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Stuart C Althorpe - One of the best experts on this subject based on the ideXlab platform.

  • on the uniqueness of t 0 quantum transition state theory
    Journal of Chemical Physics, 2013
    Co-Authors: Timothy J H Hele, Stuart C Althorpe
    Abstract:

    It was shown recently that there exists a true quantum transition-state theory (QTST) corresponding to the t → 0+ limit of a (new form of) quantum Flux-side time-correlation function. Remarkably, this QTST is identical to ring-polymer molecular dynamics (RPMD) TST. Here, we provide evidence which suggests very strongly that this QTST (≡ RPMD-TST) is unique, in the sense that the t → 0+ limit of any other Flux-side time-correlation function gives either non-positive-definite quantum statistics or zero. We introduce a Generalized Flux-side time-correlation function which includes all other (known) Flux-side time-correlation functions as special limiting cases. We find that the only non-zero t → 0+ limit of this function that contains positive-definite quantum statistics is RPMD-TST.

  • On the uniqueness of t → 0+ quantum transition-state theory
    The Journal of Chemical Physics, 2013
    Co-Authors: Timothy J H Hele, Stuart C Althorpe
    Abstract:

    It was shown recently that there exists a true quantum transition-state theory (QTST) corresponding to the t → 0+ limit of a (new form of) quantum Flux-side time-correlation function. Remarkably, this QTST is identical to ring-polymer molecular dynamics (RPMD) TST. Here, we provide evidence which suggests very strongly that this QTST (≡ RPMD-TST) is unique, in the sense that the t → 0+ limit of any other Flux-side time-correlation function gives either non-positive-definite quantum statistics or zero. We introduce a Generalized Flux-side time-correlation function which includes all other (known) Flux-side time-correlation functions as special limiting cases. We find that the only non-zero t → 0+ limit of this function that contains positive-definite quantum statistics is RPMD-TST.

Timothy J H Hele - One of the best experts on this subject based on the ideXlab platform.

  • on the uniqueness of t 0 quantum transition state theory
    Journal of Chemical Physics, 2013
    Co-Authors: Timothy J H Hele, Stuart C Althorpe
    Abstract:

    It was shown recently that there exists a true quantum transition-state theory (QTST) corresponding to the t → 0+ limit of a (new form of) quantum Flux-side time-correlation function. Remarkably, this QTST is identical to ring-polymer molecular dynamics (RPMD) TST. Here, we provide evidence which suggests very strongly that this QTST (≡ RPMD-TST) is unique, in the sense that the t → 0+ limit of any other Flux-side time-correlation function gives either non-positive-definite quantum statistics or zero. We introduce a Generalized Flux-side time-correlation function which includes all other (known) Flux-side time-correlation functions as special limiting cases. We find that the only non-zero t → 0+ limit of this function that contains positive-definite quantum statistics is RPMD-TST.

  • On the uniqueness of t → 0+ quantum transition-state theory
    The Journal of Chemical Physics, 2013
    Co-Authors: Timothy J H Hele, Stuart C Althorpe
    Abstract:

    It was shown recently that there exists a true quantum transition-state theory (QTST) corresponding to the t → 0+ limit of a (new form of) quantum Flux-side time-correlation function. Remarkably, this QTST is identical to ring-polymer molecular dynamics (RPMD) TST. Here, we provide evidence which suggests very strongly that this QTST (≡ RPMD-TST) is unique, in the sense that the t → 0+ limit of any other Flux-side time-correlation function gives either non-positive-definite quantum statistics or zero. We introduce a Generalized Flux-side time-correlation function which includes all other (known) Flux-side time-correlation functions as special limiting cases. We find that the only non-zero t → 0+ limit of this function that contains positive-definite quantum statistics is RPMD-TST.

Zohar Yosibash - One of the best experts on this subject based on the ideXlab platform.

  • GFIFs Computation for Two-Dimensional Heat Conduction Problems
    Interdisciplinary Applied Mathematics, 2011
    Co-Authors: Zohar Yosibash
    Abstract:

    Having computed the eigenpairs associated with a 2-D singular point, the next task is the computation of the coefficients of the series expansion Ai ’s, called for the heat conduction equation “Generalized Flux intensity functions” (GFIFs). The eigenpairs may be viewed as characterizing the straining modes, and their amplitudes (the GFIFs) quantify the amount of “energy” residing in particular straining modes. For this reason, failure theories directly or indirectly involve the GFIFs. As a simple example, consider a solution for which all eigenpairs are given. Although the first eigenvalue may be very small, if the corresponding GFIF is zero, the solution does not manifest this singular behavior.

  • On solutions of two-dimensional linear elastostatic and heat-transfer problems in the vicinity of singular points
    International Journal of Solids and Structures, 1997
    Co-Authors: Zohar Yosibash
    Abstract:

    Singular points associated with the linear theories of steady-state heat transfer and elasticity are discussed. Exact solutions for a set of benchmark problems consisting of crack tips, wedge corners of different angles and materials and internal multi-material interfaces in isotropic as well as anisotropic materials are provided and described in detail. Both the Generalized Flux/stress intensity factors (GFIFs/GSIFs) and the eigenfunctions are explicitly presented. The efficiency, robustness and accuracy of new numerical methods based on the p-version of the finite element method are demonstrated on the basis of the benchmark problems.

  • NUMERICAL ANALYSIS OF SINGULARITIES IN TWO DIMENSIONS. PART 2: COMPUTATION OF Generalized Flux/STRESS INTENSITY FACTORS
    International Journal for Numerical Methods in Engineering, 1996
    Co-Authors: Barna A. Szabó, Zohar Yosibash
    Abstract:

    SUMMARY A numerical method for the computation of the Generalized Flux/stress intensity factors (GFIFs/GSIFs) for the asymptotic solution of linear second-order elliptic partial differential equations in two dimensions in the vicinity of singular points is described. Special attention is given to heat transfer and elasticity problems. The singularities may be caused by re-entrant corners and abrupt changes in material properties. Such singularities are of great interest from the point of view of failure initiation: The eigenpairs, computed in a companion paper,' characterize the straining modes and their amplitudes (the GFIFs/GSIFs) quantify the amount of energy residing in particular straining modes. For this reason, failure theories directly or indirectly involve the GFIFs/GSIFs. This paper addresses a general method based on the complementary weak formulation for determining the GFIFs/GSIFs numerically as a post-solution operation on the finite element solution vector. Importantly, the method is applicable to anisotropic materials, multi-material interfaces, and cases where the singularities are characterized by complex eigenpairs. An error analysis is sketched and numerical examples are presented to illustrate the effectiveness of the technique.

  • numerical analysis of singularities in two dimensions part 2 computation of Generalized Flux stress intensity factors
    International Journal for Numerical Methods in Engineering, 1996
    Co-Authors: Barna A. Szabó, Zohar Yosibash
    Abstract:

    SUMMARY A numerical method for the computation of the Generalized Flux/stress intensity factors (GFIFs/GSIFs) for the asymptotic solution of linear second-order elliptic partial differential equations in two dimensions in the vicinity of singular points is described. Special attention is given to heat transfer and elasticity problems. The singularities may be caused by re-entrant corners and abrupt changes in material properties. Such singularities are of great interest from the point of view of failure initiation: The eigenpairs, computed in a companion paper,' characterize the straining modes and their amplitudes (the GFIFs/GSIFs) quantify the amount of energy residing in particular straining modes. For this reason, failure theories directly or indirectly involve the GFIFs/GSIFs. This paper addresses a general method based on the complementary weak formulation for determining the GFIFs/GSIFs numerically as a post-solution operation on the finite element solution vector. Importantly, the method is applicable to anisotropic materials, multi-material interfaces, and cases where the singularities are characterized by complex eigenpairs. An error analysis is sketched and numerical examples are presented to illustrate the effectiveness of the technique.

Pramod Shukla - One of the best experts on this subject based on the ideXlab platform.

  • T -dualizing de Sitter no-go scenarios
    Physical Review D, 2020
    Co-Authors: Pramod Shukla
    Abstract:

    In the context of realizing de-Sitter vacua and the slow-roll inflation, several no-go conditions have been found in the framework of type IIA (Generalized) Flux compactifications. In this article, using our recently proposed $T$-dual dictionary in arXiv:1909.07391, we translate various such type IIA no-go conditions which subsequently leads to some interesting de-Sitter no-go scenarios in the presence of (non-)geometric Fluxes on the dual type IIB side. We also present the relevance of using $K3/{\mathbb T}^4$-fibred Calabi Yau threefolds in order to facilitate one particular class of the de-Sitter no-go conditions. This analysis helps in refining certain corners of the vast non-geometric Flux landscape for the hunt of de-Sitter vacua.

  • Implementing odd-axions in dimensional oxidation of 4D non-geometric type IIB scalar potential
    Nuclear Physics B, 2016
    Co-Authors: Pramod Shukla
    Abstract:

    In a setup of type IIB superstring compactification on an orientifold of a T6/Z4 sixfold, the presence of geometric Flux (ω) and non-geometric Fluxes (Q, R) is implemented along with the standard NS–NS and RR three-form Fluxes (H, F). After computing the F/D-term contributions to the N=1 four dimensional effective scalar potential, we rearrange the same into ‘suitable’ pieces by using a set of new Generalized Flux orbits. Subsequently, we dimensionally oxidize the various pieces of the total four dimensional scalar potential to guess their ten-dimensional origin.

  • On modular completion of Generalized Flux orbits
    Journal of High Energy Physics, 2015
    Co-Authors: Pramod Shukla
    Abstract:

    In the context of type IIB orientifold compactification with the presence of (non-)geometric Fluxes, we conjecture a modular completed version of the Generalized Flux- orbits of various NS-NS and RR Fluxes. Subsequently, considering two explicit examples with frozen complex structure moduli, we illustrate the utility of these new Flux orbits in a very compact rearrangement of the four dimensional effective scalar potential.

  • Dimensional oxidation and modular completion of non-geometric type IIB action
    Journal of High Energy Physics, 2015
    Co-Authors: Xin Gao, Pramod Shukla
    Abstract:

    Utilizing a setup of type IIB superstring theory compactified on an orientifold of T 6 / ℤ 2 × ℤ 2 $$ {\mathbb{T}}^6/\left({\mathbb{Z}}_2\times {\mathbb{Z}}_2\right) $$ , we propose a modular invariant dimensional oxidation of the four- dimensional scalar potential. In the oxidized ten-dimensional supergravity action, the standard NS-NS and RR three form Fluxes ( H -, F -) as well as the non-geometric Fluxes ( Q -, P -) are found to nicely rearrange themselves to form Generalized Flux-combinations. As an application towards moduli stabilization, using the same S-duality invariant scalar potential, we examine the recently proposed No-Go theorem [1] about creating a mass-hierarchy between universal-axion and the dilaton relevant for axionic-inflation. Considering a two-field dynamics of universal axion and dilator while assuming the other moduli/axions being stabilized, we find a part of the No-Go arguments to be quite robust even with the inclusion of non-geometric ( Q -, P -) Fluxes.

T M Rice - One of the best experts on this subject based on the ideXlab platform.

  • Variational Monte Carlo study of Generalized Flux phases in the t-J model.
    Physical Review B, 1991
    Co-Authors: Masao Ogata, B Douçot, T M Rice
    Abstract:

    Etude des fonctions d'onde des phases de Flux generalisees par la methode Monte Carlo variationnelle. Les tubes de Flux sont lies aux trous, ce qui produit des facteurs de phase en plus de ceux dus au mouvement des electrons. Les facteurs de phase s'annulent entre eux lorsque les electrons et les trous intervertissent leur position a certaines densites d'electrons speciales et il en resulte une absence de courants orbitaux dans ces etats. On examine specialement le cas du remplissage au tiers et on trouve une energie cinetique legerement plus basse que celle de la phase de Flux commensurable. Calcul de la chiralite pour confirmer que la symetrie d'inversion du temps est brisee dans ces etats

  • Variational Monte Carlo study for Generalized Flux phases in the t-J model
    Physica B-condensed Matter, 1990
    Co-Authors: Masao Ogata, T M Rice
    Abstract:

    We study new wavefunctions for Generalized Flux phases by the variational Monte Carlo method, in which the motion of holes produces additional phase factors besides those due to the motion of electrons. The phase factors cancel each other at some special electron densities and, as a result, there are no orbital currents in these states. We investigate especially the 1/3-filled case and find a wavefunction with lower kinetic energy than the original commensurate Flux phase. We also calculate the chirality to confirm that time reversal symmetry is broken also in these states.