The Percus-Yevick theory for monodisperse hard spheres gives very good results for the pressure and structure factor of the system in a whole range of densities that lie within the liquid phase. However, the equation seems to lead to a very unacceptable result beyond that region. Namely, the Percus-Yevick theory predicts a smooth behavior of the pressure that diverges only when the volume fraction $\eta$ approaches unity. Thus, within the theory there seems to be no indication for the termination of the liquid phase and the transition to a solid or to a glass. In the present article we study the Percus-Yevick hard-sphere pair distribution function, $g_2\left(r\right)$, for various spatial dimensions. We find that beyond a certain critical volume fraction ${\eta }_c$, the pair distribution function, $g_2\left(r\right)$, which should be positive definite, becomes negative at some distances. We also present an intriguing observation that the critical ${\eta }_c$ values we find are consistent with volume fractions where onsets of random close packing (or maximally random jammed states) are reported in the literature for various dimensions. That observation is supported by an intuitive argument. This work may have important implications for other systems for which a Percus-Yevick theory exists.

The elasticity of the DNA double helix varies with the underlying base pair sequence. This allows one to put mechanical cues into sequences that in turn influence the packaging of DNA into nucleosomes, DNA-wrapped protein cylinders. Nucleosomes dictate a broad range of biological processes, ranging from gene regulation, recombination, and replication to chromosome condensation. Here we map base pair sequences onto graphs and use shortest paths algorithms to determine which DNA stretches are easiest or hardest to bend inside a nucleosome. We further demonstrate how genetic and mechanical information can be multiplexed by studying paths through graphs of synonymous codons. Using this method we find that nucleosomes can be placed by mechanical cues nearly everywhere on the genome of baker's yeast (Saccharomyces cerevisiae).

Generation of homogeneous isotropic turbulence was attempted using an innovative “multifan wind tunnel” with 99 fans installed. The driving method used is based on a principle that the shear layers generated between outflows from the adjacent ducts lead to turbulent flow downstream. First, a signal composed of two frequency components is set, and then it is fed to all the fans for three kinds of arrangements of phases. Here, parameter $N$ is introduced as the number of phases used for the 99 fans, which represents a variety of emanated shear layers. Furthermore, $S$ is introduced as a measure of shear magnitude at the inlet of the test section. Relative importance of the initial conditions ($N$ and $S$) in the development of turbulence was investigated. To estimate the contribution from naturally induced turbulence, we numerically decomposed the resulting velocity fluctuations into the periodic and nonperiodic component. Energy spectra for three values of $N$ were calculated using nonperiodic data. The inertial subrange of a gradient of $-5/3$ widens with increasing $N$. The value $S$ is the largest for $N=2$, but the turbulence intensity of the nonperiodic component is the largest for $N=99$. Hence, it might be suggested that the shear magnitude at the inlet of the test section is not as important as the variety of shear layers for effective generation of high-Reynolds-number turbulence.

The conditions for the amplitude instability onset in a two-dimensional Yukawa cluster system consisting of seven particles are investigated for the case of sufficiently large thermal particle displacements. We consider here an analytical approach to derive the criterion for such instability onset, which is based on searching an energetically favorable inflection point of the system potential energy. We show that there is a proportionality between melting curve for an “infinite” two-dimensional system with the hexagonal lattice and analytical curve of critical points for the seven-particle Yukawa cluster. We use numerical simulations to study the structural and dynamical properties of the system near the critical point of the amplitude instability. The obtained results are compared to the criteria for melting of the “infinite” two-dimensional system.

A multiple-relaxation-time discrete Boltzmann model (DBM) is developed for compressible thermal reactive flows. A unified Boltzmann equation set is solved for hydrodynamic and thermodynamic quantities as well as higher order kinetic moments. The collision, reaction, and force terms are uniformly calculated with a matrix inversion method, which is physically accurate, numerically efficient, and convenient for coding. Via the Chapman-Enskog analysis, the DBM is demonstrated to recover reactive Navier-Stokes (NS) equations in the hydrodynamic limit. Both specific heat ratio and Prandtl number are adjustable. Moreover, it provides quantification of hydrodynamic and thermodynamic nonequilibrium effects beyond the NS equations. The capability of the DBM is demonstrated through simulations of chemical reactions in the free falling process, sound wave, thermal Couette flow, and steady and unsteady detonation cases. Moreover, nonequilibrium effects on the predicted physical quantities in unsteady combustion are quantified via the DBM. It is demonstrated that nonequilibrium effects suppress detonation instability and dissipate small oscillations of fluid flows.

Recent advances in experimental techniques for complex systems and the corresponding theoretical findings show that in many cases random parametrization of the diffusion coefficients gives adequate descriptions of the observed fractional dynamics. In this paper we introduce two statistical methods which can be effectively applied to analyze and estimate parameters of superstatistical fractional Brownian motion with random scale parameter. The first method is based on the analysis of the increments of the process, the second one takes advantage of the variation of the trajectories of the process. We prove the effectiveness of the methods using simulated data. Also, we apply it to the experimental data describing random motion of individual molecules inside the cell of E.coli. We show that fractional Brownian motion with Weibull-distributed diffusion coefficient gives adequate description of this experimental data.

We study the excitation conditions of antidark solitons and nonrational W-shaped solitons in a nonlinear fiber with both third-order and fourth-order effects. We show that the relative phase can be used to distinguish antidark solitons and nonrational W-shaped solitons. The excitation conditions of these well-known fundamental nonlinear waves (on a continuous-wave background) can be clarified clearly by the relative phase and three previously reported parameters (background frequency, perturbation frequency, and perturbation energy). Moreover, the numerical simulations from the nonideal initial states also support these theoretical results. These results provide an important complement for the studies on relationship between modulation instability and nonlinear wave excitations, and are helpful for controllable nonlinear excitations in experiments.

Animals having a tendency to align their velocities to an average of those of their neighbors may flock as illustrated by the Vicsek model and its variants. If, in addition, they feel a systematic contrarian trend, the result may be a time periodic adjustment of the flock or period doubling in time. These exotic phases are predicted from kinetic theory and numerically found in a modified two-dimensional Vicsek model of self-propelled particles. Numerical simulations demonstrate striking effects of alignment noise on the polarization order parameter measuring particle flocking: maximum polarization length is achieved at an optimal nonzero noise level. When contrarian compulsions are more likely than conformist ones, nonuniform polarized phases appear as the noise surpasses threshold.

The rheology of semidilute bacterial suspensions is studied with the tools of kinetic theory, considering binary interactions, going beyond the ideal gas approximation. Two models for the interactions are considered, which encompass both the steric and short-range interactions. In these, swimmers can either align polarly regardless of the state previous to the collision, or they can align axially, ending up antiparallel if the relative angle between directors is large. In both cases, it is found that an ordered phase develops when increasing the density, where the shear stress oscillates with large amplitudes, when a constant shear rate is imposed. This oscillation disappears for large shear rates in a continuous or discontinuous transition, depending on if the aligning is polar or axial, respectively. For pusher swimmers these nonlinear effects can produce an increase on the shear stress, contrary to the prediction of a viscosity reduction made for the dilute regime with the ideal gas approximation.

This paper addresses the phenomenon of random packing of sedimenting grains in the context of metallic alloy solidification from a dynamics perspective. More precisely, we investigate the evolution of the grains from the initial steady-state sedimentation until the final mechanical equilibrium—packing—is achieved. The packing dynamics of two grain geometries (spherical and nonconvex) is investigated for a hydrodynamic condition of a low ratio of grain inertia to viscous dissipation, given by a low Stokes number, St, of $o\left({10}^{-3}\right)$, which is typical in solidification. An experimental setup that consists of a vertical column filled with glycerol is employed to reproduce the packing of the sedimenting grains by means of two different protocols (sequential and collective), enabling to track the trajectory of the grains. The grain packing is also simulated by means of a discrete element method for both grain geometries in case of collective packing protocol, complementing the experimental work—trajectory tracking—with the time evolution of the local solid fraction, of the local number of contacting neighbors and of the grain orientation during the packing dynamics.

We report Stokesian dynamics simulations of bidensity suspensions rotating in a horizontal cylinder. We studied the phase space and radial and axial patterns in settling as well as floating systems. Each system was composed of particle mixtures of two different densities. As many as eight unique phases are identified for each system along the radial plane. The bidensity system shows similarity to the monodisperse case only when the radial distribution of the particles is completely uniform. Characteristic behavior of the bidensity systems is identical at low rotation rates and contrasting when centrifugal force dominates. Expressing the phase boundaries in terms of dimensionless parameters $U_s/\left(\mathrm{\Omega }R\right)$ and $g/\left({\mathrm{\Omega }}^{2}R\right)$ gives a linear fit unifying the data in the gravity-dominated regime. At high rotation rates, the behavior is opposing for either system though linear in nature. In the axial direction, number density profiles of both systems affirm the phenomenon of band formation. Location of the axial bands remains the same for heavy and light particles in both systems. We have also reestablished that an inhomogeneous particle configuration in the radial plane induces growing instabilities in the axial plane which amplify to form particle bands similar to monodisperse suspensions.

Stochastic resets have lately emerged as a mechanism able to generate finite equilibrium mean-square displacement (MSD) when they are applied to diffusive motion. Furthermore, walkers with an infinite mean first-arrival time (MFAT) to a given position $x$ may reach it in a finite time when they reset their position. In this work we study these emerging phenomena from a unified perspective. On one hand, we study the existence of a finite equilibrium MSD when resets are applied to random motion with ${\langle x^2\left(t\right)\rangle }_m\sim t^p$ for $0<p\le 2$. For exponentially distributed reset times, a compact formula is derived for the equilibrium MSD of the overall process in terms of the mean reset time and the motion MSD. On the other hand, we also test the robustness of the finiteness of the MFAT for different motion dynamics which are subject to stochastic resets. Finally, we study a biased Brownian oscillator with resets with the general formulas derived in this work, finding its equilibrium first moment and MSD and its MFAT to the minimum of the harmonic potential.

We define a structural property of real-world large-scale communication networks consisting of the recurring patterns of communication among individuals, which we term persistent cascades. Using methods of inexact tree matching and agglomerative clustering, we group these patterns into classes which we claim represent some underlying way in which individuals tend to disseminate information. We extend methods from epidemic modeling to offer a way to analytically model this recurring structure in a random network, and comparing to the data, we find that the real cascading structure is significantly larger and more recurrent than the random model. We find that the cascades reveal a habitual hierarchy of spreading, alternative roles in weekday vs weekend spreading, and the existence of hidden spreaders. Finally, we show that cascade membership increases the likelihood of receiving information spreading through the network through simulation on the real order of communication events.

Noncoding RNA molecules take part in many biological processes, while metal ions play crucial roles in helping RNAs to perform their functions. However, the statics and dynamics of these metal ions around RNA molecules are still not well understood. In this work, we report a detailed molecular dynamics study of the type-I $\mathrm{pre}{\mathrm{Q}}_1\text{−}\mathrm{bound}$ riboswitch aptamer domain (PRAD) at different ionic conditions (${\mathrm{K}}^{+}$, $\mathrm{N}{\mathrm{a}}^{+}$, and $\mathrm{M}{\mathrm{g}}^{2+}$). The results show that the structural properties and flexibility of the PRAD molecule greatly influence the distributions and dynamics of metal ions around it. Simultaneously, $\mathrm{N}{\mathrm{a}}^{+}$ ions show a stronger competitiveness with $\mathrm{M}{\mathrm{g}}^{2+}$ ions than ${\mathrm{K}}^{+}$ ions, and the three types of metal ions have different modes of interaction with the RNA molecule. Furthermore, we have also investigated specific binding sites of metal ions on the PRAD molecule and found that the dynamics and hydration structures of metal ions located at the ion-binding sites were obviously affected by the RNA structure near these ion-binding sites. These results may be useful to understand the role of the metal ions in noncoding RNA functions.

Brain connectivity and structure-function relationships are analyzed from a physical perspective in place of common graph-theoretic and statistical approaches that overwhelmingly ignore the brain's physical structure and geometry. Field theory is used to define connectivity tensors in terms of bare and dressed propagators, and discretized representations are implemented that respect the physical nature and dimensionality of the quantities involved, retain the correct continuum limit, and enable diagrammatic analysis. Eigenfunction analysis is used to simultaneously characterize and probe patterns of brain connectivity and activity, in place of statistical or phenomenological patterns. Physically based measures that characterize the connectivity are then developed in coordinate and spectral domains; some of which generalize or rectify graph-theoretic measures to implement correct dimensionality and continuum limits, and some replace graph-theoretic quantities. Traditional graph-based measures are shown to be highly prone to artifacts introduced by discretization and threshold, often because essential physical constraints have not been imposed, dimensionality has not been included, and/or distinctions between scalar, vector, and tensor quantities have not been considered. The results can replace them in ways that converge correctly and measure properties of brain structure, rather than of its discretization, and thus potentially enable physical interpretation of the many phenomenological results in the literature. Geometric effects are shown to dominate in determining many brain properties and care must be taken not to interpret geometric differences as differences in intrinsic neural connectivity. The results demonstrate the need to use systematic physical methods to analyze the brain and the potential of such methods to obtain new insights from data, make new predictions for experimental test, and go beyond phenomenological classification to dynamics and mechanisms.

The bent-core liquid crystals (LCs) are highly regarded as the next-generation materials for electro-optic devices. The nematic (N) phase of these LCs possesses highly ordered smecticlike cybotactic clusters which are promising for electro-optic applications. We have studied a one-dimensional Landau–de Gennes model of spatially inhomogeneous order parameters for the N phase of bent-core LCs. We investigate the effects of spatial confinement and coupling (between these clusters and the surrounding LC molecules modeled by a coupling parameter γ) on the order parameters. The coupling is found to increase the cluster order parameter significantly, suggesting enhancement in cluster formation, and also predicts a transition to a phase with weak nematiclike ordering above the nematic supercooling temperature.

The dramatic effect kirigami, such as hole cutting, has on the elastic properties of thin sheets invites a study of the mechanics of thin elastic frames under an external load. Such frames can be thought of as modular elements needed to build any kirigami pattern. Here we develop the technique of elastic charges to address a variety of elastic problems involving thin sheets with perforations, focusing on frames with sharp corners. We find that holes generate elastic defects (partial disclinations), which act as sources of geometric incompatibility. Numerical and analytic studies are made of three different aspects of loaded frames—the deformed configuration itself, the effective mechanical properties in the form of force-extension curves, and the buckling transition triggered by defects. This allows us to understand generic kirigami mechanics in terms of a set of force-dependent elastic charges with long-range interactions.

We propose the clock Monte Carlo technique for sampling each successive chain step in constant time. It is built on a recently proposed factorized transition filter and its core features include its O(1) computational complexity and its generality. We elaborate how it leads to the clock factorized Metropolis (clock FMet) method, and discuss its application in other update schemes. By grouping interaction terms into boxes of tunable sizes, we further formulate a variant of the clock FMet algorithm, with the limiting case of a single box reducing to the standard Metropolis method. A theoretical analysis shows that an overall acceleration of $\mathrm{O}\left(N^{\kappa }\right)$ ($0\le \kappa \le 1$) can be achieved compared to the Metropolis method, where $N$ is the system size and the $\kappa$ value depends on the nature of the energy extensivity. As a systematic test, we simulate long-range $\mathrm{O}\left(n\right)$ spin models in a wide parameter regime: for $n=1,2,3$, with disordered, algebraically decaying or oscillatory Ruderman-Kittel-Kasuya-Yosida-type interactions and with and without external fields, and in spatial dimensions from $d=1,2,3$ to the mean field. The O(1) computational complexity is demonstrated, and the expected acceleration is confirmed. Its flexibility and its independence from the interaction range guarantee that the clock method would find decisive applications in systems with many interaction terms.

We apply Pontryagin's principle to drive rapidly a trapped overdamped Brownian particle in contact with a thermal bath between two equilibrium states corresponding to different trap stiffness $\kappa$. We work out the optimal time dependence $\kappa \left(t\right)$ by minimizing the work performed on the particle under the nonholonomic constraint $0\le \kappa \le {\kappa }_{max}$, an experimentally relevant situation. Several important differences arise, as compared with the case of unbounded stiffness that has been analyzed in the literature. First, two arbitrary equilibrium states may not always be connected. Second, depending on the operating time $t_{\text{f}}$ and the desired compression ratio ${\kappa }_{\text{f}}/{\kappa }_{\text{i}}$, different types of solutions emerge. Finally, the differences in the minimum value of the work brought about by the bounds may become quite large, which may have a relevant impact on the optimization of heat engines.

The structure of flow networks determines their function under normal conditions as well as their response to perturbative damage. Brain vasculature often experiences transient or permanent occlusions in the finest vessels, but it is not clear how these microclots affect the large-scale blood flow or to what extent they decrease functionality. Motivated by this, we investigate how flow is rerouted after the occlusion of a single edge in networks with a hierarchy in edge conductances. We find that in two-dimensional networks, vessels formed by highly conductive edges serve as barriers to contain the displacement of flow due to a localized perturbation. In this way, the vein provides shielding from damage to surrounding edges. We show that once the conductance of the vein surpasses an initial minimal value, further increasing the conductance can no longer extend the shielding provided by the vein. Rather, the length scale of the shielding is set by the network topology. Upon understanding the effects of a single vein, we investigate the global resilience of networks with complex hierarchical order. We find that a system of veins arranged in a grid is able to modestly increase the overall network resilience, outperforming a parallel vein pattern.