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B. Zheng

Publications and source records attributed to B. Zheng.

At least 55 records · Page 3Linked to original sources
arXiv2005

Persistence Probabilities of the German DAX and Shanghai Index

We present a relatively detailed analysis of the persistence probability distributions in financial dynamics. Compared with the auto-correlation function, the persistence probability distributions describe dynamic correlations non-local in time. Universal and non-universal behaviors of the German DAX and Shanghai Index are analyzed, and numerical simulations of some microscopic models are also performed. Around the fixed point $z_0=0$, the interacting herding model produces the scaling behavior of the real markets.

nlin.AO↗
arXiv2001

Monte Carlo Simulations of Short-time Critical Dynamics with a Conserved Quantity

With Monte Carlo simulations, we investigate short-time critical dynamics of the three-dimensional anti-ferromagnetic Ising model with a globally conserved magnetization $m_s$ (not the order parameter). From the power law behavior of the staggered magnetization (the order parameter), its second moment and the auto-correlation, we determine all static and dynamic critical exponents as well as the critical temperature. The universality class of $m_s=0$ is the same as that without a conserved quantity, but the universality class of non-zero $m_s$ is different.

cond-mat.stat-mech↗
arXiv2001

Phase Ordering Dynamics of $ϕ^4$ Theory with Hamiltonian Equations of Motion

Phase ordering dynamics of the (2+1)- and (3+1)-dimensional $ϕ^4$ theory with Hamiltonian equations of motion is investigated numerically. Dynamic scaling is confirmed. The dynamic exponent $z$ is different from that of the Ising model with dynamics of model A, while the exponent $λ$ is the same.

cond-mat.stat-mech↗
arXiv2001

Corrections to Scaling for the Two-dimensional Dynamic XY Model

With large-scale Monte Carlo simulations, we confirm that for the two-dimensional XY model, there is a logarithmic correction to scaling in the dynamic relaxation starting from a completely disordered state, while only an inverse power law correction in the case of starting from an ordered state. The dynamic exponent $z$ is $z=2.04(1)$.

cond-mat.stat-mech↗
arXiv2000

Long-range effects in granular avalanching

We introduce a model for granular flow in a one-dimensional rice pile that incorporates rolling effects through a long-range rolling probability for the individual rice grains proportional to $r^{-ρ}$, $r$ being the distance traveled by a grain in a single topling event. The exponent $ρ$ controls the average rolling distance. We have shown that the crossover from power law to stretched exponential behaviors observed experimentally in the granular dynamics of rice piles can be well described as a long-range effect resulting from a change in the transport properties of individual grains. We showed that stretched exponential avalanche distributions can be associated with a long-range regime for $1<ρ<2$ where the average rolling distance grows as a power law with the system size, while power law distributions are associated with a short range regime for $ρ>2$, where the average rolling distance is independent of the system size.

cond-mat.dis-nn↗
arXiv2000

Dynamic Approach to Weak First Order Phase Transitions

A short-time dynamic approach to weak first order phase transitions is proposed. Taking the 2-dimensional Potts models as examples, from short-time behaviour of non-equilibrium relaxational processes starting from high temperature and zero temperature states,x pseudo critical points K^{*} and K^{**} are determined. A clear difference of the values for K^{*} and K^{**} distinguishes a weak first order transition from a second order one. At the pseudo critical points, pseudo critical exponents can be estimated.

cond-mat.soft↗
arXiv1999

Deterministic Equations of Motion and Phase Ordering Dynamics

We numerically solve microscopic deterministic equations of motion for the 2D $ϕ^4$ theory with random initial states. Phase ordering dynamics is investigated. Dynamic scaling is found and it is dominated by a fixed point corresponding to the minimum energy of random initial states.

cond-mat.stat-mech↗
arXiv1999

Deterministic Equations of Motion and Dynamic Critical Phenomena

Taking the two-dimensional $ϕ^4$ theory as an example, we numerically solve the deterministic equations of motion with random initial states. Short-time behavior of the solutions is systematically investigated. Assuming that the solutions generate a microcanonical ensemble of the system, we demonstrate that the second order phase transition point can be determined already from the short-time dynamic behavior. Initial increase of the magnetization and critical slowing down are observed. The dynamic critical exponent z, the new exponent $θ$ and the static exponents $β$ and $ν$ are estimated. Interestingly, the deterministic dynamics with random initial states is in a same dynamic universality class of Monte Carlo dynamics.

cond-mat.stat-mech↗
arXiv1999

The Critical Exponent $θ'$ in Spin Glasses

Short-time dynamic scaling behavior of the 3D $\pm J$ Ising spin glass is studied by Monte Carlo methods. Starting the replicas with independent initial configurations with a small pseudo magnetization, the dynamic evolution of the overlap q(t) between two replicas is measured. The initial increase of the overlap q(t) is observed and the corresponding exponent $θ'$ is obtained. From the scaling relation $λ=d/z-θ'$, the dynamic exponent z is estimated.

cond-mat.stat-mech↗
arXiv1999

Microscopic Deterministic Dynamics and Persistence Exponent

Numerically we solve the microscopic deterministic equations of motion with random initial states for the two-dimensional $ϕ^4$ theory. Scaling behavior of the persistence probability at criticality is systematically investigated and the persistence exponent is estimated.

cond-mat.stat-mech↗
arXiv1998

Monte Carlo Simulations of a Generalized n--spin facilitated kinetic Ising Model

A kinetic Ising model is analyzed where spin variables correspond to lattice cells with mobile or immobile particles. Introducing additional restrictions for the flip processes according to the n-spin facilitated kinetic Ising model and using Monte Carlo methods we study the freezing process under the influence of an additional nearest-neighbor interaction. The stretched exponential decay of the auto-correlation function is observed and the exponent $γ$ as well as the relaxation time are determined depending on the activation energy $h$ and the short range coupling $J$. The magnetization corresponding to the density of immobile particles is found to be the controlling parameter for the dynamic evolution.

cond-mat.dis-nn↗
arXiv1998

Dynamic Simulations of the Kosterlitz-Thouless Phase Transition

Based on the short-time dynamic scaling form, a novel dynamic approach is proposed to tackle numerically the Kosterlitz-Thouless phase transition. Taking the two-dimensional XY model as an example, the exponential divergence of the spatial correlation length, the transition temperature $T_{KT}$ and all critical exponents are computed. Compared with Monte Carlo simulations in equilibrium, we obtain data at temperatures nearer to $T_{KT}$.

cond-mat.stat-mech↗
arXiv1998

Critical Relaxation and Critical Exponents

Dynamic relaxation of the XY model and fully frustrated XY model quenched from an initial ordered state to the critical temperature or below is investigated with Monte Carlo methods. Universal power law scaling behaviour is observed. The dynamic critical exponent $z$ and the static exponent $η$ are extracted from the time-dependent Binder cumulant and magnetization. The results are competitive to those measured with traditional methods.

cond-mat.stat-mech↗
arXiv1998

Short-time Dynamic Behaviour of Critical XY Systems

Using Monte Carlo methods, the short-time dynamic scaling behaviour of two-dimensional critical XY systems is investigated. Our results for the XY model show that there exists universal scaling behaviour already in the short-time regime, but the values of the dynamic exponent $z$ differ for different initial conditions. For the fully frustrated XY model, power law scaling behaviour is also observed in the short-time regime. However, a violation of the standard scaling relation between the exponents is detected.

cond-mat.stat-mech↗
arXiv1998

Short-time Critical Dynamics of the 3-Dimensional Ising Model

Comprehensive Monte Carlo simulations of the short-time dynamic behaviour are reported for the three-dimensional Ising model at criticality. Besides the exponent $θ$ of the critical initial increase and the dynamic exponent $z$, the static critical exponents $ν$ and $β$ as well as the critical temperature are determined from the power-law scaling behaviour of observables at the beginning of the time evolution. States of very high temperature as well as of zero temperature are used as initial states for the simulations.

cond-mat.stat-mech↗