Lattice gas simulations of two-dimensional liquid foams

Liquid foam is a dense random packing of gas bubbles in a small amount of immiscible liquid containing surfactants. The liquid within the Plateau borders, although small in volume, causes considerable difficulties to investigations of the physical properties of foams, and the situation becomes even more complicated if the flow of the liquid through the foam is considered too. Here we propose a fresh approach to tackling these issues by introducing a discrete two-dimensional hybrid lattice gas model of liquid foams. While lattice gas models have been used to model two-phase liquids in the past, their application to the study of liquid foams is novel and proves promising. We represent bubble surfaces by a finite number of nodes, and model the surrounding liquid as a lattice gas (with a finite number of liquid particles). The gas in the bubbles is treated as an ideal gas at constant temperature. The model is tested by choosing an arbitrarily shaped bubble that evolves into a circular shape in agreement with Laplaces law. The model is then employed to simulate periodic ordered and disordered dry and wet foams. Since our model is specifically designed to handle wet foams up to a critical liquid fraction of 0.16 (void fraction of random packing of disks), we are able to compute the variation in coordination number (average number of neighbours of a bubble) over the whole range of liquid fractions, and we find it to be a linear function of the shear modulus.This paper was presented at the first Annual European Rheology Conference (AERC) held in Guimarães, Portugal, 11–13 September 2003.     

Development and optimisation of a novel genetic algorithm for studying model protein folding

Determination of the native state of a protein from its amino acid sequence is the goal of protein folding simulations, with potential applications in gene therapy and drug design. Location of the global minimum structure for a given sequence, however, is a difficult optimisation problem. In this paper, we describe the development and application of a genetic algorithm (GA) to find the lowest-energy conformations for the 2D HP lattice bead protein model. Optimisation of the parameters of our standard GA program reveals that the GA is most successful (at finding the lowest-energy conformations) for high rates of mating and mutation and relatively high elitism. We have also introduced a number of new genetic operators: a duplicate predator—which maintains population diversity by eliminating duplicate structures; brood selection—where two parent structures undergo crossover and give rise to a brood of (not just two) offspring; and a Monte Carlo based local search algorithm—to explore the neighbourhood of all members of the population. It is shown that these operators lead to significant improvements in the success and efficiency of the GA, both compared with our standard GA and with previously published GA studies for benchmark HP sequences with up to 50 beads.     

Reduction of spin glasses applied to the Migdal-Kadanoff hierarchical lattice

A reduction procedure to obtain ground states of spin glasses on sparse graphs is developed and tested on the hierarchical lattice associated with the Migdal-Kadanoff approximation for low-dimensional lattices. While more generally applicable, these rules here lead to a complete reduction of the lattice. The stiffness exponent governing the scaling of the defect energy E with system size L, (E) ~L ^y, is obtained as y ₃ = 0.25546(3) by reducing the equivalent of lattices up to L = 2¹⁰⁰ in d = 3, and as y ₄ = 0.76382(4) for up to L = 2³⁵ in d = 4. The reduction rules allow the exact determination of the ground state energy, entropy, and also provide an approximation to the overlap distribution. With these methods, some well-know and some new features of diluted hierarchical lattices are calculated.     

Efficient Hopfield pattern recognition on a scale-free neural network

Neural networks are supposed to recognise blurred images (or patterns) of N pixels (bits) each. Application of the network to an initial blurred version of one of P pre-assigned patterns should converge to the correct pattern. In the “standard" Hopfield model, the N “neurons” are connected to each other via N² bonds which contain the information on the stored patterns. Thus computer time and memory in general grow with N². The Hebb rule assigns synaptic coupling strengths proportional to the overlap of the stored patterns at the two coupled neurons. Here we simulate the Hopfield model on the Barabási-Albert scale-free network, in which each newly added neuron is connected to only m other neurons, and at the end the number of neurons with q neighbours decays as 1/q ³. Although the quality of retrieval decreases for small m, we find good associative memory for 1 ≪ m ≪ N. Hence, these networks gain a factor N/m ≫ 1 in the computer memory and time. Received 12 January 2003 Published online 11 April 2003 RID="a" ID="a"e-mail: stauffer@thp.uni-koeln.de     

Nature of the Peierls- to Mott-insulator transition in 1D

In order to clarify the physics of the crossover from a Peierls band insulator to a correlated Mott-Hubbard insulator, we analyze ground-state and spectral properties of the one-dimensional half-filled Holstein-Hubbard model using quasi-exact numerical techniques. In the adiabatic limit the transition is connected to the band to Mott insulator transition of the ionic Hubbard model. Depending on the strengths of the electron-phonon coupling and the Hubbard interaction the transition is either first order or evolves continuously across a narrow intermediate phase with finite spin, charge, and optical excitation gaps. Received 7 July 2002 / Received in final form 21 October 2002 Published online 27 January 2003 RID="a" ID="a"e-mail: holger.fehske@physik.uni-greifswald.de     

Persistent currents in a lattice correlated electron ring with a magnetic impurity

The behavior of charge and spin persistent currents in an integrable lattice ring of strongly correlated electrons with a magnetic impurity is exactly studied. Our results manifest that the oscillations of charge and spin persistent currents are similar to the ones, earlier obtained for integrable continuum models with a magnetic impurity. The difference is due to two (instead of one) Fermi velocities of low-lying excitations. The form of oscillations in the ground state is “saw-tooth”-like, generic for any multi-particle coherent one-dimensional models. The integrable magnetic impurity introduces net charge and spin chiralities in the generic integrable lattice system, which determine the initial phase shifts of charge and spin persistent currents. We show that the magnitude of the charge persistent current in the generic Kondo situation does not depend on the parameters of the magnetic impurity, unlike the (magneto)resistivity of transport currents. Received 30 January 2003 / Received in final form 12 March 2003 Published online 11 April 2003 RID="a" ID="a"e-mail: zvyagin@fy.chalmers.se     

Infrared gluon and ghost propagators from lattice QCD

We report on the infrared limit of the quenched lattice Landau gauge gluon and ghost propagators as well as the strong-coupling constant computed from large asymmetric lattices. The infrared lattice propagators are compared with the pure power law solutions from Dyson-Schwinger equations (DSE). For the gluon propagator, the lattice data is compatible with the DSE solution. The preferred measured gluon exponent being ∼0.52, favouring a vanishing propagator at zero momentum. The lattice ghost propagator shows finite-volume effects and, for the volumes considered, the propagator does not follow a pure power law. Furthermore, the strong-coupling constant is computed and its infrared behaviour investigated.     

格结构在晶体梳状滤波器设计中的应用

利用数字信号处理中的格滤波器理论,研究了晶体梳状滤波器的设计方法.当传输函数满足对称和功率互补时,分析指出滤波器的阶数是奇数,N阶滤波器只需要(N+1)/2个波片,且所用波片的厚度比为1∶2∶2…2或2∶2…2∶1；提出了对半带滤波器传输函数作谱分解得到光梳状滤波器传输函数的方法.在此基础上总结出根据应用要求设计晶体梳状滤波器传输函数和结构参量的方法,通过设计一个7阶滤波器,表明提出的方法设计过程简单,且设计结果符合梳状滤波特征.     

Understanding nucleon structure using lattice simulations

This review focuses on the discussion of three key results of nucleon structure calculations on the lattice. These three results are the quark contribution to the nucleon spin, J_q, the nucleon-Δ transition form factors, and the nucleon axial coupling, g_A. The importance for phenomenology and experiment is discussed and the requirements for future simulations are pointed out.     

表面杂质对NO+CO/Pt(100)反应体系振荡动力学的影响

提出了一个格气模型， 探讨催化表面的惰性杂质对NO+CO/Pt(100)反应体系振荡动力学行为的影响．研究发现表面杂质较少时，反应进程中表面重构能够形成相连通的1*1相和持续的振荡行为．当表面杂质不断增加时，反应进程中1*1相只能形成许多孤立的畴，从而在1*1相形成的随机的局域振荡的空间关联被削弱，因而体系全局的持续振荡行为演变为衰减振荡行为．当表面吸附的CO和NO的扩散速率增加时，局域振荡的空间协同又得到加强，体系又呈现出持续振荡行为．