Narrow Results

The purpose of this paper is to investigate the length scale effects of small protein folding by lattice modeling. Heat capacity is computed to analyze folding transition temperature of the model proteins of different lengths. The results show that there is an evident phase transition when the lengths of the model proteins are similar to those of foldons. Furthermore, it is found that the folding transition temperature is proportional to the sequence length.

In this paper, the lattice model which depends not only on the difference of the optimal current and the local current but also on the relative current is presented and analyzed in detail. We derive the stability condition of the extended model by considering a small perturbation around the homogeneous flow solution with finding that the improvement in the stability of the traffic flow is obtained by taking into account the relative current, which is also confirmed by direct simulations. Moreover, from the nonlinear analysis to the extended models, the relative current dependence of the propagating kink solutions for traffic jam is obtained by deriving the modified KdV equation near the critical point by using the reductive perturbation method.

In this paper, a new lattice model is presented with the consideration of the honk effect. The stability condition is obtained by the linear stability analysis. The modified Korteweg–de Vries (KdV) equation is derived to describe the phase transition of traffic flow through nonlinear analysis. The space is divided into three regions: the stable region, the metastable region and the unstable region, respectively. And numerical simulation is carried out to validate the analytic results. The results implied that the honk effect could stabilize traffic flow and suppress the traffic jam in lattice model of traffic flow.

A novel lattice traffic flow model with a slope effect is proposed. Neutral stability condition is obtained by the use of the linear stability theory. The standard KdV equation is derived in the meta-stable region and soliton solution is obtained near the neutral stability line. The solitary waves are reproduced through the numerical simulations. Results show that the solitary density wave appears in upward form when the average density is less than critical density, otherwise it exhibits downward form.

In this paper, a new two-lane lattice model of traffic flow is proposed with the consideration of multi-anticipation effect. The linear stability condition of two-lane traffic is derived with the multi-anticipation effect term by linear stability analysis, which shows that the stable region enlarges with the number of multi-anticipation sites increasing. Nonlinear analysis near the critical point is carried out to obtain kink–antikink soliton solution of the mKdV equation with the multi-anticipation effect term. Numerical simulation also shows that the multi-anticipation effect can suppress the traffic jam efficiently with lane changing in two-lane system.

The spread and burned areas of wildfires in Alberta, Canada during a 50 year period, from 1961 through 2010 are studied here. Meteorological factors that control the spread and burn area have been discussed for a long time. In this paper, we analyze the temperature rise that could drastically enhance the spread and average burned area of wildfires. A simple lattice model that mimics meteorological factors is also introduced to simulate the temperature effect on the spread and burned areas of wildfires. The numerical results demonstrate the temperature effects on wildfires when compared to the empirical data.

In this paper, a new lattice model for bidirectional pedestrian flow on single path which involves the effect of friction parameter is presented. Linear stability analysis is used to obtain the stability condition. The modified Korteweg–de Vries (mKdV) equation and time-dependent Ginzburg–Landan (TDGL) equation are deduced by means of the reductive perturbation method respectively. Further, the influence of the friction parameters upon pedestrian flow has been discussed. Our results also indicate that pedestrians moving along both directions uniformly are most stable.

Due to the existence of curved roads in real traffic situation, a novel lattice traffic flow model on a curved road is proposed by taking the effect of friction coefficient and radius into account. The stability condition is obtained by using linear stability theory. The result shows that the traffic flow becomes stable with the decrease of friction coefficient and radius of the curved road. Using nonlinear analysis method, the Korteweg–de Vries (KdV) and modified Korteweg–de Vries (mKdV) equation are derived to describe soliton waves and the kink–antikink waves in the meta-stable region and unstable region, respectively. Numerical simulations are carried out and the results are consistent with the theoretical results.

In this paper, the original lattice hydrodynamic model of traffic flow is extended to take into account the traffic current cooperation among three consecutive sites. The basic idea of the new consideration is that the cooperative traffic current of the considered site is determined by the traffic currents of the site itself, the immediately preceding site and the immediately following one. The stability criterion of the extended model is obtained by applying the linear stability analysis. The result reveals the traffic current cooperation of the immediately preceding site is positive correlation with the stability of traffic system, while negative correlation is found between the traffic stability and the traffic current cooperation of the nearest follow site. To describe the phase transition, the modified KdV equation near the critical point is derived by using the reductive perturbation method, with obtaining the dependence of the propagation kink solution for traffic jams on the traffic current cooperation among three consecutive sites. The direct numerical are conducted to verify the results of theoretical analysis, and explore the effects of the traffic current cooperation on the traffic flux of the vehicle flow system.

A new lattice model is proposed by taking into account the interruption probability with passing for two-lane freeway. The effect of interruption probability with passing is investigated about the linear stability condition and the mKdV equation through linear stability analysis and nonlinear analysis, respectively. Furthermore, numerical simulation is carried out to study traffic phenomena resulted from the interruption probability with passing in two-lane system. The results show that the interruption probability with passing can improve the stability of traffic flow for low reaction coefficient while the interruption probability with passing can destroy the stability of traffic flow for high reaction coefficient on two-lane highway.

In order to investigate the effect of driver’s memory during a period of time upon traffic dynamics, an extended lattice hydrodynamic model for traffic flow is proposed and studied analytically and numerically in this paper. The linear stability analysis reveals that the time length of driver’s memory has an important effect on stability of traffic flow. The factor will lead to the occurrence of traffic congestion. Three typical nonlinear wave equations including Burgers, Korteweg-de Vries and modified Korteweg-de Vries equation are derived to describe the evolution of density wave for traffic flow in three different regions, which are stable, meta-stable and unstable region, respectively. The simulations are given to illustrate and clarify the analytical results. The results indicate that the time length of driver’s memory has a negative effect upon stability of traffic flow.

A lattice model is proposed for three-lane traffic flow. The extended lane-changing rates are presented to mimic the lane-changing behavior by considering the congestion degree at the present site and the acceptance degree at the targeted site. The stability condition of the model is derived by applying the linear stability method. The spatiotemporal evolution of traffic flow transfer rates is investigated. The results demonstrate that the new model can reproduce the characteristics of lane changing.

In the process of traffic information transmission, traffic flux delay often occurs. To solve traffic jams resulting from traffic flux delay, we put forward a novel feedback control mode to establish a lattice model accounting for the difference between the optimal estimation and the delayed flux (called for OEDF model). The stability condition, which is closely related to the OEDF model, is derived according to the linear stability analysis. Moreover, the important positive contribution of the OEDF model is demonstrated via numerical simulation from two aspects including density evolution and hysteresis loop, respectively.

We have studied the aggregation of model amphiphilic molecules on a square lattice through Monte Carlo simulations via Metropolis. Amphiphilic molecules are modeled with a hydrophilic head represented by a small set of "water-loving" sites whereas the hydrophobic double-tail is represented by a second set of oil-loving sites. We have compared aggregation properties of single-stail (detergents) and double-tail (phospholipids) amphiphiles with equivalent hydrophobicity ratios. Equilibrium quantities such as average particle energy, specific heat, free amphiphile density show similar behavior for both model systems. The transition region associated with aggregation occurs at high temperatures for phospholipids as compared to detergents.

The nascent peptide folding in vivo is different from the denatured peptide refolding in vitro and can be divided into two stages. In the first stage, the peptide is folding as it is being synthesized until the whole peptide chain is synthesized. The final conformation formed in this stage is called as nascent state. In the second stage, the protein folds beginning with the nascent state formed in the first stage into the native state. We use a lattice model to simulate these two stages and investigate the folding time of the nascent peptide comparing with that of the denatured peptide refolding. Our results show that the synthesis process may affect the folding time of the nascent peptide. This may be helpful to understand why the former folds faster than the latter.

In this paper, the effect of multi-phase optimal velocity (OV) on a lattice model accounting for driver’s characteristics in a unidirectional traffic system is investigated. From theoretical analysis, it is found that the presence of aggressive drivers enlarges the stability region on the phase diagram in density-sensitive phase plane. As the number of stages in multi-phase transition is closely related to the number of critical points, two stage (three-phase) OV function is considered and the simulation is carried out to find the effect of sensitivity and drivers behavior on traffic dynamics. Further, with the variation of traffic density, multiple phase transitions are reported which not only depend on sensitivity but are also strongly influenced by the driver’s characteristics. Finally, the numerical simulations are performed which verify the theoretical findings.

xProtein folding in a two-dimensional lattice with an unrestricted boundary is simulated by means of the simplified HP model. The proteins are regarded as peptide chains and fold into compact structures. These structures are classified by the number of core sites. It is found that the number of structures with the given designability and given number of core sites versus designability appears as the normal distribution. The simulation shows that the structures with a large number of core sites have a high designability.

In this paper, new lattice model for the gradient elasticity is suggested. This lattice model gives a microstructural basis for second-order strain-gradient elasticity of continuum that is described by the linear elastic constitutive relation with the negative sign in front of the gradient. Moreover, the suggested lattice model allows us to have a unified description of gradient models with positive and negative signs of the strain gradient terms. Possible generalizations of this model for the high-order gradient elasticity and three-dimensional case are also suggested.

In this paper, a new lattice model is proposed with the consideration of the multiple optimal current differences for two-lane traffic system. The linear stability condition and the mKdV equation are obtained with the considered multiple optimal current differences effect by making use of linear stability analysis and nonlinear analysis, respectively. Numerical simulation shows that the multiple optimal current differences effect can efficiently improve the stability of two-lane traffic flow. Furthermore, the three front sites considered, is the optimal state of two-lane freeway.

An extended two-lane lattice model of traffic flow with consideration of the slope effect is proposed. The slope effect is reflected in both the maximal velocity and the relative current. The stability condition of the model is derived by applying the linear stability method. By using the nonlinear analysis method, we obtain the Korteweg–de Vries (KdV) equation near the neutral stability line and the modified Korteweg–de Vries (mKdV) equation near the critical point. The analytical and numerical results demonstrate that the stability of traffic flow is enhanced on the uphill but is weakened on the downhill when the slope angle increases.