Soliton topology versus discrete symmetry in optical lattices

We address the existence of vortex solitons supported by azimuthally modulated lattices and reveal how the global lattice discrete symmetry has fundamental implications on the possible topological charges of solitons. We set a general ``charge rule'' using group-theory techniques, which holds for all lattices belonging to a given symmetry group. Focusing in the case of Bessel lattices allows us to derive also a overall stability rule for the allowed vortex solitons.Comment: 4 pages, 3 figures. To appear in Phys. Rev. Let

Drinfeld Twists and Symmetric Bethe Vectors of Supersymmetric Fermion Models

We construct the Drinfeld twists (factorizing $F$-matrices) of the $gl(m|n)$-invariant fermion model. Completely symmetric representation of the pseudo-particle creation operators of the model are obtained in the basis provided by the $F$-matrix (the $F$-basis). We resolve the hierarchy of the nested Bethe vectors in the $F$-basis for the $gl(m|n)$ supersymmetric model.Comment: Latex File, 24 pages, no figure, some misprints are correcte

Determinant representations of scalar products for the open XXZ chain with non-diagonal boundary terms

With the help of the F-basis provided by the Drinfeld twist or factorizing F-matrix for the open XXZ spin chain with non-diagonal boundary terms, we obtain the determinant representations of the scalar products of Bethe states of the model.Comment: Latex file, 28 pages, based on the talk given by W. -L. Yang at Statphys 24, Cairns, Australia, 19-23 July, 201

Determinant Representations of Correlation Functions for the Supersymmetric t-J Model

Working in the $F$-basis provided by the factorizing $F$-matrix, the scalar products of Bethe states for the supersymmetric t-J model are represented by determinants. By means of these results, we obtain determinant representations of correlation functions for the model.Comment: Latex File, 41 pages, no figure; V2: minor typos corrected, V3: This version will appear in Commun. Math. Phy

Full-Field Numerical Simulation of Halite Dynamic Recrystallization From Subgrain Rotation to Grain Boundary Migration

Full-field numerical modeling is a useful method to gain understanding of rock salt deformation at multiple scales, but it is quite challenging due to the anisotropic and complex plastic behavior of halite, together with dynamic recrystallization processes. This contribution presents novel results of full-field numerical simulations of coupled dislocation glide and dynamic recrystallization of halite polycrystalline aggregates during simple shear deformation, including both subgrain rotation and grain boundary migration (GBM) recrystallization. The results demonstrate that the numerical approach successfully replicates the evolution of pure halite microstructures from laboratory torsion deformation experiments at 100–300°C. Temperature determines the competition between (a) grain size reduction controlled by dislocation glide and subgrain rotation recrystallization (at low temperature) and (b) grain growth associated with GBM (at higher temperature), while the resulting crystallographic preferred orientations are similar for all cases. The relationship between subgrain misorientation and strain follows a power law relationship with a universal exponent of 2/3 at low strain. However, dynamic recrystallization causes a progressive deviation from this relationship when strain increases, as revealed by the skewness of the subgrain misorientation distribution. A systematic investigation of the subgrain misorientation evolution shows that strain or temperature prediction from microstructures requires careful calibration

A numerical method to solve the Boltzmann equation for a spin valve

We present a numerical algorithm to solve the Boltzmann equation for the electron distribution function in magnetic multilayer heterostructures with non-collinear magnetizations. The solution is based on a scattering matrix formalism for layers that are translationally invariant in plane so that properties only vary perpendicular to the planes. Physical quantities like spin density, spin current, and spin-transfer torque are calculated directly from the distribution function. We illustrate our solution method with a systematic study of the spin-transfer torque in a spin valve as a function of its geometry. The results agree with a hybrid circuit theory developed by Slonczewski for geometries typical of those measured experimentally.Comment: 13 pages, 8 figure

Non-polynomial Worst-Case Analysis of Recursive Programs

We study the problem of developing efficient approaches for proving worst-case bounds of non-deterministic recursive programs. Ranking functions are sound and complete for proving termination and worst-case bounds of nonrecursive programs. First, we apply ranking functions to recursion, resulting in measure functions. We show that measure functions provide a sound and complete approach to prove worst-case bounds of non-deterministic recursive programs. Our second contribution is the synthesis of measure functions in nonpolynomial forms. We show that non-polynomial measure functions with logarithm and exponentiation can be synthesized through abstraction of logarithmic or exponentiation terms, Farkas' Lemma, and Handelman's Theorem using linear programming. While previous methods obtain worst-case polynomial bounds, our approach can synthesize bounds of the form $\mathcal{O}(n\log n)$ as well as $\mathcal{O}(n^r)$ where $r$ is not an integer. We present experimental results to demonstrate that our approach can obtain efficiently worst-case bounds of classical recursive algorithms such as (i) Merge-Sort, the divide-and-conquer algorithm for the Closest-Pair problem, where we obtain $\mathcal{O}(n \log n)$ worst-case bound, and (ii) Karatsuba's algorithm for polynomial multiplication and Strassen's algorithm for matrix multiplication, where we obtain $\mathcal{O}(n^r)$ bound such that $r$ is not an integer and close to the best-known bounds for the respective algorithms.Comment: 54 Pages, Full Version to CAV 201

Resistance distance, information centrality, node vulnerability and vibrations in complex networks

We discuss three seemingly unrelated quantities that have been introduced in different fields of science for complex networks. The three quantities are the resistance distance, the information centrality and the node displacement. We first prove various relations among them. Then we focus on the node displacement, showing its usefulness as an index of node vulnerability.We argue that the node displacement has a better resolution as a measure of node vulnerability than the degree and the information centrality

Superior effects of modified chen-style Tai Chi versus 24-style Tai Chi on cognitive function, fitness, and balance performance in adults over 55

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. Background: Cognitive decline and balance impairment are prevalent in the aging population. Previous studies investigated the beneficial effects of 24-style Tai Chi (TC-24) on either cognitive function or balance performance of older adults. It still remains largely unknown whether modified Chen-style TC (MTC) that includes 18 complex movements is more beneficial for these age-related health outcomes, as compared to TC-24. Objective: We investigated if MTC would show greater effects than TC-24 on global cognitive function and balance-related outcomes among older adults. Methods: We conducted a randomized trial where 80 eligible adults aged over 55 were allocated into two different styles of Tai Chi (TC) arms (sixty-minute session × three times per week, 12 weeks). Outcome assessments were performed at three time periods (baseline, Week 6, and Week 12) and included the Chinese Version of the Montreal Cognitive Assessment (MoCA) for overall cognitive function, One-leg Standing Test (LST) for static balance, Timed Up and Go Test (TUGT) for dynamic balance, chair Stand Test (CST) for leg power, and the six-meter Walk Test (6MWT) for aerobic exercise capacity. Results: Compared to TC-24 arm, MTC arm demonstrated significantly greater improvements in MoCA, LST, TUGT, CST, and 6MWT (all p \u3c 0.05). Conclusions: Both forms of TC were effective in enhancing global cognitive function, balance, and fitness. Furthermore, MTC was more effective than TC-24 in enhancing these health-related parameters in an aging population