scholarly journals Six-vertex Models and the GUE-corners Process

2018 ◽  
Vol 2020 (6) ◽  
pp. 1794-1881
Author(s):  
Evgeni Dimitrov
Keyword(s):  
Correlation Functions ◽  
Probability Distributions ◽  
Gibbs Measures ◽  
Descent Method ◽  
Steepest Descent Method ◽  
Difference Operators ◽  
Vertex Model ◽  
Gaussian Unitary Ensemble ◽  
Vertex Models ◽  
Higher Spin

Abstract We consider a class of probability distributions on the six-vertex model, which originates from the higher spin vertex models of [13]. We define operators, inspired by the Macdonald difference operators, which extract various correlation functions, measuring the probability of observing different arrow configurations. For the class of models we consider, the correlation functions can be expressed in terms of multiple contour integrals, which are suitable for asymptotic analysis. For a particular choice of parameters we analyze the limit of the correlation functions through the steepest descent method. Combining this asymptotic statement with some new results about Gibbs measures on Gelfand–Tsetlin cones and patterns, we show that the asymptotic behavior of our six-vertex model near the boundary is described by the Gaussian Unitary Ensemble-corners process.

MEAN STAGGERED POLARIZATION FOR THE HIGHER SPIN ANALOG OF THE 6-VERTEX MODEL

1992 ◽  
Vol 07 (supp01a) ◽  
pp. 151-163 ◽  
Author(s):  
ETSURO DATE ◽  
MICHIO JIMBO ◽  
KEI MIKI ◽  
MASATO OKADO
Keyword(s):  
Vertex Model ◽  
Vertex Models ◽  
Higher Spin ◽  
The Mean ◽  
Spin Representations

We compute the mean staggered polarization of the vertex models corresponding to higher spin representations of [Formula: see text]. This generalizes a result of Baxter for spin 1/2.

CORRELATION FUNCTIONS IN QUANTUM SPIN CHAINS AND VERTEX MODELS

2001 ◽  
Vol 16 (11) ◽  
pp. 1875-1887
Author(s):  
VIERI MASTROPIETRO
Keyword(s):  
Correlation Functions ◽  
Spin Chain ◽  
Nearest Neighbor ◽  
Quantum Spin ◽  
Spin Chains ◽  
Vertex Model ◽  
Quantum Spin Chains ◽  
Neighbor Interaction ◽  
Vertex Models

Some correlation functions of critical models, like the anisotropic spin chain with nearest and next-to-nearest neighbor interaction, or the eight vertex model, are computed as a corollary of the study of the XYZ model in [2].

Solution of inverse coefficient problem for fractional anomalous diffusion equation

2012 ◽  
Vol 9 (2) ◽  
pp. 65-70
Author(s):  
E.V. Karachurina ◽  
S.Yu. Lukashchuk
Keyword(s):  
Anomalous Diffusion ◽  
Fractional Derivatives ◽  
Descent Method ◽  
Extremum Problem ◽  
Steepest Descent Method ◽  
Coefficient Problem ◽  
Caputo Fractional Derivatives ◽  
Inverse Coefficient Problem ◽  
Residual Functional ◽  
Inverse Coefficient

An inverse coefficient problem is considered for time-fractional anomalous diffusion equations with the Riemann-Liouville and Caputo fractional derivatives. A numerical algorithm is proposed for identification of anomalous diffusivity which is considered as a function of concentration. The algorithm is based on transformation of inverse coefficient problem to extremum problem for the residual functional. The steepest descent method is used for numerical solving of this extremum problem. Necessary expressions for calculating gradient of residual functional are presented. The efficiency of the proposed algorithm is illustrated by several test examples.

scholarly journals Improved Immune Algorithm Combined with Steepest Descent Method for Optimal Design of IPMSM for FCEV Traction Motor

Energies ◽  
2021 ◽  
Vol 14 (13) ◽  
pp. 3904
Author(s):  
Ji-Chang Son ◽  
Myung-Ki Baek ◽  
Sang-Hun Park ◽  
Dong-Kuk Lim
Keyword(s):  
Optimal Design ◽  
Permanent Magnet Synchronous Motor ◽  
Torque Ripple ◽  
Descent Method ◽  
Immune Algorithm ◽  
Electric Machines ◽  
Steepest Descent Method ◽  
Superior Performance ◽  
Element Analysis ◽  
Traction Motor

In this paper, an improved immune algorithm (IIA) was proposed for the torque ripple reduction optimal design of an interior permanent magnet synchronous motor (IPMSM) for a fuel cell electric vehicle (FCEV) traction motor. When designing electric machines, both global and local solutions of optimal designs are required as design result should be compared in various aspects, including torque, torque ripple, and cogging torque. To lessen the computational burden of optimization using finite element analysis, the IIA proposes a method to efficiently adjust the generation of additional samples. The superior performance of the IIA was verified through the comparison of optimization results with conventional optimization methods in three mathematical test functions. The optimal design of an IPMSM using the IIA was conducted to verify the applicability in the design of practical electric machines.

Controlling Chaos by Hybrid System Based on FREN and Sliding Mode Control

2005 ◽  
Vol 128 (2) ◽  
pp. 352-358 ◽  
Author(s):  
C. Treesatayapun ◽  
S. Uatrongjit
Keyword(s):  
Sliding Mode ◽  
Adaptive Controller ◽  
Descent Method ◽  
Fuzzy Rules ◽  
System Stability ◽  
Steepest Descent Method ◽  
Upper And Lower Bounds ◽  
Adaptation Algorithm ◽  
Control Effort ◽  
Fine Tune

This paper presents a direct adaptive controller for chaotic systems. The proposed adaptive controller is constructed using the network called fuzzy rules emulated network (FREN). FREN’s structure is based on human knowledge in the form of fuzzy rules. Parameter adaptation algorithm based on the steepest descent method is presented to fine tune the controller’s performance. To improve the system stability, the modified sliding mode algorithm is applied to estimate the upper and lower bounds of the control effort. The suitable control effort is generated by FREN and kept within these bounds. Some computer simulations of using the controller to control the Hénon map have been performed to demonstrate the performance of the proposed controller.

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