Statistical models of hadron production—simple models for complicated processes

Thermal statistical models are a simple and effective tool to describe particle production in high energy heavy ion collision. It is shown that for higher moments finite volume corrections become important observable quantities. They make it possible to differentiate between different statistical ensembles even in the thermodynamic limit. The text was submitted by the author in English.     

Analytic models for organic field-effect transistors based on exponential and power mobility models

The fundamental I–V formula of an organic field effect transistor(OFET) is improved to overcome the divergence of the integrand, so it is very convenient for both numerical calculations and analytic derivations. The analytic I–V formulae are derived based on the exponential mobility model and power-function mobility model, respectively, and the derived analytic formulae are applied to three OFET devices. The results calculated from the reformulated analytic I–V formulae taking in exponential and...     

A simple geometric representative for μ of a point

ForSU(2) (orSO(3)) Donaldson theory on a 4-manifoldX, we construct a simple geometric representative for of a point. Letp be a generic point inX. Then the set {[A]F _A ^– (p) is reducible}, with coefficient –1/4 and appropriate orientation, is our desired geometric representative. The construction is an exercise in real algebraic geometry in the style of Ehresmann and Pontryagin.This work is partially supported by an NSF Mathematical Sciences Postdoctoral Fellowship and Texas Advanced Research Project grant ARP-037.     

Correlation inequalities for two-component hypercubicϕ 4 models

A collection of new and already known correlation inequalities is found for a family of two-component hypercubic ⁴ models, using techniques of duplicated variables, rotated correlation inequalities, and random walk representation. Among the interesting new inequalities are: rotated very special Dunlop-Newman inequality _1,x ² ; _1,z ² + _2g ² 0, rotated Griffiths I inequality _{1,x 1,y} ; _1z ² 0, and anti-Lebowitz inequalityu ₄ ¹¹¹¹ >-0.     

BRST symmetry for Regge–Teitelboim-based minisuperspace models

The Einstein–Hilbert action in the context of higher derivative theories is considered for finding their BRST symmetries. Being a constraint system, the model is transformed in the minisuperspace language with the FRLW background and the gauge symmetries are explored. Exploiting the first order formalism developed by Banerjee et al. the diffeomorphism symmetry is extracted. From the general form of the gauge transformations of the field, the analogous BRST transformations are calculated. The effective Lagrangian is constructed by considering two gauge-fixing conditions. Further, the BRST (conserved) charge is computed, which plays an important role in defining the physical states from the total Hilbert space of states. The finite field-dependent BRST formulation is also studied in this context where the Jacobian for the functional measure is illustrated specifically.     

Separation of variables for integrable spin–boson models

We formulate the functional Bethe ansatz for bosonic (infinite dimensional) representations of the Yang–Baxter algebra. The main deviation from the standard approach consists in a half infinite Sklyanin lattice made of the eigenvalues of the operator zeros of the Bethe annihilation operator. By a separation of variables, functional TQ-equations are obtained for this half infinite lattice. They provide valuable information about the spectrum of a given Hamiltonian model. We apply this procedure to integrable spin–boson models subject to both twisted and open boundary conditions. In the case of general twisted and certain open boundary conditions polynomial solutions to these TQ-equations are found and we compute the spectrum of both the full transfer matrix and its quasi-classical limit. For generic open boundaries we present a two-parameter family of Bethe equations, derived from TQ-equations that are compatible with polynomial solutions for Q. A connection of these parameters to the boundary fields is still missing.     

Perturbation calculation for the eight-vertex model around the Ising point for T → Tc−

The dispersion expansion for the two-point electric correlation function in the eight-vertex model is calculated to first order in the four-spin coupling in the scaling limit. The dispersion expansion for the spin-spin-energy density correlation function in the Ising model is used. The result is not a simple extension of the Fredholm structure in the Ising model.     

Existence of a homoclinic point for the Hénon map

We prove analytically that for the Hénon map of the plane into itself (s, t)(t+1–1.4a ², 0.3s), there exists a transversal homoclinic point.     

Pure point spectrum for discrete almost periodic Schrödinger operators

The finite difference Schrödinger operator on ? ^m is considered $$Hu_j = \left( {\sum\limits_{v = 1}^m { D_v^2 } } \right)u_j + \frac{1}{\varepsilon }q_j u_j ,u \in \ell ^2 (\mathbb{Z}^m ),$$ where \(\sum\limits_{v = 1}^m { D_v^2 } \) is the difference Laplacian inm dimensions. For ? sufficiently small almost periodic potentialsq _j are constructed such that the operatorH has only pure point spectrum. The method is an inverse spectral procedure, which is a modification of the Kolmogorov-Arnol'd-Moser technique.     

Coupling of two-dimensional atomistic and continuum models for dynamic crack

A concurrent multiscale method of coupling atomistic and continuum models is presented in the two-dimensional system. The atomistic region is governed by molecular dynamics while the continuum region is represented by construct- ing the mass and stiffness matrix dependent on the coarsening of the grids, which ensures that they merge seamlessly. The low-pass phonon filter embedded in the handshaking region is utilized to effectively eliminate the spurious reflection of high-frequency phonons, while keeping the low-frequency phonons transparent. These schemes are demonstrated by numerically calculating the reflection and transmission coefficient, and by the further application of dynamic crack propa- gation subjected to mode-I tensile loading.     

Constructing refined null models for statistical analysis of signed networks

The establishment of effective null models can provide reference networks to accurately describe statistical properties of real-life signed networks.At present,two classical null models of signed networks(i.e.,sign and full-edge randomized models)shuffle both positive and negative topologies at the same time,so it is difficult to distinguish the effect on network topology of positive edges,negative edges,and the correlation between them.In this study,we construct three re-fined edge-randomized null models by only randomizing link relationships without changing positive and negative degree distributions.The results of nontrivial statistical indicators of signed networks,such as average degree connectivity and clustering coefficient,show that the position of positive edges has a stronger effect on positive-edge topology,while the signs of negative edges have a greater influence on negative-edge topology.For some specific statistics(e.g.,embeddedness),the results indicate that the proposed null models can more accurately describe real-life networks compared with the two existing ones,which can be selected to facilitate a better understanding of complex structures,functions,and dynamical behaviors on signed networks.     

Target models for range performance prediction of infrared imaging system

This paper describes a commonly used target model and two improved models for range performance prediction of infrared imaging system in an original explicit way.We conclude the basic assumptions of each model,define the temperature difference,and give the mathematical equation to calculate the measurement of resolvable target details.The flow path for using the measurement to evaluate the range performance is briefly introduced.The features of these models are compared.     

Exotic nuclei – a challenge for nuclear mean field models

We present a brief overview of the interplay between exotic nuclei and the development of nuclear mean field models. This is exemplified with four test cases addressing the topics of shape coexistence, isotope shifts, long isotopic chains, and superheavy elements. This revised version was published online in August 2006 with corrections to the Cover Date.     

Perturbation calculations for the eight-vertex model around the Ising point for T → Tc+. II

The dispersion expansion for the two-point electric correlation function in the eight-vertex model is calculated to first order in the four-spin coupling in the scaling limit in the high-temperature regime. It is found that there is a close relation between the T_c⁻ and T_c⁺ spin-spin-energy density correlation function in the Ising model. This is used to simplify tremendously the calculation in the T_c⁺ case; the result can be obtained from the T_c⁻ result by deleting two variables in the expansion.     

Prandtl–Ishlinskii hysteresis models for complex time dependent hysteresis nonlinearities

We introduce a new class of time dependent hysteresis models by combining the time dependent Prandtl–Ishlinskii model with functional nonlinearities. This combination improves the capability of the time dependent Prandtl–Ishlinskii model to characterize a class of complex time dependent hysteresis nonlinearities in smart actuators. The analytical inversion for the proposed time dependent hysteresis model is also presented in order to extend the inversion algorithm of the inverse time dependent Prandtl–Ishlinskii model for a class of complex time dependent hysteresis nonlinearities.     

A systematic study on matrix models for Chern–Simons-matter theories

We investigate the planar solution of matrix models derived from various Chern–Simons-matter theories compatible with the planar limit. The saddle-point equations for most of such theories can be solved in a systematic way. A relation to Fuchsian systems play an important role in obtaining the planar resolvents. For those theories, the eigenvalue distribution is found to be confined in a bounded region even when the ?t Hooft couplings become large. As a result, the vevs of Wilson loops are bounded in the large ?t Hooft coupling limit. This implies that many of Chern–Simons-matter theories have quite different properties from ABJM theory. If the gauge group is of the form U_(N1)k1×U_(N2)k2$\mathrm{U}{(N_1)}_{k_1}\times \mathrm{U}{(N_2)}_{k_2}$, then the resolvents can be obtained in a more explicit form than in the general cases.