We present a detailed study of the equilibriumlike invaded cluster algorithm, recently proposed as an extension of the invaded cluster algorithm, designed to drive the system to criticality while still preserving the equilibrium ensemble. We perform extensive simulations on two special cases of the Potts model and examine the precision of critical exponents by including the leading corrections. We show that both thermal and magnetic critical exponents can be obtained with high accuracy compared to the best available results. The choice of the auxiliary parameters of the algorithm is discussed in context of dynamical properties. We also discuss the relation to the Li-Sokal bound for the dynamical exponent $z$.

Molecules with complex internal structure in time-dependent periodic potentials are studied by using short Rubinstein-Duke model polymers as an example. We extend our earlier work on transport in stochastically varying potentials to cover also deterministic potential switching mechanisms, energetic efficiency, and nonuniform charge distributions. We also use currents in the nonequilibrium steady state to identify the dominating mechanisms that lead to polymer transportation and analyze the evolution of the macroscopic state (e.g., total and head-to-head lengths) of the polymers. Several numerical methods are used to solve the master equations and nonlinear optimization problems. The dominating transport mechanisms are found via graph optimization methods. The results show that small changes in the molecule structure and the environment variables can lead to large increases of the drift. The drift and the coherence can be amplified by using deterministic flashing potentials and customized polymer charge distributions. Identifying the dominating transport mechanism by graph analysis tools is found to give insight in how the molecule is transported by the ratchet effect.

The effects of bond randomness on the phase diagram and critical behavior of the square lattice ferromagnetic Blume-Capel model are discussed. The system is studied in both the pure and disordered versions by the same efficient two-stage Wang-Landau method for many values of the crystal field, restricted here in the second-order phase-transition regime of the pure model. For the random-bond version several disorder strengths are considered. We present phase diagram points of both pure and random versions and for a particular disorder strength we locate the emergence of the enhancement of ferromagnetic order observed in an earlier study in the ex-first-order regime. The critical properties of the pure model are contrasted and compared to those of the random model. Accepting, for the weak random version, the assumption of the double-logarithmic scenario for the specific heat we attempt to estimate the range of universality between the pure and random-bond models. The behavior of the strong disorder regime is also discussed and a rather complex and yet not fully understood behavior is observed. It is pointed out that this complexity is related to the ground-state structure of the random-bond version.

The trapping of excitations in systems coupled to an environment allows one to study the quantum to classical crossover by different means. We show how to combine the phenomenological description by a non-Hermitian Liouville-von Neumann equation (LvNE) approach with the numerically exact path integral Monte Carlo (PIMC) method, and exemplify our results for a system of two coupled two-level systems. By varying the strength of the coupling to the environment we are able to estimate the parameter range in which the LvNE approach yields satisfactory results. Moreover, by matching the PIMC results with the LvNE calculations, we have a powerful tool to extrapolate the numerically exact PIMC method to long times.

It has recently been shown that amplified signal response is possible in scale-free networks of two-state signaling devices [J. A. Acebron et al., Phys. Rev. Lett. 99, 128701 (2007)]. In the analysis of dynamics in networks, much emphasis is put on the hub, and consequently the applicability thereof is limited to a region of small coupling strength. In this paper, we develop a one-body theory which predicts (1) the behavior of the gain in the whole coupling strength region, and (2) the degree of the unit, which shows maximum response, as a function of the coupling strength. In order to achieve good agreement with numerical experiments effects of finite system size are taken into account when the coupling strength becomes very small and the degree $k_L$ of the maximum response unit, predicted by our theory, becomes larger than the maximum degree $k_{max}$ available to a concrete finite network.

Dense random packings of hard particles are useful models of granular media and are closely related to the structure of nonequilibrium low-temperature amorphous phases of matter. Most work has been done for random jammed packings of spheres and it is only recently that corresponding packings of nonspherical particles (e.g., ellipsoids) have received attention. Here we report a study of the maximally random jammed (MRJ) packings of binary superdisks and monodispersed superballs whose shapes are defined by ${\left|x_1\right|}^{2p}+\cdots +{\left|x_d\right|}^{2p}\le 1$ with $d=2$ and 3, respectively, where $p$ is the deformation parameter with values in the interval $\left(0,\infty \right)$. As $p$ increases from zero, one can get a family of both concave $\left(0<p<0.5\right)$ and convex $\left(p\ge 0.5\right)$ particles with square symmetry $\left(d=2\right)$, or octahedral and cubic symmetry $\left(d=3\right)$. In particular, for $p=1$ the particle is a perfect sphere (circular disk) and for $p\to \infty$ the particle is a perfect cube (square). We find that the MRJ densities of such packings increase dramatically and nonanalytically as one moves away from the circular-disk and sphere point $\left(p=1\right)$. Moreover, the disordered packings are hypostatic, i.e., the average number of contacting neighbors is less than twice the total number of degrees of freedom per particle, and yet the packings are mechanically stable. As a result, the local arrangements of particles are necessarily nontrivially correlated to achieve jamming. We term such correlated structures “nongeneric.” The degree of “nongenericity” of the packings is quantitatively characterized by determining the fraction of local coordination structures in which the central particles have fewer contacting neighbors than average. We also show that such seemingly “special” packing configurations are counterintuitively not rare. As the anisotropy of the particles increases, the fraction of rattlers decreases while the minimal orientational order as measured by the tetratic and cubatic order parameters increases. These characteristics result from the unique manner in which superballs break their rotational symmetry, which also makes the superdisk and superball packings distinctly different from other known nonspherical hard-particle packings.

Evidence is presented to show the microstructural anisotropy responsible for normal stress in sheared suspensions. Particle velocimetry is combined with three-dimensional particle locations obtained via confocal microscopy at rest. A range of volume fractions $\varphi$ and local shear rates $\dot{\gamma }$ are investigated in a weakly Brownian pressure-driven suspension. At high $\dot{\gamma }$, the pairwise distribution shows a strong probability along the axis of compression similar to observations from Stokesian dynamics simulation at $\varphi =0.32$. At the channel center where $\dot{\gamma }\to 0$, the concentrated suspension at $\varphi =0.56$ behaves as a confined isotropic fluid.

We present a method to perform in situ microrheological measurements on monolayers of soft materials undergoing viscoelastic transitions under compression. Using the combination of a Langmuir trough mounted on the inverted microscope stage of a laser scanning confocal microscope we track the motion of individual fluorescent quantum dots partly dispersed in monolayers spread at the air-water interface. From the calculated mean square displacement of the probe particles and extending a well established scheme of the generalized Stokes-Einstein relation in bulk to the interface we arrive at the viscoelastic modulus for the respective monolayers as a function of surface density. Measurements on monolayers of glassy as well as nonglassy polymers and a standard fatty acid clearly show sensitivity of our technique to subtle variations, in the viscoelastic properties of the highly confined materials under compression. Evidence for possible spatial variations of such viscoelastic properties at a given surface density for the fatty acid monolayer is also provided.

Although widely used in practice, the behavior and accuracy of the popular module identification technique called modularity maximization is not well understood in practical contexts. Here, we present a broad characterization of its performance in such situations. First, we revisit and clarify the resolution limit phenomenon for modularity maximization. Second, we show that the modularity function $Q$ exhibits extreme degeneracies: it typically admits an exponential number of distinct high-scoring solutions and typically lacks a clear global maximum. Third, we derive the limiting behavior of the maximum modularity $Q_{\text{max}}$ for one model of infinitely modular networks, showing that it depends strongly both on the size of the network and on the number of modules it contains. Finally, using three real-world metabolic networks as examples, we show that the degenerate solutions can fundamentally disagree on many, but not all, partition properties such as the composition of the largest modules and the distribution of module sizes. These results imply that the output of any modularity maximization procedure should be interpreted cautiously in scientific contexts. They also explain why many heuristics are often successful at finding high-scoring partitions in practice and why different heuristics can disagree on the modular structure of the same network. We conclude by discussing avenues for mitigating some of these behaviors, such as combining information from many degenerate solutions or using generative models.

The appearance of mathematical regularities in the disposition of leaves on a stem, scales on a pine-cone, and spines on a cactus has puzzled scholars for millennia; similar so-called phyllotactic patterns are seen in self-organized growth, polypeptides, convection, magnetic flux lattices and ion beams. Levitov showed that a cylindrical lattice of repulsive particles can reproduce phyllotaxis under the (unproved) assumption that minimum of energy would be achieved by two-dimensional Bravais lattices. Here we provide experimental and numerical evidence that the Phyllotactic lattice is actually a ground state. When mechanically annealed, our experimental “magnetic cactus” precisely reproduces botanical phyllotaxis, along with domain boundaries (called transitions in Botany) between different phyllotactic patterns. We employ a structural genetic algorithm to explore the more general axially unconstrained case, which reveals multijugate (multiple spirals) as well as monojugate (single-spiral) phyllotaxis.

The Hirota equation is a modified nonlinear Schrödinger equation (NLSE) that takes into account higher-order dispersion and time-delay corrections to the cubic nonlinearity. In describing wave propagation in the ocean and optical fibers, it can be viewed as an approximation which is more accurate than the NLSE. We have modified the Darboux transformation technique to show how to construct the hierarchy of rational solutions of the Hirota equation. We present explicit forms for the two lower-order solutions. Each one is a regular (nonsingular) rational solution with a single maximum that can describe a rogue wave in this model. Numerical simulations reveal the appearance of these solutions in a chaotic field generated from a perturbed continuous wave solution.

We describe an approach to numerical simulation of spiral waves dynamics of large spatial extent, using small computational grids.

We perform numerical simulations to examine particle diffusion at steady shear in a soft-disk model in two dimensions and zero temperature around the jamming density. We find that the diffusion constant depends on shear rate as $D\sim \dot{\gamma }$ below jamming and as $D\sim {\dot{\gamma }}^{q_D}$ with $q_D<1$ at the transition and set out to relate this to properties of the velocity autocorrelation function. It is found that this correlation function is governed by two processes with different time scales. The first time scale, the inverse of the externally applied shear rate, controls an exponential decay of the correlations whereas the second time scale, equal to the inverse shear stress, governs an algebraic decay with time. The obtained value of $q_D$ is related to these properties of the correlation function.

There exists a variety of theories of the glass transition and many more numerical models. But because the models need built-in complexity to prevent crystallization, comparisons with theory can be difficult. We study the dynamics of a deeply supersaturated monodisperse four-dimensional (4D) hard-sphere fluid, which has no such complexity, but whose strong intrinsic geometrical frustration inhibits crystallization, even when deeply supersaturated. As an application, we compare its behavior to the mode-coupling theory (MCT) of glass formation. We find MCT to describe this system better than any other structural glass formers in lower dimensions. The reduction in dynamical heterogeneity in 4D suggested by a milder violation of the Stokes-Einstein relation could explain the agreement. These results are consistent with a mean-field scenario of the glass transition.

The concept of midpoint percolation has recently been applied to characterize the double percolation transitions in negatively curved structures. Regular $d$-dimensional hypercubic lattices are investigated in the present work using the same concept. Specifically, the site-percolation transitions at the critical thresholds are investigated for dimensions up to $d=10$ by means of the Leath algorithm. It is shown that the explicit inclusion of the boundaries provides a straightforward way to obtain critical indices, both for the bulk and surface parts. At and above the critical dimension $d=6$, it is found that the percolation cluster contains only a finite number of surface points in the infinite-size limit. This is in accordance with the expectation from studies of lattices with negative curvature. It is also found that the number of surface points, reached by the percolation cluster in the infinite limit, approaches $2d$ for large dimensions $d$. We also note that the size dependence in proliferation of percolating clusters for $d\ge 7$ can be obtained by solely counting surface points of the midpoint cluster.

We investigate the effects of quenched bond randomness on the critical properties of the two-dimensional ferromagnetic Ising model embedded in a triangular lattice. The system is studied in both the pure and disordered versions by the same efficient two-stage Wang-Landau method. In the first part of our study, we present the finite-size scaling behavior of the pure model, for which we calculate the critical amplitude of the specific heat’s logarithmic expansion. For the disordered system, the numerical data and the relevant detailed finite-size scaling analysis along the lines of the two well-known scenarios—logarithmic corrections versus weak universality—strongly support the field-theoretically predicted scenario of logarithmic corrections. A particular interest is paid to the sample-to-sample fluctuations of the random model and their scaling behavior that are used as a successful alternative approach to criticality.

The jamming transition of an isotropically compressed granular packing is studied by means of molecular dynamics simulations. The system is shown to undergo a critical transition which is analyzed by looking at the topological structure of the force network. At the critical packing fraction there is a sudden growth of the number of polygons in the network. Above the critical packing fraction the number of triangles keeps growing while the number of the rest of polygons is weakly reduced. Then, we prove that in the jammed regime, there is a linear relationship between the number of triangles and the coordination number. Furthermore, the presence of these minimal structures is revealed to be connected with the evolution of some important topological properties, suggesting its importance to understand the physical properties of the packing and the onset of rigidity during the compression.

Shear-driven segregation of dense granular mixtures has been associated with a number of interesting pattern formation problems. We use experimental and computational split-bottom cells to isolate segregation effects associated with shear gradients from those associated with gravity. We find the effect of shear gradients much less dramatic than initial observations of segregation suggest. While a segregation pattern emerges in a circular split-bottom cell that appears coincident with the shear gradient, we find the pattern is orthogonal to the active segregation flux. We measure a toroidal convection roll that, in conjunction with gravity-driven segregation, is likely responsible for the dramatic horizontal segregation pattern. On the other hand, computational results from a parallel split-bottom cell indicate a subtle segregation flux associated with the shear gradient. The nature of the driving mechanism is unknown. A current predictive form of kinetic theory based on binary collisions dominating the particle dynamics predicts segregation in the opposite direction from observed trends. This indicates the direction of shear-driven segregation depends on the nature of the flow itself, collisional or frictional.

The behavior of particles driven through a narrow constriction is investigated in experiment and simulation. The system of particles adapts to the confining potentials and the interaction energies by a self-consistent arrangement of the particles. It results in the formation of layers throughout the channel and of a density gradient along the channel. The particles accommodate to the density gradient by reducing the number of layers one by one when it is energetically favorable. The position of the layer reduction zone fluctuates with time while the particles continuously pass this zone. The flow behavior of the particles is studied in detail. The velocities of the particles and their diffusion behavior reflect the influence of the self-organized order of the system.

Nearly all glass-forming liquids feature, along with the structural $\alpha$-relaxation process, a faster secondary process ($\beta$ relaxation), whose nature belongs to the great mysteries of glass physics. However, for some of these liquids, no well-pronounced secondary relaxation is observed. A prominent example is the archetypical glass-forming liquid glycerol. In the present work, by performing dielectric spectroscopy under superhigh pressures up to 6 GPa, we show that in glycerol a significant secondary relaxation peak appears in the dielectric loss at $P>3\text{GPa}$. We identify this $\beta$ relaxation to be of Johari-Goldstein type and discuss its relation to the excess wing. We provide evidence for a smooth but significant increase in glass-transition temperature and fragility on increasing pressure.