He-Ping Ying

A determination of the low energy parameters of the 2-d Heisenberg antiferromagnet

We perform numerical simulations of the 2-d Heisenberg antiferromagnet using a cluster algorithm. Comparing the size and temperature effects of various quantities with results from chiral perturbation theory we determine the low energy parameters of the system very precisely. We finde0=−0.6693(1)J/a2 for the ground state energy density, ℳs = 0.3074(4)/a2 for the staggered magnetization,ħc=1.68(1)J a for the spin wave velocity andps=0.186(4)J for the spin stiffness. Our results agree with experimental data for the precursor insulators of high-Tc superconductors.

Pade - Z(2) estimator of determinants

We introduce the Pade-Z2 (PZ) stochastic estimator for calculating determinants and determinant ratios. The estimator is applied to the calculation of fermion determi- nants from the two ends of the Hybrid Monte Carlo trajectories with pseudofermions. Our results on the 8 3 × 12 lattice with Wilson action show that the statistical errors from the stochastic estimator can be reduced by more than an order of magnitude by employing an unbiased variational subtraction scheme which utilizes the off-diagonal matrices from the hopping expansion. Having been able to reduce the error of the determinant ratios to about 20 % with a relatively small number of noise vectors, this may become a feasible algorithm for simulating dynamical fermions in full QCD. We also discuss the application to the density of states in Hamiltonian systems.

Blockspin cluster algorithms for quantum spin systems

Abstract 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 mapped 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.

Liberation of a pinned spiral wave by a rotating electric pulse

Spiral waves may be pinned to anatomical heterogeneities in the cardiac tissue, which leads to monomorphic ventricular tachycardia. Wave emission from heterogeneities (WEH) induced by electric pulses in one direction (EP) is a promising method for liberating such waves by using heterogeneities as internal virtual pacing sites. Here, based on the WEH effect, a new mechanism of liberation by means of a rotating electric pulse (REP) is proposed in a generic model of excitable media. Compared with the EP, the REP has the advantage of opening wider time window to liberate pinned spiral. The influences of rotating direction and frequency of the REP, and the radius of the obstacles on this new mechanism are studied. We believe this strategy may improve manipulations with pinned spiral waves in heart experiments.

Drift of rigidly rotating spirals under periodic and noisy illuminations

Under the weak deformation approximation, the motion of rigidly rotating spirals induced by periodic and noisy illuminations are investigated analytically. We derive an approximate but explicit formula of the spiral drift velocity directly from the original reaction-diffusion equation. With this formula we are able to explain the main features in the periodic and noisy illuminations induced spiral drift problems. Numerical computations of the Oregonator model are carried out as well, and they agree with the main qualitative conclusions of our analytical results.

Influences of periodic mechanical deformation on pinned spiral waves

In a generic model of excitable media, we study the behavior of spiral waves interacting with obstacles and their dynamics under the influences of simple periodic mechanical deformation (PMD). Depending on the characteristics of the obstacles, i.e., size and excitability, the rotation of a pinned spiral wave shows different scenarios, e.g., embedding into or anchoring on an obstacle. Three different drift phenomena induced by PMD are observed: scattering on small partial-excitable obstacles, meander-induced unpinning on big partial-excitable obstacles, and drifting around small unexcitable obstacles. Their underlying mechanisms are discussed. The dependence of the threshold amplitude of PMD on the characteristics of the obstacles to successfully remove pinned spiral waves on big partial-excitable obstacles is studied.

Loop-cluster algorithm: an application for the 2D quantum Heisenberg antiferromagnet

Abstract A new type of cluster algorithm that strongly reduces the critical slowing down and frustration effects is developed to stimulate the spin one half quantum Heisenberg antiferromagnet. The numerical results for the 2D system show that the method can be applied to study efficiently quantum spin systems at lower temperatures with large Trotter number.

Emitting waves from heterogeneity by a rotating electric field.

In a generic model of excitable media, we simulate wave emission from a heterogeneity (WEH) induced by an electric field. Based on the WEH effect, a rotating electric field is proposed to terminate existed spatiotemporal turbulence. Compared with the effects resulted by a periodic pulsed electric field, the rotating electric field displays several improvements, such as lower required intensity, emitting waves on smaller obstacles, and shorter suppression time. Furthermore, due to rotation of the electric field, it can automatically source waves from the boundary of an obstacle with small curvature.

Short-time dynamics and magnetic critical behavior of the two-dimensional random-bond potts model

The critical behavior in the short-time dynamics for the random-bond Potts ferromagnet in two dimensions is investigated by short-time dynamic Monte Carlo simulations. The numerical calculations show that this dynamic approach can be applied efficiently to study the scaling characteristic, which is used to estimate the critical exponents straight theta,beta/nu, and z, for quenched disordered systems from the power-law behavior of the kth moments of magnetization.

Controlling synchronous patterns in complex networks

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.