Exact partition functions and correlation functions of multiple Hamiltonian walks on the Manhattan lattice

This is a general and exact study of multiple Hamiltonian walks (HAW) filling the two-dimensional (2D) Manhattan lattice. We generalize the original exact solution for a single HAW by Kasteleyn to a system ofmultiple closed walks, aimed at modeling a polymer melt. In 2D, two basic nonequivalent topological situations are distinguished. (1) the Hamiltonian loops are allrooted andcontractible to a point:adjacent one to another, and, on a torus,homotopic to zero. (2) the loops can encircle one another and, on a torus, canwind around it. Forcase 1, the grand canonical partition function and multiple correlation functions are calculated exactly as those of multiple rooted spanningtrees or of a massive 2Dfree field, critical at zero mass (zero fugacity). The conformally invariant continuum limit on a Manhattantorus is studied in detail. The melt entropy is calculated exactly. We also consider the relevant effect of free boundary conditions. The number of single HAWs on Manhattan lattices with other perimeter shapes (rectangular, Kagomé, triangular, and arbitrary) is studied and related to the spectral theory of the Dirichlet Laplacian. This allows the calculation of exact shape-dependent configuration exponents y. An exact surface critical exponent is obtained. Forcase 2, nested and winding Hamiltonian circuits are allowed. An exact equivalence to thecritical Q-state Potts model exists, whereQ ^1/2 is the walk fugacity. The Hamiltonian system is then always critical (forQ<-4). The exact critical exponents, in infinite numbers, are universal and identical to those of theO(n=Q ^1/2) model in its low-temperature phase, i.e. are those of dense polymers. The exact critical partition functions on the torus are given from conformai invariance theory. These models 1 and 2 yield the two first exactly solved models of polymer melts.     

LARGE MAGNETIC ENTROPY CHANGE NEAR CHARGE-ORDERED TRANSITION TEMPERATURE IN PEROVSKITE-TYPE MANGANITE

The magnetocaloric effect in polycrystalline of Pr_1-xSr_xMnO₃ (x=0.33, 0.43, 0.50) has been investigated. A large magnetic entropy change (7.1J/kgK) was discovered in Pr_0.5Sr_0.5MnO₃ under a low magnetic field of 1T at charge-ordered state transition temperature (161K). The physical mechanism is related to a drastic magnetization change at a temperature where the field-induced magnetic, electron and structural phase transitions occur (from the antiferromagnetic charge-ordered state to the ferromagnetic charge-disordered state).     

La_(0.8-x)Ca_(0.2)MnO_3纳米颗粒的居里温度与磁热效应

采用溶胶 凝胶法制备了系列La0 .8-xCa0 .2 MnO3 多晶样品 ,用X射线衍射分析确定了样品的钙钛矿结构 ,用透射电子显微镜观察了样品的形貌及粒径分布情况 ,用PAR15 5型振动样品磁强计测量了样品的磁性随外场和温度的变化 ,确定样品的居里温度并计算了各样品的磁熵变 .磁测量及计算结果表明制备的各样品的居里温度在180— 2 6 0K的范围内且随焙烧温度和La3 离子空位浓度的不同而变化 ,不同温度焙烧的样品均有较大的磁熵变值 ,其中 110 0℃焙烧的La0 77Ca0 .2 MnO3,多晶样品在 2 40 5K ,H =1 0T的外场下的磁熵变达 3 76J/kg·K ,对实验结果做了定性的分析 .该材料具有较高的居里温度和较大的磁熵变 ,所需外场强度适中 ,电阻率高 ,性能稳定 ,适合做高温磁制冷材料 .     

35MeV/u~(40)Ar ~(197)Au中的熵产生

根据量子统计模型 (QSM )的计算分析 ,找到了一个提取核反应过程中熵产生的新的可观测量 .核反应过程中约化d的产额d/ (d t 3 He 4 He)和熵有单调的函数关系 ,并且和体系的碎裂密度 (ρ/ ρ0 )及体系的N/Z都无关 ,可以作为提取核反应过程中熵产生的一个观测量 .和目前已经有的其他方法相比 ,约化d产额这一提取熵方法可以用于较低能量的重离子核反应中 ,并且数据处理分析简单 .对于 35MeV/u4 0 Ar 197Au的核反应过程所提取的熵和利用约化带电粒子多重性提取的熵结果一致 .结合后角类靶热核发射体系实验提取的同位素核温度为 4 7±1 2MeV及S/A =2 5± 0 5 ,根据熵和核温度的关联关系 ,可以确定其Breakup密度接近但小于 0 1(ρ/ ρ0 )     

On the convergence of a class of derivative-free minimization algorithms

A convergence analysis is presented for a general class of derivative-free algorithms for minimizing a functionf(x) for which the analytic form of the gradient and the Hessian is impractical to obtain. The class of algorithms accepts finite-difference approximation to the gradient, with stepsizes chosen in such a way that the length of the stepsize must meet two conditions involving the previous stepsize and the distance from the last estimate of the solution to the current estimate. The algorithms also maintain an approximation to the second-derivative matrix and require that the change inx made at each iteration be subject to a bound that is also revised automatically. The convergence theorems have the features that the starting pointx ¹ need not be close to the true solution andf(x) need not be convex. Furthermore, despite the fact that the second-derivative approximation may not converge to the true Hessian at the solution, the rate of convergence is still Q-superlinear. The theorry is also shown to be applicable to a modification of Powell's dog-leg algorithm.     

L1-optimal estimates for a regression type function in R

Let X₁, X₂, …, X_n be random vectors that take values in a compact set in R^d, d ≥ 1. Let Y₁, Y₂, …, Y_n be random variables (“the responses”) which conditionally on X₁ = x₁, …, X_n = x_n are independent with densities f(y | x_i, θ(x_i)), i = 1, …, n. Assuming that θ lives in a sup-norm compact space Θ_q,d of real valued functions, an optimal L₁-consistent estimator of θ is constructed via empirical measures. The rate of convergence of the estimator to the true parameter θ depends on Kolmogorov's entropy of Θ_q,d.     

Direct measurement of the magnetocaloric effect in La0.67Ca0.33MnO3

Polycrystalline perovskite La_0.67Ca_0.33MnO₃ was synthesized by a sol–gel method. Its adiabatic temperature change ΔT_ad induced by a magnetic field change was measured directly. At 268 K, near its Curie temperature T_C, ΔT_ad of La_0.67Ca_0.33MnO₃ induced by a magnetic field change of 2.02 T reaches 2.4 K. The latent heat Q and magnetic entropy change −ΔS_M induced by a magnetic field change were calculated from the temperature dependence of ΔT_ad and zero-field heat capacity C_p. The maximum values of Q and −ΔS_M in La_0.67Ca_0.33MnO₃ induced by a magnetic field change of 2.02 T are 1.85 J g⁻¹ and 6.9 J kg⁻¹ K⁻¹, respectively. The former is larger than the phase transition latent heat of heating or cooling, which is about 1.70 J g⁻¹.     

一般加速带电带磁的动态黑洞中标量场的熵

在一般加速带电带磁的动态黑洞中,化简Klein-Gordon场方程,利用乌龟坐标变换,得到在视界面附近的辐射温度.用薄膜brick-wall模型,选择适当的截断因子和薄膜厚度,得到在视界面附近薄膜上的熵,结果表明黑洞熵与视界面积成正比. 关键词： 黑洞 Hawking温度 薄膜brick-wall模型 熵     

小波双线性插值搜索算法及其在光学遥感图像中的应用

详细分析了在小波双线性插值中高频外推阈值门限与峰值信噪比的变化关系,提出了基于峰值信噪比最大的小波双线性插值搜索算法。提出的算法能够自动搜索到峰值信噪比最大的高频外推最佳阈值门限,实现了在不破坏光学遥感图像原始信息的情况下,提高了图像的空间分辨率,有利于对图像的细节信息进行观察分析。实验结果表明:该算法能够得到比双线性插值和全小波插值更高的峰值信噪比、熵值和更好的图像细节效果,是一种适合提高光学遥感图像分辨率的有效算法。     

图像局部熵用于小目标检测研究

分析了局部熵用于小目标检测时造成目标范围扩散等问题的原因,并提出了熵增长方法.该方法用于点目标检测可避免发生目标范围扩散现象.由于边缘纹理和点目标在熵增长处理过程中表现出截然相反的属性,故可避免边缘纹理对于小目标检测产生的严重干扰.该方法也可用于不受噪声干扰的边缘检测.针对相同信噪比目标在不同背景亮度中具有不同熵值和增长量的问题,提出用方差增长替代熵增长,使相同信噪比目标在不同背景亮度中表现出相同的增长量值,降低了后续目标分割的难度.试验表明,熵增长方法和方差增长方法能够有效检测1或2像素大小的点目标,并不受背景中边缘纹理的干扰.对算法的复杂度进行了分析,并提出采用双通道并行流水线方式实现工程化的设计思路.