We perform numerical simulations of the 2-d antiferromagnetic quantum Heisenberg model using an efficient cluster algorithm. Comparing the finite size and finite temperature effects of various quantities with recent results from chiral perturbation theory we are able to determine the low energy parameters of the system very precisely. We find e 0 = −0.6693(1)J/a 2 for the ground state energy density, M s = 0.3074(4)/a 2 for the staggered magnetization, hc = 1.68(1)Ja for the spin wave velocity and ρ s = 0.186(4)J for the spin stiffness. Our results agree with experimental data for the undoped precursor insulators of high-T c superconductors.

The occurrence of Winfree turbulence is currently regarded as one of the principal mechanisms underlying cardiac fibrillation. We develop a local stimulation method that suppresses Winfree turbulence in three-dimensional excitable media. We find that Winfree turbulence can be effectively suppressed by locally injecting periodic signals to only a very small subset (around some surface region) of total space sites. Our method for the first time demonstrates the effectiveness of local low-amplitude periodic excitations in suppressing turbulence in 3D excitable media and has fundamental improvements in efficiency, convenience, and turbulence suppression speed compared with previous strategies. Therefore, it has great potential for developing into a practical low-amplitude defibrillation approach.

Realistic neurons may hold complex anatomical structure, for example, autapse connection to some internuncial neurons, which this specific synapse can connect to its body via a close loop. Continuous exchanges of charged ions across the membrane can induce complex distribution fluctuation of intracellular and extracellular charged ions of cell, and a time-varying electromagnetic field is set to modulate the membrane potential of neuron. In this paper, an autapse-modulated neuron model is presented and the effect of electromagnetic induction is considered by using magnetic flux. Bifurcation analysis and sampled time series for membrane potentials are calculated to investigate the mode transition in electrical activities and the biological function of autapse connection is discussed. Furthermore, the Gaussian white noise and electromagnetic radiation are considered on the improved neuron model, it is found appropriate setting and selection for feedback gain and time delay in autapse can suppress the bursting in neuronal behaviors. It indicates the formation of autapse can enhance the self-adaption of neuron so that appropriate response to external forcing can be selected, this biological function is helpful for encoding and signal propagation of neurons. It can be useful for investigation about collective behaviors in neuronal networks exposed to electromagnetic radiation.

Cluster algorithms are developed for simulating quantum spin systems like the one-and two-dimensional Heisenberg ferro-and anti-ferromagnets. The corresponding two-and three-dimensional classical spin models with four-spin couplings are maped to blockspin models with two-blockspin interactions. Clusters of blockspins are updated collectively. The efficiency of the method is investigated in detail for one-dimensional spin chains. Then in most cases the new algorithms solve the problems of slowing down from which standard algorithms are suffering.Two-dimensional quantum spin systems are relevant for the description of the undoped anti-ferromagnetic precursor insulators of high-T c superconductors. Presumably understanding the physics of the superconductors requires an understanding of their precursor insulators. This already is a nontrivial problem, which most likely does not allow for a complete analytic solution. Therefore it is natural to use a numerical approach to compute the properties of these materials. At present different methods are used in numerical studies of quantum spin systems (for a recent review see for example ref.[1]). Small systems can be solved completely by a direct diagonalization of the hamiltonian. For larger systems one can use Monte-Carlo methods. For this purpose the finite temperature partition function of the d-dimensional quantum spin system is expressed as a pathintegral of a (d + 1)-dimensional classical system of Ising-like spin variables with four-spin couplings. The classical system is then simulated on a euclidean time lattice with lattice spacing ǫ using importance 1

Using a model of long-range interactions between vortices, we numerically investigate the dynamics of a driven vortex lattice subject to the randomly distributed pointlike pinning centers in a thin superconducting film. At zero temperature, crossover from elastic to plastic depinnings is observed with increasing density of pinning centers. With the lattice softness, the scaling fit between force and velocity obtained in the elastic regime becomes invalid when the plastic flow appears. The peak effect occurs when one enters the plastic regime and the lattice tearing first enhances the critical current density j c and then suppresses it. ''Steps'' in the curve of velocity-force dependence and its differential are also found in the plastic regime. For the finitetemperature case, we see evidence of plastic and filamentary flow at low driving forces and temperatures. At high driving forces and low enough temperatures, evidence of an ordering of the moving vortices is seen in the flux flow regime. Our results are in agreement with all the previous simulations and recent experiments.

Although the set of permutation symmetries of a complex network could be very large, few of them give rise to stable synchronous patterns. Here we present a general framework and develop techniques for controlling synchronization patterns in complex network of coupled chaotic oscillators. Specifically, according to the network permutation symmetry, we design a small-size and weighted network, namely the control network, and use it to control the large-size complex network by means of pinning coupling. We argue mathematically that for any of the network symmetries, there always exists a critical pinning strength beyond which the unstable synchronous pattern associated to this symmetry can be stabilized. The feasibility of the control method is verified by numerical simulations of both artificial and real-world networks and demonstrated experimentally in systems of coupled chaotic circuits. Our studies show the controllability of synchronous patterns in complex networks of coupled chaotic oscillators.

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