Steady and transient two-dimensional thin-jet flow of a viscoelastic is examined theoretically. The influence of inertia, elasticity, and gravity is emphasized. The fluid is assumed to emerge from a vertical channel and to be driven by a pressure gradient and/or gravity. The boundary-layer equations are generalized for a viscoelastic thin film obeying the Oldroyd-B constitutive model. In contrast to the commonly used depth-averaging solution method, the strong nonlinearities are preserved in the present formulation as the viscoelastic boundary-layer equations are solved by expanding the flow field in terms of orthonormal shape functions. It is found that elasticity and gravity have the most profound effect on the steady state as well as the transient behavior of the viscoelastic film. The initial conditions strongly determine the stability of the film, which for all transient cases examined were shown to be stable despite the presence of initial instabilities.

The occurrence of the limit-point instability is an intriguing phenomenon observed during stretching of hyperelastic membranes. In toy rubber balloons, this phenomenon may be experienced in the sudden reduction in the level of difficulty of blowing the balloon accompanied by its rapid inflation. The present paper brings out a link between the geometry and strain-hardening parameter of the membrane, and the occurrence of the limit-point instability. Inflation of membranes with different geometries and boundary conditions is considered, and the corresponding limit-point pressures are obtained for different strain-hardening parameter values. Interestingly, it is observed that the limit-point pressure for the different geometries is inversely proportional to a geometric parameter of the uninflated membrane. This dependence is shown analytically, which can be extended to a general membrane geometry. More surprisingly, the proportionality constant has a power-law dependence on the nondimensional material strain-hardening parameter. The constants involved in the power-law relation are universal constants for a particular membrane geometry.

Diffusion in a tube of periodically varying diameter occurs slower than that in a cylindrical tube because diffusing particles get trapped in wells of the periodic entropy potential which is due to variation of the tube cross-section area. To quantify the slowdown one has to establish a relation between the effective diffusion coefficient of the particle and the tube geometry, which is a very complicated problem. Here we show how to overcome the difficulties in the case of a periodically expanded conical tube, where we find an approximate solution for the effective diffusion coefficient as a function of the parameters determining the tube geometry.

We study the effect of a gradient of solvent quality on the coil-globule transition for a polymer in a narrow pore. A simple self-attracting, self-avoiding walk model of a polymer in solution shows that the variation in the strength of the interaction across the pore leads the system to go from one regime (good solvent) to the other (poor solvent) across the channel. This may be thought to be analogous to thermophoresis, where the polymer goes from the hot region to the cold region under the temperature gradient. The behavior of short chains is studied using exact enumeration while the behavior of long chains is studied using transfer matrix techniques. The distribution of the monomer density across the layer suggests that a gatelike effect can be created, with potential applications as a sensor.

Novel dynamic experiments have enabled the identification of a macroscopic solidlike response in the isotropic phase of a low molecular weight liquid crystal, 4,4'-$n$-octylcyanobiphenyl (8CB). This unknown property indicates that the low frequency shear elasticity identified in the isotropic phase of liquid crystal polymers is not reminiscent from the glass transition but reveals likely a generic property of the liquid state. The comparison to high molecular weight liquid crystals indicates, however, that the shear modulus is much enhanced when the liquid crystal moieties are attached to a polymer chain. The macroscopic length scales probed (0.050–0.100 mm) exclude wall-induced effects.

Defect dynamics in a thin active nematic layer is studied by asymptotic matching of solutions in the defect core and the far field. The analysis is facilitated by the correspondence between the two-dimensional nematic and complex scalar field models. Self-propulsion and topological interactions are identified as the primary drivers of the defect motion, surpassing the influence of both passive backflow and active flow induced by other defects.

We develop a theoretical framework for the study of epidemiclike social contagion in large scale social systems. We consider the most general setting in which different communication platforms or categories form multiplex networks. Specifically, we propose a contact-based information spreading model, and show that the critical point of the multiplex system associated with the active phase is determined by the layer whose contact probability matrix has the largest eigenvalue. The framework is applied to a number of different situations, including a real multiplex system. Finally, we also show that when the system through which information is disseminating is inherently multiplex, working with the graph that results from the aggregation of the different layers is inaccurate.

The statistics of rare events, the so-called black-swan events, is governed by non-Gaussian distributions with heavy power-like tails. We calculate the Green functions of the associated Fokker-Planck equations and solve the related stochastic differential equations. We also discuss the subject in the framework of path integration.

Under the assumption that the physically appropriate entropy of generic complex systems satisfies thermodynamic extensivity, we investigate the recently introduced entropy $S_{\delta }$ (which recovers the usual Boltzmann-Gibbs form for $\delta =1$) and establish the microcanonical and canonical extremizing distributions. Using a generalized version of the H theorem, we find the nonlinear Fokker-Planck equation associated with that entropic functional and calculate the stationary-state probability distributions. We demonstrate that both approaches yield one and the same equation, which in turn uniquely determines the probability distribution. We show that the equilibrium distributions asymptotically behave like stretched exponentials, and that, in appropriate probability-energy variables, an interesting return occurs at $\delta =4/3$. As a mathematically simple illustration, we consider the one-dimensional harmonic oscillator and calculate the generalized chemical potential for different values of $\delta$.

We report on the viscosity of a dilute suspension of cube-shaped particles. Irrespective of the particle size, size distribution, and surface chemistry, we find empirically that cubes manifest an intrinsic viscosity $\left[\eta \right]=3.1\pm 0.2$, which is substantially higher than the well-known value for spheres, $\left[\eta \right]=2.5$. The orientation-dependent intrinsic viscosity of cubic particles is determined theoretically using a finite-element solution of the Stokes equations. For isotropically oriented cubes, these calculations show $\left[\eta \right]=3.1$, in excellent agreement with our experimental observations.

Protein structure prediction (PSP) is a classical NP-hard problem in computational biology. The energy-landscape paving (ELP) method is a class of heuristic global optimization algorithm, and has been successfully applied to solving many optimization problems with complex energy landscapes in the continuous space. By putting forward a new update mechanism of the histogram function in ELP and incorporating the generation of initial conformation based on the greedy strategy and the neighborhood search strategy based on pull moves into ELP, an improved energy-landscape paving (ELP+) method is put forward. Twelve general benchmark instances are first tested on both two-dimensional and three-dimensional (3D) face-centered-cubic (fcc) hydrophobic-hydrophilic (HP) lattice models. The lowest energies by ELP+ are as good as or better than those of other methods in the literature for all instances. Then, five sets of larger-scale instances, denoted by S, R, F90, F180, and CASP target instances on the 3D FCC HP lattice model are tested. The proposed algorithm finds lower energies than those by the five other methods in literature. Not unexpectedly, this is particularly pronounced for the longer sequences considered. Computational results show that ELP+ is an effective method for PSP on the fcc HP lattice model.

Adaptive social networks, in which nodes and network structure coevolve, are often described using a mean-field system of equations for the density of node and link types. These equations constitute an open system due to dependence on higher-order topological structures. We propose a new approach to moment closure based on the analytical description of the system in an asymptotic regime. We apply the proposed approach to two examples of adaptive networks: recruitment to a cause model and adaptive epidemic model. We show a good agreement between the improved mean-field prediction and simulations of the full network system.

We consider the interfacial motion between two immiscible viscous fluids in the confined geometry of a radial Hele-Shaw cell. In this framework, we investigate the influence of a thin wetting film trailing behind the displaced fluid on the linear and weakly nonlinear dynamics of the system. More specifically, we examine how the interface instability and the pattern formation mechanisms of finger tip splitting and finger competition are affected by the presence of such a film in the low capillary number limit. Our theoretical analysis is carried out by employing a mode-coupling theory, which allows analytic assess to wetting-induced changes in pattern morphology at the onset of nonlinearities.

Cellular senescence is thought to play a major role in age-related diseases, which cause nearly 67% of all human deaths worldwide. Recent research in mice showed that exercising mice had higher levels of telomerase, an enzyme that helps maintain telomere length, than nonexercising mice. A commonly used model for biological aging was proposed by Penna. I propose a modification of the Penna model that incorporates cellular senescence and find an analytical steady-state solution following Coe, Mao, and Cates [Phys. Rev. Lett. 89, 288103 (2002)]. I find that models corresponding to delayed cellular senescence have younger populations that live longer. I fit the model to the United Kingdom's death distribution, which the original Penna model cannot do.

The effect of magnesium ion Mg${}^{2+}$ on the dielectric relaxation of semidilute DNA aqueous solutions has been studied by means of dielectric spectroscopy in the 100 Hz–100 MHz frequency range. de Gennes–Pfeuty–Dobrynin semidilute solution correlation length is the pertinent fundamental length scale for sufficiently low concentration of added salt, describing the collective properties of Mg-DNA solutions. No relaxation fingerprint of the DNA denaturation bubbles, leading to exposed hydrophobic core scaling, was detected at low DNA concentrations, thus indicating an increased stability of the double-stranded conformation in Mg-DNA solutions as compared to the case of Na-DNA solutions. Some changes are detected in the behavior of the fundamental length scale pertaining to the single molecule DNA properties, reflecting modified electrostatic screening effects of the Odijk-Skolnick-Fixman type. All results consistently demonstrate that Mg${}^{2+}$ ions interact with DNA in a similar way as Na${}^{1+}$ ions do, their effect being mostly describable through an enhanced screening.

We investigate mobility regimes for localized modes in the discrete nonlinear Schrödinger (DNLS) equation with the cubic-quintic on-site terms. Using the variational approximation, the largest soliton's total power admitting progressive motion of kicked discrete solitons is predicted by comparing the effective kinetic energy with the respective Peierls-Nabarro (PN) potential barrier. The prediction, for the DNLS model with the cubic-only nonlinearity too, demonstrates a reasonable agreement with numerical findings. A small self-focusing quintic term quickly suppresses the mobility. In the case of the competition between the cubic self-focusing and quintic self-defocusing terms, we identify parameter regions where odd and even fundamental modes exchange their stability, involving intermediate asymmetric modes. In this case, stable solitons can be set in motion by kicking, so as to let them pass the PN barrier. Unstable solitons spontaneously start oscillatory or progressive motion, if they are located, respectively, below or above a mobility threshold. Collisions between moving discrete solitons, at the competing nonlinearities frame, are studied too.

Extremal spacings between eigenphases of random unitary matrices of size $N$ pertaining to circular ensembles are investigated. Explicit probability distributions for the minimal spacing for various ensembles are derived for $N=4$. We study ensembles of tensor product of $k$ random unitary matrices of size $n$ which describe independent evolution of a composite quantum system consisting of $k$ subsystems. In the asymptotic case, as the total dimension $N=n^k$ becomes large, the nearest neighbor distribution $P\left(s\right)$ becomes Poissonian, but statistics of extreme spacings $P\left(s_{\min }\right)$ and $P\left(s_{\max }\right)$ reveal certain deviations from the Poissonian behavior.

Long-range power-law correlated percolation is investigated using Monte Carlo simulations. We obtain several static and dynamic critical exponents as functions of the Hurst exponent $H$, which characterizes the degree of spatial correlation among the occupation of sites. In particular, we study the fractal dimension of the largest cluster and the scaling behavior of the second moment of the cluster size distribution, as well as the complete and accessible perimeters of the largest cluster. Concerning the inner structure and transport properties of the largest cluster, we analyze its shortest path, backbone, red sites, and conductivity. Finally, bridge site growth is also considered. We propose expressions for the functional dependence of the critical exponents on $H$.

We investigate the validity and accuracy of weak-noise (saddle-point or instanton) approximations for piecewise-smooth stochastic differential equations (SDEs), taking as an illustrative example a piecewise-constant SDE, which serves as a simple model of Brownian motion with solid friction. For this model, we show that the weak-noise approximation of the path integral correctly reproduces the known propagator of the SDE at lowest order in the noise power, as well as the main features of the exact propagator with higher-order corrections, provided the singularity of the path integral associated with the nonsmooth SDE is treated with some heuristics. We also show that, as in the case of smooth SDEs, the deterministic paths of the noiseless system correctly describe the behavior of the nonsmooth SDE in the low-noise limit. Finally, we consider a smooth regularization of the piecewise-constant SDE and study to what extent this regularization can rectify some of the problems encountered when dealing with discontinuous drifts and singularities in SDEs.

We present a model of multiplicative Langevin dynamics that is based on two foundations: the Langevin equation and the notion of multiplicative evolution. The model is a nonlinear mechanism transforming a white-noise input to a dynamic-equilibrium output, using a single control: an underlying convex U-shaped potential function. The output is quantified by a stationary density which can attain a given number of shapes and a given number of randomness categories. The model generates each admissible combination of the output's shape and randomness in a universal and robust fashion. Moreover, practically all the probability distributions that are supported on the positive half-line, and that are commonly encountered and applied across the sciences, can be reverse engineered by this model. Hence, this model is a universal equilibrium mechanism, in the context of multiplicative dynamics, for the robust generation of “chance”: the model's output. In turn, the properties of the produced “chance,” the output's shape and randomness, are determined with mathematical precision by the control's landscape, its topography. Thus, a topographic map of chance is established. As a particular application, probability distributions with power-law tails are shown to be universally and robustly generated by controls on the “edge of convexity”: convex U-shaped potential functions with asymptotically linear wings.