We have obtained “iso-osmobars,” which refer to lines with constant osmotic pressures, and coexistence curve of the volume phase transition of $N$-isopropylacrylamide gel using a very simple method: hanging gels above NaCl solution having a given concentration in a sealed container that was placed in a temperature controlled bath. Since the chemical potential of the water molecules in the gel is equal to that of the water molecules in the NaCl solution, the osmotic pressure of the gel became the same value with that of the NaCl solution. Thus, air that separated the gel and the NaCl solution played a role of infinitely flexible semipermeable membrane. We have succeeded to obtain the coexistence curve and related critical exponent $\beta$ from the series of the iso-osmobars of the gel. The value of $\beta$ we obtained was $0.38\left(1.5\right)$.

The dynamics of a diffusing particle in a potential field is ubiquitous in physics, and it plays a pivotal role in single-molecule studies. We present a formalism for analyzing the dynamics of diffusing particles in harmonic potentials at low Reynolds numbers using the time evolution of the particle probability distribution function. We demonstrate the power of the formalism by simulation and by measuring and analyzing a nanobead tethered to a single DNA molecule. It allows one to simultaneously extract all the parameters that describe the system, namely, the diffusion coefficient and the restoring-force constant.

Virus capsid assembly has traditionally been considered as a process that can be described primarily via self-assembly of the capsid proteins, neglecting interactions with other viral or cellular components. Our recent work on several ssRNA viruses, a major class of viral pathogens containing important human, animal, and plant viruses, has shown that this protein-centric view is too simplistic. Capsid assembly for these viruses relies strongly on a number of cooperative roles played by the genomic RNA. This realization requires a new theoretical framework for the modeling and prediction of the assembly behavior of these viruses. In a seminal paper Zlotnick [J. Mol. Biol. 241, 59 (1994)] laid the foundations for the modeling of capsid assembly as a protein-only self-assembly process, illustrating his approach using the example of a dodecahedral study system. We describe here a generalized framework for modeling assembly that incorporates the regulatory functions provided by cognate protein–nucleic-acid interactions between capsid proteins and segments of the genomic RNA, called packaging signals, into the model. Using the same dodecahedron system we demonstrate, using a Gillespie-type algorithm to deal with the enhanced complexity of the problem instead of a master equation approach, that assembly kinetics and yield strongly depend on the distribution and nature of the packaging signals, highlighting the importance of the crucial roles of the RNA in this process.

Replication and transcription are two important processes in living systems. To execute such processes, various proteins work far away from equilibrium in a staggered way. Motivated by this, aspects of hysteresis during unzipping of DNA under a periodic drive are studied. A steady-state phase diagram of a driven DNA is proposed which is experimentally verifiable. As a two-state system, we also compare the results of DNA with that of an Ising magnet under an asymmetrical variation of the magnetic field.

The return-to-origin probability and the first-passage-time distribution are essential quantities for understanding transport phenomena in diverse systems. The behaviors of these quantities typically depend on the spectral dimension $d_s$. However, it was recently revealed that in scale-free networks these quantities show a crossover between two power-law regimes characterized by $d_s$ and the so-called hub spectral dimension $d_s^{\left(\mathrm{hub}\right)}$ due to the heterogeneity of connectivities of each node. To understand the origin of $d_s^{\left(\mathrm{hub}\right)}$ from a theoretical perspective, we study a random walk problem on hierarchical scale-free networks by using the renormalization group (RG) approach. Under the RG transformation, not only the system size but also the degree of each node changes due to the scale-free nature of the degree distribution. We show that the anomalous behavior of random walks involving the hub spectral dimension $d_s^{\left(\mathrm{hub}\right)}$ is induced by the conservation of the power-law degree distribution under the RG transformation.

In recent years, the theory and application of complex networks have been quickly developing in a markable way due to the increasing amount of data from real systems and the fruitful application of powerful methods used in statistical physics. Many important characteristics of social or biological systems can be described by the study of their underlying structure of interactions. Hierarchy is one of these features that can be formulated in the language of networks. In this paper we present some (qualitative) analytic results on the hierarchical properties of random network models with zero correlations and also investigate, mainly numerically, the effects of different types of correlations. The behavior of the hierarchy is different in the absence and the presence of giant components. We show that the hierarchical structure can be drastically different if there are one-point correlations in the network. We also show numerical results suggesting that the hierarchy does not change monotonically with the correlations and there is an optimal level of nonzero correlations maximizing the level of hierarchy.

In social animals, the presence of conflicts of interest or multiple leaders can promote the emergence of two or more subgroups. Such subgroups are easily recognizable by human observers, yet a quantitative and objective measure of group fragmentation is currently lacking. In this paper, we explore the feasibility of detecting group fragmentation by embedding the raw data from the individuals' motions on a low-dimensional manifold and analyzing the topological features of this manifold. To perform the embedding, we employ the isomap algorithm, which is a data-driven machine learning tool extensively used in computer vision. We implement this procedure on a data set generated by a modified à la Vicsek model, where agents are partitioned into two or more subsets and an independent leader is assigned to each subset. The dimensionality of the embedding manifold is shown to be a measure of the number of emerging subgroups in the selected observation window and a cluster analysis is proposed to aid the interpretation of these findings. To explore the feasibility of using this approach to characterize group fragmentation in real time and thus reduce the computational cost in data processing and storage, we propose an interpolation method based on an inverse mapping from the embedding space to the original space. The effectiveness of the interpolation technique is illustrated on a test-bed example with potential impact on the regulation of collective behavior of animal groups using robotic stimuli.

We experimentally investigate the Lagrangian-Eulerian dynamics of fluid motion and wave-form evolution for a breaking shallow water wave approaching a slope by tracking tracer motions. It is found that, before breaking, the surface element can climb over the crest and exhibits cyclic oscillation with small forward drift. The increasing asymmetric tangential compression (accumulation) and rarefaction (depletion) in the crest front and the crest are the keys for the crest front steepening with the increasing particle cyclic excursion and forward Stoke drift. Eventually, the surface layer cannot climb over the crest with the vertical front. It curls up and forms an overhanging plunging jet leading the crest, while the lower flow still can reach the crest rear. This process leads to wave breaking with the rapid drop of crest height and the transition from slow divergence to rapid divergence of the adjacent fluid trajectories.

We use direct numerical simulations to compute turbulent transport coefficients for passive scalars in turbulent rotating flows. Effective diffusion coefficients in the directions parallel and perpendicular to the rotation axis are obtained by studying the diffusion of an imposed initial profile for the passive scalar, and calculated by measuring the scalar average concentration and average spatial flux as a function of time. The Rossby and Schmidt numbers are varied to quantify their effect on the effective diffusion. It is found that rotation reduces scalar diffusivity in the perpendicular direction. The perpendicular diffusion can be estimated from mixing length arguments using the characteristic velocities and lengths perpendicular to the rotation axis. Deviations are observed for small Schmidt numbers, for which turbulent transport decreases and molecular diffusion becomes more significant.

Localized states are found in many pattern forming systems. The aim of this paper is to investigate the occurrence of oscillatory localized states in two-dimensional Boussinesq magnetoconvection. Initially considering an idealized model, in which the vertical structure of the system has been simplified by a projection onto a small number of Fourier modes, we find that these states are restricted to the low $\zeta$ regime (where $\zeta$ represents the ratio of the magnetic to thermal diffusivities). These states always exhibit bistability with another nontrivial solution branch; in other words, they show no evidence of subcritical behavior. This is due to the weak flux expulsion that is exhibited by these time-dependent solutions. Using the results of this parameter survey, we locate corresponding states in a fully resolved two-dimensional system, although the mode of oscillation is more complex in this case. This is the first time that a localized oscillatory state, of this kind, has been found in a fully resolved magnetoconvection simulation.

We present a theory for the quantum-electrodynamical (QED) parametric scattering instability of an intense photon pulse in an incoherent radiation background. The pump electromagnetic (EM) wave can decay into a scattered daughter EM wave and an acousticlike wave due to the QED vacuum polarization nonlinearity. By a linear instability analysis we obtain a nonlinear dispersion relation for the growth rate of the scattering instability. The nonlinear QED scattering instability can give rise to the exchange of orbital angular momentum between intense Laguerre-Gaussian mode photon pulses and the two daughter waves, which may be a useful method to detect the highly energetic photon gases existing in the vicinity of rotating dense bodies in the Universe, such as pulsars and magnetars. The observation of the scattered waves may reveal information about the twisted acoustic waves in the incoherent photon gas.

A model of a semiflexible magnetic filament with magnetization frozen in the direction perpendicular to the tangent of its center line is formulated. It is shown that if the rod is magnetized at its ends in opposite directions, an AC magnetic field causes parametric excitation of bending deformations. Neutral curves of parametric excitation are calculated both analytically and numerically. The shapes arising upon parametric excitation of bending deformations are chiral. Periodic rotation of the chiral filament due to nonhomogeneous twist in a nonhomogeneous AC field causes its unidirectional motion.

Using numerical simulations we consider an amorphous particle mixture which exhibits shear localization, and find that the addition of even a small fraction of chains strongly enhances the material strength, creating pronounced overshoot features in the stress-strain curves. The strengthening occurs in the case where the chains are initially perpendicular to the shear direction, leading to a suppression of the shear band. This also leads to stiffening effects that are typical of polymeric systems. For large strain, the chains migrate to the region where a shear band forms, resulting in a stress drop. For chains larger than the linear system size we find oscillatory behavior, which does not resemble polymeric systems since the second stress peak is larger than the first. Our results are also useful for providing insights into methods of controlling and strengthening granular materials against failure.

We show that the replica approach to glassy dynamics provides, in spite of its static nature, a characterization of critical dynamics in the $\beta$ regime of supercooled liquids that is equivalent to the one of mode-coupling-theory, both qualitatively and quantitatively. The nature and extent of this equivalence is discussed in connection to the main open problems of the current theory.

We study the problem of diffusing particles which coalesce upon contact. With the aid of a nonperturbative renormalization group, we first analyze the dynamics emerging below the critical dimension two, where strong fluctuations imply anomalously slow decay. Above two dimensions, the long-time, low-density behavior is known to conform with the law of mass action. For this case, we establish an exact mapping between the physics at the microscopic scale (lattice structure, particle shape and size) and the macroscopic decay rate in the law of mass action. In addition, we identify a term violating this classical law. It originates in long-range and many-particle fluctuations and is a simple, universal function of the macroscopic decay rate.

We study the instabilities of a harmonic oscillator subject to additive and dichotomous multiplicative noise, focusing on the dependence of the instability threshold on the mass. For multiplicative noise in the damping, the energy instability threshold is crossed as the mass is decreased, as long as the smaller damping is in fact negative. For multiplicative noise in the stiffness, the situation is more complicated and in fact the energy transition is reentrant for intermediate noise strength and damping. For multiplicative noise in the mass, the results depend on the implementation of the noise. One can take the velocity or the momentum to be conserved as the mass is changed. In these cases increasing the mass destabilizes the system. Alternatively, if the change in mass is caused by the accretion and loss of particles to the Brownian particle, these processes are asymmetric with momentum conserved upon accretion and velocity upon loss. In this case, there is no instability, as opposed to the other two implementations. We also present the mass dependence of the instability threshold for the first moment. Finally, we study the distribution of the energy, finding a power-law cutoff at a value that increases with time.

We consider a Brownian particle in a harmonic trap. The location of the trap is modulated according to an Ornstein-Uhlenbeck process. We investigate the fluctuation of the work done by the modulated trap on the Brownian particle in a given time interval in the steady state. We compute the large deviation as well as the complete asymptotic form of the probability density function of the work done. The theoretical asymptotic forms of the probability density function are in very good agreement with the numerics. We also discuss the validity of the fluctuation theorem for this system.

Two-dimensional spouted bed, capable to provide both dilute granular gas and dense granular solid flow patterns in one system, was selected as a prototypical system for studying granular materials. Effects of liquid cohesion on such kind of complex granular patterns were studied using particle image velocimetry. It is seen that the addition of liquid oils by a small fraction of 10${}^{-3}$–10${}^{-2}$ causes a remarkable narrowing (about 15$\%$) of the spout area. In the dense annulus, as the liquid fraction increases, the downward particle velocity gradually decreases and approaches a minimum where, at a microscopic grain scale, the liquid bridge reaches spherical regimes with a maximum capillarity. Viscous lubrication effect is observed at a much higher fraction but is really weak with respect to the capillary effect. In the dilute spout, in contrast to the dry grains, the wet grains have a lightly smaller acceleration in the initial 1/3 of the spout, but have a dramatically higher acceleration in the rest of the spout. We attribute the former to the additional work needed to overcome interparticle cohesion during particle entrainment at the spout-annulus interface. Then, using mass and momentum balances, the latter is explained by the relative higher drag force resulting from both higher gas velocities and higher voidages due to spout narrowing in the wet system. The experimental findings will provide useful data for the validation of discrete element simulation of cohesive granular-fluid flows.

We consider the stationary state of a fluid comprised of inelastic hard spheres or disks under the influence of a random, momentum-conserving external force. Starting from the microscopic description of the dynamics, we derive a nonlinear equation of motion for the coherent scattering function in two and three space dimensions. A glass transition is observed for all coefficients of restitution, $\varepsilon$, at a critical packing fraction ${\phi }_c\left(\varepsilon \right)$ below random close packing. The divergence of timescales at the glass transition implies a dependence on compression rate upon further increase of the density—similar to the cooling-rate dependence of a thermal glass. The critical dynamics for coherent motion as well as tagged particle dynamics is analyzed and shown to be nonuniversal with exponents depending on space dimension and degree of dissipation.

In this paper, a systematic method is presented for developing microstructure-statistics-property relations of anisotropic polydisperse particulate composites using microcomputer tomography (micro-CT). Micro-CT is used to obtain a detailed three-dimensional representation of polydisperse microstructures, and an image processing pipeline is developed for identifying particles. In this work, particles are modeled as idealized shapes in order to guide the image processing steps and to provide a description of the discrete micro-CT data set in continuous Euclidean space. $n$-point probability functions used to describe the morphology of mixtures are calculated directly from real microstructures. The statistical descriptors are employed in the Hashin-Shtrikman variational principle to compute overall anisotropic bounds and self-consistent estimates of the thermal-conductivity tensor. We make no assumptions of statistical isotropy nor ellipsoidal symmetry, and the statistical description is obtained directly from micro-CT data. Various mixtures consisting of polydisperse ellipsoidal and spherical particles are prepared and studied to show how the morphology impacts the overall anisotropic thermal-conductivity tensor.