Numerical simulations of the dynamical behavior of the SK model

We study the dynamical behavior of the Sherrington Kirkpatrick model. Thanks to the APE supercomputer we are able to analyze large lattice volumes, and to investigate the low T region. We present a new and precise determination of the remnant magnetization and of its time decay exponent, of the energy time decay exponent, and we discuss aging phenomena in the model. We exclude validity of naive aging, and propose different options that fit the numerical data. Received: 14 August 1997 / Revised: 2 December 1997 / Accepted: 30 January 1998     

Spread and Quote-Update Frequency of the Limit-Order Driven Sergei Maslov Model

We perform numerical simulations of the limit-order driven Sergei Maslov （SM） model and investigate the probability distribution and autocorrelation function of the bid-ask spread S and the quote-update frequency U. For the probability distribution, the model successfully reproduces the power law decay of the spread and the exponential decay of the quote-update frequency. For the autocorrelation function, both the spread and the quote-update frequency of the model decay by a power law, which is consistent with the empirical study. We obtain the power law exponent 0.54 for the spread, which is in good agreement with the real financial market.     

Casimir amplitudes in a quantum spherical model with long-range interaction

A d-dimensional quantum model system confined to a general hypercubical geometry with linear spatial size L and “temporal size” 1/T ( T - temperature of the system) is considered in the spherical approximation under periodic boundary conditions. For a film geometry in different space dimensions , where is a parameter controlling the decay of the long-range interaction, the free energy and the Casimir amplitudes are given. We have proven that, if , the Casimir amplitude of the model, characterizing the leading temperature corrections to its ground state, is . The last implies that the universal constant of the model remains the same for both short, as well as long-range interactions, if one takes the normalization factor for the Gaussian model to be such that . This is a generalization to the case of long-range interaction of the well-known result due to Sachdev. That constant differs from the corresponding one characterizing the leading finite-size corrections at zero temperature which for is . Received 3 June 1999 and Received in final form 16 August 1999     

Delay, feedback and quenching in financial markets

An asset whose price exhibits geometric Brownian motion is analysed. The basic Brownian motion model is modified to account for the effects of market delay and investor feedback. A Langevin equation model is appropriate. When the feedback coupling is sufficiently strong, the market dynamics switches from a slow random walk behaviour to a rapid unstable behaviour with a fast time scale characteristic of the market delay. The unstable runaway behaviour is subsequently quenched by investors deserting a collapsing market or saturating a booming one. This quenching effect is sufficient to ensure long term bounding of the asset price. A form of market sabotage is demonstrated in which investors can push the market from a stable to an unstable regime. Received 24 February 2000     

Stylized facts from a threshold-based heterogeneous agent model

A class of heterogeneous agent models is investigated where investors switch trading position whenever their motivation to do so exceeds some critical threshold. These motivations can be psychological in nature or reflect behaviour suggested by the efficient market hypothesis (EMH). By introducing different propensities into a baseline model that displays EMH behaviour, one can attempt to isolate their effects upon the market dynamics. The simulation results indicate that the introduction of a herding propensity results in excess kurtosis and power-law decay consistent with those observed in actual return distributions, but not in significant long-term volatility correlations. Possible alternatives for introducing such long-term volatility correlations are then identified and discussed.     

Classical dielectric models of fullerenes and estimation of heat radiation

With the aim of describing the cooling of highly excited fullerene molecules by heat radiation, we consider simple classical, dielectric models for calculation of the electromagnetic response and show that the overall distribution of oscillator strength for electronic transitions can be represented fairly well by such a model. The connection to a layer model for graphite is discussed. For thermal emission of radiation from fullerenes, which depends on the oscillator strength at low frequencies only, the classical dielectric model leads to a prediction which should be applicable at high temperatures where the fine structure of the oscillator strength distribution is smeared out. We also estimate the emission from infrared-active vibrations, which dominate at low temperatures but play a minor role at the high temperatures where formation and decay of fullerene molecules take place. Received 22 November 1999 and Received in final form 19 April 2000     

γ辐射引发淀粉目由基衰减的动力学研究

用ESR方法研究了红薯淀粉在y射线预辐照下,产生的淀粉自由基特性及其室温下的自由基衰减动力学反应。结果表明在室温条件下,淀粉自由基的相对浓度随辐射剂量的增大而增加。自由基相对浓度的室温衰减用二级反应动力学处理,求得了衰减速率常数和淀粉自由基反应的半衰期。     

Critical behavior of a three-state Potts model on a Voronoi lattice

We use the single-histogram technique to study the critical behavior of the three-state Potts model on a (random) Voronoi-Delaunay lattice with size ranging from 250 to 8 000 sites. We consider the effect of an exponential decay of the interactions with the distance, , with a>0, and observe that this system seems to have critical exponents and which are different from the respective exponents of the three-state Potts model on a regular square lattice. However, the ratio remains essentially the same. We find numerical evidences (although not conclusive, due to the small range of system size) that the specific heat on this random system behaves as a power-law for a=0 and as a logarithmic divergence for a=0.5 and a=1.0 Received 5 April 2000     

Quantum Entropy Controlling in the Damping Jaynes-Cummings Model

The quantum entropy of the damping Jaynes-Cummings model is investigated in different decay coefficients under detuning conditions. The results indicate that the larger the decay coefficient is, the more quickly the entropy decays. The detuning of the atom and field frequencies reduce the entanglement maximum in short time regions, but delays the damping process of the entanglement. The sine modulation enhances the entanglement in short time regions.     

Mechanism of Proton-Induced Reactions on Targets ^16O, ^27Al, ^56Fe, ^112Cd, ^184W and ^208Pb At Ep = 800 MeV

We investigate the 800 MeV proton-induced spallation reactions on various targets by the improved quantum molecular dynamics （ImQMD05） model incorporated with a statistical decay model （SDM）. The influence of the nucleon-nucleon effective interaction on proton induced spallation reactions is studied by using different Skyrme interactions. It is found that the low energy part of the neutron double differential cross sections （DDCS）, which is mainly contributed from the decay of the excited residue, is influenced by the effective nucleon-nucleon interaction strongly., while the high energy part of neutron DDCS is influenced weakly. Among the Skyrme interactions used in the calculations, the calculation results with SkP give the best agreement with the experimental data.     

Interaction-dependent enhancement of the localisation length for two interacting particles in a one-dimensional random potential

We present calculations of the localisation length, , for two interacting particles (TIP) in a one-dimensional random potential, presenting its dependence on disorder, interaction strength U and system size. is computed by a decimation method from the decay of the Green function along the diagonal of finite samples. Infinite sample size estimates are obtained by finite-size scaling. For U=0 we reproduce approximately the well-known dependence of the one-particle localisation length on disorder while for finite U, we find that with varying between and . We test the validity of various other proposed fit functions and also study the problem of TIP in two different random potentials corresponding to interacting electron-hole pairs. As a check of our method and data, we also reproduce well-known results for the two-dimensional Anderson model without interaction. Received 19 June 1998 and Received in final form 29 October 1998     

Interactions between charged rods near salty surfaces

Using both theoretical modeling and computer simulations we study a model system for DNA interactions in the vicinity of charged membranes. We focus on the polarization of the mobile charges in the membranes due to the nearby charged rods (DNA) and the resulting screening of their fields and inter-rod interactions. We find, both within a Debye-Hückel model and in Brownian dynamics simulations, that the confinement of the mobile charges to the surface leads to a qualitative reduction in their ability to screen the charged rods to the degree that the fields and resulting interactions are not finite-ranged as in systems including a bulk salt concentration, but rather decay algebraically and the screening effect is more like an effective increase in the multipole moment of the charged rod. Received 28 September 1999     

Dynamics of reorientation of a constrained nematic elastomer

A model is proposed for the reorientation dynamics of a confined nematic liquid crystal elastomer, where the effect of crosslinks is to couple the director to deformations of the elastic matrix. The model combines the (equilibrium) `neo-classical' theory of liquid crystal rubber elasticity with the simplest time evolution equations for a system described by two coupled, non-conserved order parameters. Relaxation from an orientation imposed by an electric field is studied as a function of elastic softness, starting angle, surface pretilt, and the relative mobilities of director and strain. Most importantly, the absence of a `semi-soft' elastic threshold changes the long-time behaviour of the effective refractive index of the medium from exponential to inverse power law decay. Predictions are compatible with recent experimental results by Chang, Chien and Meyer [Phys. Rev. E 56, 595 (1997)]. Received 22 June 1998     

Persistence and financial markets

The persistence phenomenon is studied in a financial context by using a novel mapping of the time evolution of the values of shares in a portfolio onto Ising spins. The method is applied to historical data from the London Financial Times Stock Exchange 100 index (FTSE 100) over an arbitrarily chosen period. By following the time dependence of the spins, we find evidence for a power law decay of the proportion of shares that remain either above or below their ‘starting’ values. As a result, we estimate a persistence exponent for the underlying financial market to be ≈0.5. Preliminary results from computer simulations on persistence in the economic dynamics of a toy model appear to reproduce the behaviour observed in real markets.     

Wetting of phospholipid membranes on hydrophilic surfaces - Concepts towards self-healing membranes

We report on the wetting behavior of phospholipid membranes on solid surfaces immersed in aqueous solution. Using fluorescence microscopy, the spreading velocity of fluid bilayers advancing from a lipid source is investigated. The kinetic spreading coefficient was measured as a function of temperature for pure DMPC membranes and as a function of charge density and cholesterol content for binary membranes. A theoretical model for the membrane flow is presented, which takes into account the liquid crystalline bilayer architecture of the lipid membrane. The spreading power results from the membrane-solid VdW interaction and is dissipated in hydrodynamic shear flow as well as by inter-monolayer friction within the bilayer. The frictional drag causes a dynamic tension gradient in the spreading membrane, which is manifested by a single exponential decay of the fluorescence intensity profile along the spreading direction. Obstacles are shown to act as pinning centers deforming the advancing line interface. However, no depinning was observed, since the centers are circumflown without abrupt relaxation. Received 6 November 1998     

Short-time behaviour of demand and price viewed through an exactly solvable model for heterogeneous interacting market agents

We introduce a stochastic heterogeneous interacting-agent model for the short-time non-equilibrium evolution of excess demand and price in a stylized asset market. We consider a combination of social interaction within peer groups and individually heterogeneous fundamentalist trading decisions which take into account the market price and the perceived fundamental value of the asset. The resulting excess demand is coupled to the market price. Rigorous analysis reveals that this feedback may lead to price oscillations, a single bounce, or monotonic price behaviour. The model is a rare example of an analytically tractable interacting-agent model which allows us to deduce in detail the origin of these different collective patterns. For a natural choice of initial distribution, the results are independent of the graph structure that models the peer network of agents whose decisions influence each other.     

On the role of volatility in the evolution of social networks

We study how the volatility, node- or link-based, affects the evolution of social networks in simple models. The model describes the competition betweenorder – promoted by the efforts of agents to coordinate – and disorder induced byvolatility in the underlying social network.We find that when volatility affects mostly the decay of links, the model exhibit a sharp transition between an ordered phase with a dense network and a disordered phase with a sparse network. When volatility is mostly node-based, instead, only the symmetric (disordered) phase existsThese two regimes are separated by a second order phase transition of unusual type, characterized by an order parameter critical exponent β = 0⁺.We argue that node volatility has the same effect in a broader class of models, and provide numerical evidence in this direction.