The stochastic dynamics of gene expression is often described by highly abstract models involving only the key molecular actors DNA, RNA, and protein, neglecting all further details of the transcription and translation processes. One example of such models is the “gene gate model,” which contains a minimal set of actors and kinetic parameters, which allows us to describe the regulation of a gene by both repression and activation. Based on this approach, we formulate a master equation for the case of a single gene regulated by its own product—a transcription factor—and solve it exactly. The obtained gene product distributions display features of mono- and bimodality, depending on the choice of parameters. We discuss our model in the perspective of other models in the literature.

The attractor dimension at the transition to complete synchronization in a network of chaotic units with time-delayed couplings is investigated. In particular, we determine the Kaplan-Yorke dimension from the spectrum of Lyapunov exponents for iterated maps and for two coupled semiconductor lasers. We argue that the Kaplan-Yorke dimension must be discontinuous at the transition and compare it to the correlation dimension. For a system of Bernoulli maps, we indeed find a jump in the correlation dimension. The magnitude of the discontinuity in the Kaplan-Yorke dimension is calculated for networks of Bernoulli units as a function of the network size. Furthermore, the scaling of the Kaplan-Yorke dimension as well as of the Kolmogorov entropy with system size and time delay is investigated.

We study the dynamic response of a granular chain of particles with a resonant inclusion (i.e., a particle attached to a harmonic oscillator, or a mass-with-mass defect). We focus on the response of granular chains excited by an impulse, with no static precompression. We find that the presence of the harmonic oscillator can be used to tune the transmitted and reflected energy of a mechanical pulse by adjusting the ratio between the harmonic resonator mass and the bead mass. Furthermore, we find that this system has the capability of asymptotically trapping energy, a feature that is not present in granular chains containing other types of defects. Finally, we study the limits of low and high resonator mass, and the structure of the reflected and transmitted pulses.

Quantum wires and electromagnetic waveguides possess common features since their physics is described by the same wave equation. We exploit this analogy to investigate experimentally with microwave waveguides and theoretically with the help of an effective potential approach the occurrence of bound states in sharply bent quantum wires. In particular, we compute the bound states, study the features of the transition from a bound to an unbound state caused by the variation of the bending angle, and determine the critical bending angles at which such a transition takes place. The predictions are confirmed by calculations based on a conventional numerical method as well as experimental measurements of the spectra and electric field intensity distributions of electromagnetic waveguides.

We study numerically the process of quasistatic invasion of a fluid in thin porous layers from multiple inlet injection sources focusing on the effect of trapping or mixed wettability, that is, when hydrophobic and hydrophilic pores coexist in the system. Two flow scenarios are considered. In the first one, referred to as the sequential scenario, the injection bonds at the inlet are activated one after the other. In the second one, referred to as the kinetic scenario, the injection bonds at the inlet are activated simultaneously. In contrast with the case of purely hydrophobic systems with no trapping, studied in a previous work, it is shown that the invasion pattern and the breakthrough point statistics at the end of the displacement depend on the flow scenario when trapping or mixed wettability effects are taken into account. The transport properties of the defending phase are also studied and it is shown that a one-to-one relationship between the overall diffusive conductance and the mean saturation cannot be expected in a thin system. In contrast with thick systems, the diffusive conductance also depends on the thickness when the system is thin. After consideration of various generic aspects characterizing thin porous systems, the main results are briefly discussed in relation with the water management problem in proton exchange membrane fuel cells.

A simple model for a swimmer consisting of three colinearly linked spheres attached by rods and oscillating out of phase to break reciprocal motion is analyzed. With a prescribed forcing of the rods acting on the three spheres, the swimming dynamics are determined analytically in both a Newtonian Stokes fluid and a zero Reynolds number, nonlinear, Oldroyd-B viscoelastic fluid with Deborah numbers of order one (or less), highlighting the effects of viscoelasticity on the net displacement of swimmer. For instance, the model predicts that the three-sphere swimmer with a sinusoidal, but nonreciprocal, forcing cycle within an Oldroyd-B representation of a polymeric Boger fluid moves a greater distance with enhanced efficiency in comparison with its motility in a Newtonian fluid of the same viscosity. Furthermore, the nonlinear contributions to the viscoelastic constitutive relation, while dynamically nontrivial, are predicted a posteriori to have no effect on swimmer motility at leading order, given a prescribed forcing between spheres.

We present an effective-medium theory that includes bending as well as stretching forces, and we use it to calculate the mechanical response of a diluted filamentous triangular lattice. In this lattice, bonds are central-force springs, and there are bending forces between neighboring bonds on the same filament. We investigate the diluted lattice in which each bond is present with a probability $p$. We find a rigidity threshold $p_{\mathrm{b}}$ which has the same value for all positive bending rigidity and a crossover characterizing bending, stretching, and bend-stretch coupled elastic regimes controlled by the central-force rigidity percolation point at $p_{\mathrm{CF}}\simeq 2/3$ of the lattice when fiber bending rigidity vanishes.

The diluted kagome lattice, in which bonds are randomly removed with probability $1-p$, consists of straight lines that intersect at points with a maximum coordination number of 4. If lines are treated as semiflexible polymers and crossing points are treated as cross-links, this lattice provides a simple model for two-dimensional filamentous networks. Lattice-based effective-medium theories and numerical simulations for filaments modeled as elastic rods, with stretching modulus $\mu$ and bending modulus $\kappa$, are used to study the elasticity of this lattice as functions of $p$ and $\kappa$. At $p=1$, elastic response is purely affine, and the macroscopic elastic modulus $G$ is independent of $\kappa$. When $\kappa =0$, the lattice undergoes a first-order rigidity-percolation transition at $p=1$. When $\kappa >0$, $G$ decreases continuously as $p$ decreases below one, reaching zero at a continuous rigidity-percolation transition at $p=p_b\approx 0.605$ that is the same for all nonzero values of $\kappa$. The effective-medium theories predict scaling forms for $G$, which exhibit crossover from bending-dominated response at small $\kappa /\mu$ to stretching-dominated response at large $\kappa /\mu$ near both $p=1$ and $p_b$, that match simulations with no adjustable parameters near $p=1$. The affine response as $p\to 1$ is identified with the approach to a state with sample-crossing straight filaments treated as elastic rods.

We report numerical evidence showing that periodic oscillations can produce unexpected and wide-ranging zig-zag parameter networks embedded in chaos in the control space of nonlinear systems. Such networks interconnect shrimplike windows of stable oscillations and are illustrated here for a tunnel diode, for an erbium-doped fiber-ring laser, and for the Hénon map, a proxy of certain CO${}_2$ lasers. Networks in maps can be studied without the need for solving differential equations. Tuning parameters along zig-zag networks allows one to continuously modify wave patterns without changing their chaotic or periodic nature. In addition, we report convenient parameter ranges where such networks can be detected experimentally.

This paper deals with amplitude death in time-delayed oscillators coupled by a delayed connection with topology uncertainty. A systematic procedure without trial-and-error testing for designing connection parameters is proposed from a robust control theory viewpoint. This procedure has the following two advantages: the designed connection parameters are valid for any network topology and the procedure is valid even for long-delay oscillators. These analytical results are verified by some numerical simulations.

We examine the effects of symmetry-preserving and -breaking interactions in a drive-response system where the response has an invariant symmetry in the absence of the drive. Subsequent to the onset of generalized synchronization, we find that there can be more than one stable attractor. Numerical as well as analytical results establish the presence of phase synchrony in such coexisting attractors. These results are robust to external noise.

We consider the dynamics of a compressible fluid under the influence of electrostrictive ponderomotive forces in strong inhomogeneous nonstationary electric fields. It is shown that if the fronts of the voltage rise at a sharp, needlelike electrode are rather steep (less than or about nanoseconds), the region of negative pressure arises, which can reach values at which the fluid loses its continuity with the formation of cavitation ruptures. If the voltage on the electrode is not large enough or the front is flatter, the cavitation in the liquid does not occur. However, a sudden shutdown of the field results in a reverse flow of liquid from the electrode, which leads to appearance of negative pressure, and, possibly, cavitation.

Iterative methods that operate with the full Hamiltonian matrix in the untrimmed Hilbert space of a finite system continue to be important tools for the study of one- and two-dimensional quantum spin models, in particular in the presence of frustration. To reach sensible system sizes such numerical calculations heavily depend on the use of symmetries. We describe a divide-and-conquer strategy for implementing translation symmetries of finite spin clusters, which efficiently uses and extends the “sublattice coding” of H. Q. Lin [Phys. Rev. B 42, 6561 (1990)]. With our method, the Hamiltonian matrix can be generated on-the-fly in each matrix vector multiplication, and problem dimensions beyond ${10}^{11}$ become accessible.

We present a study of the existence, stability, and bifurcation structure of families of dark breathers in a one-dimensional uniform chain of spherical beads under static load. A defocusing nonlinear Schrödinger equation (NLS) is derived for frequencies that are close to the edge of the phonon band and is used to construct targeted initial conditions for numerical computations. Salient features of the system include the existence of large amplitude solutions that emerge from the small amplitude solutions described by the NLS equation, and the presence of a nonlinear instability that, to the best of the authors’ knowledge, has not been observed in classical Fermi-Pasta-Ulam lattices. Finally, it is also demonstrated that these dark breathers can be detected in a physically realistic experimental settings by merely actuating the ends of an initially at rest chain of beads and inducing destructive interference between their signals.

Texture observations in $B2$ phase of bent-shape molecules showed a coexistence of so-called dark conglomerate (DC) structure with fan-shaped texture composed of focal conic domains (FCDs). A model of DC structure based on grains of dimensions lower than visible wavelengths is proposed and used to compare the energies of DC and FCD structures. The comparison of energies of both structures enables the estimation of approximate model parameters. Reorientation of smectic layers in grains under an electric field and transformation into the system of FCD structure are discussed.

The spatial rock-paper-scissors ecosystem, where three species interact cyclically, is a model example of how spatial structure can maintain biodiversity. We here consider such a system for a broad range of interaction rates. When one species grows very slowly, this species and its prey dominate the system by self-organizing into a labyrinthine configuration in which the third species propagates. The cluster size distributions of the two dominating species have heavy tails and the configuration is stabilized through a complex spatial feedback loop. We introduce a statistical measure that quantifies the amount of clustering in the spatial system by comparison with its mean-field approximation. Hereby, we are able to quantitatively explain how the labyrinthine configuration slows down the dynamics and stabilizes the system.

The phenomenon of crisis in systems evolving in high-dimensional phase space can show unexpected and interesting features. We study this phenomenon in the context of a system of coupled sine circle maps. We establish that the origins of this crisis lie in a tangent bifurcation in high dimensions, and identify the routes that lead to the crisis. Interestingly, multiple routes to crisis are seen depending on the initial conditions of the system, due to the high dimensionality of the space in which the system evolves. The statistical behavior seen in the phase diagram of the system is also seen to change due to the dynamical phenomenon of crisis, which leads to transitions from nonspreading to spreading behavior across an infection line in the phase diagram. Unstable dimension variability is seen in the neighborhood of the infection line. We characterize this crisis and unstable dimension variability using dynamical characterizers, such as finite-time Lyapunov exponents and their distributions. The phase diagram also contains regimes of spatiotemporal intermittency and spatial intermittency, where the statistical quantities scale as power laws. We discuss the signatures of these regimes in the dynamic characterizers, and correlate them with the statistical characterizers and bifurcation behavior. We find that it is necessary to look at both types of correlators together to build up an accurate picture of the behavior of the system.

The inertia-induced forces on two identical spherical bubbles in a simple shear flow at small but finite Reynolds number, for the case when the bubbles are within each other's inner viscous region, are calculated making use of the reciprocal theorem. This interaction force is further employed to model the dynamics of air bubbles injected to a viscous fluid sheared in a Couette device at the first shear flow instability where the bubbles are trapped inside the stable Taylor vortex. It was shown that, during a long time scale, the inertial interaction between the bubbles in the primary shear flow drives them away from each other and, as a result, equal-size bubbles eventually assume an ordered string with equal separation distances between all neighbors. We report on experiments showing the dynamic evolution of various numbers of bubbles. The results of the theory are in good agreement with the experimental observations.

Thermal convection in a dielectric fluid layer between two parallel plates subjected to an alternating electric field and a temperature gradient is investigated under microgravity conditions. A thermoelectric coupling resulting from the thermal variation of the electric permittivity of the fluid produces the dielectrophoretic (DEP) body force, which can be regarded as thermal buoyancy due to an effective gravity. This electric gravity can destabilize a stationary conductive state of the fluid to develop convection. The similarity of the DEP thermal convection with the Rayleigh-Bénard (RB) convection is examined by considering its behavior in detail by a linear stability theory and a two-dimensional direct numerical simulation. The results are analyzed from an energetic viewpoint and in the framework of the Ginzburg-Landau (GL) equation. The stabilizing effects of a thermoelectric feedback make the critical parameters different from those in the RB instability. The nonuniformity of the electric gravity arising from the finite variation of permittivity also affects the critical parameters. The characteristic constants of the GL equation are comparable with those for the RB convection. The heat transfer in the DEP convection is weaker than in the RB convection as a consequence of the feedback that impedes the convection.

For sensory networks, we determine the rate with which they acquire information about the changing external conditions. Comparing this rate with the thermodynamic entropy production that quantifies the cost of maintaining the network, we find that there is no universal bound restricting the rate of obtaining information to be less than this thermodynamic cost. These results are obtained within a general bipartite model consisting of a stochastically changing environment that affects the instantaneous transition rates within the system. Moreover, they are illustrated with a simple four-states model motivated by cellular sensing. On the technical level, we obtain an upper bound on the rate of mutual information analytically and calculate this rate with a numerical method that estimates the entropy of a time series generated with a simulation.