We study fluctuation effects of nonsteric molecular interactions between RNA polymerase (RNAP) motors that move simultaneously on the same DNA track during transcription elongation. Based on a stochastic model that allows for the exact analytical computation of the stationary distribution of RNAPs as a function of their density, interaction strength, nucleoside triphosphate concentration, and rate of pyrophosphate release we predict an almost geometric headway distribution of subsequent RNAP transcribing on the same DNA segment. The localization length which characterizes the decay of the headway distribution depends directly only the average density of RNAP and the interaction strength, but not on specific single-RNAP properties. Density correlations are predicted to decay exponentially with the distance (in units of DNA base pairs), with a correlation length that is significantly shorter than the localization length.

Using computer simulation we explore how two-dimensional systems of colloids with a combination of short-range attractive and long-range repulsive interactions generate complex structures and kinetics. Cooperative effects mean the attractive potential, despite being very short-ranged compared to the repulsion, can have significant effects on large-scale structure. By considering the number of particles occupying a notional “repulsion zone” defined by the repulsion length scale, we classify different characteristic structural regimes in which the combination of attraction and repulsion leads to different structural and kinetic outcomes, such as compact clustering, chain labyrinths, and coexisting clusters and chains. In some regimes small changes in repulsion range and/or area fraction can change timescales of structural evolution by many orders of magnitude.

The packing fraction dynamics of a wet granular material submitted to freeze-thaw cycling is investigated experimentally. The dynamics is strongly influenced by the liquid volume fraction $\omega$ in the considered range of $0.03<\omega <0.32$. This range of liquid contents covers different regimes of wetness from the creation of the capillary network until the formation of large clusters and finally close to the saturated case. For the liquid contents $\omega \gtrsim 0.15$, the pile experiences a decompaction until a particular value of the packing fraction 0.56 corresponding to a random loose packing configuration for monosized spheres. Moreover, the decompaction starts after a cycling number that decreases exponentially with the liquid content. Finally, we show that the packing dynamics can be well modeled on the basis of a Landau potential with an asymmetric double-well structure. The onset of decompaction represents the tendency of the system to stay in a metastable state. After several cycles, the forces induced by the thermal cycling and local stochastic rearrangements of the grains can drive the system to overcome the energy barrier of the cohesive forces.

The transport of chemical species in porous media is ubiquitous in subsurface processes, including contaminant transport, soil drying, and soil remediation. We study vapor transport in a multiscale porosity material, a smectite clay, in which water molecules travel in mesopores and macropores between the clay grains but can also intercalate inside the nanoporous grains, making them swell. The intercalation dynamics is known to be controlled by the type of cation that is present in the nanopores; in this case exchanging the cations from ${\mathrm{Na}}^{+}$ to ${\mathrm{Li}}^{+}$ accelerates the dynamics. By inferring spatial profiles of mesoporous humidity from a space-resolved measurement of grain swelling, and analyzing them with a fractional diffusion equation, we show that exchanging the cations changes mesoporous transport from Fickian to markedly subdiffusive. This results both from modifying the exchange dynamics between the mesoporous and nanoporous phases, and from the feedback of transport on the medium's permeability due to grain swelling. An important practical implication is a large difference in the time needed for vapor to permeate a given length of the clay depending on the type of intercalated cation.

Molecular dynamics represents a key enabling technology for applications ranging from biology to the development of new materials. However, many real-world applications remain inaccessible to fully resolved simulations due to their unsustainable computational costs and must therefore rely on semiempirical coarse-grained models. Significant efforts have been devoted in the last decade towards improving the predictivity of these coarse-grained models and providing a rigorous justification of their use, through a combination of theoretical studies and data-driven approaches. One of the most promising research efforts is the (re)discovery of the Mori-Zwanzig projection as a generic, yet systematic, theoretical tool for deriving coarse-grained models. Despite its clean mathematical formulation and generality, there are still many open questions about its applicability and assumptions. In this work, we propose a detailed derivation of a hybrid multiscale system, generalizing and further investigating the approach developed in Español [Europhys. Lett. 88, 40008 (2009)]. Issues such as the general coexistence of atoms (fully resolved degrees of freedom) and beads (larger coarse-grained units), the role of the fine-to-coarse mapping chosen, and the approximation of effective potentials are discussed. The theoretical discussion is supported by numerical simulations of a monodimensional nonlinear periodic benchmark system with an open-source parallel Julia code, easily extensible to arbitrary potential models and fine-to-coarse mapping functions. The results presented highlight the importance of introducing, in the macroscopic model, nonconstant fluctuating and dissipative terms, given by the Mori-Zwanzig approach, to correctly reproduce the reference fine-grained results, without requiring ad hoc calibration of interaction potentials and thermostats.

An isolated quantum system in a pure state may be perceived as thermal if only a substantially small fraction of all degrees of freedom is probed. We propose that in a quantum chaotic many-body system all states with sufficiently small energy fluctuations are approximately thermal. We refer to this hypothesis as canonical universality (CU). The CU hypothesis complements the eigenstate thermalization hypothesis which proposes that for chaotic systems individual energy eigenstates are thermal. Integrable and many-body localization systems do not satisfy CU. We provide theoretical and numerical evidence supporting the CU hypothesis.

A novel form of amorphous matter characterized by marginal stability was recently discovered in the mean-field theory of structural glasses. Using this approach, we provide complete phase diagrams delimiting the location of the marginally stable glass phase for a large variety of pair interactions and physical conditions, extensively exploring physical regimes relevant to granular matter, foams, emulsions, hard and soft colloids, and molecular glasses. We find that all types of glasses may become marginally stable, but the extent of the marginally stable phase highly depends on the preparation protocol. Our results suggest that marginal phases should be observable for colloidal and non-Brownian particles near jamming and for poorly annealed glasses. For well-annealed glasses, two distinct marginal phases are predicted. Our study unifies previous results on marginal stability in mean-field models and will be useful to guide numerical simulations and experiments aimed at detecting marginal stability in finite-dimensional amorphous materials.

Different aspects of synchronization emerging in networks of coupled oscillators have been examined prominently in the last decades. Nevertheless, little attention has been paid on the emergence of this imperative collective phenomenon in networks displaying temporal changes in the connectivity patterns. However, there are numerous practical examples where interactions are present only at certain points of time owing to physical proximity. In this work, we concentrate on exploring the emergence of interlayer and intralayer synchronization states in a multiplex dynamical network comprising of layers having mobile nodes performing two-dimensional lattice random walk. We thoroughly illustrate the impacts of the network parameters, in particular, the vision range $\varphi$ and the step size $u$ together with the inter- and intralayer coupling strengths $\epsilon$ and $k$ on these synchronous states arising in coupled Rössler systems. The presented numerical results are very well validated by analytically derived necessary conditions for the emergence and stability of the synchronous states. Furthermore, the robustness of the states of synchrony is studied under both structural and dynamical perturbations. We find interesting results on interlayer synchronization for a continuous removal of the interlayer links as well as for progressively created static nodes. We demonstrate that the mobility parameters responsible for intralayer movement of the nodes can retrieve interlayer synchrony under such structural perturbations. For further analysis of survivability of interlayer synchrony against dynamical perturbations, we proceed through the investigation of single-node basin stability, where again the intralayer mobility properties have noticeable impacts. We also discuss the scenarios related mainly to effects of the mobility parameters in cases of varying lattice size and percolation of the whole network.

We explore the effect of the magnetic Prandtl number Pm on energy and dissipation in fully resolved direct numerical simulations of steady-state, mechanically forced, homogeneous magnetohydrodynamic turbulence in the range $1/32<\mathrm{Pm}<32$. We compare the spectra and show that if the simulations are not fully resolved, the steepness of the scaling of the kinetic-to-magnetic dissipation ratio with Pm is overestimated. We also present results of decaying turbulence with helical and nonhelical magnetic fields, where we find nonhelical reverse spectral transfer for $\mathrm{Pm}<1$. The results of this systematic analysis have applications including stars, planetary dynamos, and accretion disks.

In their Comment, Rehman and Ahmad have noted that the damping rate of Langmuir oscillations in a $q$-nonextensive electron-positron plasma is always negative and so resulting only in Landau damped oscillations and no unstable modes. As a Reply, I would like to resolve the origin of the misleading result in Phys. Rev. E 87, 053112 (2013), which had arisen from a misprint in numerical programming of one of the equations there. Furthermore, I would like to point out that this picture is not solely connected to the problem of Langmuir oscillations in an electron-positron plasma, but this is in fact a reemphasizing of the stability of $q$ distribution as a decreasing function with velocity. In this Reply, the corrected and modified pattern of the Landau damping rate of Langmuir oscillations in an electron-positron plasma is given in the superextensive region $q<1$ (the subsection involved an inappropriate result) and the modified results are confirmed. Hereby, it is confirmed that all analytical solutions of Phys. Rev. E 87, 053112 (2013) are true and the misleading result there arose from a misprint in numerical programming of one of the equations.

We consider the overdamped dynamics of a Brownian particle in an arbitrary spatial periodic and time-dependent potential on the basis of an exact solution for the probability density in the form of a power series in the inverse friction coefficient. The expression for the average velocity of a Brownian ratchet is simplified in the high-temperature consideration when only the first terms of the series can be used. For the potential of an additive-multiplicative form (a sum of a time-independent contribution and a time-dependent multiplicative perturbation), general explicit expressions are obtained which allow comparative analysis of frequency dependencies of the average velocity, implying deterministic and stochastic potential energy fluctuations. For qualitative and quantitative analysis of these dependences, we choose illustrative examples for spatial harmonic fluctuations: with deterministic time dependences of a relaxation type and stochastic time dependences describing Markovian dichotomous and harmonic noise processes. We explore the influence of fluctuation types on the ratchet effect and demonstrate its enhancement in the case of harmonic noise.

The time evolution of a system of coagulating particles under the product kernel and arbitrary initial conditions is studied. Using the improved Marcus-Lushnikov approach, the master equation is solved for the probability $W(Q,t)$ to find the system in a given mass spectrum $Q=\{n_1,n_2,\cdots ,n_g\cdots \}$, with $n_g$ being the number of particles of size $g$. The exact expression for the average number of particles $\langle n_g\left(t\right)\rangle$ at arbitrary time $t$ is derived and its validity is confirmed in numerical simulations of several selected initial mass spectra.

We study theoretically the size distributions of nanoparticles (surface islands, droplets, molecular chains, and semiconductor nanowires) which grow without decay and with arbitrary size and time-dependent growth rates. Using a special transformation of variables, the analytic Green's function is obtained in the form of a Gaussian the variance of which is determined by the size dependence of the growth rate $k\left(s\right)$. In the case of the power-law growth rates $k\left(s\right)={(a+s)}^{\alpha }$, the explicit formulas for the expectation and variance are given that contain earlier results in the limiting regimes. In the case of heterogeneous nucleation in a closed system, by convoluting Green's function with the exponential nucleation rate, we find an analytic size distribution which takes into account a delay in forming the smallest dimer and shows how it affects the distribution shapes. The recently discovered sub-Poissonian narrowing of the size distribution by nucleation antibunching is also included in the treatment. We briefly consider the length distribution of vapor-liquid-solid nanowires in the context of the obtained results. Overall, simple analytic size distributions obtained here under rather general assumptions may be useful for understanding and modeling statistical properties of different growth systems.

We suggest a method for calculation of parameters of dispersive shock waves in the framework of Whitham modulation theory applied to nonintegrable wave equations with a wide class of initial conditions corresponding to propagation of a pulse into a medium at rest. The method is based on universal applicability of Whitham's “number of waves conservation law” as well as on the conjecture of applicability of its soliton counterpart to the above mentioned class of initial conditions which is substantiated by comparison with similar situations in the case of completely integrable wave equations. This allows one to calculate the limiting characteristic velocities of the Whitham modulation equations at the boundary with the smooth part of the pulse whose evolution obeys the dispersionless approximation equations. We show that explicit analytic expressions can be obtained for laws of motion of the edges. The validity of the method is confirmed by its application to similar situations described by the integrable Korteweg–de Vries (KdV) and nonlinear Schrödinger (NLS) equations and by comparison with the results of numerical simulations for the generalized KdV and NLS equations.

Synchronization phenomena are of broad interest across disciplines and increasingly of interest in a multiplex network setting. For the multiplex network of coupled Rössler oscillators, here we show how the master stability function, a celebrated framework for analyzing synchronization on a single network, can be extended to certain classes of multiplex networks with different intralayer and interlayer coupling functions. We derive three master stability equations that determine, respectively, the necessary regions of complete synchronization, intralayer synchronization, and interlayer synchronization. We calculate these three regions explicitly for the case of a two-layer network of Rössler oscillators and show that the overlap of the regions determines the type of synchronization achieved. In particular, if the interlayer or intralayer coupling function is such that the interlayer or intralayer synchronization region is empty, complete synchronization cannot be achieved regardless of the coupling strength. Furthermore, for any network structure, the occurrence of intralayer and interlayer synchronization depends mainly on the coupling functions of nodes within a layer and across layers, respectively. Our mathematical analysis requires that the intralayer and interlayer supra-Laplacians commute. But, we show this is only a sufficient, and not necessary, condition and that the results can be applied more generally.

The area of networks is very interdisciplinary and exhibits many applications in several fields of science. Nevertheless, there are few studies focusing on geographically located $d$-dimensional networks. In this paper, we study the scaling properties of a wide class of $d$-dimensional geographically located networks which grow with preferential attachment involving Euclidean distances through $r_{ij}^{-{\alpha }_A}$ (${\alpha }_A\ge 0$). We have numerically analyzed the time evolution of the connectivity of sites, the average shortest path, the degree distribution entropy, and the average clustering coefficient for $d=1,2,3,4$ and typical values of ${\alpha }_A$. Remarkably enough, virtually all the curves can be made to collapse as functions of the scaled variable ${\alpha }_A/d$. These observations confirm the exist- ence of three regimes. The first one occurs in the interval ${\alpha }_A/d\in [0,1]$; it is non-Boltzmannian with very-long-range interactions in the sense that the degree distribution is a $q$ exponential with $q$ constant and above unity. The critical value ${\alpha }_A/d=1$ that emerges in many of these properties is replaced by ${\alpha }_A/d=1/2$ for the $\beta$ exponent which characterizes the time evolution of the connectivity of sites. The second regime is still non-Boltzmannian, now with moderately-long-range interactions, and reflects in an index $q$ monotonically decreasing with ${\alpha }_A/d$ increasing from its critical value to a characteristic value ${\alpha }_A/d\simeq 5$. Finally, the third regime is Boltzmannian-like (with $q\simeq 1$) and corresponds to short-range interactions.

In a multivariate evolutionary system, the present state of a variable is a resultant outcome of all interacting variables through the temporal history of the system. How can we quantify the information transfer from the history of all variables to the outcome of a specific variable at a specific time? We develop information theoretic metrics to quantify the information transfer from the entire history, called causal history. Further, we partition this causal history into immediate causal history, as a function of lag $\tau$ from the recent time, to capture the influence of recent dynamics, and the complementary distant causal history. Further, each of these influences are decomposed into self- and cross-feedbacks. By employing a Markov property for directed acyclic time-series graph, we reduce the dimensions of the proposed information-theoretic measure to facilitate an efficient estimation algorithm. This approach further reveals an information aggregation property, that is, the information from historical dynamics are accumulated at the preceding time directly influencing the present state of variable(s) of interest. These formulations allow us to analyze complex inter-dependencies in unprecedented ways. We illustrate our approach for: (1) characterizing memory dependency by analyzing a synthetic system with short memory; (2) distinguishing from traditional methods such as lagged mutual information using the Lorenz chaotic model; (3) comparing the memory dependencies of two long-memory processes with and without the strange attractor using the Lorenz model and a linear Ornstein-Uhlenbeck process; and (4) illustrating how dynamics in a complex system is sustained through the interactive contribution of self- and cross-dependencies in both immediate and distant causal histories, using the Lorenz model and observed stream chemistry data known to exhibit $1/f$ long memory.

We study a simple run-and-tumble random walk whose switching frequencies between run mode and tumble mode depend on a stochastic signal. We consider a particularly sharp, steplike dependence, where the run-to-tumble switching probability jumps from zero to one as the signal crosses a particular value (say $y_1$) from below. Similarly, tumble-to-run switching probability also shows a jump like this as the signal crosses another value ($y_2<y_1$) from above. We are interested in characterizing the effect of signaling noise on the long-time behavior of the random walker. We consider two different time-evolutions of the stochastic signal. In one case, the signal dynamics is an independent stochastic process and does not depend on the run-and-tumble motion. In this case we can analytically calculate the mean value and the complete distribution function of the run duration and tumble duration. In the second case, we assume that the signal dynamics is influenced by the spatial location of the random walker. For this system, we numerically measure the steady state position distribution of the random walker. We discuss some similarities and differences between our system and Escherichia coli chemotaxis, which is another well-known run-and-tumble motion encountered in nature.

Hybrid lipid-polymer vesicles can integrate benefits of liposomes and polymersomes. In this work, the phase behavior of hybrid membranes containing lipids and diblock copolymers is explored by dissipative particle dynamics simulations. The influences of lipid unsaturation and thickness mismatch between lipids and polymers are considered. The transition from the mixing state (homogeneous distribution) to the demixing state (formation of bilayered lipid-rich domains) is always observed as the lipid concentration (${\phi }_l$) exceeds a critical value, which increases with the degree of unsaturation. It is found that phase separation is driven by weak energy incompatibility between the hydrophobic segments of lipids and polymers. When the effect of thickness mismatch becomes significant, the occurrence of the demixing state is retarded, and monolayer lipid rafts emerge before phase separation. Lipid fluidity associated with the physical state of a hybrid membrane can be characterized by lateral lipid diffusivity ($D_l$). In the polymer-rich membrane, $D_l$ is higher in the mixing state, but decreases generally with ${\phi }_l$ due to lipid-lipid interactions and interdigitation.