Living cells often alternate between proliferating and nonproliferating states as part of individual or collective strategies to adapt to complex and changing environments. To this aim, they have evolved a biochemical regulatory network enabling them to switch between cell-division cycles (i.e., oscillatory state) and cell-cycle arrests (i.e., steady state) in response to extracellular cues. This can be achieved by means of a variety of bifurcation mechanisms that potentially give rise to qualitatively distinct cell-cycle arrest properties. In this paper, we study the dynamics of a minimal biochemical network model in which a cell-division oscillator and a differentiation switch mutually antagonize. We identify the existence of three biologically plausible bifurcation scenarios organized around a codimension-four swallowtail-homoclinic singularity. As a result, the model exhibits a broad repertoire of cell-cycle arrest properties in terms of reversibility of these arrests, tunability of interdivision time, and ability to track time-varying signals. This dynamic versatility would explain the diversity of cell-cycle arrest strategies developed in different living species and functional contexts.

We all use path routing everyday as we take shortcuts to avoid traffic jams, or by using faster traffic means. Previous models of traffic flow of RNA polymerase II (RNAPII) during transcription, however, were restricted to one dimension along the DNA template. Here we report the modeling and application of traffic flow in transcription that allows preferential paths of different dimensions only restricted to visit some transit points, as previously introduced between the $5^{\prime }$ and $3^{\prime }$ end of the gene. According to its position, an RNAPII protein molecule prefers paths obeying two types of time-evolution rules. One is an asymmetric simple exclusion process (ASEP) along DNA, and the other is a three-dimensional jump between transit points in DNA where RNAPIIs are staying. Simulations based on our model, and comparison experimental results, reveal how RNAPII molecules are distributed at the DNA-loop-formation-related protein binding sites as well as CTCF insulator proteins (or exons). As time passes after the stimulation, the RNAPII density at these sites becomes higher. Apparent far-distance jumps in one dimension are realized by short-range three-dimensional jumps between DNA loops. We confirm the above conjecture by applying our model calculation to the SAMD4A gene by comparing the experimental results. Our probabilistic model provides possible scenarios for assembling RNAPII molecules into transcription factories, where RNAPII and related proteins cooperatively transcribe DNA.

A spin-oscillator system models unzipping of biomolecules (such as DNA, RNA, or proteins) subject to an external force. The system comprises a macroscopic degree of freedom, represented by a one-dimensional oscillator, and internal degrees of freedom, represented by Glauber spins with nearest-neighbor interaction and a coupling constant proportional to the oscillator position. At a critical value $F_c$ of an applied external force $F$, the oscillator rest position (order parameter) changes abruptly and the system undergoes a first-order phase transition. When the external force is cycled at different rates, the extension given by the oscillator position exhibits a hysteresis cycle at high loading rates, whereas it moves reversibly over the equilibrium force-extension curve at very low loading rates. Under constant force, the logarithm of the residence time at the stable and metastable oscillator rest position is proportional to $F-F_c$ as in an Arrhenius law.

Brain electrical stimulation (BES) has long been suggested as a means of controlling pathological brain activity. In epilepsy, control of a spatially localized source, the seizure focus, may normalize neuronal dynamics. Consequently, most BES research has been directed at controlling small, local, neuronal populations. At a higher level, pathological seizure activity can be viewed as a network event that may begin without a clear spatial focus or in multiple sites and spread rapidly through a distributed cortical network. In this paper, we begin to address the implications of local control in a network scenario. To do so, we explore the efficacy of local BES when deployed over a larger-scale neuronal network, for instance, using a grid of stimulating electrodes on the cortex. By introducing a mean-field model of neuronal interactions we are able to identify limitations in network controllability based on physiological constraints that suggest the need for more nuanced network control strategies.

The detection of community structure in networks is intimately related to finding a concise description of the network in terms of its modules. This notion has been recently exploited by the map equation formalism [Rosvall and Bergstrom, Proc. Natl. Acad. Sci. USA 105, 1118 (2008)] through an information-theoretic description of the process of coding inter- and intracommunity transitions of a random walker in the network at stationarity. However, a thorough study of the relationship between the full Markov dynamics and the coding mechanism is still lacking. We show here that the original map coding scheme, which is both block-averaged and one-step, neglects the internal structure of the communities and introduces an upper scale, the “field-of-view” limit, in the communities it can detect. As a consequence, map is well tuned to detect clique-like communities but can lead to undesirable overpartitioning when communities are far from clique-like. We show that a signature of this behavior is a large compression gap: The map description length is far from its ideal limit. To address this issue, we propose a simple dynamic approach that introduces time explicitly into the map coding through the analysis of the weighted adjacency matrix of the time-dependent multistep transition matrix of the Markov process. The resulting Markov time sweeping induces a dynamical zooming across scales that can reveal (potentially multiscale) community structure above the field-of-view limit, with the relevant partitions indicated by a small compression gap.

A dripping faucet is an example of an everyday system that exhibits surprisingly rich dynamics ranging from periodic to chaotic. Using a simple capacitive device, we experimentally demonstrate that the dynamics is determined by the degree of synchronization between two temporally disparate processes: the time at which a drop attains a critical mass and an oscillatory process that accompanies the formation of a drop. We present a full experimental phase-space reconstruction of the ensuing dynamics.

The branching process (BP) approach has been successful in explaining the avalanche dynamics in complex networks. However, its applications are mainly focused on unipartite networks, in which all nodes are of the same type. Here, motivated by a need to understand avalanche dynamics in metabolic networks, we extend the BP approach to a particular bipartite network composed of Boolean AND and OR logic gates. We reduce the bipartite network into a unipartite network by integrating out OR gates and obtain the effective branching ratio for the remaining AND gates. Then the standard BP approach is applied to the reduced network, and the avalanche-size distribution is obtained. We test the BP results with simulations on the model networks and two microbial metabolic networks, demonstrating the usefulness of the BP approach.

We investigate through a generalized Langevin formalism the phenomenon of anomalous diffusion for asymptotic times, and we generalized the concept of the diffusion exponent. A method is proposed to obtain the diffusion coefficient analytically through the introduction of a time scaling factor $\lambda$. We obtain as well an exact expression for $\lambda$ for all kinds of diffusion. Moreover, we show that $\lambda$ is a universal parameter determined by the diffusion exponent. The results are then compared with numerical calculations and very good agreement is observed. The method is general and may be applied to many types of stochastic problem.

We investigate the scaling properties of phase transitions between survival and extinction (active-to-absorbing-state phase transition, AAPT) in a model that by itself belongs to the directed percolation (DP) universality class, interacting with a spatiotemporally fluctuating environment having its own nontrivial dynamics. We model the environment by (i) a randomly stirred fluid, governed by the Navier-Stokes (NS) equation, and (ii) a fluctuating surface, described either by the Kardar-Parisi-Zhang (KPZ) or the Edward-Wilkinson (EW) equations. We show, by using a one-loop perturbative field theoretic setup that, depending upon the spatial scaling of the variance of the external forces that drive the environment (i.e., the NS, KPZ, or EW equations), the system may show weak or strong dynamic scaling at the critical point of active-to-absorbing-state phase transitions. In the former case AAPT displays scaling belonging to the DP universality class, whereas in the latter case the universal behavior is different.

We study both theoretically and experimentally a process of subdiffusion in a system with two thin membranes. The theoretical model uses Green's functions obtained for the membrane system by means of the generalized method of images. These Green's functions are combinations of the fundamental solutions to a fractional subdiffusion equation describing subdiffusion in a homogenous, unbounded system. Using Green's functions we find analytical formulas describing the time evolution of concentration profiles and the time evolution of the amount of substance that remains in the region between the membranes. The concentration profiles fulfill a new boundary condition at the membrane, in which the membrane permeability is assumed to change over time according to the special formula presented in the paper. These concentration profiles fulfill a standard subdiffusion equation with fractional Riemann-Liouville time derivative only approximately, but they coincide very well with the experimental data. Fitting the theoretical functions in with the experimental results, we also estimate the subdiffusion coefficient of polyethylene glycol 2000 in agarose hydrogel.

In this paper, molecular dynamics simulations of a simple Lennard-Jones fluid confined in narrow slit pores and undergoing shear have been performed. The aim is to investigate the effects of density inhomogeneities at the fluid-solid interfaces on the shear viscosity profiles. It has been found that the local viscosity was varying strongly with the distance from the solid walls for both dilute and dense fluid states with oscillations correlated to the density ones. To describe the computed viscosity profiles, we propose a scheme that uses the local average density model, combined with an adequate weight function, for the configurational viscosity and a semiempirical model for the translational viscosity. It is shown that the proposed approach is able to provide viscosity profiles in good agreement with those coming from simulations for different pore widths and for different fluid states (dilute to dense).

Previous studies on wetted, particle-particle collisions have been limited to head-on collisions, but in many-particle flows, collisions are inherently oblique. In this work, we explore such oblique collisions experimentally and theoretically. Whereas in normal collisions particles rebound only due to solid deformation, we observe in oblique collisions a new outcome where the particles initially form a rotating doublet and then deagglomerate at a later time due to so-called centrifugal forces. Surprisingly, we discover the essential role of capillary forces in oblique collisions even when the capillary number (viscous over capillary forces) is high. This recognition leads to the introduction of a dimensionless number, the centrifugal number (centrifugal over capillary forces), which together with the previously established Stokes number characterizes the regime map of outcomes. Unexpectedly, we observe a normal restitution coefficient greater than unity at large impact angles, the mechanism for which may also be observed in other agglomerating systems.

We experimentally investigate the behavior of a pinned water droplet evaporating into air. The influence of the substrate temperature and substrate thermal properties on the evaporation process are studied in both hydrophilic and hydrophobic conditions. Our objective is to understand the effect of thermal mechanisms on the droplet evaporation process. The experimental results are compared with the quasisteady, diffusion-driven evaporation model, which is implemented under the influence of the temperature; the model assumes the isothermia of the droplet at the substrate temperature. The results highlight a favorable correlation between the model and the experimental data at ambient temperatures for most situations considered here. The model works to qualitatively describe the influence of the substrate temperature on the evaporation process. However, with an increase in the substrate temperature, the role of the thermal-linked mechanisms becomes increasingly important; this experiment highlights the need for more accurate models to account for the buoyant convection in vapor transport and the evaporative cooling and heat conduction between the droplet and the substrate. Finally, the experimental data reveal the modification of contact angle evolution as the temperature increases and the crucial role played by the nature of the substrate in the evaporation of a sessile droplet. The influence of the substrate thermal properties on the global evaporation rate is explained by the parallel thermal effusivity of the liquid and solid phases.

Dense grain flows in nature consist of a mixture of solid constituents that are immersed in an ambient fluid. In order to obtain a good representation of these flows, the interaction mechanisms between the different constituents of the mixture should be considered. In this article, we study the dynamics of a dense granular flow composed of a binary mixture of small and large grains immersed in an ambient fluid. In this context, we extend the two-phase approach proposed by Meruane et al. [J. Fluid Mech. 648, 381 (2010)] to the case of flowing dense binary mixtures of solid particles, by including in the momentum equations a constitutive relation that describes the interaction mechanisms between the solid constituents in a dense regime. These coupled equations are solved numerically and validated by comparing the numerical results with experimental measurements of the front speed of gravitational granular flows resulting from the collapse, in ambient air or water, of two-dimensional granular columns that consisted of mixtures of small and large spherical particles of equal mass density. Our results suggest that the model equations include the essential features that describe the dynamics of grains flows of binary mixtures in an ambient fluid. In particular, it is shown that segregation of small and large grains can increase the front speed because of the volumetric expansion of the flow. This increase in flow speed is damped by the interaction forces with the ambient fluid, and this behavior is more pronounced in water than in air.

The blossoming of interest in colloids and nanoparticles has given renewed impulse to the study of hard-body systems. In particular, hard spheres have become a real test system for theories and experiments. It is therefore necessary to study the complex dynamics of such systems in presence of a solvent; disregarding hydrodynamic interactions, the simplest model is the Langevin equation. Unfortunately, standard algorithms for the numerical integration of the Langevin equation require that interactions are slowly varying during an integration time step. This is not the case for hard-body systems, where there is no clear-cut distinction between the correlation time of the noise and the time scale of the interactions. Starting first from a splitting of the Fokker-Plank operator associated with the Langevin dynamics, and then from an approximation of the two-body Green's function, we introduce and test two algorithms for the simulation of the Langevin dynamics of hard spheres.

It was shown earlier that some classes of three-dimensional contact problems can be mapped onto one-dimensional systems without loss of essential macroscopic information, thus allowing for immense acceleration of numerical simulations. The validity of this method of reduction of dimensionality has been strictly proven for contact of any axisymmetric bodies, both with and without adhesion. In [T. Geike and V. L. Popov, Phys. Rev. E 76, 036710 (2007)], it was shown that this method is valid “with empirical accuracy” for the simulation of contacts between randomly rough surfaces. In the present paper, we compare exact calculations of contact stiffness between elastic bodies with fractal rough surfaces (carried out by means of the boundary element method) with results of the corresponding one-dimensional model. Both calculations independently predict the contact stiffness as a function of the applied normal force to be a power law, with the exponent varying from 0.50 to 0.85, depending on the fractal dimension. The results strongly support the application of the method of reduction of dimensionality to a general class of randomly rough surfaces. The mapping onto a one-dimensional system drastically decreases the computation time.

We study quantum resonance behavior of the infinite-range kinetic Ising model at zero temperature. Numerical integration of the time-dependent Schrödinger equation in the presence of an external magnetic field in the $z$ direction is performed at various transverse field strengths $g$. It is revealed that two resonance peaks occur when the energy gap matches the external driving frequency at two distinct values of $g$, one below and the other above the quantum phase transition. From the similar observations already made in classical systems with phase transitions, we propose that the double resonance peaks should be a generic feature of continuous transitions, for both quantum and classical many-body systems.

A model of self-driven particles similar to the Vicsek model [Phys. Rev. Lett. 75, 1226 (1995)] but with metric-free interactions is studied by means of a novel Enskog-type kinetic theory. In this model, $N$ particles of constant speed $v_0$ try to align their travel directions with the average direction of a fixed number of closest neighbors. At strong alignment a global flocking state forms. The alignment is defined by a stochastic rule, not by a Hamiltonian. The corresponding interactions are of genuine multibody nature. The theory is based on a Master equation in $3N$-dimensional phase space, which is made tractable by means of the molecular chaos approximation. The phase diagram for the transition to collective motion is calculated and compared to direct numerical simulations. A linear stability analysis of a homogeneous ordered state is performed using the kinetic but not the hydrodynamic equations in order to achieve high accuracy. In contrast to the regular metric Vicsek-model no instabilities occur. This confirms previous direct simulations that, for Vicsek-like models with metric-free interactions, there is no formation of density bands and that the flocking transition is continuous.

Based on the results of computer simulation of transport coefficients in a Lennard-Jones fluid, it has been shown that in ($p$,$T)$ coordinates, lines of constant values of coefficients of self-diffusion $D$ and excess shear viscosity $\Delta \eta$ extended into the region of superheated liquid and supersaturated vapor have an envelope. Each of the ensembles of such lines is divided into two parts by a critical isoline, where the conditions $\varphi ={\varphi }_c=\mathrm{const}$ $(\varphi =D,\Delta \eta )$ are fulfilled. One part of this ensemble has as an envelope the branch of the spinodal that refers to superheated liquid; the other part has the branch of the spinodal of supersaturated vapor. The critical point of liquid-vapor equilibrium is the cusp of the spinodal, at which the critical isolines have a common tangent line with the spinodal and the binodal. Thus, at the approach to the spinodal, the relations ${(\partial D/\partial p)}_T\to \infty$ and ${(\partial \Delta \eta /\partial p)}_T\to \infty$ hold.

We show that a large class of pulse-coupled oscillators converge with high probability from random initial conditions on a large class of graphs with time delays. Our analysis combines previous local convergence results, probabilistic network analysis, and a classification scheme for type-II phase response curves to produce rigorous lower bounds for convergence probabilities based on network density. These results suggest methods for the analysis of pulse-coupled oscillators, and provide insights into the balance of excitation and inhibition in the operation of biological type-II phase response curves and also the design of decentralized and minimal clock synchronization schemes in sensor nets.