We consider a partially directed walk model of a strictly alternating copolymer adsorbing on a striped surface where the energy is associated with the numbers of the two types of monomers adsorbed on the two types of surface sites. A force is applied to the last monomer and the polymer responds to this force, sometimes by desorbing. The force can be applied at various angles, with the surface component parallel or perpendicular (or at some other angle) to the stripe direction. The desorption behavior is strongly dependent on the force direction and the response gives information about the shape and direction of the polymer adsorbed on the surface, especially at low temperatures. In some cases the ground state is degenerate and this also has an important effect on the temperature dependence of the critical force needed for desorption. We give a complete solution of the problem using generating function techniques and an approximate treatment that is especially useful at low temperatures and helps in our physical understanding of the situation.

This work discusses the sedimentation stability and aging of aqueous suspensions of Laponite in the presence of cetyltrimethylammonium bromide (CTAB). The concentration of Laponite was fixed at a constant level $C_l=2$ %wt, which corresponds to the threshold between equilibrium gel IG${}_1$ and glass IG${}_2$ states. The concentration of CTAB $C_s$ was within 0–0.3 %wt. In the presence of CTAB, the Laponite aqueous suspensions were unstable against sedimentation and separated into the upper and bottom layers (U and B layers, respectively). The dynamic light-scattering technique has revealed that addition of CTAB even at a rather small concentration, $C_s=0.0164$ %wt (0.03 cation exchange capacity), induced noticeable changes in the aging dynamics of the U layer. It was explained by equilibration of CTAB molecules that were initially nonuniformly distributed between different Laponite particles. Accelerated stability analysis by means of analytical centrifugation with rotor speed $\omega =500$–4000 rpm revealed three sedimentation regimes: continuous (I, $C_s<0.14$ %wt), zonelike (II, $0.14<C_s<0.2$ %wt), and gel-like (III, $C_s>0.2$ %wt). It was demonstrated that the B layer was “soft” in the zonelike regime. The increase of $\omega$ resulted in its supplementary compressing and collapse of “soft” sediment above certain critical centrifugal acceleration. The physical nature of the observed behavior, accounting for enhancement of hydrophobic interactions between Laponite particles, is discussed.

When loaded in simple shear deformation, polymeric materials may develop so-called normal stresses: stresses perpendicular to the direction of the applied shear. These normal stresses are intrinsically nonlinear: basic symmetry considerations dictate they may only enter at $O\left({\gamma }^2\right)$, with $\gamma$ the dimensionless shear strain. There is no fundamental restriction on their sign, and normal stresses may be positive (pushing outward) or negative (pulling inward). Most materials tend to dilate in the normal direction, but a wide variety of biopolymer networks including fibrin and actin gels have been reported to present anomalously large, negative normal stresses—a feature which has been ascribed to the intrinsic elastic nonlinearity of semiflexible fibers. In this work, we present analytical results on a model nonlinear network, which we expand to the required nonlinear order to show that due to geometric, rather than elastic, nonlinearities (negative) normal stresses generically arise in filamentous networks—even in networks composed of linear, Hookean springs. We investigate analytically and numerically how the subsequent addition of elastic nonlinearities, nonaffine deformations, and filament persistence through cross-linkers augment this basic behavior.

RNA molecules form three-dimensional structures via base pairing that determine the function and biochemical activity of the molecule. Here we introduce a structure-based method for studying the folding dynamics of RNA secondary structures. The approach focuses on native contacts that are parametrized with standard empirical free energies. Kinetic Monte Carlo simulations for free folding of simple hairpins and complex structures such as a tRNA as well as for folding in the presence of an external force show good agreement with experimental data. A systematic comparison of simulated and experimental folding rates for various structures shows a strong correlation, indicating that the approach can predict folding rates within about an order of magnitude.

It is well known that sexually transmitted diseases (STD) spread across a network of human sexual contacts. This network is most often bipartite, as most STD are transmitted between men and women. Even though network models in epidemiology have quite a long history now, there are few general results about bipartite networks. One of them is the simple dependence, predicted using the mean field approximation, between the epidemic threshold and the average and variance of the degree distribution of the network. Here we show that going beyond this approximation can lead to qualitatively different results that are supported by numerical simulations. One of the new features, that can be relevant for applications, is the existence of a critical value for the infectivity of each population, below which no epidemics can arise, regardless of the value of the infectivity of the other population.

As a fundamental problem in network study, community identification has attracted much attention from different fields. Representing a seminal work in this area, the modularity optimization method has been widely applied and studied. However, this method has issues in resolution limit and extreme degeneracy and may not perform well for networks with unbalanced structures. Although several methods have been proposed to overcome these limitations, they are all based on the original idea of defining modularity through comparing the total number of edges within the putative communities in the observed network with that in an equivalent randomly generated network. In this paper, we show that this modularity definition is not suitable to analyze some networks such as those with unbalanced structures. Instead, we propose to define modularity through the average degree within the communities and formulate modularity as comparing the sum of average degree within communities of the observed network to that of an equivalent randomly generated network. In addition, we also propose a degree-adjusted approach for further improvement when there are unbalanced structures. We analyze the theoretical properties of our degree adjusted method. Numerical experiments for both artificial networks and real networks demonstrate that average degree plays an important role in network community identification, and our proposed methods have better performance than existing ones.

In the voter and many other opinion formation models, agents are assumed to behave as congregators (also called the conformists); they are attracted to the opinions of others. In this study I investigate linear extensions of the voter model with contrarian agents. An agent is either congregator or contrarian and assumes a binary opinion. I investigate three models that differ in the behavior of the contrarian toward other agents. In model 1, contrarians mimic the opinions of other contrarians and oppose (i.e., try to select the opinion opposite to) those of congregators. In model 2, contrarians mimic the opinions of congregators and oppose those of other contrarians. In model 3, contrarians oppose anybody. In all models, congregators are assumed to like anybody. I show that even a small number of contrarians prohibits the consensus in the entire population to be reached in all three models. I also obtain the equilibrium distributions using the van Kampen small-fluctuation approximation and the Fokker-Planck equation for the case of many contrarians and a single contrarian, respectively. I show that the fluctuation around the symmetric coexistence equilibrium is much larger in model 2 than in models 1 and 3 when contrarians are rare.

Electrorheological fluids are suspensions that are characterized by a strong functional dependence of the constitutive behavior of the fluids on the electric field. In this work, we consider electro-osmosis of an electrorheological fluid through a channel where a transverse, nonuniform electric field is spontaneously induced due to the presence of an electric double layer that is manifested due to surface charge density at the channel wall. We reveal a nonlinear interplay between the applied electric field, the induced electric field, and the observed flow profiles, which is fundamentally distinctive from other types of nonlinear electrokinetic effects that have been extensively discussed in the literature, in a sense that here an interaction between the applied electric field, the induced electric field, and the dependence of the rheology on the resultant electric field happens to be the focal source of nonlinearity in the observed phenomena. We analyze the electro-osmotic flow control through the exploitation of a combined nonlinear interplay of the driving electrokinetic forces and the resistive viscous interactions, which gives rise to distinctive flow regimes as compared to those realized in cases of either Newtonian fluids or non-Newtonian fluids having electric-field-independent flow rheology.

The effect of an electric field on the shear wave instability pertaining to a gravity driven conducting liquid film is studied based on the Chebyshev-Tau method. The shear wave appears at very large values of the Reynolds number when the inclination angle is sufficiently small. The presence of an electric field shows peculiar behavior on the critical Reynolds number corresponding to the shear mode. It suppresses shear wave instability through the amplification of the critical Reynolds number and leads to a nontrivial stabilizing effect when inclination angle $B\ge 3^{\prime }$. On the other hand, the reduction of the critical Reynolds number is found if the inclination angle is further lowered in magnitude.

The density of states of continuous models is known to span many orders of magnitudes at different energies due to the small volume of phase space near the ground state. Consequently, the traditional Wang-Landau sampling which uses the same trial move for all energies faces difficulties sampling the low-entropic states. We developed an adaptive variant of the Wang-Landau algorithm that very effectively samples the density of states of continuous models across the entire energy range. By extending the acceptance ratio method of Bouzida, Kumar, and Swendsen such that the step size of the trial move and acceptance rate are adapted in an energy-dependent fashion, the random walker efficiently adapts its sampling according to the local phase space structure. The Wang-Landau modification factor is also made energy dependent in accordance with the step size, enhancing the accumulation of the density of states. Numerical simulations show that our proposed method performs much better than the traditional Wang-Landau sampling.

We present an error-diagnostic validation method for posterior distributions in Bayesian signal inference, an advancement of a previous work. It transfers deviations from the correct posterior into characteristic deviations from a uniform distribution of a quantity constructed for this purpose. We show that this method is able to reveal and discriminate several kinds of numerical and approximation errors, as well as their impact on the posterior distribution. For this we present four typical analytical examples of posteriors with incorrect variance, skewness, position of the maximum, or normalization. We show further how this test can be applied to multidimensional signals.

We developed a lattice Boltzmann method coupled with the Oldroyd-B constitutive equation to simulate a viscoelastic fluid. In this work, the flow field of the solvent is solved using an incompressible lattice Boltzmann Bhatnagar-Gross-Krook (BGK) model, while the advection operator of the polymer stress tensor is directly calculated with the help of the particle distribution functions. Specifically, we present a numerical scheme for the advection of the polymer stress tensor through the truncation of second-order Taylor expansion, which does not need to introduce the extra distribution functions and has better numerical accuracy. We consider two types of numerical tests to examine the performance of the presented method, including a two-dimensional (2D) channel flow and the 4:1 contraction problem. Our numerical results for the 2D channel flow agree well with the analytical results and some experimental results reported in the previous studies. Moreover, the numerical results also indicate that the current method can capture some complex rheological behaviors of the 4:1 contraction flow.

The local order units of dense simple liquid are typically three-dimensional (close packed) clusters: hcp, fcc, and icosahedrons. We show that the fluid demonstrates the superstable tetrahedral local order up to temperatures several orders of magnitude higher than the melting temperature and down to critical density. While the solid-like local order (hcp, fcc) disappears in the fluid at much lower temperatures and far above critical density. We conclude that the supercritical fluid shows the temperature (density)-driven two-stage “melting” of the three-dimensional local order. We also find that the structure relaxation times in the supercritical fluid are much larger than ones estimated for weakly interactive gas even far above the melting line.

The internal structures of most periodic crystalline solids contain defects. This affects various important mechanical and thermal properties of crystals. Since it is very difficult and expensive to track the motion of individual atoms in real solids, macroscopic model systems, such as complex plasmas, are often used. Complex plasmas consist of micrometer-sized grains immersed into an ion-electron plasma. They exist in solidlike, liquidlike, and gaseouslike states and exhibit a range of nonlinear and dynamic effects, most of which have direct analogies in solids and liquids. Slabs of a monolayer hexagonal complex plasma were subjected to a cycle of uniaxial compression and decompression of large amplitudes to achieve plastic deformations, both in experiments and simulations. During the cycle, the internal structure of the lattice exhibited significant rearrangements. Dislocations (point defects) were generated and displaced in the stressed lattice. They tended to glide parallel to their Burgers vectors under load. It was found that the deformation cycle was macroscopically reversible but irreversible at the particle scale.

We show that any Monte Carlo (MC) algorithm using joint updates of more than a single variable at each step produces time-shifted correlations between variables—even if the equilibrium probabilities of the variables are independent. These spurious time-shifted correlations will affect both the magnitudes of correlation times and the values of optimal acceptance ratios. In particular, correlation times computed with local variables will not generally give the same predictions of efficiency or optimal acceptance ratios as those computed with global variables. Gelman, Roberts, and Gilks [Bayesian Statistics, edited by J. M. Bernardo, J. O. Berger, A. P. Dawid, and A. R. M. Smith, Vol. 5 (Oxford University Press, 1996), pp. 599–607] have used a local measure of efficiency to prove a theorem for global MC updating that predicts an optimal acceptance ratio of 0.234 as the number of variables goes to infinity. We show that global measures of efficiency can produce different, and arguably more appropriate, optimal acceptance ratios. More importantly, global updating is inherently far less efficient than updating variables separately or in small groups. We suggest that previously determined optimal acceptance ratios and their implications for practical applications should be reconsidered in the context of these findings.

We describe a mean field interacting particle system in any number of dimensions and in a generic external potential as an ideal gas with fractional exclusion statistics (FES). We define the FES quasiparticle energies, we calculate the FES parameters of the system and we deduce the equations for the equilibrium particle populations. The FES gas is “ideal,” in the sense that the quasiparticle energies do not depend on the other quasiparticle levels’ populations and the sum of the quasiparticle energies is equal to the total energy of the system. We prove that the FES formalism is equivalent to the semiclassical or Thomas Fermi limit of the self-consistent mean-field theory and the FES quasiparticle populations may be calculated from the Landau quasiparticle populations by making the correspondence between the FES and the Landau quasiparticle energies. The FES provides a natural semiclassical ideal gas description of the interacting particle gas.

Fast phase transitions under lack of local thermalization between successive elementary steps of the physical process are treated analytically. Non-Markovian master equations are derived for fast processes, which do not have enough time to reach energy or momentum thermalization during rapid phase change or freezing of a highly nonequilibrium system. These master equations provide a further physical basis for evolution and transport equations of the phase-field model used previously in the analyses of fast phase transitions.

The location and nature of the percolation transition in random networks is a subject of intense interest. Recently, a series of graph evolution processes have been introduced that lead to discontinuous percolation transitions where the addition of a single edge causes the size of the largest component to exhibit a significant macroscopic jump in the thermodynamic limit. These processes can have additional exotic behaviors, such as displaying a “Devil's staircase” of discrete jumps in the supercritical regime. Here we investigate whether the location of the largest jump coincides with the percolation threshold for a range of processes, such as Erdős-Rényipercolation, percolation via edge competition and via growth by overtaking. We find that the largest jump asymptotically occurs at the percolation transition for Erdős-Rényiand other processes exhibiting global continuity, including models exhibiting an “explosive” transition. However, for percolation processes exhibiting genuine discontinuities, the behavior is substantially richer. In percolation models where the order parameter exhibits a staircase, the largest discontinuity generically does not coincide with the percolation transition. For the generalized Bohman-Frieze-Wormald model, it depends on the model parameter. Distinct parameter regimes well in the supercritical regime feature unstable discontinuous transitions—a novel and unexpected phenomenon in percolation. We thus demonstrate that seemingly and genuinely discontinuous percolation transitions can involve a rich behavior in supercriticality, a regime that has been largely ignored in percolation.

We propose and validate a three-dimensional continuum modeling approach that predicts small-amplitude acoustic behavior of dense-packed granular media. The model is obtained through a joint experimental and finite-element study focused on the benchmark example of a vibrated container of grains. Using a three-parameter linear viscoelastic constitutive relation, our continuum model is shown to quantitatively predict the effective mass spectra in this geometry, even as geometric parameters for the environment are varied. Further, the model's predictions for the surface displacement field are validated mode-by-mode against experiment. A primary observation is the importance of the boundary condition between grains and the quasirigid walls.

Mutual diffusion coefficients, shear viscosities, and broadband ultrasonic attenuation spectra in the frequency range 100 kHz to 300 MHz have been measured for solutions of polystyrene in cyclohexane at two degrees of polymerization $N$ and various temperatures near the critical. The exponent $y_{\eta }$ in the power law representation of the critical part in the viscosity deviates substantially from the universal value $y_{\eta }$ $=$ 0.0435: $y_{\eta }$ $=$ 0.028 ($N$ $=$ 288) and $y_{\eta }$ $=$ 0.014 ($N$ $=$ 6242). Also, the adiabatic coupling constant $g$ and the amplitudes ξ${}_0$ and Γ${}_0$ in the power laws of the correlation length and the relaxation rate of fluctuations, respectively, depend on $N$. This is especially obvious with the relaxation rates, for which Γ${}_0$ $=$ 5.8×10${}^9$ at $N$ $=$ 288 and Γ${}_0$ $=$ 6.1×10${}^7$ with the larger polymer results. A noteworthy feature is the difference between the relaxation rates from the diffusion coefficients and shear viscosities on the one hand and from the ultrasonic spectra on the other. Near the critical temperatures the latter Γ values deviate from power law behavior, indicating a coupling between the concentration fluctuations and structural isomerizations of the polymers.