Bond percolation for homogeneous two-dimensional lattices

Bond percolation is studied for the three homogeneous two-dimensional lattices: square lattice (SL), triangular lattice (TL) and honeycomb lattice (HL). An expanding cell technique is used to obtain percolation thresholds and other relevant information for different cell sizes. We extend the analysis as to include slightly asymmetric cells in addition to the usual symmetric cells to get more points in the scaling analysis. Exact percolation functions are obtained for each size. Then, the percolation threshold is obtained by means of two complementary methods: one based on the well-known renormalization techniques and the other one introduced here which is based upon determining the inflection point of the percolation curves. A comparison of the results obtained by these two methods is performed. The study includes iterations to extrapolate numerical results towards the thermodynamic limit. Critical exponents ν, β and γ are obtained. Values are compared with numerical results and expected theoretical estimations; present results show agreement and even improvement (in the case of γ) with respect to some numeric values available in the literature. Comparison tables are provided.     

Percolation of dimers on square lattices

A theoretical approach, based on exact calculations of configurations on finite rectangular cells, is applied to study the percolation of homonuclear dimers on square lattices. An efficient algorithm allows us to calculate the detailed structure of the configuration space for M=_Lx×_Ly$M=L_x\times L_y$ cells, with M$M$ varying from 16 to 36. The percolation process has been monitored by following the percolation function, defined as the ratio between the number of percolating configurations and the total number of available configurations for a given cell size and concentration of occupied sites. The percolation threshold has been calculated by means of two complementary methods: one based on well-known renormalization techniques and the other based on determining the inflection point of the percolation function curves. A comparison of the results obtained by these two methods has been performed. The study includes the use of finite-size scaling theory to extrapolate numerical results towards the thermodynamic limit. The effect of jamming due to dimers is also established. Finally, the critical exponents ν$\nu$, β$\beta$ and γ$\gamma$ have been obtained and values compared with numerical results and expected theoretical estimations. The present results show agreement and even improvement (in the case of γ$\gamma$) with respect to some numeric values available in the literature.     

Modeling of femtosecond laser damage threshold on the two-layer metal films

The heating processes of the single-layer gold thin film and the two-layer film assembly of gold padded with other metal (silver, copper and nickel) irradiated by femtosecond laser pulse are studied by the two-temperature model. It is found that the substrate metal can change energy transport, which is corresponding to the temperature changing process, and the thermal equilibrium time. Compared with the single-layer gold film at the same laser fluence, the two-layer film structure can change the damage threshold of the gold surface. Our results indicate that we can maximize the damage threshold of the gold film surface by altering the thickness ratio of the gold layer and the substrate layer in the two-layer film assembly.     

Percolation Phenomena in Low and High Density Systems

We consider the 2D quenched–disordered q–state Potts ferromagnets and show that in the translation invariant measure, averaged over the disorder, at self–dual points any amalgamation of q?1 species will fail to percolate despite an overall (high) density of 1?q ^?1. Further, in the dilute bond version of these systems, if the system is just above threshold, then throughout the low temperature phase there is percolation of a single species despite a correspondingly small density. Finally, we demonstrate both phenomena in a single model by considering a “perturbation” of the dilute model that has a self–dual point. We also demonstrate that these phenomena occur, by a similar mechanism, in a simple coloring model invented by O. Häggström.     

随机阈值冲击模型金属化膜脉冲电容器可靠性分析

基于惯性约束聚变强激光装置中金属化膜脉冲电容器自愈的失效机理,提出了更为适合的冲击模型金属化膜脉冲电容器可靠性评估方法。现有的加速退化试验中,失效阈值往往是事先确定的,但考虑可靠性产品个体差异及环境影响的不同,这是不合理的,针对此问题提出了基于随机阈值的冲击模型金属化膜脉冲电容器退化建模的方法。由于模型过于复杂,采用MCMC方法进行参数估计。最后通过对电容器的仿真实验,将随机阈值下的评估结果与固定阈值的情况相对比,说明了该模型和方法的合理性,并进一步分析了不同的阈值分布均值和方差对产品可靠性的影响。     

激光波长及脉宽对光学材料抗损伤性能的影响

 基于能带理论,利用激光与光学材料相互作用的理论模型,研究了激光辐照下材料导带自由电子数密度的变化,讨论了材料损伤阈值与激光波长、脉冲宽度、材料禁带宽度之间的关系,数值分析了激光波长和脉冲宽度对损伤阈值的影响。结果表明:当脉宽小于1 ps时,材料损伤阈值随脉宽增大而减小;当脉宽大于1 ps时,材料损伤阈值随脉宽增大而增大;激光波长为10 fs~10 ns,损伤阈值随着波长的减小而减小。     

Two-parameter analysis of the scaling behavior at the onset of chaos: tricritical and pseudo-tricritical points

We discuss the so-called tricritical points at the border of the period-doubling transition to chaos and examine to what extent the associated universality applies to 2D dissipative maps. As a concrete example, the Ikeda map is studied together with its 1D analog. For the approximate 1D map, the tricritical points appear as the terminal points of Feigenbaum's critical curves in the parameter plane. For the 2D map the same type of critical behavior does not occur in a rigorous sense. It may be observed as a kind of intermediate asymptotics, however, when one considers a finite number of period doublings. We refer to the associated points in the parameter plane as pseudo-tricritical. For the Ikeda map, we present estimates of the number of period doublings, after which the departure from the tricritical universality becomes essential.     

光学膜层激光损伤阈值均匀性的实验研究

 镀制了多种氧化物介质薄膜。用R-on-1方法测定了膜层的激光损伤阈值。引入数据处理方法，对测试数据进行分析。结果表明，基片清洗后，若放置一段时间再镀膜，则会影响到镀膜后膜层损伤阈值的均匀性，但对损伤阈值自身大小没有影响。测试激光参数对阈值均匀性也有一定影响。     

透红外含碲氟铝基玻璃的激光损伤阈值

 在氟铝酸盐玻璃组分中加入适量声子能量低的重金属氧化物TeO ₂，得到一种新的氧氟化物玻璃。该材料具有良好的成玻璃性能，适合制作大尺寸红外窗口镜。研究了TeO2含量对玻璃特征温度、阿贝数和红外透过性能的影响。同时测试了这种玻璃的抗DF激光能力，结果表明： TeO ₂含量为15%的玻璃，DF激光破坏阈值达14.95 kＷ·cm^-2。分析显示，由于玻璃基质的多声子吸收，对激光能量的吸收而引起的热冲击是导致玻璃破坏的主要原因。进一步降低玻璃中水分，可以提高玻璃抗激光破坏性能。     

高反射膜激光零几率损伤阈值的实验研究

 在确定光学薄膜激光损伤阈值的实验数据处理过程中，发现一些样品的数据点分布偏离直线型式。对此，用国际标准规定的零几率来确定损伤阈值的同时，对测试数据点采用了不同的非直线拟合，也得到一个零几率损伤阈值。比较两者差异，并与实验测试结果对照，发现这些样品采用非直线拟合得出的零几率损伤阈值与实际情况更接近一些。     

Critical behavior in a model of correlated percolation

We study the critical behavior of certain two-parameter families of correlated percolation models related to the Ising model on the triangular and square lattices, respectively. These percolation models can be considered as interpolating between the percolation model given by the + and – clusters and the Fortuin-Kasteleyn correlated percolation model associated to the Ising model. We find numerically on both lattices a two-dimensional critical region in which the expected cluster size diverges, yet there is no percolation.     

熔石英亚表面划痕激光诱导损伤阈值实验研究

 用原子力显微镜和光学显微镜观测酸蚀后熔石英亚表面划痕,并根据形貌特征将其分为Boussinesq-point-force crack(BPFC)、Hertzian-conical scratch(HCS)和Plastic indent(PI)三类,测试了各类划痕的损伤阈值,讨论了激光损伤机制。结果表明锐度较大的BPFC损伤阈值不超过2.0 J/cm<>2;深度小于1 μm的 HCS阈值可达2.6 J/cm²;形变较大的PI阈值至2.8 J/cm2,形变较小的PI的激光损伤阈值与无缺陷材料相当。BPFC 和深度超过1 μm的HCS是导致熔石英损伤阈值低的主要因素。     

Design of optical system for flattop beam shaper based on the measurement of laser induced damage threshold of thin films

To solve the problem of large error when measure the laser induced damage threshold of thin films in the case of Gaussian distribution beam induced damage thin films, optical system of flattop beam shaper which is capable of redistributing a beam with a Gaussian profile to a flattop profile was designed with optical design software ZEMAX. The Fermi-Dirac beam model was chosen as the distribution function of the flattop beam in this paper, the mapping formula of the input Gaussian beam and the output flattop beam was establish, the surface coefficient of aspheric was given. The energy conversion efficiency was 95.33% and the flattened degree was 93.66% in this design. The accuracy of measurement has been improved when measure the laser induced damage threshold of thin films by the flattop beam.     

The phase transition in the fully frustrated XY model as a percolation problem

The fully frustrated planar rotator and fully frustrated XY models in two dimensions have two phase transitions: one of the Berezinskii–Kosterlitz–Thouless type and other in the Ising universality class. We use Monte Carlo simulation to study both models. We fix our attention in the Ising-like transition, which we show can be understood as a percolation transition. We obtain the critical temperature as well as the critical exponents of the mean cluster size, γ, and Fisher's exponent τ. The critical temperature agree very well with other calculations. We found that the critical exponents are smaller than in the pure two-dimensional percolation case. We interpret this as due to the long-range interaction between vortex and antivortex.     

Percolation and the Potts model

The Kasteleyn-Fortuin formulation of bond percolation as a lattice statistical model is rederived using an alternate approach. It is shown that the quantities of interest arising in the percolation problem, including the critical exponents, can be obtained from the solution of the Potts model. We also establish the Griffith inequality for critical exponents for the bond percolation problem.Work supported in part by NSF Grant No. D MR 76-20643.     

Calculation of critical properties for the anisotropic two-layer Ising model on the Kagome lattice: Cellular automata approach

The critical point (K_c) of the two-layer Ising model on the Kagome lattice has been calculated with a high precision, using the probabilistic cellular automata with the Glauber algorithm. The critical point is calculated for different values of the inter- and intra-layer couplings (K₁≠K₂≠K₃≠K_z), where K₁, K₂ and K₃ are the nearest-neighbor interactions within each layer in the 1, 2 and 3 directions, respectively, and K_z is the intralayer coupling. A general ansatz equation for the critical point is given as a function of the inter- and intra-layer interactions, ξ=K₃/K₁,σ=K₂/K₁ and ω=K_z/K₁ for the one- and two-layer Ising models on the Kagome lattice.     

A fluorescence study on the critical exponents for the linear polymerization of butyl-methacrylate

The steady-state fluorescence (SSF) technique was used to study the sol-gel transition for the linear bulk polymerization of butyl methacrylate (BMA), carried out above the glass transition temperature of polybutylmethacrylate (PBMA) (T _g?=?20°C). Pyrene (P_y) was used as the fluorescence probe. The increase in P_y intensity was monitored during free radical polymerization of BMA by using SSF technique. Changes in the viscosity of the pregel solutions due to gel formation dramatically enhance the fluorescent yield of aromatic molecules. This effect is used to monitor the sol-gel transition of BMA, as a function of time, at various temperatures. The results are interpreted in the view of percolation theory. The gel fraction exponent β?=?0.39?±?0.02 agreed the best with the static percolation values for the linear bulk BMA polymerization carried out above T _g but weight average degree of polymerization exponent,?γ?deviated from the percolation results.     

随机阈值冲击模型金属化膜脉冲电容器可靠性分析

基于惯性约束聚变强激光装置中金属化膜脉冲电容器"自愈"的失效机理,提出了更为适合的冲击模型金属化膜脉冲电容器可靠性评估方法。现有的加速退化试验中,失效阈值往往是事先确定的,但考虑可靠性产品个体差异及环境影响的不同,这是不合理的,针对此问题提出了基于随机阈值的冲击模型金属化膜脉冲电容器退化建模的方法。由于模型过于复杂,采用MCMC方法进行参数估计。最后通过对电容器的仿真实验,将随机阈值下的评估结果与固定阈值的情况相对比,说明了该模型和方法的合理性,并进一步分析了不同的阈值分布均值和方差对产品可靠性的影响。     

Finite-size scaling properties of the damage distance and dynamical critical exponent for the Ising model

With the damage spreading method, scaling properties of the damage distance on the Ising model with heat bath dynamics are studied numerically. With the parallel flipping scheme, the scaling curves fall on two curves, which depend on the odd or even lattice sizes. The both scaling curves give the consistent dynamical exponent as z = 2.16±0.04 for d = 2 and z = 2.09±0.05 for d = 3, respectively. By shifting one of them, two curves overlap each other perfectly. Meanwhile, all the scaling curves obtained by single-spin flipping processes (with different odd or even lattice sizes) fall on a single curve, from which the consistent dynamical critical exponent with the parallel scheme is obtained z = 2.18±0.02 for d = 2 and z = 2.08±0.04 for d = 3.