our findings provide an important complementarity to conventional GHZ-state distillation protocols (designed for GHZ-diagonal states) in theory, as well as having practical applications.

Iterative algorithm for joint zero diagonalization with application in blind source separation.

PubMed

Zhang, Wei-Tao; Lou, Shun-Tian

2011-07-01

A new iterative algorithm for the nonunitary joint zero diagonalization of a set of matrices is proposed for blind source separation applications. On one hand, since the zero diagonalizer of the proposed algorithm is constructed iteratively by successive multiplications of an invertible matrix, the singular solutions that occur in the existing nonunitary iterative algorithms are naturally avoided. On the other hand, compared to the algebraic method for joint zero diagonalization, the proposed algorithm requires fewer matrices to be zero diagonalized to yield even better performance. The extension of the algorithm to the complex and nonsquare mixing cases is also addressed. Numerical simulations on both synthetic data and blind source separation using time-frequency distributions illustrate the performance of the algorithm and provide a comparison to the leading joint zero diagonalization schemes.

Parallel 3D Multi-Stage Simulation of a Turbofan Engine

NASA Technical Reports Server (NTRS)

Turner, Mark G.; Topp, David A.

1998-01-01

A 3D multistage simulation of each component of a modern GE Turbofan engine has been made. An axisymmetric view of this engine is presented in the document. This includes a fan, booster rig, high pressure compressor rig, high pressure turbine rig and a low pressure turbine rig. In the near future, all components will be run in a single calculation for a solution of 49 blade rows. The simulation exploits the use of parallel computations by using two levels of parallelism. Each blade row is run in parallel and each blade row grid is decomposed into several domains and run in parallel. 20 processors are used for the 4 blade row analysis. The average passage approach developed by John Adamczyk at NASA Lewis Research Center has been further developed and parallelized. This is APNASA Version A. It is a Navier-Stokes solver using a 4-stage explicit Runge-Kutta time marching scheme with variable time steps and residual smoothing for convergence acceleration. It has an implicit K-E turbulence model which uses an ADI solver to factor the matrix. Between 50 and 100 explicit time steps are solved before a blade row body force is calculated and exchanged with the other blade rows. This outer iteration has been coined a "flip." Efforts have been made to make the solver linearly scaleable with the number of blade rows. Enough flips are run (between 50 and 200) so the solution in the entire machine is not changing. The K-E equations are generally solved every other explicit time step. One of the key requirements in the development of the parallel code was to make the parallel solution exactly (bit for bit) match the serial solution. This has helped isolate many small parallel bugs and guarantee the parallelization was done correctly. The domain decomposition is done only in the axial direction since the number of points axially is much larger than the other two directions. This code uses MPI for message passing. The parallel speed up of the solver portion (no 1/0 or body force calculation) for a grid which has 227 points axially.

Exact and Metaheuristic Approaches for a Bi-Objective School Bus Scheduling Problem.

PubMed

Chen, Xiaopan; Kong, Yunfeng; Dang, Lanxue; Hou, Yane; Ye, Xinyue

2015-01-01

As a class of hard combinatorial optimization problems, the school bus routing problem has received considerable attention in the last decades. For a multi-school system, given the bus trips for each school, the school bus scheduling problem aims at optimizing bus schedules to serve all the trips within the school time windows. In this paper, we propose two approaches for solving the bi-objective school bus scheduling problem: an exact method of mixed integer programming (MIP) and a metaheuristic method which combines simulated annealing with local search. We develop MIP formulations for homogenous and heterogeneous fleet problems respectively and solve the models by MIP solver CPLEX. The bus type-based formulation for heterogeneous fleet problem reduces the model complexity in terms of the number of decision variables and constraints. The metaheuristic method is a two-stage framework for minimizing the number of buses to be used as well as the total travel distance of buses. We evaluate the proposed MIP and the metaheuristic method on two benchmark datasets, showing that on both instances, our metaheuristic method significantly outperforms the respective state-of-the-art methods.

A practical approximation algorithm for solving massive instances of hybridization number for binary and nonbinary trees.

PubMed

van Iersel, Leo; Kelk, Steven; Lekić, Nela; Scornavacca, Celine

2014-05-05

Reticulate events play an important role in determining evolutionary relationships. The problem of computing the minimum number of such events to explain discordance between two phylogenetic trees is a hard computational problem. Even for binary trees, exact solvers struggle to solve instances with reticulation number larger than 40-50. Here we present CycleKiller and NonbinaryCycleKiller, the first methods to produce solutions verifiably close to optimality for instances with hundreds or even thousands of reticulations. Using simulations, we demonstrate that these algorithms run quickly for large and difficult instances, producing solutions that are very close to optimality. As a spin-off from our simulations we also present TerminusEst, which is the fastest exact method currently available that can handle nonbinary trees: this is used to measure the accuracy of the NonbinaryCycleKiller algorithm. All three methods are based on extensions of previous theoretical work (SIDMA 26(4):1635-1656, TCBB 10(1):18-25, SIDMA 28(1):49-66) and are publicly available. We also apply our methods to real data.

ARS-Media for Excel: A Spreadsheet Tool for Calculating Media Recipes Based on Ion-Specific Constraints

PubMed Central

Niedz, Randall P.

2016-01-01

ARS-Media for Excel is an ion solution calculator that uses “Microsoft Excel” to generate recipes of salts for complex ion mixtures specified by the user. Generating salt combinations (recipes) that result in pre-specified target ion values is a linear programming problem. Excel’s Solver add-on solves the linear programming equation to generate a recipe. Calculating a mixture of salts to generate exact solutions of complex ionic mixtures is required for at least 2 types of problems– 1) formulating relevant ecological/biological ionic solutions such as those from a specific lake, soil, cell, tissue, or organ and, 2) designing ion confounding-free experiments to determine ion-specific effects where ions are treated as statistical factors. Using ARS-Media for Excel to solve these two problems is illustrated by 1) exactly reconstructing a soil solution representative of a loamy agricultural soil and, 2) constructing an ion-based experiment to determine the effects of substituting Na+ for K+ on the growth of a Valencia sweet orange nonembryogenic cell line. PMID:27812202

ARS-Media for Excel: A Spreadsheet Tool for Calculating Media Recipes Based on Ion-Specific Constraints.

PubMed

Niedz, Randall P

2016-01-01

ARS-Media for Excel is an ion solution calculator that uses "Microsoft Excel" to generate recipes of salts for complex ion mixtures specified by the user. Generating salt combinations (recipes) that result in pre-specified target ion values is a linear programming problem. Excel's Solver add-on solves the linear programming equation to generate a recipe. Calculating a mixture of salts to generate exact solutions of complex ionic mixtures is required for at least 2 types of problems- 1) formulating relevant ecological/biological ionic solutions such as those from a specific lake, soil, cell, tissue, or organ and, 2) designing ion confounding-free experiments to determine ion-specific effects where ions are treated as statistical factors. Using ARS-Media for Excel to solve these two problems is illustrated by 1) exactly reconstructing a soil solution representative of a loamy agricultural soil and, 2) constructing an ion-based experiment to determine the effects of substituting Na+ for K+ on the growth of a Valencia sweet orange nonembryogenic cell line.

Point-particle method to compute diffusion-limited cellular uptake.

PubMed

Sozza, A; Piazza, F; Cencini, M; De Lillo, F; Boffetta, G

2018-02-01

We present an efficient point-particle approach to simulate reaction-diffusion processes of spherical absorbing particles in the diffusion-limited regime, as simple models of cellular uptake. The exact solution for a single absorber is used to calibrate the method, linking the numerical parameters to the physical particle radius and uptake rate. We study the configurations of multiple absorbers of increasing complexity to examine the performance of the method by comparing our simulations with available exact analytical or numerical results. We demonstrate the potential of the method to resolve the complex diffusive interactions, here quantified by the Sherwood number, measuring the uptake rate in terms of that of isolated absorbers. We implement the method in a pseudospectral solver that can be generalized to include fluid motion and fluid-particle interactions. As a test case of the presence of a flow, we consider the uptake rate by a particle in a linear shear flow. Overall, our method represents a powerful and flexible computational tool that can be employed to investigate many complex situations in biology, chemistry, and related sciences.

Contact Modelling of Large Radius Air Bending with Geometrically Exact Contact Algorithm

NASA Astrophysics Data System (ADS)

Vorkov, V.; Konyukhov, A.; Vandepitte, D.; Duflou, J. R.

2016-08-01

Usage of high-strength steels in conventional air bending is restricted due to limited bendability of these metals. Large-radius punches provide a typical approach for decreasing deformations during the bending process. However, as deflection progresses the loading scheme changes gradually. Therefore, modelling of the contact interaction is essential for an accurate description of the loading scheme. In the current contribution, the authors implemented a plane frictional contact element based on the penalty method. The geometrically exact contact algorithm is used for the penetration determination. The implementation is done using the OOFEM - open source finite element solver. In order to verify the simulation results, experiments have been conducted on a bending press brake for 4 mm Weldox 1300 with a punch radius of 30 mm and a die opening of 80 mm. The maximum error for the springback calculation is 0.87° for the bending angle of 144°. The contact interaction is a crucial part of large radius bending simulation and the implementation leads to a reliable solution for the springback angle.

Recovery Discontinuous Galerkin Jacobian-Free Newton-Krylov Method for All-Speed Flows

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

HyeongKae Park; Robert Nourgaliev; Vincent Mousseau

2008-07-01

A novel numerical algorithm (rDG-JFNK) for all-speed fluid flows with heat conduction and viscosity is introduced. The rDG-JFNK combines the Discontinuous Galerkin spatial discretization with the implicit Runge-Kutta time integration under the Jacobian-free Newton-Krylov framework. We solve fully-compressible Navier-Stokes equations without operator-splitting of hyperbolic, diffusion and reaction terms, which enables fully-coupled high-order temporal discretization. The stability constraint is removed due to the L-stable Explicit, Singly Diagonal Implicit Runge-Kutta (ESDIRK) scheme. The governing equations are solved in the conservative form, which allows one to accurately compute shock dynamics, as well as low-speed flows. For spatial discretization, we develop a “recovery” familymore » of DG, exhibiting nearly-spectral accuracy. To precondition the Krylov-based linear solver (GMRES), we developed an “Operator-Split”-(OS) Physics Based Preconditioner (PBP), in which we transform/simplify the fully-coupled system to a sequence of segregated scalar problems, each can be solved efficiently with Multigrid method. Each scalar problem is designed to target/cluster eigenvalues of the Jacobian matrix associated with a specific physics.« less

Development of computational methods for heavy lift launch vehicles

NASA Technical Reports Server (NTRS)

Yoon, Seokkwan; Ryan, James S.

1993-01-01

The research effort has been focused on the development of an advanced flow solver for complex viscous turbulent flows with shock waves. The three-dimensional Euler and full/thin-layer Reynolds-averaged Navier-Stokes equations for compressible flows are solved on structured hexahedral grids. The Baldwin-Lomax algebraic turbulence model is used for closure. The space discretization is based on a cell-centered finite-volume method augmented by a variety of numerical dissipation models with optional total variation diminishing limiters. The governing equations are integrated in time by an implicit method based on lower-upper factorization and symmetric Gauss-Seidel relaxation. The algorithm is vectorized on diagonal planes of sweep using two-dimensional indices in three dimensions. A new computer program named CENS3D has been developed for viscous turbulent flows with discontinuities. Details of the code are described in Appendix A and Appendix B. With the developments of the numerical algorithm and dissipation model, the simulation of three-dimensional viscous compressible flows has become more efficient and accurate. The results of the research are expected to yield a direct impact on the design process of future liquid fueled launch systems.

Assessment of a high-resolution central scheme for the solution of the relativistic hydrodynamics equations

NASA Astrophysics Data System (ADS)

Lucas-Serrano, A.; Font, J. A.; Ibáñez, J. M.; Martí, J. M.

2004-12-01

We assess the suitability of a recent high-resolution central scheme developed by \\cite{kurganov} for the solution of the relativistic hydrodynamic equations. The novelty of this approach relies on the absence of Riemann solvers in the solution procedure. The computations we present are performed in one and two spatial dimensions in Minkowski spacetime. Standard numerical experiments such as shock tubes and the relativistic flat-faced step test are performed. As an astrophysical application the article includes two-dimensional simulations of the propagation of relativistic jets using both Cartesian and cylindrical coordinates. The simulations reported clearly show the capabilities of the numerical scheme of yielding satisfactory results, with an accuracy comparable to that obtained by the so-called high-resolution shock-capturing schemes based upon Riemann solvers (Godunov-type schemes), even well inside the ultrarelativistic regime. Such a central scheme can be straightforwardly applied to hyperbolic systems of conservation laws for which the characteristic structure is not explicitly known, or in cases where a numerical computation of the exact solution of the Riemann problem is prohibitively expensive. Finally, we present comparisons with results obtained using various Godunov-type schemes as well as with those obtained using other high-resolution central schemes which have recently been reported in the literature.

TSPmap, a tool making use of traveling salesperson problem solvers in the efficient and accurate construction of high-density genetic linkage maps.

PubMed

Monroe, J Grey; Allen, Zachariah A; Tanger, Paul; Mullen, Jack L; Lovell, John T; Moyers, Brook T; Whitley, Darrell; McKay, John K

2017-01-01

Recent advances in nucleic acid sequencing technologies have led to a dramatic increase in the number of markers available to generate genetic linkage maps. This increased marker density can be used to improve genome assemblies as well as add much needed resolution for loci controlling variation in ecologically and agriculturally important traits. However, traditional genetic map construction methods from these large marker datasets can be computationally prohibitive and highly error prone. We present TSPmap , a method which implements both approximate and exact Traveling Salesperson Problem solvers to generate linkage maps. We demonstrate that for datasets with large numbers of genomic markers (e.g. 10,000) and in multiple population types generated from inbred parents, TSPmap can rapidly produce high quality linkage maps with low sensitivity to missing and erroneous genotyping data compared to two other benchmark methods, JoinMap and MSTmap . TSPmap is open source and freely available as an R package. With the advancement of low cost sequencing technologies, the number of markers used in the generation of genetic maps is expected to continue to rise. TSPmap will be a useful tool to handle such large datasets into the future, quickly producing high quality maps using a large number of genomic markers.

Real-time decay of a highly excited charge carrier in the one-dimensional Holstein model

NASA Astrophysics Data System (ADS)

Dorfner, F.; Vidmar, L.; Brockt, C.; Jeckelmann, E.; Heidrich-Meisner, F.

2015-03-01

We study the real-time dynamics of a highly excited charge carrier coupled to quantum phonons via a Holstein-type electron-phonon coupling. This is a prototypical example for the nonequilibrium dynamics in an interacting many-body system where excess energy is transferred from electronic to phononic degrees of freedom. We use diagonalization in a limited functional space (LFS) to study the nonequilibrium dynamics on a finite one-dimensional chain. This method agrees with exact diagonalization and the time-evolving block-decimation method, in both the relaxation regime and the long-time stationary state, and among these three methods it is the most efficient and versatile one for this problem. We perform a comprehensive analysis of the time evolution by calculating the electron, phonon and electron-phonon coupling energies, and the electronic momentum distribution function. The numerical results are compared to analytical solutions for short times, for a small hopping amplitude and for a weak electron-phonon coupling. In the latter case, the relaxation dynamics obtained from the Boltzmann equation agrees very well with the LFS data. We also study the time dependence of the eigenstates of the single-site reduced density matrix, which defines the so-called optimal phonon modes. We discuss their structure in nonequilibrium and the distribution of their weights. Our analysis shows that the structure of optimal phonon modes contains very useful information for the interpretation of the numerical data.

Anamorphic quasiperiodic universes in modified and Einstein gravity with loop quantum gravity corrections

NASA Astrophysics Data System (ADS)

Amaral, Marcelo M.; Aschheim, Raymond; Bubuianu, Laurenţiu; Irwin, Klee; Vacaru, Sergiu I.; Woolridge, Daniel

2017-09-01

The goal of this work is to elaborate on new geometric methods of constructing exact and parametric quasiperiodic solutions for anamorphic cosmology models in modified gravity theories, MGTs, and general relativity, GR. There exist previously studied generic off-diagonal and diagonalizable cosmological metrics encoding gravitational and matter fields with quasicrystal like structures, QC, and holonomy corrections from loop quantum gravity, LQG. We apply the anholonomic frame deformation method, AFDM, in order to decouple the (modified) gravitational and matter field equations in general form. This allows us to find integral varieties of cosmological solutions determined by generating functions, effective sources, integration functions and constants. The coefficients of metrics and connections for such cosmological configurations depend, in general, on all spacetime coordinates and can be chosen to generate observable (quasi)-periodic/aperiodic/fractal/stochastic/(super) cluster/filament/polymer like (continuous, stochastic, fractal and/or discrete structures) in MGTs and/or GR. In this work, we study new classes of solutions for anamorphic cosmology with LQG holonomy corrections. Such solutions are characterized by nonlinear symmetries of generating functions for generic off-diagonal cosmological metrics and generalized connections, with possible nonholonomic constraints to Levi-Civita configurations and diagonalizable metrics depending only on a time like coordinate. We argue that anamorphic quasiperiodic cosmological models integrate the concept of quantum discrete spacetime, with certain gravitational QC-like vacuum and nonvacuum structures. And, that of a contracting universe that homogenizes, isotropizes and flattens without introducing initial conditions or multiverse problems.

Tight-binding chains with off-diagonal disorder: Bands of extended electronic states induced by minimal quasi-one-dimensionality

NASA Astrophysics Data System (ADS)

Nandy, Atanu; Pal, Biplab; Chakrabarti, Arunava

2016-08-01

It is shown that an entire class of off-diagonally disordered linear lattices composed of two basic building blocks and described within a tight-binding model can be tailored to generate absolutely continuous energy bands. It can be achieved if linear atomic clusters of an appropriate size are side-coupled to a suitable subset of sites in the backbone, and if the nearest-neighbor hopping integrals, in the backbone and in the side-coupled cluster, bear a certain ratio. We work out the precise relationship between the number of atoms in one of the building blocks in the backbone and that in the side attachment. In addition, we also evaluate the definite correlation between the numerical values of the hopping integrals at different subsections of the chain, that can convert an otherwise point spectrum (or a singular continuous one for deterministically disordered lattices) with exponentially (or power law) localized eigenfunctions to an absolutely continuous spectrum comprising one or more bands (subbands) populated by extended, totally transparent eigenstates. The results, which are analytically exact, put forward a non-trivial variation of the Anderson localization (Anderson P. W., Phys. Rev., 109 (1958) 1492), pointing towards its unusual sensitivity to the numerical values of the system parameters and, go well beyond the other related models such as the Random Dimer Model (RDM) (Dunlap D. H. et al., Phys. Rev. Lett., 65 (1990) 88).

HST3D; a computer code for simulation of heat and solute transport in three-dimensional ground-water flow systems

USGS Publications Warehouse

Kipp, K.L.

1987-01-01

The Heat- and Soil-Transport Program (HST3D) simulates groundwater flow and associated heat and solute transport in three dimensions. The three governing equations are coupled through the interstitial pore velocity, the dependence of the fluid density on pressure, temperature, the solute-mass fraction , and the dependence of the fluid viscosity on temperature and solute-mass fraction. The solute transport equation is for only a single, solute species with possible linear equilibrium sorption and linear decay. Finite difference techniques are used to discretize the governing equations using a point-distributed grid. The flow-, heat- and solute-transport equations are solved , in turn, after a particle Gauss-reduction scheme is used to modify them. The modified equations are more tightly coupled and have better stability for the numerical solutions. The basic source-sink term represents wells. A complex well flow model may be used to simulate specified flow rate and pressure conditions at the land surface or within the aquifer, with or without pressure and flow rate constraints. Boundary condition types offered include specified value, specified flux, leakage, heat conduction, and approximate free surface, and two types of aquifer influence functions. All boundary conditions can be functions of time. Two techniques are available for solution of the finite difference matrix equations. One technique is a direct-elimination solver, using equations reordered by alternating diagonal planes. The other technique is an iterative solver, using two-line successive over-relaxation. A restart option is available for storing intermediate results and restarting the simulation at an intermediate time with modified boundary conditions. This feature also can be used as protection against computer system failure. Data input and output may be in metric (SI) units or inch-pound units. Output may include tables of dependent variables and parameters, zoned-contour maps, and plots of the dependent variables versus time. (Lantz-PTT)

Multiorbital kinetic effects on charge ordering of frustrated electrons on the triangular lattice

NASA Astrophysics Data System (ADS)

Février, C.; Fratini, S.; Ralko, A.

2015-06-01

The role of the multiorbital effects on the emergence of frustrated electronic orders on the triangular lattice at half filling is investigated through an extended spinless fermion Hubbard model. By using two complementary approaches, unrestricted Hartree-Fock and exact diagonalizations, we unravel a very rich phase diagram controlled by the strength of both local and off-site Coulomb interactions and by the interorbital hopping anisotropy ratio t'/t . Three robust unconventional electronic phases, a pinball liquid, an inverse pinball liquid, and a large-unit-cell √{12 }×√{12 } droplet phase, are found to be generic in the triangular geometry, being controlled by the band structure parameters. The latter are also stabilized in the isotropic limit of our microscopic model, which recovers the standard SU(2) spinful extended single-band Hubbard model.

Trace identities and their semiclassical implications

NASA Astrophysics Data System (ADS)

Smilansky, Uzy

2000-03-01

The compatibility of the semiclassical quantization of area-preserving maps with some exact identities which follow from the unitarity of the quantum evolution operator is discussed. The quantum identities involve relations between traces of powers of the evolution operator. For classically integrable maps, the semiclassical approximation is shown to be compatible with the trace identities. This is done by the identification of stationary phase manifolds which give the main contributions to the result. The compatibility of the semiclassical quantization with the trace identities demonstrates the crucial importance of non-diagonal contributions. The same technique is not applicable for chaotic maps, and the compatibility of the semiclassical theory in this case remains unsettled. However, the trace identities are applied to maps which appear naturally in the theory of quantum graphs, revealing some features of the periodic orbit theory for these paradigms of quantum chaos.

An exact variational method to calculate vibrational energies of five atom molecules beyond the normal mode approach

DOE PAGES

Yu, Hua-Gen

2002-01-01

We present a full dimensional variational algorithm to calculate vibrational energies of penta-atomic molecules. The quantum mechanical Hamiltonian of the system for J=0 is derived in a set of orthogonal polyspherical coordinates in the body-fixed frame without any dynamical approximation. Moreover, the vibrational Hamiltonian has been obtained in an explicitly Hermitian form. Variational calculations are performed in a direct product discrete variable representation basis set. The sine functions are used for the radial coordinates, whereas the Legendre polynomials are employed for the polar angles. For the azimuthal angles, the symmetrically adapted Fourier–Chebyshev basis functions are utilized. The eigenvalue problem ismore » solved by a Lanczos iterative diagonalization algorithm. The preliminary application to methane is given. Ultimately, we made a comparison with previous results.« less

Cobalt adatoms on graphene: Effects of anisotropies on the correlated electronic structure

NASA Astrophysics Data System (ADS)

Mozara, R.; Valentyuk, M.; Krivenko, I.; Şaşıoǧlu, E.; Kolorenč, J.; Lichtenstein, A. I.

2018-02-01

Impurities on surfaces experience a geometric symmetry breaking induced not only by the on-site crystal-field splitting and the orbital-dependent hybridization, but also by different screening of the Coulomb interaction in different directions. We present a many-body study of the Anderson impurity model representing a Co adatom on graphene, taking into account all anisotropies of the effective Coulomb interaction, which we obtained by the constrained random-phase approximation. The most pronounced differences are naturally displayed by the many-body self-energy projected onto the single-particle states. For the solution of the Anderson impurity model and analytical continuation of the Matsubara data, we employed new implementations of the continuous-time hybridization expansion quantum Monte Carlo and the stochastic optimization method, and we verified the results in parallel with the exact diagonalization method.

Fermionic Symmetry-Protected Topological Phase in a Two-Dimensional Hubbard Model

DOE PAGES

Chen, Cheng-Chien; Muechler, Lukas; Car, Roberto; ...

2016-08-25

We study the two-dimensional (2D) Hubbard model using exact diagonalization for spin-1/2 fermions on the triangular and honeycomb lattices decorated with a single hexagon per site. In certain parameter ranges, the Hubbard model maps to a quantum compass model on those lattices. On the triangular lattice, the compass model exhibits collinear stripe antiferromagnetism, implying d-density wave charge order in the original Hubbard model. On the honeycomb lattice, the compass model has a unique, quantum disordered ground state that transforms nontrivially under lattice reflection. The ground state of the Hubbard model on the decorated honeycomb lattice is thus a 2D fermionicmore » symmetry-protected topological phase. This state—protected by time-reversal and reflection symmetries—cannot be connected adiabatically to a free-fermion topological phase.« less

Conservative DEC Discretization of Incompressible Navier-Stokes Equations on Arbitrary Surface Simplicial Meshes

NASA Astrophysics Data System (ADS)

Mohamed, Mamdouh; Hirani, Anil; Samtaney, Ravi

2017-11-01

A conservative discretization of incompressible Navier-Stokes equations over surfaces is developed using discrete exterior calculus (DEC). The mimetic character of many of the DEC operators provides exact conservation of both mass and vorticity, in addition to superior kinetic energy conservation. The employment of signed diagonal Hodge star operators, while using the circumcentric dual defined on arbitrary meshes, is shown to produce correct solutions even when many non-Delaunay triangles pairs exist. This allows the DEC discretization to admit arbitrary surface simplicial meshes, in contrast to the previously held notion that DEC was limited only to Delaunay meshes. The discretization scheme is presented along with several numerical test cases demonstrating its numerical convergence and conservation properties. Recent developments regarding the extension to conservative higher order methods are also presented. KAUST Baseline Research Funds of R. Samtaney.

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.

Raman Scattering from Higgs Mode Oscillations in the Two-Dimensional Antiferromagnet Ca_{2}RuO_{4}.

PubMed

Souliou, Sofia-Michaela; Chaloupka, Jiří; Khaliullin, Giniyat; Ryu, Gihun; Jain, Anil; Kim, B J; Le Tacon, Matthieu; Keimer, Bernhard

2017-08-11

We present and analyze Raman spectra of the Mott insulator Ca_{2}RuO_{4}, whose quasi-two-dimensional antiferromagnetic order has been described as a condensate of low-lying spin-orbit excitons with angular momentum J_{eff}=1. In the A_{g} polarization geometry, the amplitude (Higgs) mode of the spin-orbit condensate is directly probed in the scalar channel, thus avoiding infrared-singular magnon contributions. In the B_{1g} geometry, we observe a single-magnon peak as well as two-magnon and two-Higgs excitations. Model calculations using exact diagonalization quantitatively agree with the observations. Together with recent neutron scattering data, our study provides strong evidence for excitonic magnetism in Ca_{2}RuO_{4} and points out new perspectives for research on the Higgs mode in two dimensions.

Electron-Phonon Systems on a Universal Quantum Computer

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

Macridin, Alexandru; Spentzouris, Panagiotis; Amundson, James

We present an algorithm that extends existing quantum algorithms forsimulating fermion systems in quantum chemistry and condensed matter physics toinclude phonons. The phonon degrees of freedom are represented with exponentialaccuracy on a truncated Hilbert space with a size that increases linearly withthe cutoff of the maximum phonon number. The additional number of qubitsrequired by the presence of phonons scales linearly with the size of thesystem. The additional circuit depth is constant for systems with finite-rangeelectron-phonon and phonon-phonon interactions and linear for long-rangeelectron-phonon interactions. Our algorithm for a Holstein polaron problem wasimplemented on an Atos Quantum Learning Machine (QLM) quantum simulatoremployingmore » the Quantum Phase Estimation method. The energy and the phonon numberdistribution of the polaron state agree with exact diagonalization results forweak, intermediate and strong electron-phonon coupling regimes.« less

Spectral function of a hole in the t - J model

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

Liu, Z.; Manousakis, E.

1991-08-01

We give numerical solutions, on finite but large-size square lattices, of the equation for the single-hole Green's function obtained by the self-consistent approach of Schmitt-Rink {ital et} {ital al}. and Kane {ital et} {ital al}. The spectral function of the hole in a quantum antiferromagnet shows that most features describing the hole motion are in close agreement with the results of the exact diagonalization on the 4{sup 2} lattice in the region of {ital J}/{ital t}{le}0.2. Our results obtained on sufficiently large-size lattices suggest that certain important features of the spectral function survive in the thermodynamic limit while others changemore » due to finite-size effects. We find that the leading nonzero vertex correction is given by a two-loop diagram, which has a small contribution.« less

Raman Scattering from Higgs Mode Oscillations in the Two-Dimensional Antiferromagnet Ca2RuO4

NASA Astrophysics Data System (ADS)

Souliou, Sofia-Michaela; Chaloupka, Jiří; Khaliullin, Giniyat; Ryu, Gihun; Jain, Anil; Kim, B. J.; Le Tacon, Matthieu; Keimer, Bernhard

2017-08-01

We present and analyze Raman spectra of the Mott insulator Ca2RuO4 , whose quasi-two-dimensional antiferromagnetic order has been described as a condensate of low-lying spin-orbit excitons with angular momentum Jeff=1 . In the Ag polarization geometry, the amplitude (Higgs) mode of the spin-orbit condensate is directly probed in the scalar channel, thus avoiding infrared-singular magnon contributions. In the B1 g geometry, we observe a single-magnon peak as well as two-magnon and two-Higgs excitations. Model calculations using exact diagonalization quantitatively agree with the observations. Together with recent neutron scattering data, our study provides strong evidence for excitonic magnetism in Ca2 RuO4 and points out new perspectives for research on the Higgs mode in two dimensions.

Excitation spectrum for an inhomogeneously dipole-field-coupled superconducting qubit chain

NASA Astrophysics Data System (ADS)

Ian, Hou; Liu, Yu-xi; Nori, Franco

2012-05-01

When a chain of N superconducting qubits couples to a coplanar resonator, each of the qubits experiences a different dipole-field coupling strength due to the wave form of the cavity field. We find that this inhomogeneous coupling leads to a dependence of the collective ladder operators of the qubit chain on the qubit-interspacing l. Varying the spacing l changes the transition amplitudes between the angular momentum levels. We derive an exact diagonalization of the general N-qubit Hamiltonian and, through the N=4 case, demonstrate how the l-dependent operators lead to a denser one-excitation spectrum and a probability redistribution of the eigenstates. Moreover, we show that the variation of l between its two limiting values coincides with the crossover between Frenkel- and Wannier-type excitons in the superconducting qubit chain.

Quantum Monte Carlo calculations of two neutrons in finite volume

DOE PAGES

Klos, P.; Lynn, J. E.; Tews, I.; ...

2016-11-18

Ab initio calculations provide direct access to the properties of pure neutron systems that are challenging to study experimentally. In addition to their importance for fundamental physics, their properties are required as input for effective field theories of the strong interaction. In this work, we perform auxiliary-field diffusion Monte Carlo calculations of the ground state and first excited state of two neutrons in a finite box, considering a simple contact potential as well as chiral effective field theory interactions. We compare the results against exact diagonalizations and present a detailed analysis of the finite-volume effects, whose understanding is crucial formore » determining observables from the calculated energies. Finally, using the Lüscher formula, we extract the low-energy S-wave scattering parameters from ground- and excited-state energies for different box sizes.« less

Why do we need three levels to understand the molecular optical response?

NASA Astrophysics Data System (ADS)

Perez-Moreno, Javier; Clays, Koen; Kuzyk, Mark G.

2011-10-01

Traditionally, the nonlinear optical response at the molecular level has been modeled using the two-level approximation, under the assumption that the behavior of the exact sum-over-states (SOS) expressions for the molecular polarizabilities is well represented by the contribution of only two levels. We show how, a rigorous application of the Thomas-Kuhn sum-rules over the SOS expression for the diagonal component of the first-hyperpolarziability proves that the two-level approximation is unphysical. In addition, we indicate how the contributions of potentially infinite number of states to the SOS expressions for the first-hyperpolarizability are well represented by the contributions of a generic three-level system. This explains why the analysis of the three-level model in conjugation with the sum rules has lead to successful paradigms for the optimization of organic chromophores.

J dependence in the LSDA+U treatment of noncollinear magnets

NASA Astrophysics Data System (ADS)

Bousquet, Eric; Spaldin, Nicola

2010-12-01

We re-examine the commonly used density-functional theory plus Hubbard U (DFT+U) method for the case of noncollinear magnets. While many studies neglect to explicitly include the exchange-correction parameter J , or consider its exact value to be unimportant, here we show that in the case of noncollinear magnetism calculations the J parameter can strongly affect the magnetic ground state. We illustrate the strong J dependence of magnetic canting and magnetocrystalline anisotropy by calculating trends in the magnetic lithium orthophosphate family LiMPO4 ( M=Fe and Ni) and difluorite family MF2 ( M=Mn , Fe, Co, and Ni). Our results can be readily understood by expanding the usual DFT+U equations within the spinor scheme, in which the J parameter acts directly on the off-diagonal components which determine the spin canting.

Formulation of the relativistic quantum Hall effect and parity anomaly

NASA Astrophysics Data System (ADS)

Yonaga, Kouki; Hasebe, Kazuki; Shibata, Naokazu

2016-06-01

We present a relativistic formulation of the quantum Hall effect on Haldane sphere. An explicit form of the pseudopotential is derived for the relativistic quantum Hall effect with/without mass term. We clarify particular features of the relativistic quantum Hall states with the use of the exact diagonalization study of the pseudopotential Hamiltonian. Physical effects of the mass term to the relativistic quantum Hall states are investigated in detail. The mass term acts as an interpolating parameter between the relativistic and nonrelativistic quantum Hall effects. It is pointed out that the mass term unevenly affects the many-body physics of the positive and negative Landau levels as a manifestation of the "parity anomaly." In particular, we explicitly demonstrate the instability of the Laughlin state of the positive first relativistic Landau level with the reduction of the charge gap.

Quantum criticality and first-order transitions in the extended periodic Anderson model

NASA Astrophysics Data System (ADS)

Hagymási, I.; Itai, K.; Sólyom, J.

2013-03-01

We investigate the behavior of the periodic Anderson model in the presence of d-f Coulomb interaction (Udf) using mean-field theory, variational calculation, and exact diagonalization of finite chains. The variational approach based on the Gutzwiller trial wave function gives a critical value of Udf and two quantum critical points (QCPs), where the valence susceptibility diverges. We derive the critical exponent for the valence susceptibility and investigate how the position of the QCP depends on the other parameters of the Hamiltonian. For larger values of Udf, the Kondo regime is bounded by two first-order transitions. These first-order transitions merge into a triple point at a certain value of Udf. For even larger Udf valence skipping occurs. Although the other methods do not give a critical point, they support this scenario.

Ground state of a Heisenberg chain with next-nearest-neighbor bond alternation

NASA Astrophysics Data System (ADS)

Capriotti, Luca; Becca, Federico; Sorella, Sandro; Parola, Alberto

2003-05-01

We investigate the ground-state properties of the spin-half J1-J2 Heisenberg chain with a next-nearest-neighbor spin-Peierls dimerization using conformal field theory and Lanczos exact diagonalizations. In agreement with the results of a recent bosonization analysis by Sarkar and Sen [Phys. Rev. B 65, 172408 (2002)], we find that for small frustration (J2/J1) the system is in a Luttinger spin-fluid phase, with gapless excitations, and a finite spin-wave velocity. In the regime of strong frustration the ground state is spontaneously dimerized and the bond alternation reduces the triplet gap, leading to a slight enhancement of the critical point separating the Luttinger phase from the gapped one. An accurate determination of the phase boundary is obtained numerically from the study of the excitation spectrum.

Parallel Optimization of Polynomials for Large-scale Problems in Stability and Control

NASA Astrophysics Data System (ADS)

Kamyar, Reza

In this thesis, we focus on some of the NP-hard problems in control theory. Thanks to the converse Lyapunov theory, these problems can often be modeled as optimization over polynomials. To avoid the problem of intractability, we establish a trade off between accuracy and complexity. In particular, we develop a sequence of tractable optimization problems --- in the form of Linear Programs (LPs) and/or Semi-Definite Programs (SDPs) --- whose solutions converge to the exact solution of the NP-hard problem. However, the computational and memory complexity of these LPs and SDPs grow exponentially with the progress of the sequence - meaning that improving the accuracy of the solutions requires solving SDPs with tens of thousands of decision variables and constraints. Setting up and solving such problems is a significant challenge. The existing optimization algorithms and software are only designed to use desktop computers or small cluster computers --- machines which do not have sufficient memory for solving such large SDPs. Moreover, the speed-up of these algorithms does not scale beyond dozens of processors. This in fact is the reason we seek parallel algorithms for setting-up and solving large SDPs on large cluster- and/or super-computers. We propose parallel algorithms for stability analysis of two classes of systems: 1) Linear systems with a large number of uncertain parameters; 2) Nonlinear systems defined by polynomial vector fields. First, we develop a distributed parallel algorithm which applies Polya's and/or Handelman's theorems to some variants of parameter-dependent Lyapunov inequalities with parameters defined over the standard simplex. The result is a sequence of SDPs which possess a block-diagonal structure. We then develop a parallel SDP solver which exploits this structure in order to map the computation, memory and communication to a distributed parallel environment. Numerical tests on a supercomputer demonstrate the ability of the algorithm to efficiently utilize hundreds and potentially thousands of processors, and analyze systems with 100+ dimensional state-space. Furthermore, we extend our algorithms to analyze robust stability over more complicated geometries such as hypercubes and arbitrary convex polytopes. Our algorithms can be readily extended to address a wide variety of problems in control such as Hinfinity synthesis for systems with parametric uncertainty and computing control Lyapunov functions.

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

Jin Jiasen; Yu Changshui; Song Heshan

We propose a scheme for identifying an unknown Bell diagonal state. In our scheme the measurements are performed on the probe qubits instead of the Bell diagonal state. The distinct advantage is that the quantum state of the evolved Bell diagonal state ensemble plus probe states will still collapse on the original Bell diagonal state ensemble after the measurement on probe states; i.e., our identification is quantum state nondestructive. How to realize our scheme in the framework of cavity electrodynamics is also shown.

A Comparative Study of Randomized Constraint Solvers for Random-Symbolic Testing

NASA Technical Reports Server (NTRS)

Takaki, Mitsuo; Cavalcanti, Diego; Gheyi, Rohit; Iyoda, Juliano; dAmorim, Marcelo; Prudencio, Ricardo

2009-01-01

The complexity of constraints is a major obstacle for constraint-based software verification. Automatic constraint solvers are fundamentally incomplete: input constraints often build on some undecidable theory or some theory the solver does not support. This paper proposes and evaluates several randomized solvers to address this issue. We compare the effectiveness of a symbolic solver (CVC3), a random solver, three hybrid solvers (i.e., mix of random and symbolic), and two heuristic search solvers. We evaluate the solvers on two benchmarks: one consisting of manually generated constraints and another generated with a concolic execution of 8 subjects. In addition to fully decidable constraints, the benchmarks include constraints with non-linear integer arithmetic, integer modulo and division, bitwise arithmetic, and floating-point arithmetic. As expected symbolic solving (in particular, CVC3) subsumes the other solvers for the concolic execution of subjects that only generate decidable constraints. For the remaining subjects the solvers are complementary.

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

Adaptive relaxation for the steady-state analysis of Markov chains

NASA Technical Reports Server (NTRS)

Horton, Graham

1994-01-01

We consider a variant of the well-known Gauss-Seidel method for the solution of Markov chains in steady state. Whereas the standard algorithm visits each state exactly once per iteration in a predetermined order, the alternative approach uses a dynamic strategy. A set of states to be visited is maintained which can grow and shrink as the computation progresses. In this manner, we hope to concentrate the computational work in those areas of the chain in which maximum improvement in the solution can be achieved. We consider the adaptive approach both as a solver in its own right and as a relaxation method within the multi-level algorithm. Experimental results show significant computational savings in both cases.

Pattern-set generation algorithm for the one-dimensional multiple stock sizes cutting stock problem

NASA Astrophysics Data System (ADS)

Cui, Yaodong; Cui, Yi-Ping; Zhao, Zhigang

2015-09-01

A pattern-set generation algorithm (PSG) for the one-dimensional multiple stock sizes cutting stock problem (1DMSSCSP) is presented. The solution process contains two stages. In the first stage, the PSG solves the residual problems repeatedly to generate the patterns in the pattern set, where each residual problem is solved by the column-generation approach, and each pattern is generated by solving a single large object placement problem. In the second stage, the integer linear programming model of the 1DMSSCSP is solved using a commercial solver, where only the patterns in the pattern set are considered. The computational results of benchmark instances indicate that the PSG outperforms existing heuristic algorithms and rivals the exact algorithm in solution quality.

Pressure profiles in detonation cells with rectangular and diagonal structures

NASA Astrophysics Data System (ADS)

Hanana, M.; Lefebvre, M. H.

Experimental results presented in this work enable us to classify the three-dimensional structure of the detonation into two fundamental types: a rectangular structure and a diagonal structure. The rectangular structure is well documented in the literature and consists of orthogonal waves travelling independently from each another. The soot record in this case shows the classical diamond detonation cell exhibiting `slapping waves'. The experiments indicate that the diagonal structure is a structure with the triple point intersections moving along the diagonal line of the tube cross section. The axes of the transverse waves are canted at 45 degrees to the wall, accounting for the lack of slapping waves. It is possible to reproduce these diagonal structures by appropriately controlling the experimental ignition procedure. The characteristics of the diagonal structure show some similarities with detonation structure in round tube. Pressure measurements recorded along the central axis of the cellular structure show a series of pressure peaks, depending on the type of structure and the position inside the detonation cell. Pressure profiles measured for the whole length of the two types of detonation cells show that the intensity of the shock front is higher and the length of the detonation cell is shorter for the diagonal structures.

2. VIEW OF CENTRAL BEND OF LOWER DIAGONAL NO. 1 ...

Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

2. VIEW OF CENTRAL BEND OF LOWER DIAGONAL NO. 1 DRAIN, LOOKING 2932 EAST OF NORTH. - Truckee-Carson Irrigation District, Lower Diagonal No. 1 Drain, Bounded by West Gate Road & Weapons Delivery Road, Naval Air Station Fallon, Fallon, Churchill County, NV

Efficient three-dimensional Poisson solvers in open rectangular conducting pipe

NASA Astrophysics Data System (ADS)

Qiang, Ji

2016-06-01

Three-dimensional (3D) Poisson solver plays an important role in the study of space-charge effects on charged particle beam dynamics in particle accelerators. In this paper, we propose three new 3D Poisson solvers for a charged particle beam in an open rectangular conducting pipe. These three solvers include a spectral integrated Green function (IGF) solver, a 3D spectral solver, and a 3D integrated Green function solver. These solvers effectively handle the longitudinal open boundary condition using a finite computational domain that contains the beam itself. This saves the computational cost of using an extra larger longitudinal domain in order to set up an appropriate finite boundary condition. Using an integrated Green function also avoids the need to resolve rapid variation of the Green function inside the beam. The numerical operational cost of the spectral IGF solver and the 3D IGF solver scales as O(N log(N)) , where N is the number of grid points. The cost of the 3D spectral solver scales as O(Nn N) , where Nn is the maximum longitudinal mode number. We compare these three solvers using several numerical examples and discuss the advantageous regime of each solver in the physical application.

Examples of Linking Codes Within GeoFramework

NASA Astrophysics Data System (ADS)

Tan, E.; Choi, E.; Thoutireddy, P.; Aivazis, M.; Lavier, L.; Quenette, S.; Gurnis, M.

2003-12-01

Geological processes usually encompass a broad spectrum of length and time scales. Traditionally, a modeling code (solver) is written to solve a problem with specific length and time scales in mind. The utility of the solver beyond the designated purpose is usually limited. Furthermore, two distinct solvers, even if each can solve complementary parts of a new problem, are difficult to link together to solve the problem as a whole. For example, Lagrangian deformation model with visco-elastoplastic crust is used to study deformation near plate boundary. Ideally, the driving force of the deformation should be derived from underlying mantle convection, and it requires linking the Lagrangian deformation model with a Eulerian mantle convection model. As our understanding of geological processes evolves, the need of integrated modeling codes, which should reuse existing codes as much as possible, begins to surface. GeoFramework project addresses this need by developing a suite of reusable and re-combinable tools for the Earth science community. GeoFramework is based on and extends Pyre, a Python-based modeling framework, recently developed to link solid (Lagrangian) and fluid (Eulerian) models, as well as mesh generators, visualization packages, and databases, with one another for engineering applications. Under the framework, a solver is aware of the existence of other solvers and can interact with each other via exchanging information across adjacent boundary. A solver needs to conform a standard interface and provide its own implementation for exchanging boundary information. The framework also provides facilities to control the coordination between interacting solvers. We will show an example of linking two solvers within GeoFramework. CitcomS is a finite element code which solves for thermal convection within a 3D spherical shell. CitcomS can solve for problems either within a full spherical (global) domain or a restricted (regional) domain of a full sphere by using different meshers. We can embed a regional CitcomS solver within a global CitcomS solver. We not that linking instances of the same solver is conceptually equivalent to linking to different solvers. The global solver has a coarser grid and a longer stable time step than the regional solver. Therefore, a global-solver time step consists of several regional-solver time steps. The time-marching scheme is described below. First, the global solver is advanced one global-solver time step. Then, the regional solver is advanced for several regional-solver time steps until it catches up global solver. Within each regional-solver time step, the velocity field of the global solver is interpolated in time and then is imposed to the regional solver as boundary conditions. Finally, the temperature field of the regional solver is extrapolated in space and is fed back to the global. These two solvers are linked and synchronized by the time-marching scheme. An effort to embed a visco-elastoplastic representation of the crust within viscous mantle flow is underway.

Tradeoffs between oscillator strength and lifetime in terahertz quantum cascade lasers

DOE PAGES

Chan, Chun Wang I.; Albo, Asaf; Hu, Qing; ...

2016-11-14

Contemporary research into diagonal active region terahertz quantum cascade lasers for high temperature operation has yielded little success. We present evidence that the failure of high diagonality alone as a design strategy is due to a fundamental trade-off between large optical oscillator strength and long upper-level lifetime. Here, we hypothesize that diagonality needs to be paired with increased doping in order to succeed, and present evidence that highly diagonal designs can benefit from much higher doping than normally found in terahertz quantum cascade lasers. In assuming the benefits of high diagonality paired with high doping, we also highlight important challengesmore » that need to be overcome, specifically the increased importance of carrier induced band-bending and impurity scattering.« less

6. VIEW OF WEST GATE ROAD CULVERT OF LOWER DIAGONAL ...

Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

6. VIEW OF WEST GATE ROAD CULVERT OF LOWER DIAGONAL NO. 1 DRAIN, LOOKING 2502 EAST OF NORTH. - Truckee-Carson Irrigation District, Lower Diagonal No. 1 Drain, Bounded by West Gate Road & Weapons Delivery Road, Naval Air Station Fallon, Fallon, Churchill County, NV

7. VIEW OF WEAPONS DELIVERY ROAD CULVERT OF LOWER DIAGONAL ...

Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

7. VIEW OF WEAPONS DELIVERY ROAD CULVERT OF LOWER DIAGONAL NO. 1 DRAIN, LOOKING 522 EAST OF NORTH. - Truckee-Carson Irrigation District, Lower Diagonal No. 1 Drain, Bounded by West Gate Road & Weapons Delivery Road, Naval Air Station Fallon, Fallon, Churchill County, NV

5. VIEW OF WEST GATE ROAD CULVERT OF LOWER DIAGONAL ...

Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

5. VIEW OF WEST GATE ROAD CULVERT OF LOWER DIAGONAL NO. 1 DRAIN, LOOKING 323' EAST OF NORTH. - Truckee-Carson Irrigation District, Lower Diagonal No. 1 Drain, Bounded by West Gate Road & Weapons Delivery Road, Naval Air Station Fallon, Fallon, Churchill County, NV

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.

Formalism for the solution of quadratic Hamiltonians with large cosine terms

NASA Astrophysics Data System (ADS)

Ganeshan, Sriram; Levin, Michael

2016-02-01

We consider quantum Hamiltonians of the form H =H0-U ∑jcos(Cj) , where H0 is a quadratic function of position and momentum variables {x1,p1,x2,p2,⋯} and the Cj's are linear in these variables. We allow H0 and Cj to be completely general with only two restrictions: we require that (1) the Cj's are linearly independent and (2) [Cj,Ck] is an integer multiple of 2 π i for all j ,k so that the different cosine terms commute with one another. Our main result is a recipe for solving these Hamiltonians and obtaining their exact low-energy spectrum in the limit U →∞ . This recipe involves constructing creation and annihilation operators and is similar in spirit to the procedure for diagonalizing quadratic Hamiltonians. In addition to our exact solution in the infinite U limit, we also discuss how to analyze these systems when U is large but finite. Our results are relevant to a number of different physical systems, but one of the most natural applications is to understanding the effects of electron scattering on quantum Hall edge modes. To demonstrate this application, we use our formalism to solve a toy model for a fractional quantum spin Hall edge with different types of impurities.

Line mixing effects in isotropic Raman spectra of pure N{sub 2}: A classical trajectory study

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

Ivanov, Sergey V., E-mail: serg.vict.ivanov@gmail.com; Boulet, Christian; Buzykin, Oleg G.

2014-11-14

Line mixing effects in the Q branch of pure N{sub 2} isotropic Raman scattering are studied at room temperature using a classical trajectory method. It is the first study using an extended modified version of Gordon's classical theory of impact broadening and shift of rovibrational lines. The whole relaxation matrix is calculated using an exact 3D classical trajectory method for binary collisions of rigid N{sub 2} molecules employing the most up-to-date intermolecular potential energy surface (PES). A simple symmetrizing procedure is employed to improve off-diagonal cross-sections to make them obeying exactly the principle of detailed balance. The adequacy of themore » results is confirmed by the sum rule. The comparison is made with available experimental data as well as with benchmark fully quantum close coupling [F. Thibault, C. Boulet, and Q. Ma, J. Chem. Phys. 140, 044303 (2014)] and refined semi-classical Robert-Bonamy [C. Boulet, Q. Ma, and F. Thibault, J. Chem. Phys. 140, 084310 (2014)] results. All calculations (classical, quantum, and semi-classical) were made using the same PES. The agreement between classical and quantum relaxation matrices is excellent, opening the way to the analysis of more complex molecular systems.« less

Comparing direct and iterative equation solvers in a large structural analysis software system

NASA Technical Reports Server (NTRS)

Poole, E. L.

1991-01-01

Two direct Choleski equation solvers and two iterative preconditioned conjugate gradient (PCG) equation solvers used in a large structural analysis software system are described. The two direct solvers are implementations of the Choleski method for variable-band matrix storage and sparse matrix storage. The two iterative PCG solvers include the Jacobi conjugate gradient method and an incomplete Choleski conjugate gradient method. The performance of the direct and iterative solvers is compared by solving several representative structural analysis problems. Some key factors affecting the performance of the iterative solvers relative to the direct solvers are identified.

The diagonalization of cubic matrices

NASA Astrophysics Data System (ADS)

Cocolicchio, D.; Viggiano, M.

2000-08-01

This paper is devoted to analysing the problem of the diagonalization of cubic matrices. We extend the familiar algebraic approach which is based on the Cardano formulae. We rewrite the complex roots of the associated resolvent secular equation in terms of transcendental functions and we derive the diagonalizing matrix.

Chaos in non-diagonal spatially homogeneous cosmological models in spacetime dimensions <=10

NASA Astrophysics Data System (ADS)

Demaret, Jacques; de Rop, Yves; Henneaux, Marc

1988-08-01

It is shown that the chaotic oscillatory behaviour, absent in diagonal homogeneous cosmological models in spacetime dimensions between 5 and 10, can be reestablished when off-diagonal terms are included. Also at Centro de Estudios Cientificos de Santiago, Casilla 16443, Santiago 9, Chile

4. VIEW OF EAST PORTION OF LOWER DIAGONAL NO. 1 ...

Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

4. VIEW OF EAST PORTION OF LOWER DIAGONAL NO. 1 DRAIN LOOKING TOWARDS THE CENTRAL BEND, LOOKING 270t EAST OF NORTH. - Truckee-Carson Irrigation District, Lower Diagonal No. 1 Drain, Bounded by West Gate Road & Weapons Delivery Road, Naval Air Station Fallon, Fallon, Churchill County, NV

1. VIEW OF WEST PORTION OF LOWER DIAGONAL NO. 1 ...

Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

1. VIEW OF WEST PORTION OF LOWER DIAGONAL NO. 1 DRAIN LOOKING TOWARDS THE WEST GATE ROAD CULVERT, LOOKING 3052 EAST OF NORTH. - Truckee-Carson Irrigation District, Lower Diagonal No. 1 Drain, Bounded by West Gate Road & Weapons Delivery Road, Naval Air Station Fallon, Fallon, Churchill County, NV

3. VIEW OF EAST PORTION OF LOWER DIAGONAL NO. 1 ...

Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

3. VIEW OF EAST PORTION OF LOWER DIAGONAL NO. 1 DRAIN LOOKING TOWARDS THE CENTRAL BEND, LOOKING 2742 EAST OF NORTH. - Truckee-Carson Irrigation District, Lower Diagonal No. 1 Drain, Bounded by West Gate Road & Weapons Delivery Road, Naval Air Station Fallon, Fallon, Churchill County, NV

Simplicity and Typical Rank Results for Three-Way Arrays

ERIC Educational Resources Information Center

ten Berge, Jos M. F.

2011-01-01

Matrices can be diagonalized by singular vectors or, when they are symmetric, by eigenvectors. Pairs of square matrices often admit simultaneous diagonalization, and always admit block wise simultaneous diagonalization. Generalizing these possibilities to more than two (non-square) matrices leads to methods of simplifying three-way arrays by…

A cross-sectional study comparing lateral and diagonal maximum weight shift in people with stroke and healthy controls and the correlation with balance, gait and fear of falling

PubMed Central

Meyer, Sarah; Beyens, Hilde; Dejaeger, Eddy; Verheyden, Geert

2017-01-01

Impaired balance is common post stroke and can be assessed by means of force-platforms measuring center of pressure (COP) displacements during static standing, or more dynamically during lateral maximum weight shift (MWS). However, activities of daily life also include diagonal MWS and since force platforms are nowadays commercially available, investigating lateral and diagonal MWS in a clinical setting might be feasible and clinically relevant. We investigated lateral and diagonal MWS while standing in patients with stroke (PwS) and healthy controls (HC), evaluated MWS towards the affected and the non-affected side for PwS and correlated MWS with measures of balance, gait and fear of falling. In a cross-sectional observational study including 36 ambulatory sub-acute inpatients and 32 age-matched HC, a force platform (BioRescue, RM Ingénierie, France) was used to measure lateral and diagonal MWS in standing. Clinical outcome measures collected were Berg Balance Scale and Community Balance and Mobility Scale (CBMS) for balance, 10-meter walk test (10MWT) for gait speed and Falls Efficacy Scale–international version for fear of falling. MWS for PwS towards the affected side was significantly smaller compared to HC (lateral: p = 0.029; diagonal-forward: p = 0.000). MWS for PwS was also significantly reduced towards the affected side in the diagonal-forward direction (p = 0.019) compared to the non-affected side of PwS. Strong correlations were found for MWS for PwS in the diagonal-forward direction towards the affected side, and clinical measures of balance (CBMS: r = 0.66) and gait speed (10MWT: r = 0.66). Our study showed that ambulatory sub-acute PwS, in comparison to HC, have decreased ability to shift their body weight diagonally forward in standing towards their affected side. This reduced ability is strongly related to clinical measures of balance and gait speed. Our results suggest that MWS in a diagonal-forward direction should receive attention in rehabilitation of ambulatory sub-acute PwS in an inpatient setting. PMID:28809939

A cross-sectional study comparing lateral and diagonal maximum weight shift in people with stroke and healthy controls and the correlation with balance, gait and fear of falling.

PubMed

van Dijk, Margaretha M; Meyer, Sarah; Sandstad, Solveig; Wiskerke, Evelyne; Thuwis, Rhea; Vandekerckhove, Chesny; Myny, Charlotte; Ghosh, Nitesh; Beyens, Hilde; Dejaeger, Eddy; Verheyden, Geert

2017-01-01

Impaired balance is common post stroke and can be assessed by means of force-platforms measuring center of pressure (COP) displacements during static standing, or more dynamically during lateral maximum weight shift (MWS). However, activities of daily life also include diagonal MWS and since force platforms are nowadays commercially available, investigating lateral and diagonal MWS in a clinical setting might be feasible and clinically relevant. We investigated lateral and diagonal MWS while standing in patients with stroke (PwS) and healthy controls (HC), evaluated MWS towards the affected and the non-affected side for PwS and correlated MWS with measures of balance, gait and fear of falling. In a cross-sectional observational study including 36 ambulatory sub-acute inpatients and 32 age-matched HC, a force platform (BioRescue, RM Ingénierie, France) was used to measure lateral and diagonal MWS in standing. Clinical outcome measures collected were Berg Balance Scale and Community Balance and Mobility Scale (CBMS) for balance, 10-meter walk test (10MWT) for gait speed and Falls Efficacy Scale-international version for fear of falling. MWS for PwS towards the affected side was significantly smaller compared to HC (lateral: p = 0.029; diagonal-forward: p = 0.000). MWS for PwS was also significantly reduced towards the affected side in the diagonal-forward direction (p = 0.019) compared to the non-affected side of PwS. Strong correlations were found for MWS for PwS in the diagonal-forward direction towards the affected side, and clinical measures of balance (CBMS: r = 0.66) and gait speed (10MWT: r = 0.66). Our study showed that ambulatory sub-acute PwS, in comparison to HC, have decreased ability to shift their body weight diagonally forward in standing towards their affected side. This reduced ability is strongly related to clinical measures of balance and gait speed. Our results suggest that MWS in a diagonal-forward direction should receive attention in rehabilitation of ambulatory sub-acute PwS in an inpatient setting.

Exact and Metaheuristic Approaches for a Bi-Objective School Bus Scheduling Problem

PubMed Central

Chen, Xiaopan; Kong, Yunfeng; Dang, Lanxue; Hou, Yane; Ye, Xinyue

2015-01-01

As a class of hard combinatorial optimization problems, the school bus routing problem has received considerable attention in the last decades. For a multi-school system, given the bus trips for each school, the school bus scheduling problem aims at optimizing bus schedules to serve all the trips within the school time windows. In this paper, we propose two approaches for solving the bi-objective school bus scheduling problem: an exact method of mixed integer programming (MIP) and a metaheuristic method which combines simulated annealing with local search. We develop MIP formulations for homogenous and heterogeneous fleet problems respectively and solve the models by MIP solver CPLEX. The bus type-based formulation for heterogeneous fleet problem reduces the model complexity in terms of the number of decision variables and constraints. The metaheuristic method is a two-stage framework for minimizing the number of buses to be used as well as the total travel distance of buses. We evaluate the proposed MIP and the metaheuristic method on two benchmark datasets, showing that on both instances, our metaheuristic method significantly outperforms the respective state-of-the-art methods. PMID:26176764

The Finite-Surface Method for incompressible flow: a step beyond staggered grid

NASA Astrophysics Data System (ADS)

Hokpunna, Arpiruk; Misaka, Takashi; Obayashi, Shigeru

2017-11-01

We present a newly developed higher-order finite surface method for the incompressible Navier-Stokes equations (NSE). This method defines the velocities as a surface-averaged value on the surfaces of the pressure cells. Consequently, the mass conservation on the pressure cells becomes an exact equation. The only things left to approximate is the momentum equation and the pressure at the new time step. At certain conditions, the exact mass conservation enables the explicit n-th order accurate NSE solver to be used with the pressure treatment that is two or four order less accurate without loosing the apparent convergence rate. This feature was not possible with finite volume of finite difference methods. We use Fourier analysis with a model spectrum to determine the condition and found that the range covers standard boundary layer flows. The formal convergence and the performance of the proposed scheme is compared with a sixth-order finite volume method. Finally, the accuracy and performance of the method is evaluated in turbulent channel flows. This work is partially funded by a research colloaboration from IFS, Tohoku university and ASEAN+3 funding scheme from CMUIC, Chiang Mai University.

Highly efficient and exact method for parallelization of grid-based algorithms and its implementation in DelPhi

PubMed Central

Li, Chuan; Li, Lin; Zhang, Jie; Alexov, Emil

2012-01-01

The Gauss-Seidel method is a standard iterative numerical method widely used to solve a system of equations and, in general, is more efficient comparing to other iterative methods, such as the Jacobi method. However, standard implementation of the Gauss-Seidel method restricts its utilization in parallel computing due to its requirement of using updated neighboring values (i.e., in current iteration) as soon as they are available. Here we report an efficient and exact (not requiring assumptions) method to parallelize iterations and to reduce the computational time as a linear/nearly linear function of the number of CPUs. In contrast to other existing solutions, our method does not require any assumptions and is equally applicable for solving linear and nonlinear equations. This approach is implemented in the DelPhi program, which is a finite difference Poisson-Boltzmann equation solver to model electrostatics in molecular biology. This development makes the iterative procedure on obtaining the electrostatic potential distribution in the parallelized DelPhi several folds faster than that in the serial code. Further we demonstrate the advantages of the new parallelized DelPhi by computing the electrostatic potential and the corresponding energies of large supramolecular structures. PMID:22674480

Adaptive Osher-type scheme for the Euler equations with highly nonlinear equations of state

NASA Astrophysics Data System (ADS)

Lee, Bok Jik; Toro, Eleuterio F.; Castro, Cristóbal E.; Nikiforakis, Nikolaos

2013-08-01

For the numerical simulation of detonation of condensed phase explosives, a complex equation of state (EOS), such as the Jones-Wilkins-Lee (JWL) EOS or the Cochran-Chan (C-C) EOS, are widely used. However, when a conservative scheme is used for solving the Euler equations with such equations of state, a spurious solution across the contact discontinuity, a well known phenomenon in multi-fluid systems, arises even for single materials. In this work, we develop a generalised Osher-type scheme in an adaptive primitive-conservative framework to overcome the aforementioned difficulties. Resulting numerical solutions are compared with the exact solutions and with the numerical solutions from the Godunov method in conjunction with the exact Riemann solver for the Euler equations with Mie-Grüneisen form of equations of state, such as the JWL and the C-C equations of state. The adaptive scheme is extended to second order and its empirical convergence rates are presented, verifying second order accuracy for smooth solutions. Through a suite of several tests problems in one and two space dimensions we illustrate the failure of conservative schemes and the capability of the methods of this paper to overcome the difficulties.

A full 3D model of fluid flow and heat transfer in an E.B. heated liquid metal bath

NASA Astrophysics Data System (ADS)

Matveichev, A.; Jardy, A.; Bellot, J. P.

2016-07-01

In order to study the dissolution of exogeneous inclusions in the liquid metal during processing of titanium alloys, a series of dipping experiments has been performed in an Electron Beam Melting laboratory furnace. Precise determination of the dissolution kinetics requires knowing and mastering the exact thermohydrodynamic behavior of the melt pool, which implies full 3D modeling of the process. To achieve this goal, one needs to describe momentum and heat transfer, phase change, as well as the development of flow turbulence in the liquid. EB power input, thermal radiation, heat loss through the cooling circuit, surface tension effects (i.e. Marangoni-induced flow) must also be addressed in the model. Therefore a new solver dealing with all these phenomena was implemented within OpenFOAM platform. Numerical results were compared with experimental data from actual Ti melting, showing a pretty good agreement. In the second stage, the immersion of a refractory sample rod in the liquid pool was simulated. Results of the simulations showed that the introduction of the sample slightly disturbs the flow field inside the bath. The amount of such disturbance depends on the exact location of the dipping.

Entangled scalar and tensor fluctuations during inflation

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

Collins, Hael; Vardanyan, Tereza

2016-11-29

We show how the choice of an inflationary state that entangles scalar and tensor fluctuations affects the angular two-point correlation functions of the T, E, and B modes of the cosmic microwave background. The propagators for a state starting with some general quadratic entanglement are solved exactly, leading to predictions for the primordial scalar-scalar, tensor-tensor, and scalar-tensor power spectra. These power spectra are expressed in terms of general functions that describe the entangling structure of the initial state relative to the standard Bunch-Davies vacuum. We illustrate how such a state would modify the angular correlations in the CMB with amore » simple example where the initial state is a small perturbation away from the Bunch-Davies state. Because the state breaks some of the rotational symmetries, the angular power spectra no longer need be strictly diagonal.« less

Anisotropic exchange interaction induced by a single photon in semiconductor microcavities

NASA Astrophysics Data System (ADS)

Chiappe, G.; Fernández-Rossier, J.; Louis, E.; Anda, E. V.

2005-12-01

We investigate coupling of localized spins in a semiconductor quantum dot embedded in a microcavity. The lowest cavity mode and the quantum dot exciton are coupled and close in energy, forming a polariton. The fermions forming the exciton interact with localized spins via exchange. Exact diagonalization of a Hamiltonian in which photons, spins, and excitons are treated quantum mechanically shows that a single polariton induces a sizable indirect anisotropic exchange interaction between spins. At sufficiently low temperatures strong ferromagnetic correlations show up without an appreciable increase in exciton population. In the case of a (Cd,Mn)Te quantum dot, Mn-Mn ferromagnetic coupling is still significant at 1 K : spin-spin correlation around 3 for exciton occupation smaller than 0.3. We find that the interaction mediated by photon-polaritons is 10 times stronger than the one induced by a classical field for equal Rabi splitting.

Ground-state information geometry and quantum criticality in an inhomogeneous spin model

NASA Astrophysics Data System (ADS)

Ma, Yu-Quan

2015-09-01

We investigate the ground-state Riemannian metric and the cyclic quantum distance of an inhomogeneous quantum spin-1/2 chain in a transverse field. This model can be diagonalized by using a general canonical transformation to the fermionic Hamiltonian mapped from the spin system. The ground-state Riemannian metric is derived exactly on a parameter manifold ring S1, which is introduced by performing a gauge transformation to the spin Hamiltonian through a twist operator. The cyclic ground-state quantum distance and the second derivative of the ground-state energy are studied in different exchange coupling parameter regions. Particularly, we show that, in the case of exchange coupling parameter Ja = Jb, the quantum ferromagnetic phase can be characterized by an invariant quantum distance and this distance will decay to zero rapidly in the paramagnetic phase. Project supported by the National Natural Science Foundation of China (Grant Nos. 11404023 and 11347131).

Magnetic Phase Diagrams and Magnetization Plateaus of the Spin-1/2 Antiferromagnetic Heisenberg Model on a Square-Kagome Lattice with Three Nonequivalent Exchange Interactions

NASA Astrophysics Data System (ADS)

Morita, Katsuhiro; Tohyama, Takami

2018-04-01

Magnetization plateaus in quantum spin systems emerge in two-dimensional frustrated systems such as a kagome lattice. The spin-1/2 antiferromagnetic Heisenberg model on a square-kagome lattice is also appropriate for the study of the magnetization plateau. Motivated by recent experimental findings of such a square kagome lattice with three nonequivalent bonds, we investigate the phase diagrams and magnetization plateaus of the lattice using the exact diagonalization method. In addition to the previously reported 1/3 and 2/3 plateaus in the model with two equivalent bonds, we find a new 2/3 plateau whose magnetic structure is characterized by spontaneously broken four-fold rotational symmetry. The plateau appears only in the case of three nonequivalent bonds. We propose the possibility of finding plateaus including the new one.

Criticality of the low-frequency conductivity for the bilayer quantum Heisenberg model

NASA Astrophysics Data System (ADS)

Nishiyama, Yoshihiro

2018-04-01

The criticality of the low-frequency conductivity for the bilayer quantum Heisenberg model was investigated numerically. The dynamical conductivity (associated with the O(3) symmetry) displays the inductor σ( ω) = ( iωL)-1 and capacitor iωC behaviors for the ordered and disordered phases, respectively. Both constants, C and L, have the same scaling dimension as that of the reciprocal paramagnetic gap Δ -1. Then, there arose a question to fix the set of critical amplitude ratios among them. So far, the O(2) case has been investigated in the context of the boson-vortex duality. In this paper, we employ the exact diagonalization method, which enables us to calculate the paramagnetic gap Δ directly. Thereby, the set of critical amplitude ratios as to C, L and Δ are estimated with the finite-size-scaling analysis for the cluster with N ≤ 34 spins.

Role of spin-orbit coupling in the Kugel-Khomskii model on the honeycomb lattice

NASA Astrophysics Data System (ADS)

Koga, Akihisa; Nakauchi, Shiryu; Nasu, Joji

2018-03-01

We study the effective spin-orbital model for honeycomb-layered transition metal compounds, applying the second-order perturbation theory to the three-orbital Hubbard model with the anisotropic hoppings. This model is reduced to the Kitaev model in the strong spin-orbit coupling limit. Combining the cluster mean-field approximations with the exact diagonalization, we treat the Kugel-Khomskii type superexchange interaction and spin-orbit coupling on an equal footing to discuss ground-state properties. We find that a zigzag ordered state is realized in the model within nearest-neighbor interactions. We clarify how the ordered state competes with the nonmagnetic state, which is adiabatically connected to the quantum spin liquid state realized in a strong spin-orbit coupling limit. Thermodynamic properties are also addressed. The present paper should provide another route to account for the Kitaev-based magnetic properties in candidate materials.

Scrambling of quantum information in quantum many-body systems

NASA Astrophysics Data System (ADS)

Iyoda, Eiki; Sagawa, Takahiro

2018-04-01

We systematically investigate scrambling (or delocalizing) processes of quantum information encoded in quantum many-body systems by using numerical exact diagonalization. As a measure of scrambling, we adopt the tripartite mutual information (TMI) that becomes negative when quantum information is delocalized. We clarify that scrambling is an independent property of the integrability of Hamiltonians; TMI can be negative or positive for both integrable and nonintegrable systems. This implies that scrambling is a separate concept from conventional quantum chaos characterized by nonintegrability. Specifically, we argue that there are a few exceptional initial states that do not exhibit scrambling, and show that such exceptional initial states have small effective dimensions. Furthermore, we calculate TMI in the Sachdev-Ye-Kitaev (SYK) model, a fermionic toy model of quantum gravity. We find that disorder does not make scrambling slower but makes it smoother in the SYK model, in contrast to many-body localization in spin chains.

Concurrence of dynamical phase transitions at finite temperature in the fully connected transverse-field Ising model

NASA Astrophysics Data System (ADS)

Lang, Johannes; Frank, Bernhard; Halimeh, Jad C.

2018-05-01

We construct the finite-temperature dynamical phase diagram of the fully connected transverse-field Ising model from the vantage point of two disparate concepts of dynamical criticality. An analytical derivation of the classical dynamics and exact diagonalization simulations are used to study the dynamics after a quantum quench in the system prepared in a thermal equilibrium state. The different dynamical phases characterized by the type of nonanalyticities that emerge in an appropriately defined Loschmidt-echo return rate directly correspond to the dynamical phases determined by the spontaneous breaking of Z2 symmetry in the long-time steady state. The dynamical phase diagram is qualitatively different depending on whether the initial thermal state is ferromagnetic or paramagnetic. Whereas the former leads to a dynamical phase diagram that can be directly related to its equilibrium counterpart, the latter gives rise to a divergent dynamical critical temperature at vanishing final transverse-field strength.

Wave Function and Emergent SU(2) Symmetry in the νT=1 Quantum Hall Bilayer

NASA Astrophysics Data System (ADS)

Lian, Biao; Zhang, Shou-Cheng

2018-02-01

We propose a trial wave function for the quantum Hall bilayer system of total filling factor νT=1 at a layer distance d to magnetic length ℓ ratio d /ℓ=κc 1≈1.1 , where the lowest charged excitation is known to have a level crossing. The wave function has two-particle correlations, which fit well with those in previous numerical studies, and can be viewed as a Bose-Einstein condensate of free excitons formed by composite bosons and anticomposite bosons in different layers. We show the free nature of these excitons indicating an emergent SU(2) symmetry for the composite bosons at d /ℓ=κc 1, which leads to the level crossing in low-lying charged excitations. We further show the overlap between the trial wave function, and the ground state of a small size exact diagonalization is peaked near d /ℓ=κc 1, which supports our theory.

Magnetic anisotropy in the Kitaev model systems Na2IrO3 and RuCl3

NASA Astrophysics Data System (ADS)

Chaloupka, Jiří; Khaliullin, Giniyat

2016-08-01

We study the ordered moment direction in the extended Kitaev-Heisenberg model relevant to honeycomb lattice magnets with strong spin-orbit coupling. We utilize numerical diagonalization and analyze the exact cluster ground states using a particular set of spin-coherent states, obtaining thereby quantum corrections to the magnetic anisotropy beyond conventional perturbative methods. It is found that the quantum fluctuations strongly modify the moment direction obtained at a classical level and are thus crucial for a precise quantification of the interactions. The results show that the moment direction is a sensitive probe of the model parameters in real materials. Focusing on the experimentally relevant zigzag phases of the model, we analyze the currently available neutron-diffraction and resonant x-ray-diffraction data on Na2IrO3 and RuCl3 and discuss the parameter regimes plausible in these Kitaev-Heisenberg model systems.

Singular perturbations and time scales in the design of digital flight control systems

NASA Technical Reports Server (NTRS)

Naidu, Desineni S.; Price, Douglas B.

1988-01-01

The results are presented of application of the methodology of Singular Perturbations and Time Scales (SPATS) to the control of digital flight systems. A block diagonalization method is described to decouple a full order, two time (slow and fast) scale, discrete control system into reduced order slow and fast subsystems. Basic properties and numerical aspects of the method are discussed. A composite, closed-loop, suboptimal control system is constructed as the sum of the slow and fast optimal feedback controls. The application of this technique to an aircraft model shows close agreement between the exact solutions and the decoupled (or composite) solutions. The main advantage of the method is the considerable reduction in the overall computational requirements for the evaluation of optimal guidance and control laws. The significance of the results is that it can be used for real time, onboard simulation. A brief survey is also presented of digital flight systems.

Maximal coherence and the resource theory of purity

NASA Astrophysics Data System (ADS)

Streltsov, Alexander; Kampermann, Hermann; Wölk, Sabine; Gessner, Manuel; Bruß, Dagmar

2018-05-01

The resource theory of quantum coherence studies the off-diagonal elements of a density matrix in a distinguished basis, whereas the resource theory of purity studies all deviations from the maximally mixed state. We establish a direct connection between the two resource theories, by identifying purity as the maximal coherence which is achievable by unitary operations. The states that saturate this maximum identify a universal family of maximally coherent mixed states. These states are optimal resources under maximally incoherent operations, and thus independent of the way coherence is quantified. For all distance-based coherence quantifiers the maximal coherence can be evaluated exactly, and is shown to coincide with the corresponding distance-based purity quantifier. We further show that purity bounds the maximal amount of entanglement and discord that can be generated by unitary operations, thus demonstrating that purity is the most elementary resource for quantum information processing.

Anomalous bulk behavior in the free parafermion Z (N ) spin chain

NASA Astrophysics Data System (ADS)

Alcaraz, Francisco C.; Batchelor, Murray T.

2018-06-01

We demonstrate using direct numerical diagonalization and extrapolation methods that boundary conditions have a profound effect on the bulk properties of a simple Z (N ) model for N ≥3 for which the model Hamiltonian is non-Hermitian. For N =2 the model reduces to the well-known quantum Ising model in a transverse field. For open boundary conditions, the Z (N ) model is known to be solved exactly in terms of free parafermions. Once the ends of the open chain are connected by considering the model on a ring, the bulk properties, including the ground-state energy per site, are seen to differ dramatically with increasing N . Other properties, such as the leading finite-size corrections to the ground-state energy, the mass gap exponent, and the specific-heat exponent, are also seen to be dependent on the boundary conditions. We speculate that this anomalous bulk behavior is a topological effect.

Emergence of chiral spin liquids via quantum melting of noncoplanar magnetic orders

DOE PAGES

Hickey, Ciarán; Cincio, Lukasz; Papić, Zlatko; ...

2017-09-11

Quantum spin liquids (QSLs) are highly entangled states of quantum magnets which lie beyond the Landau paradigm of classifying phases of matter via broken symmetries. A physical route to arriving at QSLs is via frustration-induced quantum melting of ordered states such as valence bond crystals or magnetic orders. Using extensive exact diagonalization (ED) and density-matrix renormalization group (DMRG)we show studies of concrete S U ( 2 ) invariant spin models on honeycomb, triangular, and square lattices, that chiral spin liquids (CSLs) emerge as descendants of triple- Q spin crystals with tetrahedral magnetic order and a large scalar spin chirality. Suchmore » ordered-to-CSL melting transitions may yield lattice realizations of effective Chern-Simons-Higgs field theories. We provides a distinct unifying perspective on the emergence of CSLs and suggests that materials with certain noncoplanar magnetic orders might provide a good starting point to search for CSLs.« less

Effects of geometrical frustration on ferromagnetism in the Hubbard model on the generalised Shastry-Sutherland lattice

NASA Astrophysics Data System (ADS)

Farkašovský, Pavol

2018-05-01

The small-cluster exact-diagonalization calculations and the projector quantum Monte Carlo method are used to examine the competing effects of geometrical frustration and interaction on ferromagnetism in the Hubbard model on the generalised Shastry-Sutherland lattice. It is shown that the geometrical frustration stabilizes the ferromagnetic state at high electron concentrations ( n ≳ 7/4), where strong correlations between ferromagnetism and the shape of the noninteracting density of states are observed. In particular, it is found that ferromagnetism is stabilized for these values of frustration parameters, which lead to the single-peaked noninterating density of states at the band edge. Once, two or more peaks appear in the noninteracting density of states at the band edge the ferromagnetic state is suppressed. This opens a new route towards the understanding of ferromagnetism in strongly correlated systems.

Nuclear spin-lattice relaxation at field-induced level crossings in a Cr8F8 pivalate single crystal

NASA Astrophysics Data System (ADS)

Yamamoto, Shoji

2016-01-01

We construct a microscopic theory for the proton spin-lattice relaxation-rate 1 /T1 measurements around field-induced level crossings in a single crystal of the trivalent chromium ion wheel complex [Cr8F8(OOCtBu)16] at sufficiently low temperatures [E. Micotti et al., Phys. Rev. B 72 (2005) 020405(R)]. Exactly diagonalizing a well-equipped spin Hamiltonian for the individual clusters and giving further consideration to their possible interactions, we reveal the mechanism of 1 /T1 being single-peaked normally at the first level crossing but double-peaked intriguingly around the second level crossing. We wipe out the doubt about poor crystallization and find out a solution-intramolecular alternating Dzyaloshinsky-Moriya interaction combined with intermolecular coupling of antiferromagnetic character, each of which is so weak as several tens of mK in magnitude.

Phase Space Approach to Dynamics of Interacting Fermions

NASA Astrophysics Data System (ADS)

Davidson, Shainen; Sels, Dries; Kasper, Valentin; Polkovnikov, Anatoli

Understanding the behavior of interacting fermions is of fundamental interest in many fields ranging from condensed matter to high energy physics. Developing numerically efficient and accurate simulation methods is an indispensable part of this. Already in equilibrium, fermions are notoriously hard to handle due to the sign problem. Out of equilibrium, an important outstanding problem is the efficient numerical simulation of the dynamics of these systems. In this work we develop a new semiclassical phase-space approach (a.k.a. the truncated Wigner approximation) for simulating the dynamics of interacting lattice fermions in arbitrary dimensions. We demonstrate the strength of the method by comparing the results to exact diagonalization (ED) on small 1D and 2D systems. We furthermore present results on Many-Body Localized (MBL) systems in 1D and 2D, and demonstrate how the method can be used to determine the MBL transition.

Crossover from Super- to Subdiffusive Motion and Memory Effects in Crystalline Organic Semiconductors

NASA Astrophysics Data System (ADS)

De Filippis, G.; Cataudella, V.; Mishchenko, A. S.; Nagaosa, N.; Fierro, A.; de Candia, A.

2015-02-01

The transport properties at finite temperature of crystalline organic semiconductors are investigated, within the Su-Schrieffer-Heeger model, by combining an exact diagonalization technique, Monte Carlo approaches, and a maximum entropy method. The temperature-dependent mobility data measured in single crystals of rubrene are successfully reproduced: a crossover from super- to subdiffusive motion occurs in the range 150 ≤T ≤200 K , where the mean free path becomes of the order of the lattice parameter and strong memory effects start to appear. We provide an effective model, which can successfully explain features of the absorption spectra at low frequencies. The observed response to slowly varying electric field is interpreted by means of a simple model where the interaction between the charge carrier and lattice polarization modes is simulated by a harmonic interaction between a fictitious particle and an electron embedded in a viscous fluid.

Crossover from super- to subdiffusive motion and memory effects in crystalline organic semiconductors.

PubMed

De Filippis, G; Cataudella, V; Mishchenko, A S; Nagaosa, N; Fierro, A; de Candia, A

2015-02-27

The transport properties at finite temperature of crystalline organic semiconductors are investigated, within the Su-Schrieffer-Heeger model, by combining an exact diagonalization technique, Monte Carlo approaches, and a maximum entropy method. The temperature-dependent mobility data measured in single crystals of rubrene are successfully reproduced: a crossover from super- to subdiffusive motion occurs in the range 150≤T≤200  K, where the mean free path becomes of the order of the lattice parameter and strong memory effects start to appear. We provide an effective model, which can successfully explain features of the absorption spectra at low frequencies. The observed response to slowly varying electric field is interpreted by means of a simple model where the interaction between the charge carrier and lattice polarization modes is simulated by a harmonic interaction between a fictitious particle and an electron embedded in a viscous fluid.

Nonholonomic relativistic diffusion and exact solutions for stochastic Einstein spaces

NASA Astrophysics Data System (ADS)

Vacaru, S. I.

2012-03-01

We develop an approach to the theory of nonholonomic relativistic stochastic processes in curved spaces. The Itô and Stratonovich calculus are formulated for spaces with conventional horizontal (holonomic) and vertical (nonholonomic) splitting defined by nonlinear connection structures. Geometric models of the relativistic diffusion theory are elaborated for nonholonomic (pseudo) Riemannian manifolds and phase velocity spaces. Applying the anholonomic deformation method, the field equations in Einstein's gravity and various modifications are formally integrated in general forms, with generic off-diagonal metrics depending on some classes of generating and integration functions. Choosing random generating functions we can construct various classes of stochastic Einstein manifolds. We show how stochastic gravitational interactions with mixed holonomic/nonholonomic and random variables can be modelled in explicit form and study their main geometric and stochastic properties. Finally, the conditions when non-random classical gravitational processes transform into stochastic ones and inversely are analyzed.

Electronic excitations in γ -Li2IrO3

NASA Astrophysics Data System (ADS)

Li, Ying; Winter, Stephen M.; Jeschke, Harald O.; Valentí, Roser

2017-01-01

We investigate the electronic properties of the three-dimensional stripyhoneycomb γ -Li2IrO3 via relativistic density functional theory calculations as well as exact diagonalization of finite clusters and explore the details of the optical conductivity. Our analysis of this quantity reveals the microscopic origin of the experimentally observed (i) optical transitions and (ii) anisotropic behavior along the various polarization directions. In particular, we find that the optical excitations are overall dominated by transitions between jeff=1 /2 and 3/2 states and the weight of transitions between jeff=1 /2 states at low frequencies can be correlated to deviations from a pure Kitaev description. We furthermore reanalyze within this approach the electronic excitations in the known two-dimensional honeycomb systems α -Li2IrO3 and Na2IrO3 and discuss the results in comparison to γ -Li2IrO3 .

Using nonequilibrium dynamics to probe competing orders in a Mott-Peierls system

DOE PAGES

Wang, Y.; Moritz, B.; Chen, C. -C.; ...

2016-02-24

Competition between ordered phases, and their associated phase transitions, are significant in the study of strongly correlated systems. Here, we examine one aspect, the nonequilibrium dynamics of a photoexcited Mott-Peierls system, using an effective Peierls-Hubbard model and exact diagonalization. Near a transition where spin and charge become strongly intertwined, we observe antiphase dynamics and a coupling-strength-dependent suppression or enhancement in the static structure factors. The renormalized bosonic excitations coupled to a particular photoexcited electron can be extracted, which provides an approach for characterizing the underlying bosonic modes. The results from this analysis for different electronic momenta show an uneven softeningmore » due to a stronger coupling near k F. As a result, this behavior reflects the strong link between the fermionic momenta, the coupling vertices, and ultimately, the bosonic susceptibilities when multiple phases compete for the ground state of the system.« less

Electronic entanglement in late transition metal oxides.

PubMed

Thunström, Patrik; Di Marco, Igor; Eriksson, Olle

2012-11-02

We present a study of the entanglement in the electronic structure of the late transition metal monoxides--MnO, FeO, CoO, and NiO--obtained by means of density-functional theory in the local density approximation combined with dynamical mean-field theory. The impurity problem is solved through exact diagonalization, which grants full access to the thermally mixed many-body ground state density operator. The quality of the electronic structure is affirmed through a direct comparison between the calculated electronic excitation spectrum and photoemission experiments. Our treatment allows for a quantitative investigation of the entanglement in the electronic structure. Two main sources of entanglement are explicitly resolved through the use of a fidelity based geometrical entanglement measure, and additional information is gained from a complementary entropic entanglement measure. We show that the interplay of crystal field effects and Coulomb interaction causes the entanglement in CoO to take a particularly intricate form.

Emergence of chiral spin liquids via quantum melting of noncoplanar magnetic orders

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

Hickey, Ciarán; Cincio, Lukasz; Papić, Zlatko

Quantum spin liquids (QSLs) are highly entangled states of quantum magnets which lie beyond the Landau paradigm of classifying phases of matter via broken symmetries. A physical route to arriving at QSLs is via frustration-induced quantum melting of ordered states such as valence bond crystals or magnetic orders. Using extensive exact diagonalization (ED) and density-matrix renormalization group (DMRG)we show studies of concrete S U ( 2 ) invariant spin models on honeycomb, triangular, and square lattices, that chiral spin liquids (CSLs) emerge as descendants of triple- Q spin crystals with tetrahedral magnetic order and a large scalar spin chirality. Suchmore » ordered-to-CSL melting transitions may yield lattice realizations of effective Chern-Simons-Higgs field theories. We provides a distinct unifying perspective on the emergence of CSLs and suggests that materials with certain noncoplanar magnetic orders might provide a good starting point to search for CSLs.« less

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.

A tensor network approach to many-body localization

NASA Astrophysics Data System (ADS)

Yu, Xiongjie; Pekker, David; Clark, Bryan

Understanding the many-body localized phase requires access to eigenstates in the middle of the many-body spectrum. While exact-diagonalization is able to access these eigenstates, it is restricted to systems sizes of about 22 spins. To overcome this limitation, we develop tensor network algorithms which increase the accessible system size by an order of magnitude. We describe both our new algorithms as well as the additional physics about MBL we can extract from them. For example, we demonstrate the power of these methods by verifying the breakdown of the Eigenstate Thermalization Hypothesis (ETH) in the many-body localized phase of the random field Heisenberg model, and show the saturation of entanglement in the MBL phase and generate eigenstates that differ by local excitations. Work was supported by AFOSR FA9550-10-1-0524 and FA9550-12-1-0057, the Kaufmann foundation, and SciDAC FG02-12ER46875.

Stability of the wobbling motion in the triaxially deformed odd-A nucleus

NASA Astrophysics Data System (ADS)

Tanabe, Kosai; Sugawara-Tanabe, Kazuko

2017-12-01

In order to analyze the content of the exact solutions for particle-rotor models with both the rigid and the hydrodynamical moments of inertia (MoI), as a theoretical probe we apply the Holstein-Primakoff (HP) boson expansion method to the total angular momentum I and the single-particle angular momentum j. We study the competition between Coriolis force and the single-particle potential by employing the different choices of the diagonal HP boson representations for the components of I and j along a common coordinate axis, and along perpendicular axes. We do not find any wobbling level sequence associated with the rotation around the principal axis with the medium MoI. The staggering in the alignments of I about the axis with the medium MoI is found in the limited range of I, while the vector R(=I-j) is confined about the axis with the largest MoI.

Role of heat equation in lap joint for welding process

NASA Astrophysics Data System (ADS)

Kumar, P.; Rohit, Sooraj

2017-07-01

Welding is predominantly used in industrial purposes and growth in their industry, which gives exact welding and more efficient. The major advantage of using this welding technique at initial stage it takes very low heat to weld the portion and gives a good result of low distortion in modules. In this context, two dissimilar metals copper and nickel are chosen for analysis in tungsten inert gas welding (TIG) in which length is 300 mm and breadth is 100 mm thickness 15 mm welded at room temperature a welded portion zone is formed simulation analysis has done on CATIA® and ANSYS®and MATLAB® code is generated for calculating temperatures at each node to calculate temperature at each node a new technique is used tri-diagonal matrix algorithm is used (TDMA) Steady state one dimension heat is calculated results compared between simulation analysis and analytical analysis temperature at each node is calculated both the temperatures are equal with error.

Steering Bell-diagonal states

PubMed Central

Quan, Quan; Zhu, Huangjun; Liu, Si-Yuan; Fei, Shao-Ming; Fan, Heng; Yang, Wen-Li

2016-01-01

We investigate the steerability of two-qubit Bell-diagonal states under projective measurements by the steering party. In the simplest nontrivial scenario of two projective measurements, we solve this problem completely by virtue of the connection between the steering problem and the joint-measurement problem. A necessary and sufficient criterion is derived together with a simple geometrical interpretation. Our study shows that a Bell-diagonal state is steerable by two projective measurements iff it violates the Clauser-Horne-Shimony-Holt (CHSH) inequality, in sharp contrast with the strict hierarchy expected between steering and Bell nonlocality. We also introduce a steering measure and clarify its connections with concurrence and the volume of the steering ellipsoid. In particular, we determine the maximal concurrence and ellipsoid volume of Bell-diagonal states that are not steerable by two projective measurements. Finally, we explore the steerability of Bell-diagonal states under three projective measurements. A simple sufficient criterion is derived, which can detect the steerability of many states that are not steerable by two projective measurements. Our study offers valuable insight on steering of Bell-diagonal states as well as the connections between entanglement, steering, and Bell nonlocality. PMID:26911250

Accelerating solutions of one-dimensional unsteady PDEs with GPU-based swept time-space decomposition

NASA Astrophysics Data System (ADS)

Magee, Daniel J.; Niemeyer, Kyle E.

2018-03-01

The expedient design of precision components in aerospace and other high-tech industries requires simulations of physical phenomena often described by partial differential equations (PDEs) without exact solutions. Modern design problems require simulations with a level of resolution difficult to achieve in reasonable amounts of time-even in effectively parallelized solvers. Though the scale of the problem relative to available computing power is the greatest impediment to accelerating these applications, significant performance gains can be achieved through careful attention to the details of memory communication and access. The swept time-space decomposition rule reduces communication between sub-domains by exhausting the domain of influence before communicating boundary values. Here we present a GPU implementation of the swept rule, which modifies the algorithm for improved performance on this processing architecture by prioritizing use of private (shared) memory, avoiding interblock communication, and overwriting unnecessary values. It shows significant improvement in the execution time of finite-difference solvers for one-dimensional unsteady PDEs, producing speedups of 2 - 9 × for a range of problem sizes, respectively, compared with simple GPU versions and 7 - 300 × compared with parallel CPU versions. However, for a more sophisticated one-dimensional system of equations discretized with a second-order finite-volume scheme, the swept rule performs 1.2 - 1.9 × worse than a standard implementation for all problem sizes.

Efficient Iterative Methods Applied to the Solution of Transonic Flows

NASA Astrophysics Data System (ADS)

Wissink, Andrew M.; Lyrintzis, Anastasios S.; Chronopoulos, Anthony T.

1996-02-01

We investigate the use of an inexact Newton's method to solve the potential equations in the transonic regime. As a test case, we solve the two-dimensional steady transonic small disturbance equation. Approximate factorization/ADI techniques have traditionally been employed for implicit solutions of this nonlinear equation. Instead, we apply Newton's method using an exact analytical determination of the Jacobian with preconditioned conjugate gradient-like iterative solvers for solution of the linear systems in each Newton iteration. Two iterative solvers are tested; a block s-step version of the classical Orthomin(k) algorithm called orthogonal s-step Orthomin (OSOmin) and the well-known GMRES method. The preconditioner is a vectorizable and parallelizable version of incomplete LU (ILU) factorization. Efficiency of the Newton-Iterative method on vector and parallel computer architectures is the main issue addressed. In vectorized tests on a single processor of the Cray C-90, the performance of Newton-OSOmin is superior to Newton-GMRES and a more traditional monotone AF/ADI method (MAF) for a variety of transonic Mach numbers and mesh sizes. Newton-GMRES is superior to MAF for some cases. The parallel performance of the Newton method is also found to be very good on multiple processors of the Cray C-90 and on the massively parallel thinking machine CM-5, where very fast execution rates (up to 9 Gflops) are found for large problems.

Recent Advances in Agglomerated Multigrid

NASA Technical Reports Server (NTRS)

Nishikawa, Hiroaki; Diskin, Boris; Thomas, James L.; Hammond, Dana P.

2013-01-01

We report recent advancements of the agglomerated multigrid methodology for complex flow simulations on fully unstructured grids. An agglomerated multigrid solver is applied to a wide range of test problems from simple two-dimensional geometries to realistic three- dimensional configurations. The solver is evaluated against a single-grid solver and, in some cases, against a structured-grid multigrid solver. Grid and solver issues are identified and overcome, leading to significant improvements over single-grid solvers.

Similarity-transformed equation-of-motion vibrational coupled-cluster theory.

PubMed

Faucheaux, Jacob A; Nooijen, Marcel; Hirata, So

2018-02-07

A similarity-transformed equation-of-motion vibrational coupled-cluster (STEOM-XVCC) method is introduced as a one-mode theory with an effective vibrational Hamiltonian, which is similarity transformed twice so that its lower-order operators are dressed with higher-order anharmonic effects. The first transformation uses an exponential excitation operator, defining the equation-of-motion vibrational coupled-cluster (EOM-XVCC) method, and the second uses an exponential excitation-deexcitation operator. From diagonalization of this doubly similarity-transformed Hamiltonian in the small one-mode excitation space, the method simultaneously computes accurate anharmonic vibrational frequencies of all fundamentals, which have unique significance in vibrational analyses. We establish a diagrammatic method of deriving the working equations of STEOM-XVCC and prove their connectedness and thus size-consistency as well as the exact equality of its frequencies with the corresponding roots of EOM-XVCC. We furthermore elucidate the similarities and differences between electronic and vibrational STEOM methods and between STEOM-XVCC and vibrational many-body Green's function theory based on the Dyson equation, which is also an anharmonic one-mode theory. The latter comparison inspires three approximate STEOM-XVCC methods utilizing the common approximations made in the Dyson equation: the diagonal approximation, a perturbative expansion of the Dyson self-energy, and the frequency-independent approximation. The STEOM-XVCC method including up to the simultaneous four-mode excitation operator in a quartic force field and its three approximate variants are formulated and implemented in computer codes with the aid of computer algebra, and they are applied to small test cases with varied degrees of anharmonicity.

A problem with inverse time for a singularly perturbed integro-differential equation with diagonal degeneration of the kernel of high order

NASA Astrophysics Data System (ADS)

Bobodzhanov, A. A.; Safonov, V. F.

2016-04-01

We consider an algorithm for constructing asymptotic solutions regularized in the sense of Lomov (see [1], [2]). We show that such problems can be reduced to integro-differential equations with inverse time. But in contrast to known papers devoted to this topic (see, for example, [3]), in this paper we study a fundamentally new case, which is characterized by the absence, in the differential part, of a linear operator that isolates, in the asymptotics of the solution, constituents described by boundary functions and by the fact that the integral operator has kernel with diagonal degeneration of high order. Furthermore, the spectrum of the regularization operator A(t) (see below) may contain purely imaginary eigenvalues, which causes difficulties in the application of the methods of construction of asymptotic solutions proposed in the monograph [3]. Based on an analysis of the principal term of the asymptotics, we isolate a class of inhomogeneities and initial data for which the exact solution of the original problem tends to the limit solution (as \\varepsilon\\to+0) on the entire time interval under consideration, also including a boundary-layer zone (that is, we solve the so-called initialization problem). The paper is of a theoretical nature and is designed to lead to a greater understanding of the problems in the theory of singular perturbations. There may be applications in various applied areas where models described by integro-differential equations are used (for example, in elasticity theory, the theory of electrical circuits, and so on).

Similarity-transformed equation-of-motion vibrational coupled-cluster theory

NASA Astrophysics Data System (ADS)

Faucheaux, Jacob A.; Nooijen, Marcel; Hirata, So

2018-02-01

A similarity-transformed equation-of-motion vibrational coupled-cluster (STEOM-XVCC) method is introduced as a one-mode theory with an effective vibrational Hamiltonian, which is similarity transformed twice so that its lower-order operators are dressed with higher-order anharmonic effects. The first transformation uses an exponential excitation operator, defining the equation-of-motion vibrational coupled-cluster (EOM-XVCC) method, and the second uses an exponential excitation-deexcitation operator. From diagonalization of this doubly similarity-transformed Hamiltonian in the small one-mode excitation space, the method simultaneously computes accurate anharmonic vibrational frequencies of all fundamentals, which have unique significance in vibrational analyses. We establish a diagrammatic method of deriving the working equations of STEOM-XVCC and prove their connectedness and thus size-consistency as well as the exact equality of its frequencies with the corresponding roots of EOM-XVCC. We furthermore elucidate the similarities and differences between electronic and vibrational STEOM methods and between STEOM-XVCC and vibrational many-body Green's function theory based on the Dyson equation, which is also an anharmonic one-mode theory. The latter comparison inspires three approximate STEOM-XVCC methods utilizing the common approximations made in the Dyson equation: the diagonal approximation, a perturbative expansion of the Dyson self-energy, and the frequency-independent approximation. The STEOM-XVCC method including up to the simultaneous four-mode excitation operator in a quartic force field and its three approximate variants are formulated and implemented in computer codes with the aid of computer algebra, and they are applied to small test cases with varied degrees of anharmonicity.

Separability of three qubit Greenberger-Horne-Zeilinger diagonal states

NASA Astrophysics Data System (ADS)

Han, Kyung Hoon; Kye, Seung-Hyeok

2017-04-01

We characterize the separability of three qubit GHZ diagonal states in terms of entries. This enables us to check separability of GHZ diagonal states without decomposition into the sum of pure product states. In the course of discussion, we show that the necessary criterion of Gühne (2011 Entanglement criteria and full separability of multi-qubit quantum states Phys. Lett. A 375 406-10) for (full) separability of three qubit GHZ diagonal states is sufficient with a simpler formula. The main tool is to use entanglement witnesses which are tri-partite Choi matrices of positive bi-linear maps.

Parallel Solver for H(div) Problems Using Hybridization and AMG

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

Lee, Chak S.; Vassilevski, Panayot S.

2016-01-15

In this paper, a scalable parallel solver is proposed for H(div) problems discretized by arbitrary order finite elements on general unstructured meshes. The solver is based on hybridization and algebraic multigrid (AMG). Unlike some previously studied H(div) solvers, the hybridization solver does not require discrete curl and gradient operators as additional input from the user. Instead, only some element information is needed in the construction of the solver. The hybridization results in a H1-equivalent symmetric positive definite system, which is then rescaled and solved by AMG solvers designed for H1 problems. Weak and strong scaling of the method are examinedmore » through several numerical tests. Our numerical results show that the proposed solver provides a promising alternative to ADS, a state-of-the-art solver [12], for H(div) problems. In fact, it outperforms ADS for higher order elements.« less

Fully Implicit, Nonlinear 3D Extended Magnetohydrodynamics

NASA Astrophysics Data System (ADS)

Chacon, Luis; Knoll, Dana

2003-10-01

Extended magnetohydrodynamics (XMHD) includes nonideal effects such as nonlinear, anisotropic transport and two-fluid (Hall) effects. XMHD supports multiple, separate time scales that make explicit time differencing approaches extremely inefficient. While a fully implicit implementation promises efficiency without sacrificing numerical accuracy,(D. A. Knoll et al., phJ. Comput. Phys.) 185 (2), 583-611 (2003) the nonlinear nature of the XMHD system and the numerical stiffness associated with the fast waves make this endeavor difficult. Newton-Krylov methods are, however, ideally suited for such a task. These synergistically combine Newton's method for nonlinear convergence, and Krylov techniques to solve the associated Jacobian (linear) systems. Krylov methods can be implemented Jacobian-free and can be preconditioned for efficiency. Successful preconditioning strategies have been developed for 2D incompressible resistive(L. Chacón et al., phJ. Comput. Phys). 178 (1), 15- 36 (2002) and Hall(L. Chacón and D. A. Knoll, phJ. Comput. Phys.), 188 (2), 573-592 (2003) MHD models. These are based on ``physics-based'' ideas, in which knowledge of the physics is exploited to derive well-conditioned (diagonally-dominant) approximations to the original system that are amenable to optimal solver technologies (multigrid). In this work, we will describe the status of the extension of the 2D preconditioning ideas for a 3D compressible, single-fluid XMHD model.

Study of the flow field past dimpled aerodynamic surfaces: numerical simulation and experimental verification

NASA Astrophysics Data System (ADS)

Binci, L.; Clementi, G.; D'Alessandro, V.; Montelpare, S.; Ricci, R.

2017-11-01

This work presents the study of the flow field past of dimpled laminar airfoil. Fluid dynamic behaviour of these elements has been not still deeply studied in the scientific community. Therefore Computational Fluid-Dynamics (CFD) is here used to analyze the flow field induced by dimples on the NACA 64-014A laminar airfoil at Re = 1.75 · 105 at α = 0°. Reynolds Averaged Navier-Stokes (RANS) equations and Large-Eddy Simulations (LES) were compared with wind tunnel measurements in order to evaluate their effectiveness in the modeling this kind of flow field. LES equations were solved using a specifically developed OpenFOAM solver adopting an L-stable Singly Diagonally Implicit Runge-Kutta (SDIRK) technique with an iterated PISO-like procedure for handling pressure-velocity coupling within each RK stage. Dynamic Smagorinsky subgrid model was employed. LES results provided good agreement with experimental data, while RANS equations closed with \\[k-ω -γ -\\overset{}{\\mathop{{{\\operatorname{Re}}θ, \\text{t}}}} \\] approach overstimates laminar separation bubble (LSB) extension of dimpled and un-dimpled configurations. Moreover, through skin friction coefficient analysis, we found a different representation of the turbulent zone between the numerical models; indeed, with RANS model LSB seems to be divided in two different parts, meanwhile LES model shows a LSB global reduction.

Efficient block preconditioned eigensolvers for linear response time-dependent density functional theory

NASA Astrophysics Data System (ADS)

Vecharynski, Eugene; Brabec, Jiri; Shao, Meiyue; Govind, Niranjan; Yang, Chao

2017-12-01

We present two efficient iterative algorithms for solving the linear response eigenvalue problem arising from the time dependent density functional theory. Although the matrix to be diagonalized is nonsymmetric, it has a special structure that can be exploited to save both memory and floating point operations. In particular, the nonsymmetric eigenvalue problem can be transformed into an eigenvalue problem that involves the product of two matrices M and K. We show that, because MK is self-adjoint with respect to the inner product induced by the matrix K, this product eigenvalue problem can be solved efficiently by a modified Davidson algorithm and a modified locally optimal block preconditioned conjugate gradient (LOBPCG) algorithm that make use of the K-inner product. The solution of the product eigenvalue problem yields one component of the eigenvector associated with the original eigenvalue problem. We show that the other component of the eigenvector can be easily recovered in an inexpensive postprocessing procedure. As a result, the algorithms we present here become more efficient than existing methods that try to approximate both components of the eigenvectors simultaneously. In particular, our numerical experiments demonstrate that the new algorithms presented here consistently outperform the existing state-of-the-art Davidson type solvers by a factor of two in both solution time and storage.

A Distributed-Memory Package for Dense Hierarchically Semi-Separable Matrix Computations Using Randomization

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

Rouet, François-Henry; Li, Xiaoye S.; Ghysels, Pieter

In this paper, we present a distributed-memory library for computations with dense structured matrices. A matrix is considered structured if its off-diagonal blocks can be approximated by a rank-deficient matrix with low numerical rank. Here, we use Hierarchically Semi-Separable (HSS) representations. Such matrices appear in many applications, for example, finite-element methods, boundary element methods, and so on. Exploiting this structure allows for fast solution of linear systems and/or fast computation of matrix-vector products, which are the two main building blocks of matrix computations. The compression algorithm that we use, that computes the HSS form of an input dense matrix, reliesmore » on randomized sampling with a novel adaptive sampling mechanism. We discuss the parallelization of this algorithm and also present the parallelization of structured matrix-vector product, structured factorization, and solution routines. The efficiency of the approach is demonstrated on large problems from different academic and industrial applications, on up to 8,000 cores. Finally, this work is part of a more global effort, the STRUctured Matrices PACKage (STRUMPACK) software package for computations with sparse and dense structured matrices. Hence, although useful on their own right, the routines also represent a step in the direction of a distributed-memory sparse solver.« less

A Distributed-Memory Package for Dense Hierarchically Semi-Separable Matrix Computations Using Randomization

DOE PAGES

Rouet, François-Henry; Li, Xiaoye S.; Ghysels, Pieter; ...

2016-06-30

In this paper, we present a distributed-memory library for computations with dense structured matrices. A matrix is considered structured if its off-diagonal blocks can be approximated by a rank-deficient matrix with low numerical rank. Here, we use Hierarchically Semi-Separable (HSS) representations. Such matrices appear in many applications, for example, finite-element methods, boundary element methods, and so on. Exploiting this structure allows for fast solution of linear systems and/or fast computation of matrix-vector products, which are the two main building blocks of matrix computations. The compression algorithm that we use, that computes the HSS form of an input dense matrix, reliesmore » on randomized sampling with a novel adaptive sampling mechanism. We discuss the parallelization of this algorithm and also present the parallelization of structured matrix-vector product, structured factorization, and solution routines. The efficiency of the approach is demonstrated on large problems from different academic and industrial applications, on up to 8,000 cores. Finally, this work is part of a more global effort, the STRUctured Matrices PACKage (STRUMPACK) software package for computations with sparse and dense structured matrices. Hence, although useful on their own right, the routines also represent a step in the direction of a distributed-memory sparse solver.« less

Formation of current singularity in a topologically constrained plasma

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

Zhou, Yao; Huang, Yi-Min; Qin, Hong

2016-02-01

Recently a variational integrator for ideal magnetohydrodynamics in Lagrangian labeling has been developed. Its built-in frozen-in equation makes it optimal for studying current sheet formation. We use this scheme to study the Hahm-Kulsrud-Taylor problem, which considers the response of a 2D plasma magnetized by a sheared field under sinusoidal boundary forcing. We obtain an equilibrium solution that preserves the magnetic topology of the initial field exactly, with a fluid mapping that is non-differentiable. Unlike previous studies that examine the current density output, we identify a singular current sheet from the fluid mapping. These results are benchmarked with a constrained Grad-Shafranovmore » solver. The same signature of current singularity can be found in other cases with more complex magnetic topologies.« less

A new impedance accounting for short- and long-range effects in mixed substructured formulations of nonlinear problems

NASA Astrophysics Data System (ADS)

Negrello, Camille; Gosselet, Pierre; Rey, Christian

2018-05-01

An efficient method for solving large nonlinear problems combines Newton solvers and Domain Decomposition Methods (DDM). In the DDM framework, the boundary conditions can be chosen to be primal, dual or mixed. The mixed approach presents the advantage to be eligible for the research of an optimal interface parameter (often called impedance) which can increase the convergence rate. The optimal value for this parameter is often too expensive to be computed exactly in practice: an approximate version has to be sought for, along with a compromise between efficiency and computational cost. In the context of parallel algorithms for solving nonlinear structural mechanical problems, we propose a new heuristic for the impedance which combines short and long range effects at a low computational cost.

Development and Verification of the Charring, Ablating Thermal Protection Implicit System Simulator

NASA Technical Reports Server (NTRS)

Amar, Adam J.; Calvert, Nathan; Kirk, Benjamin S.

2011-01-01

The development and verification of the Charring Ablating Thermal Protection Implicit System Solver (CATPISS) is presented. This work concentrates on the derivation and verification of the stationary grid terms in the equations that govern three-dimensional heat and mass transfer for charring thermal protection systems including pyrolysis gas flow through the porous char layer. The governing equations are discretized according to the Galerkin finite element method (FEM) with first and second order fully implicit time integrators. The governing equations are fully coupled and are solved in parallel via Newton s method, while the linear system is solved via the Generalized Minimum Residual method (GMRES). Verification results from exact solutions and Method of Manufactured Solutions (MMS) are presented to show spatial and temporal orders of accuracy as well as nonlinear convergence rates.

Compressive auto-indexing in femtosecond nanocrystallography

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

Maia, Filipe; Yang, Chao; Marchesini, Stefano

2010-09-20

Ultrafast nanocrystallography has the potential to revolutionize biology by enabling structural elucidation of proteins for which it is possible to grow crystals with 10 or fewer unit cells. The success of nanocrystallography depends on robust orientation-determination procedures that allow us to average diffraction data from multiple nanocrystals to produce a 3D diffraction data volume with a high signal-to-noise ratio. Such a 3D diffraction volume can then be phased using standard crystallographic techniques."Indexing" algorithms used in crystallography enable orientation determination of a diffraction data from a single crystal when a relatively large number of reflections are recorded. Here we show thatmore » it is possible to obtain the exact lattice geometry from a smaller number of measurements than standard approaches using a basis pursuit solver.« less

An acoustic-convective splitting-based approach for the Kapila two-phase flow model

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

Eikelder, M.F.P. ten, E-mail: m.f.p.teneikelder@tudelft.nl; Eindhoven University of Technology, Department of Mathematics and Computer Science, P.O. Box 513, 5600 MB Eindhoven; Daude, F.

In this paper we propose a new acoustic-convective splitting-based numerical scheme for the Kapila five-equation two-phase flow model. The splitting operator decouples the acoustic waves and convective waves. The resulting two submodels are alternately numerically solved to approximate the solution of the entire model. The Lagrangian form of the acoustic submodel is numerically solved using an HLLC-type Riemann solver whereas the convective part is approximated with an upwind scheme. The result is a simple method which allows for a general equation of state. Numerical computations are performed for standard two-phase shock tube problems. A comparison is made with a non-splittingmore » approach. The results are in good agreement with reference results and exact solutions.« less

Multidimensional Riemann problem with self-similar internal structure - part III - a multidimensional analogue of the HLLI Riemann solver for conservative hyperbolic systems

NASA Astrophysics Data System (ADS)

Balsara, Dinshaw S.; Nkonga, Boniface

2017-10-01

Just as the quality of a one-dimensional approximate Riemann solver is improved by the inclusion of internal sub-structure, the quality of a multidimensional Riemann solver is also similarly improved. Such multidimensional Riemann problems arise when multiple states come together at the vertex of a mesh. The interaction of the resulting one-dimensional Riemann problems gives rise to a strongly-interacting state. We wish to endow this strongly-interacting state with physically-motivated sub-structure. The fastest way of endowing such sub-structure consists of making a multidimensional extension of the HLLI Riemann solver for hyperbolic conservation laws. Presenting such a multidimensional analogue of the HLLI Riemann solver with linear sub-structure for use on structured meshes is the goal of this work. The multidimensional MuSIC Riemann solver documented here is universal in the sense that it can be applied to any hyperbolic conservation law. The multidimensional Riemann solver is made to be consistent with constraints that emerge naturally from the Galerkin projection of the self-similar states within the wave model. When the full eigenstructure in both directions is used in the present Riemann solver, it becomes a complete Riemann solver in a multidimensional sense. I.e., all the intermediate waves are represented in the multidimensional wave model. The work also presents, for the very first time, an important analysis of the dissipation characteristics of multidimensional Riemann solvers. The present Riemann solver results in the most efficient implementation of a multidimensional Riemann solver with sub-structure. Because it preserves stationary linearly degenerate waves, it might also help with well-balancing. Implementation-related details are presented in pointwise fashion for the one-dimensional HLLI Riemann solver as well as the multidimensional MuSIC Riemann solver.

Diagonalization and Jordan Normal Form--Motivation through "Maple"[R

ERIC Educational Resources Information Center

Glaister, P.

2009-01-01

Following an introduction to the diagonalization of matrices, one of the more difficult topics for students to grasp in linear algebra is the concept of Jordan normal form. In this note, we show how the important notions of diagonalization and Jordan normal form can be introduced and developed through the use of the computer algebra package…

Automated enzyme-based diagonal capillary electrophoresis: application to phosphopeptide characterization

PubMed Central

Wojcik, Roza; Vannatta, Michael

2010-01-01

Diagonal capillary electrophoresis is a form of two-dimensional capillary electrophoresis that employs identical separation modes in each dimension. The distal end of the first capillary incorporates an enzyme-based microreactor. Analytes that are not modified by the reactor will have identical migration times in the two capillaries and will generate spots that fall on the diagonal in a reconstructed two-dimensional electropherogram. Analytes that undergo enzymatic modification in the reactor will have a different migration time in the second capillary and will generate spots that fall off the diagonal in the electropherogram. We demonstrate the system with immobilized alkaline phosphatase to monitor the phosphorylation status of a mixture of peptides. This enzyme-based diagonal capillary electrophoresis assay appears to be generalizable; any post-translational modification can be detected as long as an immobilized enzyme is available that reacts with the modification under electrophoretic conditions. PMID:20099889

Loads imposed on intermediate frames of stiffened shells

NASA Technical Reports Server (NTRS)

Kuhn, Paul

1939-01-01

The loads imposed on intermediate frames by the curvature of the longitudinal and by the diagonal-tension effects are treated. A new empirical method is proposed for analyzing diagonal-tension effects. The basic formulas of the pure diagonal-tension theory are used, and the part of the total shear S carried by diagonal tension is assumed to be given the expression S (sub DT) = S (1-tau sub o/tau)(sup n) where tau (sub o) is the critical shear stress, tau the total (nominal shear stress), and n = 3 - sigma/tau where sigma is the stress in the intermediate frame. Numerical examples illustrate all cases treated.

Finite temperature dynamics of a Holstein polaron: The thermo-field dynamics approach

NASA Astrophysics Data System (ADS)

Chen, Lipeng; Zhao, Yang

2017-12-01

Combining the multiple Davydov D2 Ansatz with the method of thermo-field dynamics, we study finite temperature dynamics of a Holstein polaron on a lattice. It has been demonstrated, using the hierarchy equations of motion method as a benchmark, that our approach provides an efficient, robust description of finite temperature dynamics of the Holstein polaron in the simultaneous presence of diagonal and off-diagonal exciton-phonon coupling. The method of thermo-field dynamics handles temperature effects in the Hilbert space with key numerical advantages over other treatments of finite-temperature dynamics based on quantum master equations in the Liouville space or wave function propagation with Monte Carlo importance sampling. While for weak to moderate diagonal coupling temperature increases inhibit polaron mobility, it is found that off-diagonal coupling induces phonon-assisted transport that dominates at high temperatures. Results on the mean square displacements show that band-like transport features dominate the diagonal coupling cases, and there exists a crossover from band-like to hopping transport with increasing temperature when including off-diagonal coupling. As a proof of concept, our theory provides a unified treatment of coherent and incoherent transport in molecular crystals and is applicable to any temperature.

Thermodynamic Bethe ansatz for non-equilibrium steady states: exact energy current and fluctuations in integrable QFT

NASA Astrophysics Data System (ADS)

Castro-Alvaredo, Olalla; Chen, Yixiong; Doyon, Benjamin; Hoogeveen, Marianne

2014-03-01

We evaluate the exact energy current and scaled cumulant generating function (related to the large-deviation function) in non-equilibrium steady states with energy flow, in any integrable model of relativistic quantum field theory (IQFT) with diagonal scattering. Our derivations are based on various recent results of Bernard and Doyon. The steady states are built by connecting homogeneously two infinite halves of the system thermalized at different temperatures Tl, Tr, and waiting for a long time. We evaluate the current J(Tl, Tr) using the exact QFT density matrix describing these non-equilibrium steady states and using Zamolodchikov’s method of the thermodynamic Bethe ansatz (TBA). The scaled cumulant generating function is obtained from the extended fluctuation relations which hold in integrable models. We verify our formula in particular by showing that the conformal field theory (CFT) result is obtained in the high-temperature limit. We analyze numerically our non-equilibrium steady-state TBA equations for three models: the sinh-Gordon model, the roaming trajectories model, and the sine-Gordon model at a particular reflectionless point. Based on the numerics, we conjecture that an infinite family of non-equilibrium c-functions, associated with the scaled cumulants, can be defined, which we interpret physically. We study the full scaled distribution function and find that it can be described by a set of independent Poisson processes. Finally, we show that the ‘additivity’ property of the current, which is known to hold in CFT and was proposed to hold more generally, does not hold in general IQFT—that is, J(Tl, Tr) is not of the form f(Tl) - f(Tr).

Semi-implicit iterative methods for low Mach number turbulent reacting flows: Operator splitting versus approximate factorization

NASA Astrophysics Data System (ADS)

MacArt, Jonathan F.; Mueller, Michael E.

2016-12-01

Two formally second-order accurate, semi-implicit, iterative methods for the solution of scalar transport-reaction equations are developed for Direct Numerical Simulation (DNS) of low Mach number turbulent reacting flows. The first is a monolithic scheme based on a linearly implicit midpoint method utilizing an approximately factorized exact Jacobian of the transport and reaction operators. The second is an operator splitting scheme based on the Strang splitting approach. The accuracy properties of these schemes, as well as their stability, cost, and the effect of chemical mechanism size on relative performance, are assessed in two one-dimensional test configurations comprising an unsteady premixed flame and an unsteady nonpremixed ignition, which have substantially different Damköhler numbers and relative stiffness of transport to chemistry. All schemes demonstrate their formal order of accuracy in the fully-coupled convergence tests. Compared to a (non-)factorized scheme with a diagonal approximation to the chemical Jacobian, the monolithic, factorized scheme using the exact chemical Jacobian is shown to be both more stable and more economical. This is due to an improved convergence rate of the iterative procedure, and the difference between the two schemes in convergence rate grows as the time step increases. The stability properties of the Strang splitting scheme are demonstrated to outpace those of Lie splitting and monolithic schemes in simulations at high Damköhler number; however, in this regime, the monolithic scheme using the approximately factorized exact Jacobian is found to be the most economical at practical CFL numbers. The performance of the schemes is further evaluated in a simulation of a three-dimensional, spatially evolving, turbulent nonpremixed planar jet flame.

Iterating the Number of Intersection Points of the Diagonals of Irregular Convex Polygons, or C (n, 4) the Hard Way!

ERIC Educational Resources Information Center

Hathout, Leith

2007-01-01

Counting the number of internal intersection points made by the diagonals of irregular convex polygons where no three diagonals are concurrent is an interesting problem in discrete mathematics. This paper uses an iterative approach to develop a summation relation which tallies the total number of intersections, and shows that this total can be…

Eigenvalue Solvers for Modeling Nuclear Reactors on Leadership Class Machines

DOE PAGES

Slaybaugh, R. N.; Ramirez-Zweiger, M.; Pandya, Tara; ...

2018-02-20

In this paper, three complementary methods have been implemented in the code Denovo that accelerate neutral particle transport calculations with methods that use leadership-class computers fully and effectively: a multigroup block (MG) Krylov solver, a Rayleigh quotient iteration (RQI) eigenvalue solver, and a multigrid in energy (MGE) preconditioner. The MG Krylov solver converges more quickly than Gauss Seidel and enables energy decomposition such that Denovo can scale to hundreds of thousands of cores. RQI should converge in fewer iterations than power iteration (PI) for large and challenging problems. RQI creates shifted systems that would not be tractable without the MGmore » Krylov solver. It also creates ill-conditioned matrices. The MGE preconditioner reduces iteration count significantly when used with RQI and takes advantage of the new energy decomposition such that it can scale efficiently. Each individual method has been described before, but this is the first time they have been demonstrated to work together effectively. The combination of solvers enables the RQI eigenvalue solver to work better than the other available solvers for large reactors problems on leadership-class machines. Using these methods together, RQI converged in fewer iterations and in less time than PI for a full pressurized water reactor core. These solvers also performed better than an Arnoldi eigenvalue solver for a reactor benchmark problem when energy decomposition is needed. The MG Krylov, MGE preconditioner, and RQI solver combination also scales well in energy. Finally, this solver set is a strong choice for very large and challenging problems.« less

Eigenvalue Solvers for Modeling Nuclear Reactors on Leadership Class Machines

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

Slaybaugh, R. N.; Ramirez-Zweiger, M.; Pandya, Tara

In this paper, three complementary methods have been implemented in the code Denovo that accelerate neutral particle transport calculations with methods that use leadership-class computers fully and effectively: a multigroup block (MG) Krylov solver, a Rayleigh quotient iteration (RQI) eigenvalue solver, and a multigrid in energy (MGE) preconditioner. The MG Krylov solver converges more quickly than Gauss Seidel and enables energy decomposition such that Denovo can scale to hundreds of thousands of cores. RQI should converge in fewer iterations than power iteration (PI) for large and challenging problems. RQI creates shifted systems that would not be tractable without the MGmore » Krylov solver. It also creates ill-conditioned matrices. The MGE preconditioner reduces iteration count significantly when used with RQI and takes advantage of the new energy decomposition such that it can scale efficiently. Each individual method has been described before, but this is the first time they have been demonstrated to work together effectively. The combination of solvers enables the RQI eigenvalue solver to work better than the other available solvers for large reactors problems on leadership-class machines. Using these methods together, RQI converged in fewer iterations and in less time than PI for a full pressurized water reactor core. These solvers also performed better than an Arnoldi eigenvalue solver for a reactor benchmark problem when energy decomposition is needed. The MG Krylov, MGE preconditioner, and RQI solver combination also scales well in energy. Finally, this solver set is a strong choice for very large and challenging problems.« less

Quantum Field Theory in Two Dimensions: Light-front Versus Space-like Solutions

NASA Astrophysics Data System (ADS)

Martinovic̆, L'ubomír

2017-07-01

A few non-perturbative topics of quantum field theory in D=1+1 are studied in both the conventional (SL) and light-front (LF) versions. First, we give a concise review of the recently proposed quantization of the two-dimensional massless LF fields. The LF version of bosonization follows in a simple and natural way including the bosonized form of the Thirring model. As a further application, we demonstrate the closeness of the 2D massless LF quantum fields to conformal field theory (CFT). We calculate several correlation functions including those between the components of the LF energy-momentum tensor and derive the LF version of the Virasoro algebra. Using the Euclidean time variable, we can immediately transform calculated quantities to the (anti)holomorphic form. The results found are in agreement with those from CFT. Finally, we show that the proposed framework provides us with the elements needed for an independent LF study of exactly solvable models. We compute the non-perturbative correlation functions from the exact operator solution of the LF Thirring model and compare it to the analogous results in the SL theory. While the vacuum effects are automatically taken into account in the LF case, the non-trivial vacuum structure has to be incorported by an explicit diagonalization of the SL Hamiltonians, to obtain the equivalently complete solution.

Complete devil's staircase and crystal-superfluid transitions in a dipolar XXZ spin chain: a trapped ion quantum simulation

NASA Astrophysics Data System (ADS)

Hauke, Philipp; Cucchietti, Fernando M.; Müller-Hermes, Alexander; Bañuls, Mari-Carmen; Cirac, J. Ignacio; Lewenstein, Maciej

2010-11-01

Systems with long-range interactions show a variety of intriguing properties: they typically accommodate many metastable states, they can give rise to spontaneous formation of supersolids, and they can lead to counterintuitive thermodynamic behavior. However, the increased complexity that comes with long-range interactions strongly hinders theoretical studies. This makes a quantum simulator for long-range models highly desirable. Here, we show that a chain of trapped ions can be used to quantum simulate a one-dimensional (1D) model of hard-core bosons with dipolar off-site interaction and tunneling, equivalent to a dipolar XXZ spin-1/2 chain. We explore the rich phase diagram of this model in detail, employing perturbative mean-field theory, exact diagonalization and quasi-exact numerical techniques (density-matrix renormalization group and infinite time-evolving block decimation). We find that the complete devil's staircase—an infinite sequence of crystal states existing at vanishing tunneling—spreads to a succession of lobes similar to the Mott lobes found in Bose-Hubbard models. Investigating the melting of these crystal states at increased tunneling, we do not find (contrary to similar 2D models) clear indications of supersolid behavior in the region around the melting transition. However, we find that inside the insulating lobes there are quasi-long-range (algebraic) correlations, as opposed to models with nearest-neighbor tunneling, that show exponential decay of correlations.

Ramp and periodic dynamics across non-Ising critical points

NASA Astrophysics Data System (ADS)

Ghosh, Roopayan; Sen, Arnab; Sengupta, K.

2018-01-01

We study ramp and periodic dynamics of ultracold bosons in an one-dimensional (1D) optical lattice which supports quantum critical points separating a uniform and a Z3 or Z4 symmetry broken density-wave ground state. Our protocol involves both linear and periodic drives which takes the system from the uniform state to the quantum critical point (for linear drive protocol) or to the ordered state and back (for periodic drive protocols) via controlled variation of a parameter of the system Hamiltonian. We provide exact numerical computation, for finite-size boson chains with L ≤24 using exact diagonalization (ED), of the excitation density D , the wave function overlap F , and the excess energy Q at the end of the drive protocol. For the linear ramp protocol, we identify the range of ramp speeds for which D and Q show Kibble-Zurek scaling. We find, based on numerical analysis with L ≤24 , that such scaling is consistent with that expected from critical exponents of the q -state Potts universality class with q =3 ,4 . For the periodic protocol, we show that the model displays near-perfect dynamical freezing at specific frequencies; at these frequencies D ,Q →0 and |F |→1 . We provide a semi-analytic explanation of such freezing behavior and relate this phenomenon to a many-body version of Stuckelberg interference. We suggest experiments which can test our theory.

Frustrated S = 1/2 Two-Leg Ladder with Different Leg Interactions

NASA Astrophysics Data System (ADS)

Tonegawa, Takashi; Okamoto, Kiyomi; Hikihara, Toshiya; Sakai, Tôru

2017-04-01

We explore the ground-state phase diagram of the S = 1/2 two-leg ladder. The isotropic leg interactions J1,a and J1,b between nearest neighbor spins in the legs a and b, respectively, are different from each other. The xy and z components of the uniform rung interactions are denoted by Jr and ΔJr, respectively, where Δ is the XXZ anisotropy parameter. This system has a frustration when J1,aJ1,b < 0 irrespective of the sign of Jr. The phase diagrams on the Δ (0≤Δ<1) versus J1,b plane in the cases of J1,a = - 0.2 and J1,a = 0.2 with Jr = -1 are determined numerically. We employ the physical consideration, the level spectroscopy analysis of the results obtained by the exact diagonalization method and also the density-matrix renormalization-group method. It is found that the non-collinear ferrimagnetic (NCFR) state appears as the ground state in the frustrated region of the parameters. Furthermore, the direct-product triplet-dimer (TD) state in which all rungs form the TD pair is the exact ground state, when J1,a + J1,b = 0 and 0≤ Δ ≲ 0.83. The obtained phase diagrams consist of the TD, XY and Haldane phases as well as the NCFR phase.

Abelian and non-Abelian states in ν = 2 / 3 bilayer fractional quantum Hall systems

NASA Astrophysics Data System (ADS)

Peterson, Michael; Wu, Yang-Le; Cheng, Meng; Barkeshli, Maissam; Wang, Zhenghan

There are several possible theoretically allowed non-Abelian fractional quantum Hall (FQH) states that could potentially be realized in one- and two-component FQH systems at total filling fraction ν = n + 2 / 3 , for integer n. Some of these states even possess quasiparticles with non-Abelian statistics that are powerful enough for universal topological quantum computation, and are thus of particular interest. Here we initiate a systematic numerical study, using both exact diagonalization and variational Monte Carlo, to investigate the phase diagram of FQH systems at total filling fraction ν = n + 2 / 3 , including in particular the possibility of the non-Abelian Z4 parafermion state. In ν = 2 / 3 bilayers we determine the phase diagram as a function of interlayer tunneling and repulsion, finding only three competing Abelian states, without the Z4 state. On the other hand, in single-component systems at ν = 8 / 3 , we find that the Z4 parafermion state has significantly higher overlap with the exact ground state than the Laughlin state, together with a larger gap, suggesting that the experimentally observed ν = 8 / 3 state may be non-Abelian. Our results from the two complementary numerical techniques agree well with each other qualitatively. We acknowledge the Office of Research and Sponsored Programs at California State University Long Beach and Microsoft Station Q.

General purpose nonlinear system solver based on Newton-Krylov method.

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

2013-12-01

KINSOL is part of a software family called SUNDIALS: SUite of Nonlinear and Differential/Algebraic equation Solvers [1]. KINSOL is a general-purpose nonlinear system solver based on Newton-Krylov and fixed-point solver technologies [2].

An HLLC Riemann solver for resistive relativistic magnetohydrodynamics

NASA Astrophysics Data System (ADS)

Miranda-Aranguren, S.; Aloy, M. A.; Rembiasz, T.

2018-05-01

We present a new approximate Riemann solver for the augmented system of equations of resistive relativistic magnetohydrodynamics that belongs to the family of Harten-Lax-van Leer contact wave (HLLC) solvers. In HLLC solvers, the solution is approximated by two constant states flanked by two shocks separated by a contact wave. The accuracy of the new approximate solver is calibrated through 1D and 2D test problems.

A computational study of the use of an optimization-based method for simulating large multibody systems.

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

Petra, C.; Gavrea, B.; Anitescu, M.

2009-01-01

The present work aims at comparing the performance of several quadratic programming (QP) solvers for simulating large-scale frictional rigid-body systems. Traditional time-stepping schemes for simulation of multibody systems are formulated as linear complementarity problems (LCPs) with copositive matrices. Such LCPs are generally solved by means of Lemke-type algorithms and solvers such as the PATH solver proved to be robust. However, for large systems, the PATH solver or any other pivotal algorithm becomes unpractical from a computational point of view. The convex relaxation proposed by one of the authors allows the formulation of the integration step as a QPD, for whichmore » a wide variety of state-of-the-art solvers are available. In what follows we report the results obtained solving that subproblem when using the QP solvers MOSEK, OOQP, TRON, and BLMVM. OOQP is presented with both the symmetric indefinite solver MA27 and our Cholesky reformulation using the CHOLMOD package. We investigate computational performance and address the correctness of the results from a modeling point of view. We conclude that the OOQP solver, particularly with the CHOLMOD linear algebra solver, has predictable performance and memory use patterns and is far more competitive for these problems than are the other solvers.« less

Implementation of the diagonalization-free algorithm in the self-consistent field procedure within the four-component relativistic scheme.

PubMed

Hrdá, Marcela; Kulich, Tomáš; Repiský, Michal; Noga, Jozef; Malkina, Olga L; Malkin, Vladimir G

2014-09-05

A recently developed Thouless-expansion-based diagonalization-free approach for improving the efficiency of self-consistent field (SCF) methods (Noga and Šimunek, J. Chem. Theory Comput. 2010, 6, 2706) has been adapted to the four-component relativistic scheme and implemented within the program package ReSpect. In addition to the implementation, the method has been thoroughly analyzed, particularly with respect to cases for which it is difficult or computationally expensive to find a good initial guess. Based on this analysis, several modifications of the original algorithm, refining its stability and efficiency, are proposed. To demonstrate the robustness and efficiency of the improved algorithm, we present the results of four-component diagonalization-free SCF calculations on several heavy-metal complexes, the largest of which contains more than 80 atoms (about 6000 4-spinor basis functions). The diagonalization-free procedure is about twice as fast as the corresponding diagonalization. Copyright © 2014 Wiley Periodicals, Inc.

SMITHERS: An object-oriented modular mapping methodology for MCNP-based neutronic–thermal hydraulic multiphysics

DOE PAGES

Richard, Joshua; Galloway, Jack; Fensin, Michael; ...

2015-04-04

A novel object-oriented modular mapping methodology for externally coupled neutronics–thermal hydraulics multiphysics simulations was developed. The Simulator using MCNP with Integrated Thermal-Hydraulics for Exploratory Reactor Studies (SMITHERS) code performs on-the-fly mapping of material-wise power distribution tallies implemented by MCNP-based neutron transport/depletion solvers for use in estimating coolant temperature and density distributions with a separate thermal-hydraulic solver. The key development of SMITHERS is that it reconstructs the hierarchical geometry structure of the material-wise power generation tallies from the depletion solver automatically, with only a modicum of additional information required from the user. In addition, it performs the basis mapping from themore » combinatorial geometry of the depletion solver to the required geometry of the thermal-hydraulic solver in a generalizable manner, such that it can transparently accommodate varying levels of thermal-hydraulic solver geometric fidelity, from the nodal geometry of multi-channel analysis solvers to the pin-cell level of discretization for sub-channel analysis solvers.« less

Sound-turbulence interaction in transonic boundary layers

NASA Astrophysics Data System (ADS)

Lelostec, Ludovic; Scalo, Carlo; Lele, Sanjiva

2014-11-01

Acoustic wave scattering in a transonic boundary layer is investigated through a novel approach. Instead of simulating directly the interaction of an incoming oblique acoustic wave with a turbulent boundary layer, suitable Dirichlet conditions are imposed at the wall to reproduce only the reflected wave resulting from the interaction of the incident wave with the boundary layer. The method is first validated using the laminar boundary layer profiles in a parallel flow approximation. For this scattering problem an exact inviscid solution can be found in the frequency domain which requires numerical solution of an ODE. The Dirichlet conditions are imposed in a high-fidelity unstructured compressible flow solver for Large Eddy Simulation (LES), CharLESx. The acoustic field of the reflected wave is then solved and the interaction between the boundary layer and sound scattering can be studied.

Implicit Multibody Penalty-BasedDistributed Contact.

PubMed

Xu, Hongyi; Zhao, Yili; Barbic, Jernej

2014-09-01

The penalty method is a simple and popular approach to resolving contact in computer graphics and robotics. Penalty-based contact, however, suffers from stability problems due to the highly variable and unpredictable net stiffness, and this is particularly pronounced in simulations with time-varying distributed geometrically complex contact. We employ semi-implicit integration, exact analytical contact gradients, symbolic Gaussian elimination and a SVD solver to simulate stable penalty-based frictional contact with large, time-varying contact areas, involving many rigid objects and articulated rigid objects in complex conforming contact and self-contact. We also derive implicit proportional-derivative control forces for real-time control of articulated structures with loops. We present challenging contact scenarios such as screwing a hexbolt into a hole, bowls stacked in perfectly conforming configurations, and manipulating many objects using actively controlled articulated mechanisms in real time.

Transport coefficients in ultrarelativistic kinetic theory

NASA Astrophysics Data System (ADS)

Ambruş, Victor E.

2018-02-01

A spatially periodic longitudinal wave is considered in relativistic dissipative hydrodynamics. At sufficiently small wave amplitudes, an analytic solution is obtained in the linearized limit of the macroscopic conservation equations within the first- and second-order relativistic hydrodynamics formulations. A kinetic solver is used to obtain the numerical solution of the relativistic Boltzmann equation for massless particles in the Anderson-Witting approximation for the collision term. It is found that, at small values of the Anderson-Witting relaxation time τ , the transport coefficients emerging from the relativistic Boltzmann equation agree with those predicted through the Chapman-Enskog procedure, while the relaxation times of the heat flux and shear pressure are equal to τ . These claims are further strengthened by considering a moment-type approximation based on orthogonal polynomials under which the Chapman-Enskog results for the transport coefficients are exactly recovered.

FoSSI: the family of simplified solver interfaces for the rapid development of parallel numerical atmosphere and ocean models

NASA Astrophysics Data System (ADS)

Frickenhaus, Stephan; Hiller, Wolfgang; Best, Meike

The portable software FoSSI is introduced that—in combination with additional free solver software packages—allows for an efficient and scalable parallel solution of large sparse linear equations systems arising in finite element model codes. FoSSI is intended to support rapid model code development, completely hiding the complexity of the underlying solver packages. In particular, the model developer need not be an expert in parallelization and is yet free to switch between different solver packages by simple modifications of the interface call. FoSSI offers an efficient and easy, yet flexible interface to several parallel solvers, most of them available on the web, such as PETSC, AZTEC, MUMPS, PILUT and HYPRE. FoSSI makes use of the concept of handles for vectors, matrices, preconditioners and solvers, that is frequently used in solver libraries. Hence, FoSSI allows for a flexible treatment of several linear equations systems and associated preconditioners at the same time, even in parallel on separate MPI-communicators. The second special feature in FoSSI is the task specifier, being a combination of keywords, each configuring a certain phase in the solver setup. This enables the user to control a solver over one unique subroutine. Furthermore, FoSSI has rather similar features for all solvers, making a fast solver intercomparison or exchange an easy task. FoSSI is a community software, proven in an adaptive 2D-atmosphere model and a 3D-primitive equation ocean model, both formulated in finite elements. The present paper discusses perspectives of an OpenMP-implementation of parallel iterative solvers based on domain decomposition methods. This approach to OpenMP solvers is rather attractive, as the code for domain-local operations of factorization, preconditioning and matrix-vector product can be readily taken from a sequential implementation that is also suitable to be used in an MPI-variant. Code development in this direction is in an advanced state under the name ScOPES: the Scalable Open Parallel sparse linear Equations Solver.

186 K Operation of Terahertz Quantum-Cascade Lasers Based on a Diagonal Design

NASA Technical Reports Server (NTRS)

Kumar, Sushil; Hu, Qing; Reno, John L.

2009-01-01

Resonant-phonon terahertz quantum-cascade lasers operating up to a heat-sink temperature of 186 K are demonstrated. This record temperature performance is achieved based on a diagonal design, with the objective to increase the upper-state lifetime and therefore the gain at elevated temperatures. The increased diagonality also lowers the operating current densities by limiting the flow of parasitic leakage current. Quantitatively, the diagonality is characterized by a radiative oscillator strength that is smaller by a factor of two from the least of any previously published designs. At the lasing frequency of 3.9 THz, 63 mW of peak optical power was measured at 5 K, and approximately 5 mW could still be detected at 180 K.

Adaptively Refined Euler and Navier-Stokes Solutions with a Cartesian-Cell Based Scheme

NASA Technical Reports Server (NTRS)

Coirier, William J.; Powell, Kenneth G.

1995-01-01

A Cartesian-cell based scheme with adaptive mesh refinement for solving the Euler and Navier-Stokes equations in two dimensions has been developed and tested. Grids about geometrically complicated bodies were generated automatically, by recursive subdivision of a single Cartesian cell encompassing the entire flow domain. Where the resulting cells intersect bodies, N-sided 'cut' cells were created using polygon-clipping algorithms. The grid was stored in a binary-tree data structure which provided a natural means of obtaining cell-to-cell connectivity and of carrying out solution-adaptive mesh refinement. The Euler and Navier-Stokes equations were solved on the resulting grids using an upwind, finite-volume formulation. The inviscid fluxes were found in an upwinded manner using a linear reconstruction of the cell primitives, providing the input states to an approximate Riemann solver. The viscous fluxes were formed using a Green-Gauss type of reconstruction upon a co-volume surrounding the cell interface. Data at the vertices of this co-volume were found in a linearly K-exact manner, which ensured linear K-exactness of the gradients. Adaptively-refined solutions for the inviscid flow about a four-element airfoil (test case 3) were compared to theory. Laminar, adaptively-refined solutions were compared to accepted computational, experimental and theoretical results.

Exact Dynamics via Poisson Process: a unifying Monte Carlo paradigm

NASA Astrophysics Data System (ADS)

Gubernatis, James

2014-03-01

A common computational task is solving a set of ordinary differential equations (o.d.e.'s). A little known theorem says that the solution of any set of o.d.e.'s is exactly solved by the expectation value over a set of arbitary Poisson processes of a particular function of the elements of the matrix that defines the o.d.e.'s. The theorem thus provides a new starting point to develop real and imaginary-time continous-time solvers for quantum Monte Carlo algorithms, and several simple observations enable various quantum Monte Carlo techniques and variance reduction methods to transfer to a new context. I will state the theorem, note a transformation to a very simple computational scheme, and illustrate the use of some techniques from the directed-loop algorithm in context of the wavefunction Monte Carlo method that is used to solve the Lindblad master equation for the dynamics of open quantum systems. I will end by noting that as the theorem does not depend on the source of the o.d.e.'s coming from quantum mechanics, it also enables the transfer of continuous-time methods from quantum Monte Carlo to the simulation of various classical equations of motion heretofore only solved deterministically.

Approximate tensor-product preconditioners for very high order discontinuous Galerkin methods

NASA Astrophysics Data System (ADS)

Pazner, Will; Persson, Per-Olof

2018-02-01

In this paper, we develop a new tensor-product based preconditioner for discontinuous Galerkin methods with polynomial degrees higher than those typically employed. This preconditioner uses an automatic, purely algebraic method to approximate the exact block Jacobi preconditioner by Kronecker products of several small, one-dimensional matrices. Traditional matrix-based preconditioners require O (p2d) storage and O (p3d) computational work, where p is the degree of basis polynomials used, and d is the spatial dimension. Our SVD-based tensor-product preconditioner requires O (p d + 1) storage, O (p d + 1) work in two spatial dimensions, and O (p d + 2) work in three spatial dimensions. Combined with a matrix-free Newton-Krylov solver, these preconditioners allow for the solution of DG systems in linear time in p per degree of freedom in 2D, and reduce the computational complexity from O (p9) to O (p5) in 3D. Numerical results are shown in 2D and 3D for the advection, Euler, and Navier-Stokes equations, using polynomials of degree up to p = 30. For many test cases, the preconditioner results in similar iteration counts when compared with the exact block Jacobi preconditioner, and performance is significantly improved for high polynomial degrees p.

Robust Multigrid Smoothers for Three Dimensional Elliptic Equations with Strong Anisotropies

NASA Technical Reports Server (NTRS)

Llorente, Ignacio M.; Melson, N. Duane

1998-01-01

We discuss the behavior of several plane relaxation methods as multigrid smoothers for the solution of a discrete anisotropic elliptic model problem on cell-centered grids. The methods compared are plane Jacobi with damping, plane Jacobi with partial damping, plane Gauss-Seidel, plane zebra Gauss-Seidel, and line Gauss-Seidel. Based on numerical experiments and local mode analysis, we compare the smoothing factor of the different methods in the presence of strong anisotropies. A four-color Gauss-Seidel method is found to have the best numerical and architectural properties of the methods considered in the present work. Although alternating direction plane relaxation schemes are simpler and more robust than other approaches, they are not currently used in industrial and production codes because they require the solution of a two-dimensional problem for each plane in each direction. We verify the theoretical predictions of Thole and Trottenberg that an exact solution of each plane is not necessary and that a single two-dimensional multigrid cycle gives the same result as an exact solution, in much less execution time. Parallelization of the two-dimensional multigrid cycles, the kernel of the three-dimensional implicit solver, is also discussed. Alternating-plane smoothers are found to be highly efficient multigrid smoothers for anisotropic elliptic problems.

Numerically Exact Long Time Magnetization Dynamics Near the Nonequilibrium Kondo Regime

NASA Astrophysics Data System (ADS)

Cohen, Guy; Gull, Emanuel; Reichman, David; Millis, Andrew; Rabani, Eran

2013-03-01

The dynamical and steady-state spin response of the nonequilibrium Anderson impurity model to magnetic fields, bias voltages, and temperature is investigated by a numerically exact method which allows access to unprecedentedly long times. The method is based on using real, continuous time bold Monte Carlo techniques--quantum Monte Carlo sampling of diagrammatic corrections to a partial re-summation--in order to compute the kernel of a memory function, which is then used to determine the reduced density matrix. The method owes its effectiveness to the fact that the memory kernel is dominated by relatively short-time properties even when the system's dynamics are long-ranged. We make predictions regarding the non-monotonic temperature dependence of the system at high bias voltage and the oscillatory quench dynamics at high magnetic fields. We also discuss extensions of the method to the computation of transport properties and correlation functions, and its suitability as an impurity solver free from the need for analytical continuation in the context of dynamical mean field theory. This work is supported by the US Department of Energy under grant DE-SC0006613, by NSF-DMR-1006282 and by the US-Israel Binational Science Foundation. GC is grateful to the Yad Hanadiv-Rothschild Foundation for the award of a Rothschild Fellowship.

Robust determination of the chemical potential in the pole expansion and selected inversion method for solving Kohn-Sham density functional theory

NASA Astrophysics Data System (ADS)

Jia, Weile; Lin, Lin

2017-10-01

Fermi operator expansion (FOE) methods are powerful alternatives to diagonalization type methods for solving Kohn-Sham density functional theory (KSDFT). One example is the pole expansion and selected inversion (PEXSI) method, which approximates the Fermi operator by rational matrix functions and reduces the computational complexity to at most quadratic scaling for solving KSDFT. Unlike diagonalization type methods, the chemical potential often cannot be directly read off from the result of a single step of evaluation of the Fermi operator. Hence multiple evaluations are needed to be sequentially performed to compute the chemical potential to ensure the correct number of electrons within a given tolerance. This hinders the performance of FOE methods in practice. In this paper, we develop an efficient and robust strategy to determine the chemical potential in the context of the PEXSI method. The main idea of the new method is not to find the exact chemical potential at each self-consistent-field (SCF) iteration but to dynamically and rigorously update the upper and lower bounds for the true chemical potential, so that the chemical potential reaches its convergence along the SCF iteration. Instead of evaluating the Fermi operator for multiple times sequentially, our method uses a two-level strategy that evaluates the Fermi operators in parallel. In the regime of full parallelization, the wall clock time of each SCF iteration is always close to the time for one single evaluation of the Fermi operator, even when the initial guess is far away from the converged solution. We demonstrate the effectiveness of the new method using examples with metallic and insulating characters, as well as results from ab initio molecular dynamics.

FOB-SH: Fragment orbital-based surface hopping for charge carrier transport in organic and biological molecules and materials

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

Spencer, J.; Gajdos, F.; Blumberger, J., E-mail: j.blumberger@ucl.ac.uk

2016-08-14

We introduce a fragment orbital-based fewest switches surface hopping method, FOB-SH, designed to efficiently simulate charge carrier transport in strongly fluctuating condensed phase systems such as organic semiconductors and biomolecules. The charge carrier wavefunction is expanded and the electronic Hamiltonian constructed in a set of singly occupied molecular orbitals of the molecular sites that mediate the charge transfer. Diagonal elements of the electronic Hamiltonian (site energies) are obtained from a force field, whereas the off-diagonal or electronic coupling matrix elements are obtained using our recently developed analytic overlap method. We derive a general expression for the exact forces on themore » adiabatic ground and excited electronic state surfaces from the nuclear gradients of the charge localized electronic states. Applications to electron hole transfer in a model ethylene dimer and through a chain of ten model ethylenes validate our implementation and demonstrate its computational efficiency. On the larger system, we calculate the qualitative behaviour of charge mobility with change in temperature T for different regimes of the intermolecular electronic coupling. For small couplings, FOB-SH predicts a crossover from a thermally activated regime at low temperatures to a band-like transport regime at higher temperatures. For higher electronic couplings, the thermally activated regime disappears and the mobility decreases according to a power law. This is interpreted by a gradual loss in probability for resonance between the sites as the temperature increases. The polaron hopping model solved for the same system gives a qualitatively different result and underestimates the mobility decay at higher temperatures. Taken together, the FOB-SH methodology introduced here shows promise for a realistic investigation of charge carrier transport in complex organic, aqueous, and biological systems.« less

Robust determination of the chemical potential in the pole expansion and selected inversion method for solving Kohn-Sham density functional theory.

PubMed

Jia, Weile; Lin, Lin

2017-10-14

Fermi operator expansion (FOE) methods are powerful alternatives to diagonalization type methods for solving Kohn-Sham density functional theory (KSDFT). One example is the pole expansion and selected inversion (PEXSI) method, which approximates the Fermi operator by rational matrix functions and reduces the computational complexity to at most quadratic scaling for solving KSDFT. Unlike diagonalization type methods, the chemical potential often cannot be directly read off from the result of a single step of evaluation of the Fermi operator. Hence multiple evaluations are needed to be sequentially performed to compute the chemical potential to ensure the correct number of electrons within a given tolerance. This hinders the performance of FOE methods in practice. In this paper, we develop an efficient and robust strategy to determine the chemical potential in the context of the PEXSI method. The main idea of the new method is not to find the exact chemical potential at each self-consistent-field (SCF) iteration but to dynamically and rigorously update the upper and lower bounds for the true chemical potential, so that the chemical potential reaches its convergence along the SCF iteration. Instead of evaluating the Fermi operator for multiple times sequentially, our method uses a two-level strategy that evaluates the Fermi operators in parallel. In the regime of full parallelization, the wall clock time of each SCF iteration is always close to the time for one single evaluation of the Fermi operator, even when the initial guess is far away from the converged solution. We demonstrate the effectiveness of the new method using examples with metallic and insulating characters, as well as results from ab initio molecular dynamics.

Effective model with strong Kitaev interactions for α -RuCl3

NASA Astrophysics Data System (ADS)

Suzuki, Takafumi; Suga, Sei-ichiro

2018-04-01

We use an exact numerical diagonalization method to calculate the dynamical spin structure factors of three ab initio models and one ab initio guided model for a honeycomb-lattice magnet α -RuCl3 . We also use thermal pure quantum states to calculate the temperature dependence of the heat capacity, the nearest-neighbor spin-spin correlation function, and the static spin structure factor. From the results obtained from these four effective models, we find that, even when the magnetic order is stabilized at low temperature, the intensity at the Γ point in the dynamical spin structure factors increases with increasing nearest-neighbor spin correlation. In addition, we find that the four models fail to explain heat-capacity measurements whereas two of the four models succeed in explaining inelastic-neutron-scattering experiments. In the four models, when temperature decreases, the heat capacity shows a prominent peak at a high temperature where the nearest-neighbor spin-spin correlation function increases. However, the peak temperature in heat capacity is too low in comparison with that observed experimentally. To address these discrepancies, we propose an effective model that includes strong ferromagnetic Kitaev coupling, and we show that this model quantitatively reproduces both inelastic-neutron-scattering experiments and heat-capacity measurements. To further examine the adequacy of the proposed model, we calculate the field dependence of the polarized terahertz spectra, which reproduces the experimental results: the spin-gapped excitation survives up to an onset field where the magnetic order disappears and the response in the high-field region is almost linear. Based on these numerical results, we argue that the low-energy magnetic excitation in α -RuCl3 is mainly characterized by interactions such as off-diagonal interactions and weak Heisenberg interactions between nearest-neighbor pairs, rather than by the strong Kitaev interactions.

FOB-SH: Fragment orbital-based surface hopping for charge carrier transport in organic and biological molecules and materials

NASA Astrophysics Data System (ADS)

Spencer, J.; Gajdos, F.; Blumberger, J.

2016-08-01

We introduce a fragment orbital-based fewest switches surface hopping method, FOB-SH, designed to efficiently simulate charge carrier transport in strongly fluctuating condensed phase systems such as organic semiconductors and biomolecules. The charge carrier wavefunction is expanded and the electronic Hamiltonian constructed in a set of singly occupied molecular orbitals of the molecular sites that mediate the charge transfer. Diagonal elements of the electronic Hamiltonian (site energies) are obtained from a force field, whereas the off-diagonal or electronic coupling matrix elements are obtained using our recently developed analytic overlap method. We derive a general expression for the exact forces on the adiabatic ground and excited electronic state surfaces from the nuclear gradients of the charge localized electronic states. Applications to electron hole transfer in a model ethylene dimer and through a chain of ten model ethylenes validate our implementation and demonstrate its computational efficiency. On the larger system, we calculate the qualitative behaviour of charge mobility with change in temperature T for different regimes of the intermolecular electronic coupling. For small couplings, FOB-SH predicts a crossover from a thermally activated regime at low temperatures to a band-like transport regime at higher temperatures. For higher electronic couplings, the thermally activated regime disappears and the mobility decreases according to a power law. This is interpreted by a gradual loss in probability for resonance between the sites as the temperature increases. The polaron hopping model solved for the same system gives a qualitatively different result and underestimates the mobility decay at higher temperatures. Taken together, the FOB-SH methodology introduced here shows promise for a realistic investigation of charge carrier transport in complex organic, aqueous, and biological systems.

A model for solving the prescribed burn planning problem.

PubMed

Rachmawati, Ramya; Ozlen, Melih; Reinke, Karin J; Hearne, John W

2015-01-01

The increasing frequency of destructive wildfires, with a consequent loss of life and property, has led to fire and land management agencies initiating extensive fuel management programs. This involves long-term planning of fuel reduction activities such as prescribed burning or mechanical clearing. In this paper, we propose a mixed integer programming (MIP) model that determines when and where fuel reduction activities should take place. The model takes into account multiple vegetation types in the landscape, their tolerance to frequency of fire events, and keeps track of the age of each vegetation class in each treatment unit. The objective is to minimise fuel load over the planning horizon. The complexity of scheduling fuel reduction activities has led to the introduction of sophisticated mathematical optimisation methods. While these approaches can provide optimum solutions, they can be computationally expensive, particularly for fuel management planning which extends across the landscape and spans long term planning horizons. This raises the question of how much better do exact modelling approaches compare to simpler heuristic approaches in their solutions. To answer this question, the proposed model is run using an exact MIP (using commercial MIP solver) and two heuristic approaches that decompose the problem into multiple single-period sub problems. The Knapsack Problem (KP), which is the first heuristic approach, solves the single period problems, using an exact MIP approach. The second heuristic approach solves the single period sub problem using a greedy heuristic approach. The three methods are compared in term of model tractability, computational time and the objective values. The model was tested using randomised data from 711 treatment units in the Barwon-Otway district of Victoria, Australia. Solutions for the exact MIP could be obtained for up to a 15-year planning only using a standard implementation of CPLEX. Both heuristic approaches can solve significantly larger problems, involving 100-year or even longer planning horizons. Furthermore there are no substantial differences in the solutions produced by the three approaches. It is concluded that for practical purposes a heuristic method is to be preferred to the exact MIP approach.

Mathematics of the total alkalinity-pH equation - pathway to robust and universal solution algorithms: the SolveSAPHE package v1.0.1

NASA Astrophysics Data System (ADS)

Munhoven, G.

2013-08-01

The total alkalinity-pH equation, which relates total alkalinity and pH for a given set of total concentrations of the acid-base systems that contribute to total alkalinity in a given water sample, is reviewed and its mathematical properties established. We prove that the equation function is strictly monotone and always has exactly one positive root. Different commonly used approximations are discussed and compared. An original method to derive appropriate initial values for the iterative solution of the cubic polynomial equation based upon carbonate-borate-alkalinity is presented. We then review different methods that have been used to solve the total alkalinity-pH equation, with a main focus on biogeochemical models. The shortcomings and limitations of these methods are made out and discussed. We then present two variants of a new, robust and universally convergent algorithm to solve the total alkalinity-pH equation. This algorithm does not require any a priori knowledge of the solution. SolveSAPHE (Solver Suite for Alkalinity-PH Equations) provides reference implementations of several variants of the new algorithm in Fortran 90, together with new implementations of other, previously published solvers. The new iterative procedure is shown to converge from any starting value to the physical solution. The extra computational cost for the convergence security is only 10-15% compared to the fastest algorithm in our test series.

Efficient iterative methods applied to the solution of transonic flows

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

Wissink, A.M.; Lyrintzis, A.S.; Chronopoulos, A.T.

1996-02-01

We investigate the use of an inexact Newton`s method to solve the potential equations in the transonic regime. As a test case, we solve the two-dimensional steady transonic small disturbance equation. Approximate factorization/ADI techniques have traditionally been employed for implicit solutions of this nonlinear equation. Instead, we apply Newton`s method using an exact analytical determination of the Jacobian with preconditioned conjugate gradient-like iterative solvers for solution of the linear systems in each Newton iteration. Two iterative solvers are tested; a block s-step version of the classical Orthomin(k) algorithm called orthogonal s-step Orthomin (OSOmin) and the well-known GIVIRES method. The preconditionermore » is a vectorizable and parallelizable version of incomplete LU (ILU) factorization. Efficiency of the Newton-Iterative method on vector and parallel computer architectures is the main issue addressed. In vectorized tests on a single processor of the Cray C-90, the performance of Newton-OSOmin is superior to Newton-GMRES and a more traditional monotone AF/ADI method (MAF) for a variety of transonic Mach numbers and mesh sizes. Newton- GIVIRES is superior to MAF for some cases. The parallel performance of the Newton method is also found to be very good on multiple processors of the Cray C-90 and on the massively parallel thinking machine CM-5, where very fast execution rates (up to 9 Gflops) are found for large problems. 38 refs., 14 figs., 7 tabs.« less

A Newton-Krylov solver for fast spin-up of online ocean tracers

NASA Astrophysics Data System (ADS)

Lindsay, Keith

2017-01-01

We present a Newton-Krylov based solver to efficiently spin up tracers in an online ocean model. We demonstrate that the solver converges, that tracer simulations initialized with the solution from the solver have small drift, and that the solver takes orders of magnitude less computational time than the brute force spin-up approach. To demonstrate the application of the solver, we use it to efficiently spin up the tracer ideal age with respect to the circulation from different time intervals in a long physics run. We then evaluate how the spun-up ideal age tracer depends on the duration of the physics run, i.e., on how equilibrated the circulation is.

A high-order relativistic two-fluid electrodynamic scheme with consistent reconstruction of electromagnetic fields and a multidimensional Riemann solver for electromagnetism

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

Balsara, Dinshaw S., E-mail: dbalsara@nd.edu; Amano, Takanobu, E-mail: amano@eps.s.u-tokyo.ac.jp; Garain, Sudip, E-mail: sgarain@nd.edu

In various astrophysics settings it is common to have a two-fluid relativistic plasma that interacts with the electromagnetic field. While it is common to ignore the displacement current in the ideal, classical magnetohydrodynamic limit, when the flows become relativistic this approximation is less than absolutely well-justified. In such a situation, it is more natural to consider a positively charged fluid made up of positrons or protons interacting with a negatively charged fluid made up of electrons. The two fluids interact collectively with the full set of Maxwell's equations. As a result, a solution strategy for that coupled system of equationsmore » is sought and found here. Our strategy extends to higher orders, providing increasing accuracy. The primary variables in the Maxwell solver are taken to be the facially-collocated components of the electric and magnetic fields. Consistent with such a collocation, three important innovations are reported here. The first two pertain to the Maxwell solver. In our first innovation, the magnetic field within each zone is reconstructed in a divergence-free fashion while the electric field within each zone is reconstructed in a form that is consistent with Gauss' law. In our second innovation, a multidimensionally upwinded strategy is presented which ensures that the magnetic field can be updated via a discrete interpretation of Faraday's law and the electric field can be updated via a discrete interpretation of the generalized Ampere's law. This multidimensional upwinding is achieved via a multidimensional Riemann solver. The multidimensional Riemann solver automatically provides edge-centered electric field components for the Stokes law-based update of the magnetic field. It also provides edge-centered magnetic field components for the Stokes law-based update of the electric field. The update strategy ensures that the electric field is always consistent with Gauss' law and the magnetic field is always divergence-free. This collocation also ensures that electromagnetic radiation that is propagating in a vacuum has both electric and magnetic fields that are exactly divergence-free. Coupled relativistic fluid dynamic equations are solved for the positively and negatively charged fluids. The fluids' numerical fluxes also provide a self-consistent current density for the update of the electric field. Our reconstruction strategy ensures that fluid velocities always remain sub-luminal. Our third innovation consists of an efficient design for several popular IMEX schemes so that they provide strong coupling between the finite-volume-based fluid solver and the electromagnetic fields at high order. This innovation makes it possible to efficiently utilize high order IMEX time update methods for stiff source terms in the update of high order finite-volume methods for hyperbolic conservation laws. We also show that this very general innovation should extend seamlessly to Runge–Kutta discontinuous Galerkin methods. The IMEX schemes enable us to use large CFL numbers even in the presence of stiff source terms. Several accuracy analyses are presented showing that our method meets its design accuracy in the MHD limit as well as in the limit of electromagnetic wave propagation. Several stringent test problems are also presented. We also present a relativistic version of the GEM problem, which shows that our algorithm can successfully adapt to challenging problems in high energy astrophysics.« less

A high-order relativistic two-fluid electrodynamic scheme with consistent reconstruction of electromagnetic fields and a multidimensional Riemann solver for electromagnetism

NASA Astrophysics Data System (ADS)

Balsara, Dinshaw S.; Amano, Takanobu; Garain, Sudip; Kim, Jinho

2016-08-01

In various astrophysics settings it is common to have a two-fluid relativistic plasma that interacts with the electromagnetic field. While it is common to ignore the displacement current in the ideal, classical magnetohydrodynamic limit, when the flows become relativistic this approximation is less than absolutely well-justified. In such a situation, it is more natural to consider a positively charged fluid made up of positrons or protons interacting with a negatively charged fluid made up of electrons. The two fluids interact collectively with the full set of Maxwell's equations. As a result, a solution strategy for that coupled system of equations is sought and found here. Our strategy extends to higher orders, providing increasing accuracy. The primary variables in the Maxwell solver are taken to be the facially-collocated components of the electric and magnetic fields. Consistent with such a collocation, three important innovations are reported here. The first two pertain to the Maxwell solver. In our first innovation, the magnetic field within each zone is reconstructed in a divergence-free fashion while the electric field within each zone is reconstructed in a form that is consistent with Gauss' law. In our second innovation, a multidimensionally upwinded strategy is presented which ensures that the magnetic field can be updated via a discrete interpretation of Faraday's law and the electric field can be updated via a discrete interpretation of the generalized Ampere's law. This multidimensional upwinding is achieved via a multidimensional Riemann solver. The multidimensional Riemann solver automatically provides edge-centered electric field components for the Stokes law-based update of the magnetic field. It also provides edge-centered magnetic field components for the Stokes law-based update of the electric field. The update strategy ensures that the electric field is always consistent with Gauss' law and the magnetic field is always divergence-free. This collocation also ensures that electromagnetic radiation that is propagating in a vacuum has both electric and magnetic fields that are exactly divergence-free. Coupled relativistic fluid dynamic equations are solved for the positively and negatively charged fluids. The fluids' numerical fluxes also provide a self-consistent current density for the update of the electric field. Our reconstruction strategy ensures that fluid velocities always remain sub-luminal. Our third innovation consists of an efficient design for several popular IMEX schemes so that they provide strong coupling between the finite-volume-based fluid solver and the electromagnetic fields at high order. This innovation makes it possible to efficiently utilize high order IMEX time update methods for stiff source terms in the update of high order finite-volume methods for hyperbolic conservation laws. We also show that this very general innovation should extend seamlessly to Runge-Kutta discontinuous Galerkin methods. The IMEX schemes enable us to use large CFL numbers even in the presence of stiff source terms. Several accuracy analyses are presented showing that our method meets its design accuracy in the MHD limit as well as in the limit of electromagnetic wave propagation. Several stringent test problems are also presented. We also present a relativistic version of the GEM problem, which shows that our algorithm can successfully adapt to challenging problems in high energy astrophysics.

Exact Mapping from Many-Spin Hamiltonians to Giant-Spin Hamiltonians.

PubMed

Ghassemi Tabrizi, Shadan; Arbuznikov, Alexei V; Kaupp, Martin

2018-03-26

Thermodynamic and spectroscopic data of exchange-coupled molecular spin clusters (e.g. single-molecule magnets) are routinely interpreted in terms of two different models: the many-spin Hamiltonian (MSH) explicitly considers couplings between individual spin centers, while the giant-spin Hamiltonian (GSH) treats the system as a single collective spin. When isotropic exchange coupling is weak, the physical compatibility between both spin Hamiltonian models becomes a serious concern, due to mixing of spin multiplets by local zero-field splitting (ZFS) interactions ('S-mixing'). Until now, this effect, which makes the mapping MSH→GSH ('spin projection') non-trivial, had only been treated perturbationally (up to third order), with obvious limitations. Here, based on exact diagonalization of the MSH, canonical effective Hamiltonian theory is applied to construct a GSH that exactly matches the energies of the relevant (2S+1) states comprising an effective spin multiplet. For comparison, a recently developed strategy for the unique derivation of effective ('pseudospin') Hamiltonians, now routinely employed in ab initio calculations of mononuclear systems, is adapted to the problem of spin projection. Expansion of the zero-field Hamiltonian and the magnetic moment in terms of irreducible tensor operators (or Stevens operators) yields terms of all ranks k (up to k=2S) in the effective spin. Calculations employing published MSH parameters illustrate exact spin projection for the well-investigated [Ni(hmp)(dmb)Cl] 4 ('Ni 4 ') single-molecule magnet, which displays weak isotropic exchange (dmb=3,3-dimethyl-1-butanol, hmp - is the anion of 2-hydroxymethylpyridine). The performance of the resulting GSH in finite field is assessed in terms of EPR resonances and diabolical points. The large tunnel splitting in the M=± 4 ground doublet of the S=4 multiplet, responsible for fast tunneling in Ni 4 , is attributed to a Stevens operator with eightfold rotational symmetry, marking the first quantification of a k=8 term in a spin cluster. The unique and exact mapping MSH→GSH should be of general importance for weakly-coupled systems; it represents a mandatory ultimate step for comparing theoretical predictions (e.g. from quantum-chemical calculations) to ZFS, hyperfine or g-tensors from spectral fittings. © 2018 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim.

Robotic Compliant Motion Control for Aircraft Refueling Applications

DTIC Science & Technology

1988-12-01

J. DUVALL 29 SEP 88 C-26 SUBROUTINE IMPCONST(CONST,MINV, BMAT ) Abstract: This subroutine calculates the 25 constants used by the Fortran subroutine...mass with center of gravity along the joint 6 axis. The desired mass and the damping ( BMAT ) matrices are assumed to be diagonal. Joints angles 4,5...constants. MINV -- A 2x2 matrix containing the elements of the inverse desired mass matrix (diagonal). BMAT -- A 2x2 matrix of damping coefficents (diagonal

Oasis: A high-level/high-performance open source Navier-Stokes solver

NASA Astrophysics Data System (ADS)

Mortensen, Mikael; Valen-Sendstad, Kristian

2015-03-01

Oasis is a high-level/high-performance finite element Navier-Stokes solver written from scratch in Python using building blocks from the FEniCS project (fenicsproject.org). The solver is unstructured and targets large-scale applications in complex geometries on massively parallel clusters. Oasis utilizes MPI and interfaces, through FEniCS, to the linear algebra backend PETSc. Oasis advocates a high-level, programmable user interface through the creation of highly flexible Python modules for new problems. Through the high-level Python interface the user is placed in complete control of every aspect of the solver. A version of the solver, that is using piecewise linear elements for both velocity and pressure, is shown to reproduce very well the classical, spectral, turbulent channel simulations of Moser et al. (1999). The computational speed is strongly dominated by the iterative solvers provided by the linear algebra backend, which is arguably the best performance any similar implicit solver using PETSc may hope for. Higher order accuracy is also demonstrated and new solvers may be easily added within the same framework.

Improving stochastic estimates with inference methods: calculating matrix diagonals.

PubMed

Selig, Marco; Oppermann, Niels; Ensslin, Torsten A

2012-02-01

Estimating the diagonal entries of a matrix, that is not directly accessible but only available as a linear operator in the form of a computer routine, is a common necessity in many computational applications, especially in image reconstruction and statistical inference. Here, methods of statistical inference are used to improve the accuracy or the computational costs of matrix probing methods to estimate matrix diagonals. In particular, the generalized Wiener filter methodology, as developed within information field theory, is shown to significantly improve estimates based on only a few sampling probes, in cases in which some form of continuity of the solution can be assumed. The strength, length scale, and precise functional form of the exploited autocorrelation function of the matrix diagonal is determined from the probes themselves. The developed algorithm is successfully applied to mock and real world problems. These performance tests show that, in situations where a matrix diagonal has to be calculated from only a small number of computationally expensive probes, a speedup by a factor of 2 to 10 is possible with the proposed method. © 2012 American Physical Society

The Use of Sparse Direct Solver in Vector Finite Element Modeling for Calculating Two Dimensional (2-D) Magnetotelluric Responses in Transverse Electric (TE) Mode

NASA Astrophysics Data System (ADS)

Yihaa Roodhiyah, Lisa’; Tjong, Tiffany; Nurhasan; Sutarno, D.

2018-04-01

The late research, linear matrices of vector finite element in two dimensional(2-D) magnetotelluric (MT) responses modeling was solved by non-sparse direct solver in TE mode. Nevertheless, there is some weakness which have to be improved especially accuracy in the low frequency (10-3 Hz-10-5 Hz) which is not achieved yet and high cost computation in dense mesh. In this work, the solver which is used is sparse direct solver instead of non-sparse direct solverto overcome the weaknesses of solving linear matrices of vector finite element metod using non-sparse direct solver. Sparse direct solver will be advantageous in solving linear matrices of vector finite element method because of the matrix properties which is symmetrical and sparse. The validation of sparse direct solver in solving linear matrices of vector finite element has been done for a homogen half-space model and vertical contact model by analytical solution. Thevalidation result of sparse direct solver in solving linear matrices of vector finite element shows that sparse direct solver is more stable than non-sparse direct solver in computing linear problem of vector finite element method especially in low frequency. In the end, the accuracy of 2D MT responses modelling in low frequency (10-3 Hz-10-5 Hz) has been reached out under the efficient allocation memory of array and less computational time consuming.

23. INCLINED END POST / VERTICAL / DIAGONAL / PORTAL ...

Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

23. INCLINED END POST / VERTICAL / DIAGONAL / PORTAL BRACING DETAIL. VIEW TO SOUTHEAST. - Abraham Lincoln Memorial Bridge, Spanning Missouri River on Highway 30 between Nebraska & Iowa, Blair, Washington County, NE

Entropy of isolated quantum systems after a quench.

PubMed

Santos, Lea F; Polkovnikov, Anatoli; Rigol, Marcos

2011-07-22

A diagonal entropy, which depends only on the diagonal elements of the system's density matrix in the energy representation, has been recently introduced as the proper definition of thermodynamic entropy in out-of-equilibrium quantum systems. We study this quantity after an interaction quench in lattice hard-core bosons and spinless fermions, and after a local chemical potential quench in a system of hard-core bosons in a superlattice potential. The former systems have a chaotic regime, where the diagonal entropy becomes equivalent to the equilibrium microcanonical entropy, coinciding with the onset of thermalization. The latter system is integrable. We show that its diagonal entropy is additive and different from the entropy of a generalized Gibbs ensemble, which has been introduced to account for the effects of conserved quantities at integrability.

Error due to unresolved scales in estimation problems for atmospheric data assimilation

NASA Astrophysics Data System (ADS)

Janjic, Tijana

The error arising due to unresolved scales in data assimilation procedures is examined. The problem of estimating the projection of the state of a passive scalar undergoing advection at a sequence of times is considered. The projection belongs to a finite- dimensional function space and is defined on the continuum. Using the continuum projection of the state of a passive scalar, a mathematical definition is obtained for the error arising due to the presence, in the continuum system, of scales unresolved by the discrete dynamical model. This error affects the estimation procedure through point observations that include the unresolved scales. In this work, two approximate methods for taking into account the error due to unresolved scales and the resulting correlations are developed and employed in the estimation procedure. The resulting formulas resemble the Schmidt-Kalman filter and the usual discrete Kalman filter, respectively. For this reason, the newly developed filters are called the Schmidt-Kalman filter and the traditional filter. In order to test the assimilation methods, a two- dimensional advection model with nonstationary spectrum was developed for passive scalar transport in the atmosphere. An analytical solution on the sphere was found depicting the model dynamics evolution. Using this analytical solution the model error is avoided, and the error due to unresolved scales is the only error left in the estimation problem. It is demonstrated that the traditional and the Schmidt- Kalman filter work well provided the exact covariance function of the unresolved scales is known. However, this requirement is not satisfied in practice, and the covariance function must be modeled. The Schmidt-Kalman filter cannot be computed in practice without further approximations. Therefore, the traditional filter is better suited for practical use. Also, the traditional filter does not require modeling of the full covariance function of the unresolved scales, but only modeling of the covariance matrix obtained by evaluating the covariance function at the observation points. We first assumed that this covariance matrix is stationary and that the unresolved scales are not correlated between the observation points, i.e., the matrix is diagonal, and that the values along the diagonal are constant. Tests with these assumptions were unsuccessful, indicating that a more sophisticated model of the covariance is needed for assimilation of data with nonstationary spectrum. A new method for modeling the covariance matrix based on an extended set of modeling assumptions is proposed. First, it is assumed that the covariance matrix is diagonal, that is, that the unresolved scales are not correlated between the observation points. It is postulated that the values on the diagonal depend on a wavenumber that is characteristic for the unresolved part of the spectrum. It is further postulated that this characteristic wavenumber can be diagnosed from the observations and from the estimate of the projection of the state that is being estimated. It is demonstrated that the new method successfully overcomes previously encountered difficulties.

High Maneuverability Airframe: Investigation of Fin and Canard Sizing for Optimum Maneuverability

DTIC Science & Technology

2014-09-01

overset grids (unified- grid); 5) total variation diminishing discretization based on a new multidimensional interpolation framework; 6) Riemann solvers to...Aerodynamics .........................................................................................3 3.1.1 Solver ...describes the methodology used for the simulations. 3.1.1 Solver The double-precision solver of a commercially available code, CFD ++ v12.1.1, 9

A fast direct solver for a class of two-dimensional separable elliptic equations on the sphere

NASA Technical Reports Server (NTRS)

Moorthi, Shrinivas; Higgins, R. Wayne

1992-01-01

An efficient, direct, second-order solver for the discrete solution of two-dimensional separable elliptic equations on the sphere is presented. The method involves a Fourier transformation in longitude and a direct solution of the resulting coupled second-order finite difference equations in latitude. The solver is made efficient by vectorizing over longitudinal wavenumber and by using a vectorized fast Fourier transform routine. It is evaluated using a prescribed solution method and compared with a multigrid solver and the standard direct solver from FISHPAK.

Development of axisymmetric lattice Boltzmann flux solver for complex multiphase flows

NASA Astrophysics Data System (ADS)

Wang, Yan; Shu, Chang; Yang, Li-Ming; Yuan, Hai-Zhuan

2018-05-01

This paper presents an axisymmetric lattice Boltzmann flux solver (LBFS) for simulating axisymmetric multiphase flows. In the solver, the two-dimensional (2D) multiphase LBFS is applied to reconstruct macroscopic fluxes excluding axisymmetric effects. Source terms accounting for axisymmetric effects are introduced directly into the governing equations. As compared to conventional axisymmetric multiphase lattice Boltzmann (LB) method, the present solver has the kinetic feature for flux evaluation and avoids complex derivations of external forcing terms. In addition, the present solver also saves considerable computational efforts in comparison with three-dimensional (3D) computations. The capability of the proposed solver in simulating complex multiphase flows is demonstrated by studying single bubble rising in a circular tube. The obtained results compare well with the published data.

Nonequilibrium thermo-chemical calculations using a diagonal implicit scheme

NASA Technical Reports Server (NTRS)

Imlay, Scott T.; Roberts, Donald W.; Soetrisno, Moeljo; Eberhardt, Scott

1991-01-01

A recently developed computer program for hypersonic vehicle flow analysis is described. The program uses a diagonal implicit algorithm to solve the equations of viscous flow for a gas in thermochemical nonequilibrium. The diagonal scheme eliminates the expense of inverting large block matrices that arise when species conservation equations are introduced. The program uses multiple zones of grids patched together and includes radiation wall and rarefied gas boundary conditions. Solutions are presented for hypersonic flows of air and hydrogen air mixtures.

Efficient block preconditioned eigensolvers for linear response time-dependent density functional theory

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

Vecharynski, Eugene; Brabec, Jiri; Shao, Meiyue

Within this paper, we present two efficient iterative algorithms for solving the linear response eigenvalue problem arising from the time dependent density functional theory. Although the matrix to be diagonalized is nonsymmetric, it has a special structure that can be exploited to save both memory and floating point operations. In particular, the nonsymmetric eigenvalue problem can be transformed into an eigenvalue problem that involves the product of two matrices M and K. We show that, because MK is self-adjoint with respect to the inner product induced by the matrix K, this product eigenvalue problem can be solved efficiently by amore » modified Davidson algorithm and a modified locally optimal block preconditioned conjugate gradient (LOBPCG) algorithm that make use of the K-inner product. Additionally, the solution of the product eigenvalue problem yields one component of the eigenvector associated with the original eigenvalue problem. We show that the other component of the eigenvector can be easily recovered in an inexpensive postprocessing procedure. As a result, the algorithms we present here become more efficient than existing methods that try to approximate both components of the eigenvectors simultaneously. In particular, our numerical experiments demonstrate that the new algorithms presented here consistently outperform the existing state-of-the-art Davidson type solvers by a factor of two in both solution time and storage.« less

Efficient block preconditioned eigensolvers for linear response time-dependent density functional theory

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

Vecharynski, Eugene; Brabec, Jiri; Shao, Meiyue

In this article, we present two efficient iterative algorithms for solving the linear response eigenvalue problem arising from the time dependent density functional theory. Although the matrix to be diagonalized is nonsymmetric, it has a special structure that can be exploited to save both memory and floating point operations. In particular, the nonsymmetric eigenvalue problem can be transformed into an eigenvalue problem that involves the product of two matrices M and K. We show that, because MK is self-adjoint with respect to the inner product induced by the matrix K, this product eigenvalue problem can be solved efficiently by amore » modified Davidson algorithm and a modified locally optimal block preconditioned conjugate gradient (LOBPCG) algorithm that make use of the K-inner product. The solution of the product eigenvalue problem yields one component of the eigenvector associated with the original eigenvalue problem. We show that the other component of the eigenvector can be easily recovered in an inexpensive postprocessing procedure. As a result, the algorithms we present here become more efficient than existing methods that try to approximate both components of the eigenvectors simultaneously. In particular, our numerical experiments demonstrate that the new algorithms presented here consistently outperform the existing state-of-the-art Davidson type solvers by a factor of two in both solution time and storage.« less

Efficient block preconditioned eigensolvers for linear response time-dependent density functional theory

DOE PAGES

Vecharynski, Eugene; Brabec, Jiri; Shao, Meiyue; ...

2017-12-01

In this article, we present two efficient iterative algorithms for solving the linear response eigenvalue problem arising from the time dependent density functional theory. Although the matrix to be diagonalized is nonsymmetric, it has a special structure that can be exploited to save both memory and floating point operations. In particular, the nonsymmetric eigenvalue problem can be transformed into an eigenvalue problem that involves the product of two matrices M and K. We show that, because MK is self-adjoint with respect to the inner product induced by the matrix K, this product eigenvalue problem can be solved efficiently by amore » modified Davidson algorithm and a modified locally optimal block preconditioned conjugate gradient (LOBPCG) algorithm that make use of the K-inner product. The solution of the product eigenvalue problem yields one component of the eigenvector associated with the original eigenvalue problem. We show that the other component of the eigenvector can be easily recovered in an inexpensive postprocessing procedure. As a result, the algorithms we present here become more efficient than existing methods that try to approximate both components of the eigenvectors simultaneously. In particular, our numerical experiments demonstrate that the new algorithms presented here consistently outperform the existing state-of-the-art Davidson type solvers by a factor of two in both solution time and storage.« less

Efficient block preconditioned eigensolvers for linear response time-dependent density functional theory

DOE PAGES

Vecharynski, Eugene; Brabec, Jiri; Shao, Meiyue; ...

2017-08-24

Within this paper, we present two efficient iterative algorithms for solving the linear response eigenvalue problem arising from the time dependent density functional theory. Although the matrix to be diagonalized is nonsymmetric, it has a special structure that can be exploited to save both memory and floating point operations. In particular, the nonsymmetric eigenvalue problem can be transformed into an eigenvalue problem that involves the product of two matrices M and K. We show that, because MK is self-adjoint with respect to the inner product induced by the matrix K, this product eigenvalue problem can be solved efficiently by amore » modified Davidson algorithm and a modified locally optimal block preconditioned conjugate gradient (LOBPCG) algorithm that make use of the K-inner product. Additionally, the solution of the product eigenvalue problem yields one component of the eigenvector associated with the original eigenvalue problem. We show that the other component of the eigenvector can be easily recovered in an inexpensive postprocessing procedure. As a result, the algorithms we present here become more efficient than existing methods that try to approximate both components of the eigenvectors simultaneously. In particular, our numerical experiments demonstrate that the new algorithms presented here consistently outperform the existing state-of-the-art Davidson type solvers by a factor of two in both solution time and storage.« less

Fluctuating hydrodynamics, current fluctuations, and hyperuniformity in boundary-driven open quantum chains

NASA Astrophysics Data System (ADS)

Carollo, Federico; Garrahan, Juan P.; Lesanovsky, Igor; Pérez-Espigares, Carlos

2017-11-01

We consider a class of either fermionic or bosonic noninteracting open quantum chains driven by dissipative interactions at the boundaries and study the interplay of coherent transport and dissipative processes, such as bulk dephasing and diffusion. Starting from the microscopic formulation, we show that the dynamics on large scales can be described in terms of fluctuating hydrodynamics. This is an important simplification as it allows us to apply the methods of macroscopic fluctuation theory to compute the large deviation (LD) statistics of time-integrated currents. In particular, this permits us to show that fermionic open chains display a third-order dynamical phase transition in LD functions. We show that this transition is manifested in a singular change in the structure of trajectories: while typical trajectories are diffusive, rare trajectories associated with atypical currents are ballistic and hyperuniform in their spatial structure. We confirm these results by numerically simulating ensembles of rare trajectories via the cloning method, and by exact numerical diagonalization of the microscopic quantum generator.

Fluctuating hydrodynamics, current fluctuations, and hyperuniformity in boundary-driven open quantum chains.

PubMed

Carollo, Federico; Garrahan, Juan P; Lesanovsky, Igor; Pérez-Espigares, Carlos

2017-11-01

We consider a class of either fermionic or bosonic noninteracting open quantum chains driven by dissipative interactions at the boundaries and study the interplay of coherent transport and dissipative processes, such as bulk dephasing and diffusion. Starting from the microscopic formulation, we show that the dynamics on large scales can be described in terms of fluctuating hydrodynamics. This is an important simplification as it allows us to apply the methods of macroscopic fluctuation theory to compute the large deviation (LD) statistics of time-integrated currents. In particular, this permits us to show that fermionic open chains display a third-order dynamical phase transition in LD functions. We show that this transition is manifested in a singular change in the structure of trajectories: while typical trajectories are diffusive, rare trajectories associated with atypical currents are ballistic and hyperuniform in their spatial structure. We confirm these results by numerically simulating ensembles of rare trajectories via the cloning method, and by exact numerical diagonalization of the microscopic quantum generator.

Accuracy of the microcanonical Lanczos method to compute real-frequency dynamical spectral functions of quantum models at finite temperatures

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

Okamoto, Satoshi; Alvarez, Gonzalo; Dagotto, Elbio

We examine the accuracy of the microcanonical Lanczos method (MCLM) developed by Long et al. [Phys. Rev. B 68, 235106 (2003)] to compute dynamical spectral functions of interacting quantum models at finite temperatures. The MCLM is based on the microcanonical ensemble, which becomes exact in the thermodynamic limit. To apply the microcanonical ensemble at a fixed temperature, one has to find energy eigenstates with the energy eigenvalue corresponding to the internal energy in the canonical ensemble. Here in this paper, we propose to use thermal pure quantum state methods by Sugiura and Shimizu [Phys. Rev. Lett. 111, 010401 (2013)] tomore » obtain the internal energy. After obtaining the energy eigenstates using the Lanczos diagonalization method, dynamical quantities are computed via a continued fraction expansion, a standard procedure for Lanczos-based numerical methods. Using one-dimensional antiferromagnetic Heisenberg chains with S = 1/2, we demonstrate that the proposed procedure is reasonably accurate, even for relatively small systems.« less

Characterizing the three-orbital Hubbard model with determinant quantum Monte Carlo

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

Kung, Y. F.; Chen, C. -C.; Wang, Yao

Here, we characterize the three-orbital Hubbard model using state-of-the-art determinant quantum Monte Carlo (DQMC) simulations with parameters relevant to the cuprate high-temperature superconductors. The simulations find that doped holes preferentially reside on oxygen orbitals and that the (π,π) antiferromagnetic ordering vector dominates in the vicinity of the undoped system, as known from experiments. The orbitally-resolved spectral functions agree well with photoemission spectroscopy studies and enable identification of orbital content in the bands. A comparison of DQMC results with exact diagonalization and cluster perturbation theory studies elucidates how these different numerical techniques complement one another to produce a more complete understandingmore » of the model and the cuprates. Interestingly, our DQMC simulations predict a charge-transfer gap that is significantly smaller than the direct (optical) gap measured in experiment. Most likely, it corresponds to the indirect gap that has recently been suggested to be on the order of 0.8 eV, and demonstrates the subtlety in identifying charge gaps.« less

Characterizing the three-orbital Hubbard model with determinant quantum Monte Carlo

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

Kung, Y. F.; Chen, C. -C.; Wang, Yao

We characterize the three-orbital Hubbard model using state-of-the-art determinant quantum Monte Carlo (DQMC) simulations with parameters relevant to the cuprate high-temperature superconductors. The simulations find that doped holes preferentially reside on oxygen orbitals and that the (π,π) antiferromagnetic ordering vector dominates in the vicinity of the undoped system, as known from experiments. The orbitally-resolved spectral functions agree well with photoemission spectroscopy studies and enable identification of orbital content in the bands. A comparison of DQMC results with exact diagonalization and cluster perturbation theory studies elucidates how these different numerical techniques complement one another to produce a more complete understanding ofmore » the model and the cuprates. Interestingly, our DQMC simulations predict a charge-transfer gap that is significantly smaller than the direct (optical) gap measured in experiment. Most likely, it corresponds to the indirect gap that has recently been suggested to be on the order of 0.8 eV, and demonstrates the subtlety in identifying charge gaps.« less

Accuracy of the microcanonical Lanczos method to compute real-frequency dynamical spectral functions of quantum models at finite temperatures

DOE PAGES

Okamoto, Satoshi; Alvarez, Gonzalo; Dagotto, Elbio; ...

2018-04-20

We examine the accuracy of the microcanonical Lanczos method (MCLM) developed by Long et al. [Phys. Rev. B 68, 235106 (2003)] to compute dynamical spectral functions of interacting quantum models at finite temperatures. The MCLM is based on the microcanonical ensemble, which becomes exact in the thermodynamic limit. To apply the microcanonical ensemble at a fixed temperature, one has to find energy eigenstates with the energy eigenvalue corresponding to the internal energy in the canonical ensemble. Here in this paper, we propose to use thermal pure quantum state methods by Sugiura and Shimizu [Phys. Rev. Lett. 111, 010401 (2013)] tomore » obtain the internal energy. After obtaining the energy eigenstates using the Lanczos diagonalization method, dynamical quantities are computed via a continued fraction expansion, a standard procedure for Lanczos-based numerical methods. Using one-dimensional antiferromagnetic Heisenberg chains with S = 1/2, we demonstrate that the proposed procedure is reasonably accurate, even for relatively small systems.« less

Infinite projected entangled-pair state algorithm for ruby and triangle-honeycomb lattices

NASA Astrophysics Data System (ADS)

Jahromi, Saeed S.; Orús, Román; Kargarian, Mehdi; Langari, Abdollah

2018-03-01

The infinite projected entangled-pair state (iPEPS) algorithm is one of the most efficient techniques for studying the ground-state properties of two-dimensional quantum lattice Hamiltonians in the thermodynamic limit. Here, we show how the algorithm can be adapted to explore nearest-neighbor local Hamiltonians on the ruby and triangle-honeycomb lattices, using the corner transfer matrix (CTM) renormalization group for 2D tensor network contraction. Additionally, we show how the CTM method can be used to calculate the ground-state fidelity per lattice site and the boundary density operator and entanglement entropy (EE) on an infinite cylinder. As a benchmark, we apply the iPEPS method to the ruby model with anisotropic interactions and explore the ground-state properties of the system. We further extract the phase diagram of the model in different regimes of the couplings by measuring two-point correlators, ground-state fidelity, and EE on an infinite cylinder. Our phase diagram is in agreement with previous studies of the model by exact diagonalization.