A polymer chain containing $N$ monomers confined in a finite cylindrical tube of diameter $D$ grafted at a distance $L$ from the open end of the tube may undergo a rather abrupt transition, where part of the chain escapes from the tube to form a “crownlike” coil outside of the tube. When this problem is studied by Monte Carlo simulation of self-avoiding walks on the simple cubic lattice applying a cylindrical confinement and using the standard pruned-enriched Rosenbluth method (PERM), one obtains spurious results, however, with increasing chain length the transition gets weaker and weaker, due to insufficient sampling of the “escaped” states, as a detailed analysis shows. In order to solve this problem, a new variant of a biased sequential sampling algorithm with resampling is proposed, force-biased PERM: the difficulty of sampling both phases in the region of the first order transition with the correct weights is treated by applying a force at the free end pulling it out of the tube. Different strengths of this force need to be used and reweighting techniques are applied. Using rather long chains (up to $N=18000$) and wide tubes (up to $D=29$ lattice spacings), the free energy of the chain, its end-to-end distance, the number of “imprisoned” monomers can be estimated, as well as the order parameter and its distribution. It is suggested that this algorithm should be useful for other problems involving state changes of polymers, where the different states belong to rather disjunct “valleys” in the phase space of the system.

A computer model is described which is used to assess the dynamical complexity of a class of networks of spiking neurons with small-world properties. Networks are constructed by forming an initially segregated set of highly intraconnected clusters and then applying a probabilistic rewiring method reminiscent of the Watts-Strogatz procedure to make intercluster connections. Causal density, which counts the number of independent significant interactions among a system’s components, is used to assess dynamical complexity. This measure was chosen because it employs lagged observations, and is therefore more sensitive to temporally smeared evidence of segregation and integration than its alternatives. The results broadly support the hypothesis that small-world topology promotes dynamical complexity, but reveal a narrow parameter range within which this occurs for the network topology under investigation, and suggest an inverse correlation with phase synchrony inside this range.

Community structure is common in various real-world networks; methods or algorithms for detecting such communities in complex networks have attracted great attention in recent years. We introduced a different adaptive clustering algorithm capable of extracting modules from complex networks with considerable accuracy and robustness. In this approach, each node in a network acts as an autonomous agent demonstrating flocking behavior where vertices always travel toward their preferable neighboring groups. An optimal modular structure can emerge from a collection of these active nodes during a self-organization process where vertices constantly regroup. In addition, we show that our algorithm appears advantageous over other competing methods (e.g., the Newman-fast algorithm) through intensive evaluation. The applications in three real-world networks demonstrate the superiority of our algorithm to find communities that are parallel with the appropriate organization in reality.

We study numerically the synchronization properties of two unidirectionally coupled semiconductor lasers subject to filtered optical feedback. By adding a perturbation (a message) to the output of the master laser, we show that mutual information allows distinguishing between chaotic synchronization (at low to moderate coupling strengths) and injection locking (at large coupling strength). We find that a receiver subject to a feedback similar to that of the emitter (closed-loop receiver) shows better synchronization with the master laser when compared with a receiver without feedback (open-loop receiver). Closed-loop receivers also show better capability to recover weak messages. The filter in the feedback loop allows reducing the bandwidth of the chaotic carrier, improves the synchronization with respect to the conventional feedback case, and requires less coupling strength with a minor loss in complexity.

The radiative opacity of iron plasmas at high temperatures is very important in astrophysics. The spectrally resolved radiative opacity and Rosseland and Planck means were investigated by using the detailed-level-accounting (DLA) model for iron plasmas at high temperatures and a variety of density. The accuracy of atomic data such as energy levels and transition probabilities is checked by comparison with data from the National Institute of Standards and Technology. The transmission of iron plasma at a temperature of $156\mathrm{eV}$ and an electron density of $6.9\times {10}^{21}{\mathrm{cm}}^{-3}$ is studied in detail and compared with results of a recent experiment [Bailey et al., Phys. Rev. Lett. 99, 265002 (2007)] and other theoretical results. General good agreement is found between our DLA transmission and the experimental and other theoretical results. By using our developed DLA model, we can deduce valuable information on the physical condition of the plasma created in the experiment. The information includes the fractional distribution of different ion stages and whether the plasma is in local thermodynamic equilibrium or not. Illustrative results are given for three isothermal sequences of 100, 150, and $200\mathrm{eV}$ with different mass densities and for three isodensity sequences of 0.1, 0.05, and $0.01\mathrm{g}∕{\mathrm{cm}}^3$ with different temperatures. The Rosseland and Planck mean opacities are compared with other theoretical results obtained by the Los Alamos light element detailed configuration opacity code.

A coarse-time-step method is presented that enables the execution of multiple events at each time increment of microscopic-lattice kinetic Monte Carlo simulations. The method employs the $n$-fold method to create groups of reactions in which the $\tau$-leap algorithm of Gillespie, originally proposed for well-mixed systems, is applied. Creation of groups of reactions is an essential step to avoid violation of the leap condition that arises when the $\tau$-leap algorithm is applied to a single site. The method is general, very easy to implement, and can result in substantial computational savings when global updating is employed. An illustrative example from crystal growth of a simple cubic lattice with the solid-on-solid approximation is presented.

The scaling nature of absorbing critical phenomena is well understood for the directed percolation (DP) and the directed Ising (DI) systems. However, a full analysis of the crossover behavior is still lacking, which is of our interest in this study. In one dimension, we find three different routes from the DI to the DP classes by introducing a symmetry-breaking field (SB), breaking a modulo 2 conservation (CB), or making channels connecting two equivalent absorbing states (CC). Each route can be characterized by a crossover exponent, which is found numerically as $\varphi =2.1\pm 0.1$ (SB), $4.6\pm 0.2$ (CB), and $2.9\pm 0.1$ (CC), respectively. The difference between the SB and CB crossover can be understood easily in the domain wall language, while the CC crossover involves an additional critical singularity in the auxiliary field density with the memory effect to identify itself independent.

We have studied the effect of memory on the evolution of the prisoner’s dilemma game in square lattice networks. Based on extensive simulations, we found that the density of cooperators was enhanced by an increasing memory effect for most parameters. However, we also observed that the density of cooperators decreased with an increased memory effect in the case of a large memory and moderate temptation. It is interesting to note that memory makes cooperators immune from temptation. The strength of protection reaches its maximal value only for a moderate memory effect.

Autonomous DNA computers have been attracting much attention because of their ability to integrate into living cells. Autonomous DNA computers can process information through DNA molecules and their molecular reactions. We have already proposed an idea of an autonomous molecular computer with high computational ability, which is now named Reverse-transcription-and-TRanscription-based Autonomous Computing System (RTRACS). In this study, we first report an experimental demonstration of a basic computation element of RTRACS and a mathematical modeling method for RTRACS. We focus on an AND gate, which produces an output RNA molecule only when two input RNA molecules exist, because it is one of the most basic computation elements in RTRACS. Experimental results demonstrated that the basic computation element worked as designed. In addition, its behaviors were analyzed using a mathematical model describing the molecular reactions of the RTRACS computation elements. A comparison between experiments and simulations confirmed the validity of the mathematical modeling method. This study will accelerate construction of various kinds of computation elements and computational circuits of RTRACS, and thus advance the research on autonomous DNA computers.

Rheological properties of adherent cells are essential for their physiological functions, and microrheological measurements on living cells have shown that their viscoelastic responses follow a weak power law over a wide range of time scales. This power law is also influenced by mechanical prestress borne by the cytoskeleton, suggesting that cytoskeletal prestress determines the cell’s viscoelasticity, but the biophysical origins of this behavior are largely unknown. We have recently developed a stochastic two-dimensional model of an elastically joined chain that links the power-law rheology to the prestress. Here we use a similar approach to study the creep response of a prestressed three-dimensional elastically jointed chain as a viscoelastic model of semiflexible polymers that comprise the prestressed cytoskeletal lattice. Using a Monte Carlo based algorithm, we show that numerical simulations of the chain’s creep behavior closely correspond to the behavior observed experimentally in living cells. The power-law creep behavior results from a finite-speed propagation of free energy from the chain’s end points toward the center of the chain in response to an externally applied stretching force. The property that links the power law to the prestress is the chain’s stiffening with increasing prestress, which originates from entropic and enthalpic contributions. These results indicate that the essential features of cellular rheology can be explained by the viscoelastic behaviors of individual semiflexible polymers of the cytoskeleton.

Thin, mechanically compliant coatings commonly serve as substrata for adherent cells in cell biology and biophysics studies, biological engineering applications, and biomedical device design. The deformation of such a coating at the cell-substratum interface defines the link between cellular traction, substratum stiffness, and the chemomechanical feedback mechanisms responsible for cellular mechanosensitivity. Here we apply elasticity theory to investigate how this deformation is affected by the finite thickness of such a cell substratum. The model idealizes a cellular adhesion site (e.g., a focal adhesion) as a circular area of uniform tangential traction, and compares the deformation of a compliant semi-infinite material to that of a coating of the same material supported by a rigid base. Two parameters are identified and considered: center displacement (as a measure of adhesion site displacement) and normal strain gradient (as a measure of adhesion site distortion). The attenuation of these parameters provides two measures for the influence of a finite coating thickness and underlying rigid base on cell-mediated deformation of the compliant substratum. A dimensionless term in the resulting solutions connects the coating thickness to the characteristic size of the adhesion sites. This relation, and calculations of the minimum thickness at which the rigid base is practically undetectable by an adherent cell, are supported by existing experimental literature and our observations of the projected area of fibroblasts adhered to polyacrylamide hydrogel coatings with various thicknesses atop relatively rigid glass. The model thus provides a tool for estimating the effective stiffness sensed by a cell attached to a compliant coating. We also identify and consider conceptualizations of critical thickness, or minimum suitable thickness for an application, which depend on both the frame of reference and the cell behavior of interest. The appropriate usage of different definitions resolves the disparity in values reported in the literature. Finally, the distinction between adhesion site displacement and distortion noted in this model could be useful in designing substrata to elucidate the controlling mechanisms of cellular mechanosensing.

Complex networks describe several and different real-world systems consisting of a number of interacting elements. A very important characteristic of such networks is the degree distribution that strongly controls their behavior. Based on statistical mechanics, three classes of uncorrelated complex networks are identified here, depending on the role played by the connectivities amongst elements. In particular, by identifying the connectivities of a node with the number of its nearest neighbors, we show that the power law is the most probable degree distribution that both nodes and neighbors, in a reciprocal competition, assume when the respective entropy functions reach their maxima, under mutual constraint. As a result, we obtain scaling exponent values as a function of the structural characteristics of the whole network. Moreover, our approach sheds light on the exponential and Poissonian degree distributions, derived, respectively, when connectivities are thought of as degenerated connections or as half-edges. Thus, all three classes of degree distributions are derived, starting from a common principle and leading to a general and unified framework for investigating the network structure.

We have numerically investigated Rayleigh-Bénard convection in binary mixtures assuming a thermal diffusion ratio that depends on the local temperature and changes its sign within the cell. The stationary instability has been found to precede the oscillatory one for a wide range of negative mean $\psi$ values. The bifurcation diagram for stationary rolls turns out to be qualitatively different from that for constant Soret effect. Nevertheless, it can be mapped onto this special case by using a scaling argument, taking into account the fact that for small convection amplitudes the rolls are restricted to parts of the cell where the sign of the Soret coefficient favors instability.

In previous work, we have established that the intrinsic viscosity $\left[\eta \right]$ of an object is nearly proportional to the average electrical polarizability tensor $⟨{\mathbf{\alpha }}_{\mathit{e}}⟩=\mathrm{tr}\left({\mathbf{\alpha }}_{\mathit{e}}\right)∕3$ of a conducting object having the same shape, or equivalently, to the intrinsic conductivity $\left[\sigma \right]=⟨{\mathbf{\alpha }}_{\mathit{e}}⟩∕V$, which characterizes the conductivity of a dilute mixture of randomly oriented conducting objects ($V$ being the volume of the object). This hydrodynamic-electrostatic analogy is useful because ${\mathbf{\alpha }}_{\mathit{e}}$ can be determined accurately and efficiently by numerical path integration for objects of arbitrary shape. Here, we show that the uncertainty in $\left[\eta \right]$ can be reduced to a relatively small value ($<1.5\%$ relative uncertainty) by utilizing additional information from the full tensor ${\mathbf{\alpha }}_{\mathit{e}}$, rather than just its average. Specifically, we determine the exact constant of proportionality between $\left[\eta \right]$ and $\left[\sigma \right]$ for triaxial ellipsoids as a function of the ratios of the eigenvalues of ${\mathbf{\alpha }}_{\mathit{e}}$ and apply this relation to particles of general shape. In addition to an improved estimation of $\left[\eta \right]$, the ratios of the components of ${\mathbf{\alpha }}_{\mathit{e}}$ provide useful measures of particle anisotropy. We also present an improved method for applying the technique to flexible particles, which requires performing a conformational ensemble average. Conformational averages of ${\mathbf{\alpha }}_{\mathit{e}}$ generate systematic errors that can be avoided by performing the conformational average at an earlier stage in the computation.

We calculate the static critical behavior of systems of $\mathrm{O}\left(n_{\parallel }\right)\oplus \mathrm{O}\left(n_{\perp }\right)$ symmetry by the renormalization group method within the minimal subtraction scheme in two-loop order. Summation methods lead to fixed points describing multicritical behavior. Their stability boarder lines in the space of the order parameter components $n_{\parallel }$ and $n_{\perp }$ and spatial dimension $d$ are calculated. The essential features obtained already in two-loop order for the interesting case of an antiferromagnet in a magnetic field ($n_{\parallel }=1$, $n_{\perp }=2$) are the stability of the biconical fixed point and the neighborhood of the stability border lines to the other fixed points, leading to very small transient exponents. We are also able to calculate the flow of static couplings, which allows us to consider the attraction region. Depending on the nonuniversal background parameters, the existence of different multicritical behavior (bicritical or tetracritical) is possible, including a triple point.

We calculate the relaxational dynamical critical behavior of systems of $O\left(n_{\parallel }\right)\oplus O\left(n_{\perp }\right)$ symmetry by renormalization group method within the minimal subtraction scheme in two-loop order. The three different bicritical static universality classes previously found for such systems correspond to three different dynamical universality classes within the static borderlines. The Heisenberg and the biconical fixed point lead to strong dynamic scaling whereas in the region of stability of the decoupled fixed point weak dynamic scaling holds. Due to the neighborhood of the stability border between the strong and the weak scaling dynamic fixed point to the dynamical stable fixed point a very small dynamic transient exponent of ${\omega }_v^{\mathcal{B}}=0.0044$ is present in the dynamics for the physically important case $n_{\parallel }=1$ and $n_{\perp }=2$ in $d=3$.

With each directed acyclic graph (this includes some $D$-dimensional lattices) one can associate some Abelian algebras that we call directed Abelian algebras (DAAs). On each site of the graph one attaches a generator of the algebra. These algebras depend on several parameters and are semisimple. Using any DAA, one can define a family of Hamiltonians which give the continuous time evolution of a stochastic process. The calculation of the spectra and ground-state wave functions (stationary state probability distributions) is an easy algebraic exercise. If one considers $D$-dimensional lattices and chooses Hamiltonians linear in the generators, in finite-size scaling the Hamiltonian spectrum is gapless with a critical dynamic exponent $z=D$. One possible application of the DAA is to sandpile models. In the paper we present this application, considering one- and two-dimensional lattices. In the one-dimensional case, when the DAA conserves the number of particles, the avalanches belong to the random walker universality class (critical exponent ${\sigma }_{\tau }=3∕2$). We study the local density of particles inside large avalanches, showing a depletion of particles at the source of the avalanche and an enrichment at its end. In two dimensions we did extensive Monte-Carlo simulations and found ${\sigma }_{\tau }=1.780\pm 0.005$.

We study analytically and numerically the ratchet transport of interacting particles induced by a monochromatic driving in asymmetric two-dimensional structures. The ratchet flow is preserved in the limit of strong interactions and can become even stronger compared to the noninteracting case. The developed kinetic theory gives a good description of these two limiting regimes. The numerical data show emergence of turbulence in the ratchet flow under certain conditions.

We study the packing of colloidal microspheres mixed with polymers in oil-in-water emulsion droplets by evaporation. The addition of polymers produces non-unique configurations of final clusters when the number of particles $N$ inside the droplet is larger than 4. The cluster configurations are classified into three categories based on symmetry. Stablized colloidal clusters of spherical packings are observed. Our observations on packing process suggest the mechanisms which cause different and nonunique structures. The osmotic pressure and the interparticle interaction due to polymers changes the force balance between microspheres and result in different structures.