Knotlike chi disclinations in the cholesteric liquid crystals

We investigate the topological properties of N(N >= 1) disclination lines in cholesteric liquid crystals. The topological structure of N disclination lines is obtained with the Hopf index and Brouwer degree. Furthermore, the knotted x disclination loops is proposed with the Hopf invariant. And we consider the stability of such configuration based on the higher order interaction. At last, the evolution of the disclinations is discussed.

Efficiency Dynamics on Two Coupled Small-World Networks

We investigate the effect of clusters in complex networks on efficiency dynamics by studying a simple efficiency model in two coupled small-world networks. It is shown that the critical network randomness corresponding to transition from a stagnant phase to a growing one decreases to zero as the connection strength of clusters increases. It is also shown for fixed randomness that the state of clusters transits from a stagnant phase to a growing one as the connection strength of clusters increases. This work can be useful for understanding the critical transition appearing in many dynamic processes on the cluster networks.

EFFICIENCY DYNAMICS ON SCALE-FREE NETWORKS WITH COMMUNITIES

The simple efficiency model is developed on scale-free networks with communities to study the effect of the communities in complex networks on efficiency dynamics. For some parameters, we found that the state of system will transit from a stagnant phase to a growing phase as the strength of community decreases.

Promotion of cooperation in the form C0C1D classified by 'degree grads' in a scale-free network

In this paper, we revisit the issue of the public goods game (PGG) on a heterogeneous graph. By introducing a new effective topology parameter, 'degree grads' phi, we clearly classify the agents into three kinds, namely, C-0, C-1, and D. The mechanism for the heterogeneous topology promoting cooperation is discussed in detail from the perspective of C0C1D, which reflects the fact that the unreasoning imitation behaviour of C-1 agents, who are 'cheated' by the well-paid C-0 agents inhabiting special positions, stabilizes the formation of the cooperation community. The analytical and simulation results for certain parameters are found to coincide well with each other. The C0C1D case provides a picture of the actual behaviours in real society and thus is potentially of interest.

The effect of human rhythm on packet delivery

In communication networks such as the Internet, the relationship between packet generation rate and time is similar to a rectangle wavefunction due to the rhythm of humans. Thus, we investigate the traffic dynamics on a network with a rectangle wavepacket generation rate. It is found that the critical delivering capacity parameter beta(c) (which separates the congested phase and the free phase) decreases significantly with the duty cycle r of the rectangle wave for package generation. And, in the congested phase, more collective generation of packets (smaller r) is helpful for decreasing the packet aggregation rate. Moreover, it is found that the congested phase can be divided into two regions, i.e., region1 and region2, where the distributions of queue lengths are nonlinear and linear, respectively. Also, the linear expression for the distribution of queue lengths in region2 is obtained analytically. Our work reveals an obvious effect of the rectangle wave on the traffic dynamics and the queue length distribution in the system, which is of essential interest and may provide insights into the designing of work-rest schedules and routing strategies.

Quantifying the kinetic paths of flexible biomolecular recognition

Biomolecular recognition often involves large conformational changes, sometimes even local unfolding. The identification of kinetic pathways has become a central issue in understanding the nature of binding. A new approach is proposed here to study the dynamics of this binding-folding process through the establishment of a path-integral framework on the underlying energy landscape. The dominant kinetic paths of binding and folding can be determined and quantified. The significant coupling between the binding and folding of biomolecules often exists in many important cellular processes. In this case, the corresponding kinetic paths of binding are shown to be intimately correlated with those of folding and the dynamics becomes quite cooperative. This implies that binding and folding happen concurrently. When the coupling between binding and folding is weak (strong), the kinetic process usually starts with significant folding (binding) first, with the binding (folding) later proceeding to the end. The kinetic rate can be obtained through the contributions from the dominant paths. The rate is shown to have a bell-shaped dependence on temperature in the concentration-saturated regime consistent with experiment. The changes of the kinetics that occur upon changing the parameters of the underlying binding-folding energy landscape are studied.

Energy landscape theory, funnels, specificity, and optimal criterion of biomolecular binding

We study the nature of biomolecular binding. We found that in general there exists several thermodynamic phases: a native binding phase, a non-native phase, and a glass or local trapping phase. The quantitative optimal criterion for the binding specificity is found to be the maximization of the ratio of the binding transition temperature versus the trapping transition temperature, or equivalently the ratio of the energy gap of binding between the native state and the average non-native states versus the dispersion or variance of the non-native states. This leads to a funneled binding energy landscape.

The role of Li-O bonds in calculations of nonlinear optical coefficients of LiXO3-type complex crystals

The second-order nonlinear optical (NLO) tenser coefficients of LiXO3 (X = I; Nb or Ta) type complex crystals have been calculated using the chemical bond theory of complex crystals. Contributions of each type of bond to the total second-order NLO coefficient d(ij) and the linear susceptibility X are quantitatively determined. All tensor values thus calculated are in good agreement with experimental data. The Li-O bonds are found to be an important group in the contributions to the total NLO tenser coefficient, especially for those in LiNbO3 and LiTaO3. The importance of Li-O bonds depends on the environment of Li atom in these crystals.

笼形水簇和溶解甲烷之间平均力势能的约束型分子动力学计算及其在天然气水合物成核研究中的意义

That the dodecahedral water cluster (DWC) can adsorb dissolved methane molecules, an important phenomenon related to the hydrate nucleation study, has been observed through molecular dynamics simulations, but it has not been explained satisfactorily [Guang-Jun Guo; Yi-Gang Zhang; Hua Liu. J. Phys. Chem. C, 2007, 111, 2595]. In order to explain this phenomenon by using the potential of mean force (PMF) between the DWC and the dissolved methane, we perform several series of constrained molecular dynamics simulations in the methane-water system. The distance between the center of DWC and the methane molecule is constrained from 5 Å to 18 Å by adding 0.2 Å every time. For each fixed distance, we perform 20 independent simulations to improve the statistical precision. We first get the constraint force between the DWC and the dissolved methane in each simulation and then calculate the PMF by integrating these forces. Subsequently, the radial distribution function (RDF) is obtained from the PMF through an equation of statistical mechanics. The results show that the RDF has a sharp peak at about 6.2 Å, successfully explaining why the DWC adsorbs dissolved methane molecules. The preferential binding coefficient is a positive value (=2.05±0.5), indicates that the DWC tends to adsorb dissolved methane rather than water molecules in methane aqueous solutions. The curve of PMF for the DWC encaging a methane almost coincides that for the empty DWC, meaning that it is the DWC rather than the encaged methane who could adsorb dissolved methane molecules. By comparing the curves of PMF for different directions of the DWC relative to the dissolved methane, we find that it is the cage face rather than the cage edge or vertex that plays an essential role when the DWC adsorbing dissolved methane. This research sheds light on the driving force for the methane adsorption, and it is helpful in understanding the nucleation process of methane hydrate.

Mean Field Theory for Sigmoid Belief Networks

We develop a mean field theory for sigmoid belief networks based on ideas from statistical mechanics. Our mean field theory provides a tractable approximation to the true probability distribution in these networks; it also yields a lower bound on the likelihood of evidence. We demonstrate the utility of this framework on a benchmark problem in statistical pattern recognition -- the classification of handwritten digits.

Escape times for rigid Brownian rotators in a bistable potential from the time evolution of the Green function and the characteristic time of the probability evolution

The greatest relaxation time for an assembly of three- dimensional rigid rotators in an axially symmetric bistable potential is obtained exactly in terms of continued fractions as a sum of the zero frequency decay functions (averages of the Legendre polynomials) of the system. This is accomplished by studying the entire time evolution of the Green function (transition probability) by expanding the time dependent distribution as a Fourier series and proceeding to the zero frequency limit of the Laplace transform of that distribution. The procedure is entirely analogous to the calculation of the characteristic time of the probability evolution (the integral of the configuration space probability density function with respect to the position co-ordinate) for a particle undergoing translational diffusion in a potential; a concept originally used by Malakhov and Pankratov (Physica A 229 (1996) 109). This procedure allowed them to obtain exact solutions of the Kramers one-dimensional translational escape rate problem for piecewise parabolic potentials. The solution was accomplished by posing the problem in terms of the appropriate Sturm-Liouville equation which could be solved in terms of the parabolic cylinder functions. The method (as applied to rotational problems and posed in terms of recurrence relations for the decay functions, i.e., the Brinkman approach c.f. Blomberg, Physica A 86 (1977) 49, as opposed to the Sturm-Liouville one) demonstrates clearly that the greatest relaxation time unlike the integral relaxation time which is governed by a single decay function (albeit coupled to all the others in non-linear fashion via the underlying recurrence relation) is governed by a sum of decay functions. The method is easily generalized to multidimensional state spaces by matrix continued fraction methods allowing one to treat non-axially symmetric potentials, where the distribution function is governed by two state variables. (C) 2001 Elsevier Science B.V. All rights reserved.

Current-induced forces in atomic-scale conductors

We present a self-consistent tight-binding formalism to calculate the forces on individual atoms due to the flow of electrical current in atomic-scale conductors. Simultaneously with the forces, the method yields the local current density and the local potential in the presence of current flow, allowing a direct comparison between these quantities. The method is applicable to structures of arbitrary atomic geometry and can be used to model current-induced mechanical effects in realistic nanoscale junctions and wires. The formalism is implemented within a simple Is tight-binding model and is applied to two model structures; atomic chains and a nanoscale wire containing a vacancy.

Time operators and shift representation of dynamical systems

We introduce and characterise time operators for unilateral shifts and exact endomorphisms. The associated shift representation of evolution is related to the spectral representation by a generalized Fourier transform. We illustrate the results for a simple exact system, namely the Renyi map.