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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 793 records · Page 44
All sourcesNASA NTRSDOE OSTI
DOE OSTI2018

On semi-convergence and inexact iteration of the GSS iteration method for nonsymmetric singular saddle point problems

In this paper, the generalized shift-splitting (GSS) iteration method is used to solve nonsymmetric singular saddle point systems with the positive real (1, 1)-block sub-matrix. By a careful analysis of the spectral properties of the corresponding iteration matrix, we investigate the semi-convergence property of the GSS iteration method, give the sharper bounds of the eigenvalues for the GSS iteration method and propose the inexact GSS iteration method, also. Numerical experiments are given to show the correctness of the theoretical analysis and the feasibility of the GSS preconditioner with appropriate parameters.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

A low-order block preconditioner for saddle point linear systems

A preconditioner is proposed for the large and sparse linear saddle point problems, which is based on a low-order three-by-three block saddle point form. The eigenvalue distribution and an upper bound of the degree of the minimal polynomial for the preconditioned matrix are discussed. Numerical results show that the optimal convergence behavior can be achieved when the new preconditioner is used to accelerate the convergence rate of Krylov subspace methods such as GMRES.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

On nonlinear inexact Uzawa algorithms for stabilized saddle point problems

In this paper, the nonlinear inexact Uzawa (NIU) methods for saddle point problems are studied. A further improved convergence result of the NIU algorithm for stabilized saddle point problems is presented, which results in much smaller convergence factor. This result can also be viewed as a generalization of some previous work for classical saddle point problems. Based on this result, we generalize some adaptive versions of the NIU algorithm with variable iteration parameters for classical saddle point problems to solve stabilized saddle point problems. Convergence analyses of these algorithms are presented. It shows that they converge under similar conditions as those in classical cases, which are more practical and without estimates on the extreme eigenvalues of the involved preconditioned systems. Numerical experiments are given to demonstrate the effectiveness of these algorithms over some original NIU algorithms.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

The parameterized preconditioner for the generalized saddle point problems from the incompressible Navier–Stokes equations

A parameterized preconditioner is proposed for the generalized saddle point problems arising from the incompressible Navier–Stokes equations. The eigenvalues and eigenvectors of the preconditioned matrix are analyzed. Numerical results show that the proposed preconditioner is efficient to accelerate the convergence rate of Krylov subspace methods, such as GMRES method.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

GSTS-Uzawa method for a class of complex singular saddle point problems

In this paper, we propose GSTS–Uzawa method for solving a class of complex singular saddle point problems based on generalized skew-Hermitian triangular splitting (GSTS) iteration method and classical Uzawa method. We research on its semi-convergence properties and the eigenvalues distributions of its preconditioned matrix. The resulting GSTS–Uzawa preconditioner is used to precondition Krylov subspace methods such as the restarted generalized minimal residual (GMRES) method for solving the equivalent formulation of the complex singular saddle point problems. The theoretical results and effectiveness of the GSTS–Uzawa method are supported by a numerical example.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Diagonal and circulant or skew-circulant splitting preconditioners for spatial fractional diffusion equations

We propose three new preconditioners: diagonal and optimal-circulant splitting preconditioner, diagonal and skew-circulant splitting preconditioner, and diagonal and optimal-skew-circulant splitting preconditioner for solving the diagonal-plus-Toeplitz linear system discretized from the spatial fractional diffusion equations. Theoretical analysis shows that these three preconditioners can make the eigenvalues of the preconditioned matrices be clustered around 1, especially when the grids of the discretizations are refined. These results coincide with the one about the diagonal and circulant splitting preconditioner constructed recently by Bai et al. (Numer Linear Algebra Appl 24:e2093, 2017). Numerical experiments exhibit that the proposed preconditioners can significantly improve the convergence of the Krylov subspace iteration methods like GMRES and BiCGSTAB, and they outperform the diagonal and circulant splitting preconditioner as well.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Study of excited quark propagator contributions in perturbative chiral quark model

In this work, masses of octet baryons are evaluated in the framework of the perturbative chiral quark model (PCQM) with considering both the ground and excited states in the quark propagator, in which a Cornell-like potential is first constructed by letting the predetermined ground state quark wavefunction satisfy Dirac equation, and the excited quark states are derived by resolving Dirac equation with the extracted PCQM potential numerically employing Generalized Eigenvalue & Eigenstate Problem method. The results on the octet baryon masses are found in good agreement with the experimental data, and the study reveals that the contributions of the excited quark states are considerably influential in the octet baryon masses as expected.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2018

Supersymmetric symplectic quantum mechanics

Symplectic Quantum Mechanics SQM considers a non-commutative algebra of functions on a phase space Γ and an associated Hilbert space H{sub Γ} to construct a unitary representation for the Galilei group. From this unitary representation the Schrödinger equation is rewritten in phase space variables and the Wigner function can be derived without the use of the Liouville–von Neumann equation. In this article we extend the methods of supersymmetric quantum mechanics SUSYQM to SQM. With the purpose of applications in quantum systems, the factorization method of the quantum mechanical formalism is then set within supersymmetric SQM. A hierarchy of simpler hamiltonians is generated leading to new computation tools for solving the eigenvalue problem in SQM. We illustrate the results by computing the states and spectra of the problem of a charged particle in a homogeneous magnetic field as well as the corresponding Wigner function.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

A comparative study of two-electron systems with screened Coulomb potentials

Highlights: • A comparison criterion for screened potentials is conjectured for two-electron atoms. • The limits of validity of the correlation hypothesis are discussed. • Independent Hylleraas and Lagrange mesh calculations verify the comparison criterion. - Abstract: The relative ordering of energy levels is investigated for bound two-electron systems with potentials of the form V(r{sub 1},r{sub 2},r{sub 12})=Z(v(r{sub 1})+v(r{sub 2}))-v(r{sub 12}). Given the two one-body binding potentials v{sup (1)}(r) and v{sup (2)}(r), it is argued that if f(r)≡v{sup (1)}(r)-v{sup (2)}(r) is positive and monotonically decreasing upon increasing r then the corresponding eigenvalues of the two-electron Hamiltonians H{sub i}=-(1/2)(∇{sub 1}{sup 2}+∇{sub 2}{sup 2})+Z(v{sup (i)}(r{sub 1})+v{sup (i)}(r{sub 2}))-v{sup (i)}(r{sub 12}) , i=1,2are highly likely to be pairwise ordered, i.e., E{sub n}{sup (1)}≥E{sub n}{sup (2)}, n=1,2,…, where E{sub 1}{sup (i)}≤E{sub 2}{sup (i)}≤⋯≤E{sub k}{sup (i)}≤⋯ , for both i=1 and i=2. This conjecture certainly holds at sufficiently large Z. The range of n may be finite or infinite, depending on the nature of the potentials. In fact, the range of values of n for v{sup (1)}(r) may be shorter than that of v{sup (2)}(r) (which is more binding). The one-electron potentials specifically considered are: v(r)={ v_C(r) =-(1/r) Coulomb v_D(r) =-(1/r)exp(-λr) Debye (Yukawa) v_H_u(r) =-(λ/(exp(λr)-1)) Hulthén v_E_C_S_C(r) =-(1/r)exp(-λr)cos(λr) ECSC}{sup ∗} , ){sup ∗}Exponential-Cosine-Screened-Coulomb where λ is the screening parameter. For each of the λ-dependent potentials we compare one- and two-electron spectra corresponding to distinct values of λ. This is followed by pairwise comparison of distinct potentials.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

Quantizations of the classical time of arrival and their dynamics

The classical time of arrival in the interacting case is quantized by way of quantizing its expansion about the free time of arrival. The quantization is formulated in coordinate representation which represents ordering rules in terms of two variable polynomial functions. This leads to representations of the quantized time of arrival operators as integral operators whose kernels are determined by the chosen ordering rule. The formulation lends itself to generalization which allows construction of time of arrival operators that cannot be obtained by direct quantization using particular ordering rules. Weyl, symmetric and Born–Jordan quantizations are specifically studied. The dynamics of the eigenfunctions of the different time of arrival operators are investigated. The eigenfunctions exhibit unitary arrival at the intended arrival point at their respective eigenvalues.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2019

Rationally extended many-body truncated Calogero–Sutherland model

We construct a rational extension of the truncated Calogero–Sutherland model by Pittman et al. The exact solution of this rationally extended model is obtained analytically and it is shown that while the energy eigenvalues remain unchanged, however the eigenfunctions are completely different and written in terms of exceptional X{sub 1} Laguerre orthogonal polynomials. The rational model is further extended to a more general X{sub m} case by introducing m dependent interaction term. As expected, in the special case of m=0, the extended model reduces to the conventional model of Pittman et al. In the two appropriate limits, we thereby obtain rational extensions of the celebrated Calogero–Sutherland as well as Jain–Khare models. The multi-index extension of the model is also discussed.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2019

Extended Laplace–Runge–Lentz vectors, new family of superintegrable systems and quadratic algebras

We present a useful proposition for discovering extended Laplace–Runge–Lentz vectors of certain quantum mechanical systems. We propose a new family of superintegrable systems and construct their integrals of motion. We solve these systems via separation of variables in spherical coordinates and obtain their exact energy eigenvalues and the corresponding eigenfunctions. We give the quadratic algebra relations satisfied by the integrals of motion. Remarkably these algebra relations involve the Casimir operators of certain higher rank Lie algebras in the structure constants.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2019

Holographic insulator/superconductor phase transition in higher dimensional Gauss–Bonnet gravity

In this work, we have analytically investigated the insulator/superc-onductor phase transition in the presence of d-dimensional Gauss–Bonnet AdS soliton background. Using the Sturm–Liouville eigenvalue method, we have calculated the value of the critical chemical potential μ{sub c} in any arbitrary dimension d≥5. We have then studied the condensation operator values and charge density in terms of the chemical potential and discussed the d=5,6,7 cases using our general results in d dimensions. Our analytical results agree very well with the numerical findings in the literature.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2019

Klein paradox in chaotic Dirac billiards

We investigate the Schrödinger (non-relativistic) and the Dirac (“relativistic”) billiards in the universal regime. The study is based on a non-ideal quantum resonant scattering numerical simulation. We show universal results that reveal anomalous behaviour on the conductance, on the shot-noise power and on the respective eigenvalues distributions. In particular, we demonstrate the Klein’s paradox in the graphene and tunable suppression/amplification transitions on the typical observables of the quantum dots.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2019

Comment on: “Solving many-body Schrödinger equations with kinetic energy partition method”, Ann. Phys. 388 (2018) 54–68 by Y-H. Chen and S.D. Chao

We discuss a recent test of the performance of the kinetic energy partition method (KEP) through its application to two separable quantum-mechanical models. We argue that one of the benchmark models is exceedingly simple for testing any realistic approximate method and that almost any reasonable approach yields better results. In the second example our exact benchmark eigenvalues disagree considerably with those chosen by the authors for comparison, which casts doubts on the accuracy of their KEP approach.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2019

Scattering state and bound state of scalar field in Schwarzschild spacetime: Exact solution

The main aim of this paper is twofold. (1) Exact solutions of a scalar field in the Schwarzschild spacetime are presented. The exact wave functions of scattering states and bound-states are presented. Besides the exact solution, we also provide explicit approximate expressions for bound-state eigenvalues and scattering phase shifts. (2) By virtue of the exact solutions, we give a direct calculation for the discontinuous jump on the horizon for massive scalar fields, while in literature such a jump is obtained from an asymptotic solution by an analytic extension treatment.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Relativistic levels of mesic atoms

We revisit the derivation of the covariant two-body scalar-fermion equation with a Coulomb interaction, presented in a previous paper. We show that it can be given the formal aspect of a Dirac equation, but for the fact that the eigenvalue is also contained in one of the coefficients and thus it is not linearly included. The discussion of the boundary value problem is therefore different, although some properties of the Dirac equation can be recovered in an approximation bringing back to the concept of reduced mass. We discuss a mixed analytic-numerical method of solution which allows to obtain very accurate results and we calculate the lowest levels, states and QED corrections for pionic and kaonic atoms.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

On the missing magnetic flux and topological effects of a screw dislocation on a charged particle in an inhomogeneous magnetic field

Highlights: • Aharonov–Bohm-type effect associated with the missing magnetic flux. • Persistent currents associated with the missing magnetic flux. • Aharonov–Bohm-type effect associated with the screw dislocation topology. We study the interaction of an electron/hole with inhomogeneous magnetic field in the presence of a screw dislocation. We consider the internal structure of the defect, i.e., we consider the core that gives rise to a finite size to the defect. In addition, we assume that this core determines a forbidden region for the electron/hole. Then, we solve the Schrödinger equation and show that an Aharonov–Bohm-type effect arises from the influence of the topological defect and the missing magnetic flux on the eigenvalues of energy.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗