We use a cellular automaton traffic model in order to study a nonequilibrium phase transition. We define an order parameter and show that its conjugated field is a parameter of randomness of the model. We analyze the symmetries of the free (unbroken) and of the jammed (broken) phases. Our results are consistent with a second-order phase transition at $p=0$. Nontrivial critical exponents have also been obtained.

The problem of estimating a Markov transition matrix to statistically describe the dynamics underlying an observed process is frequently found in the physical and economical sciences. However, little attention has been paid to the fact that such an estimation is associated with statistical uncertainty, which depends on the number of observed transitions between metastable states. In turn, this induces uncertainties in any property computed from the transition matrix, such as stationary probabilities, committor probabilities, or eigenvalues. Assessing these uncertainties is essential for testing the reliability of a given observation and also, if possible, to plan further simulations or measurements in such a way that the most serious uncertainties will be reduced with minimal effort. Here, a rigorous statistical method is proposed to approximate the complete statistical distribution of functions of the transition matrix provided that one can identify discrete states such that the transition process between them may be modeled with a memoryless jump process, i.e., Markov dynamics. The method is based on sampling the statistical distribution of Markov transition matrices that is induced by the observed transition events. It allows the constraint of reversibility to be included, which is physically meaningful in many applications. The method is illustrated on molecular dynamics simulations of a hexapeptide that are modeled by a Markov transition process between the metastable states. For this model the distributions and uncertainties of the stationary probabilities of metastable states, the transition matrix elements, the committor probabilities, and the transition matrix eigenvalues are estimated. It is found that the detailed balance constraint can significantly alter the distribution of some observables.

We show that a Dicke-type non-Hermitian Hamiltonian admits entirely real spectra by mapping it to the “dressed Dicke model” through a similarity transformation. We find a positive-definite metric in the Hilbert space of the non-Hermitian Hamiltonian so that the time evolution is unitary and allows a consistent quantum description. We then show that this non-Hermitian Hamiltonian describing nondissipative quantum processes undergoes quantum phase transition. The exactly solvable limit of the non-Hermitian Hamiltonian has also been discussed.

We study the fidelity susceptibility in the two-dimensional (2D) transverse-field Ising model and the 2D $XXZ$ model numerically. It is found that in both models, the fidelity susceptibility as a function of the driving parameter diverges at the critical points. The validity of the fidelity susceptibility to signal for the quantum phase transition is thus verified in these two models. We also compare the scaling behavior of the extremum of the fidelity susceptibility to that of the second derivative of the ground-state energy. From those results, the theoretical argument that fidelity susceptibility is a more sensitive seeker for a second-order quantum phase transition is also testified in the two models.

The mechanical behavior of self-assembled lipid tubules is an important property which determines their suitability for technological applications. We study the instability of multibilayer lipid tubules (with wall thickness $t$ and external radius $R_{ext}$) beyond elastic response under local radial atomic force microscopy indentations. A discontinuity in force-distance curves associated with the buckling instability of lipid tubules is observed. The critical force at which lipid tubules undergo a buckling transition linearly scales as $t/R_{ext}$. In addition, a reduced critical buckling force is found to extend a distance of $\sim 1\mu \text{m}$ from the end of lipid tubules.

Penrose and Hameroff have argued that the conventional models of a brain function based on neural networks alone cannot account for human consciousness, claiming that quantum-computation elements are also required. Specifically, in their Orchestrated Objective Reduction (Orch OR) model [R. Penrose and S. R. Hameroff, J. Conscious. Stud. 2, 99 (1995)], it is postulated that microtubules act as quantum processing units, with individual tubulin dimers forming the computational elements. This model requires that the tubulin is able to switch between alternative conformational states in a coherent manner, and that this process be rapid on the physiological time scale. Here, the biological feasibility of the Orch OR proposal is examined in light of recent experimental studies on microtubule assembly and dynamics. It is shown that the tubulins do not possess essential properties required for the Orch OR proposal, as originally proposed, to hold. Further, we consider also recent progress in the understanding of the long-lived coherent motions in biological systems, a feature critical to Orch OR, and show that no reformation of the proposal based on known physical paradigms could lead to quantum computing within microtubules. Hence, the Orch OR model is not a feasible explanation of the origin of consciousness.

Motivated by experimental observations of active (motor-driven) intracellular transport in neuronal dendrites, we analyze a stochastic model of directed intermittent search on a tree network. A particle injected from the cell body or soma into the primary branch of the dendritic tree randomly switches between a stationary search phase and a mobile nonsearch phase that is biased in the forward direction. A (synaptic) target is presented somewhere within the tree, which the particle can locate if it is within a certain range and in the searching phase. We approximate the moment generating function using Green’s function methods. The moment generating function is then used to compute the hitting probability and conditional mean first passage time to the target. We show that in contrast to a previously explored finite interval case, there is a range of parameters for which a bidirectional search strategy is more efficient than a unidirectional one in finding the target.

In this work we calculate the local elastic moduli in a weakly polydispersed two-dimensional Lennard-Jones glass undergoing a quasistatic shear deformation at zero temperature. The numerical method uses coarse-grained microscopic expressions for the strain, displacement, and stress fields. This method allows us to calculate the local elasticity tensor and to quantify the deviation from linear elasticity (local Hooke’s law) at different coarse-graining scales. From the results a clear picture emerges of an amorphous material with strongly spatially heterogeneous elastic moduli that simultaneously satisfies Hooke’s law at scales larger than a characteristic length scale of the order of five interatomic distances. At this scale, the glass appears as a composite material composed of a rigid scaffolding and of soft zones. Only recently calculated in nonhomogeneous materials, the local elastic structure plays a crucial role in the elastoplastic response of the amorphous material. For a small macroscopic shear strain, the structures associated with the nonaffine displacement field appear directly related to the spatial structure of the elastic moduli. Moreover, for a larger macroscopic shear strain we show that zones of low shear modulus concentrate most of the strain in the form of plastic rearrangements. The spatiotemporal evolution of this local elasticity map and its connection with long term dynamical heterogeneity as well as with the plasticity in the material is quantified. The possibility to use this local parameter as a predictor of subsequent local plastic activity is also discussed.

A model is proposed to understand the structuring of social networks in a fixed setting such as, for example, inside a university. The friendship formation is based on the frequency of encounters and mutual interest. The model shows distinctive single-scale behavior and reproduces accurately the measurable experimental quantities such as clustering coefficients, degree distribution, degree correlation, and friendship distribution. The model produces self-organized community structures and can be described as a network of densely interconnected networks. For the friendships, we find that the mutual interest is the dominant factor, which optimizes the network and that the number of encounters determines the statistically relevant distributions.

We consider the effects of time-varying packet generation rates in the performance of communication networks. The time variations could be a result of the patterns in human activities. As a model, we study the effects of a degree-dependent packet generation rate that includes a sinusoidal term. Applying a modified traffic awareness protocol (TAP) previously proposed for static packet generation rates to the present situation leads to an altered value of the optimization parameter, when compared to that obtained in the static case. To enhance the performance and to cope with the time-varying effects better, we propose a class of self-adjusting traffic awareness protocols that makes use of instantaneous traffic information beyond that included in the modified TAP. Two special cases that make use of global and local information, respectively, are studied. Comparing results of our proposal schemes with the modified TAP, it is shown that the present self-adjusting schemes perform more effectively.

A dissipative system with asymmetric interaction, as well as the optimal velocity model, generally shows a Hopf bifurcation concerned with the transition from homogeneous motion to the formation of nontrivial patterns. We reveal that the origin of Hopf bifurcation in macroscopic phenomena is strongly related to asymmetric interaction in a microscopic many-body system, using the continuum system derived from the original discrete system.

Event-driven simulations of inelastic smooth hard disks are used to probe the slip velocity and rheology in gravity-driven granular Poiseuille flow. It is shown that both the slip velocity $\left(U_w\right)$ and its gradient $\left(d{U}_w/dy\right)$ depend crucially on the mean density, wall roughness, and inelastic dissipation. While the gradient of slip velocity follows a single power-law relation with Knudsen number, the variation in $U_w$ with Kn shows three distinct regimes in terms of Knudsen number. An interesting possibility of Knudsen-number-dependent specularity coefficient emerges from a comparison of our results with a first-order transport theory for the slip velocity. Simulation results on stresses are compared with kinetic-theory predictions, with reasonable agreement of our data in the quasielastic limit. The deviation of simulations from theory increases with increasing dissipation which is tied to the increasing magnitude of the first normal stress difference $\left({\mathcal{N}}_1\right)$ that shows interesting nonmonotonic behavior with density. As in simple shear flow, there is a sign change of ${\mathcal{N}}_1$ at some critical density and its collisional component and the related collisional anisotropy are responsible for this sign reversal.

Monte Carlo simulations of a spherical macroion, surrounded by a size-asymmetric electrolyte in the primitive model, were performed. We considered 1:1 and 2:2 salts with a size ratio of 2 (i.e., with coions twice the size of counterions), for several surface charge densities of the macrosphere. The radial distribution functions, electrostatic potential in all the space and at the Helmholtz surfaces, and integrated charge are reported. We compare these simulational data with original results obtained from the Ornstein-Zernike integral equation, supplemented by the hypernetted chain–hypernetted chain (HNC-HNC) and hypernetted chain–mean spherical approximation (HNC-MSA) closures, and with the corresponding calculations using the modified Gouy-Chapman and unequal-radius modified Gouy-Chapman theories. The HNC-HNC and HNC-MSA integral equations formalisms show good concordance with Monte Carlo “experiments,” whereas the notable limitations of point-ion approaches are evidenced. Most importantly, the simulations confirm our previous theoretical predictions of the nondominance of the counterions in the size-asymmetric spherical electrical double layer [J. Chem. Phys. 123, 034703 (2005)], the appearance of anomalous curvatures at the outer Helmholtz plane, and the enhancement of the charge reversal and screening at high colloidal surface charge densities due to the ionic size asymmetry.

Drying processes of polymer solutions on a solid substrate enclosed by bank are studied in the slow limit of the solvent evaporation. A simple model is proposed to examine the final shape of the film after drying. Analytical expressions of the final shape in terms of the initial parameters are obtained. It is shown that the craterlike and basinlike shapes appear as final shapes of the film depending on the initial parameters. The “shape diagrams” which show parameter dependence of the final shape are presented in the absence/presence of diffusion. The final shape of the film in the geometry without bank is also discussed.

Recent experiments have exploited elastic instabilities in membranes to create complex patterns. However, the rational design of such structures poses many challenges, as they are products of nonlinear elastic behavior. We pose a simple model for determining the orientational order of such patterns using only linear elasticity theory which correctly predicts the outcomes of several experiments. Each element of the pattern is modeled by a “dislocation dipole” located at a point on a lattice, which then interacts elastically with all other dipoles in the system. We explicitly consider a membrane with a square lattice of circular holes under uniform compression and examine the changes in morphology as it is allowed to relax in a specified direction.

The effects of intrinsic noise on stochastic delay systems is studied within an expansion in the inverse system size. We show that the stochastic nature of the underlying dynamics may induce oscillatory behavior in parameter ranges where the deterministic system does not sustain cycles, and compute the power spectra of these stochastic oscillations analytically, in good agreement with simulations. The theory is developed in the context of a simple one-dimensional toy model, but is applicable more generally. Gene regulatory systems in particular often contain only a small number of molecules, leading to significant fluctuations in messenger RNA (mRNA) and protein concentrations. As an application we therefore study a minimalistic model of the expression levels of $hes1$ mRNA and Hes1 protein, representing the simple motif of an autoinhibitory feedback loop and motivated by its relevance to somite segmentation.

We investigate the physical reasons underlying the high monodispersity of empty virus capsids assembled in thermodynamical equilibrium in conditions of favorable $p\text{H}$ and ionic strength. We propose that the high fidelity of the assembly results from the effective spontaneous curvature of the viral protein assemblies and the corresponding bending rigidity that penalizes curvatures which are larger and smaller from the spontaneous one. On the example of hepatitis B virus, which has been thoroughly studied experimentally in the context of interest to us, we estimate the magnitude of bending rigidity that is needed to suppress the appearance of aberrant capsid structures $\left(\sim 60k_{B}T\right)$. Our approach also demonstrates that the aberrant capsids that can be classified within the Caspar-Klug framework are in most circumstances likely to be smaller from the regular ones, in agreement with the experimental findings.

In this paper we study the scaling behavior of the interface fluctuations (roughness) for a discrete model with conservative noise on complex networks. Conservative noise is a noise which has no external flux of deposition on the surface and the whole process is due to the diffusion. It was found that in Euclidean lattices the roughness of the steady state $W_s$ does not depend on the system size. Here, we find that for scale-free networks of $N$ nodes, characterized by a degree distribution $P\left(k\right)\sim k^{-\lambda }$, $W_s$ is independent of $N$ for any $\lambda$. This behavior is very different than the one found by Pastore y Piontti et al. [Phys. Rev. E 76, 046117 (2007)] for a discrete model with nonconservative noise, which implies an external flux, where $W_s\sim \text{ln}N$ for $\lambda <3$, and was explained by nonlinear terms in the analytical evolution equation for the interface [La Rocca et al., Phys. Rev. E 77, 046120 (2008)]. In this work we show that in these processes with conservative noise the nonlinear terms are not relevant to describe the scaling behavior of $W_s$.

We consider generalized synchronization of complex networks, which are unidirectionally coupled in the drive-response configuration. The drive network consists of linearly and diffusively coupled identical chaotic systems. By choosing suitable driving signals, we can construct the response network to generally synchronize the drive network in a predefined functional relationship. This extends both generalized synchronization of chaotic systems and synchronization inside a network. Theoretical analysis and numerical simulations fully verify our main results.