Reaction-diffusion models have been used to describe pattern formation on the cellular scale, and traditionally do not include feedback between cellular shape changes and biochemical reactions. We introduce here a distinct reaction-diffusion-elasticity approach: The reaction-diffusion part describes bistability between two actin orientations, coupled to the elastic energy of the cell membrane deformations. This coupling supports spatially localized patterns, even when such solutions do not exist in the uncoupled self-inhibited reaction-diffusion system. We apply this concept to describe the nonlinear (threshold driven) initiation mechanism of actin-based cellular protrusions and provide support by several experimental observations.

This paper is an extension of a recent study where it was shown that forces dependent on molecular helical structure may cause two DNA molecules to spontaneously braid [R. Cortini et al., Biophys. J. 101, 875 (2011)]. Here, bending fluctuations of molecular center lines about the braid axis are incorporated into the braiding theory, which may be generalized to other helix-dependent interactions and other helical molecules. The free energy of the pair of molecules is recalculated and compared to its value without incorporating undulations. We find that the loss of configurational entropy due to confinement of the molecules in the braid is quite high. This contribution to the free energy increases the amount of attraction needed for spontaneous braiding due to helix-dependent forces. The theory will be further developed for plectonemes and braids under mechanical forces in later work.

Point pattern sets arise in many different areas of physical, biological, and applied research, representing many random realizations of underlying pattern formation mechanisms. These pattern sets can be heterogeneous with respect to underlying spatial processes, which may not be visually distiguishable. This heterogeneity can be elucidated by looking at statistical measures of the patterns sets and using these measures to divide the pattern sets into distinct groups representing like spatial processes. We introduce here a numerical procedure for sorting point pattern sets into spatially homogenous groups using functional principal component analysis (FPCA) applied to the approximated Minkowski functionals of each pattern. We demonstrate that this procedure correctly sorts pattern sets into similar groups both when the patterns are drawn from similar processes and when the second-order characteristics of the pattern are identical. We highlight this routine for distinguishing the molecular patterning of fluorescently labeled cell membrane proteins, a subject of much interest in studies investigating complex spatial signaling patterns involved in the human immune response.

Inspired by the anti-Hebbian learning rule in neural systems, we study how the feedback from dynamical synchronization shapes network structure by adding new links. Through extensive numerical simulations, we find that an adaptive network spontaneously forms scale-free structure, as confirmed in many real systems. Moreover, the adaptive process produces two nontrivial power-law behaviors of deviation strength from mean activity of the network and negative degree correlation, which exists widely in technological and biological networks. Importantly, these scalings are robust to variation of the adaptive network parameters, which may have meaningful implications in the scale-free formation and manipulation of dynamical networks. Our study thus suggests an alternative adaptive mechanism for the formation of scale-free structure with negative degree correlation, which means that nodes of high degree tend to connect, on average, with others of low degree and vice versa. The relevance of the results to structure formation and dynamical property in neural networks is briefly discussed as well.

We present a method to estimate the multifractal spectrum of point distributions. The method incorporates two motivated criteria (barycentric pivot point selection and nonoverlapping coverage) in order to reduce edge effects, improve precision, and reduce computation time. Implementation of the method on synthetic benchmarks demonstrates the superior performance of the proposed method compared with existing alternatives routinely used in the literature. Finally, we use the method to estimate the multifractal properties of the widely studied growth process of diffusion-limited aggregation (DLA) and compare our results with recent and earlier studies. Our tests support the conclusion of a genuine but weak multifractality of the central core of DLA clusters, with $D_q$ decreasing from 1.75±0.01 for $q=-10$ to 1.65±0.01 for $q$  $=$+10.

We study a thin liquid film with a free surface on a planar horizontal substrate. The substrate is subjected to oscillatory accelerations in the normal and/or in the horizontal direction(s). The description is based on the longwave approximation including inertia effects, which are important due to the large velocities imparted by external vibrations. The linearized system is examined using the Floquet analysis. Pattern formation in the nonlinear regime is computed numerically from the longwave equations for the thickness and the flow rate of the fluid in two and in three spatial dimensions. For certain amplitude and frequency ranges, combined lateral and normal oscillations can give rise to one or more traveling drops, similar to recent experimental findings by Brunet et al. [Phys. Rev. Lett. 99, 144501 (2007)].

A previous model for the Rayleigh-Taylor instability [A. R. Piriz, J. J. López Cela, and N. A. Tahir, Phys. Rev. E 80, 046305 (2009)] has been extended in order to study an interface between an elastic-plastic solid and a Newtonian liquid and determine the stability region given by the initial perturbation amplitude ${\xi }_0$ and wavelength $\lambda$. The stability region is found to be enhanced by the effect of the liquid viscosity, but it reaches an asymptote for a sufficiently high viscosity. In addition, it is also found that the boundary for the transition from the elastic to the plastic regime get closer to the stability boundary up to both boundaries coincide for a high enough liquid viscosity, thus making the onset of plastic flow a sufficient condition for instability.

The effect of horizontal periodic oscillations on the interfacial instability of two immiscible, viscous fluids of different densities, confined in a vertical Hele-Shaw cell, is investigated. An inviscid linear stability analysis of the viscous basic flow leads to the periodic Mathieu oscillator describing the evolution of interfacial amplitude. We examine mainly the effect of the periodic oscillations and the influence of the viscosity on the stability of the interface. The results show that a decrease in the viscosity contrast has a stabilizing effect on the Kelvin-Helmholtz instability, which is displaced towards the long-wave region. The effects of other parameters such as the frequency number and the Weber number are also examined.

A dust grain in a plasma has a fluctuating electric charge, and past work concludes that spherical grains in a stationary, collisionless plasma have an essentially Gaussian charge probability distribution. This paper extends that work to flowing plasmas and arbitrarily large spheres, deriving analytic charge probability distributions up to normalizing constants. We find that these distributions also have good Gaussian approximations, with analytic expressions for their mean and variance.

This paper deals with the introduction of an approach for the electromagnetic characterization of homogeneous chiral layers. The proposed method is based on the state-space approach and properties of a $4\times 4$ state transition matrix. Based on this, first, the forward problem analysis through the state-space method is reviewed and properties of the state transition matrix of a chiral layer are presented and proved as two theorems. The formulation of a proposed electromagnetic characterization method is then presented. In this method, scattering data for a linearly polarized plane wave incident normally on a homogeneous chiral slab are combined with properties of a state transition matrix and provide a powerful characterization method. The main difference with respect to other well-established retrieval procedures based on the use of the scattering parameters relies on the direct computation of the transfer matrix of the slab as opposed to the conventional calculation of the propagation constant and impedance of the modes supported by the medium. The proposed approach allows avoiding nonlinearity of the problem but requires getting enough equations to fulfill the task which was provided by considering some properties of the state transition matrix. To demonstrate the applicability and validity of the method, the constitutive parameters of two well-known dispersive chiral metamaterial structures at microwave frequencies are retrieved. The results show that the proposed method is robust and reliable.

We consider a single Josephson junction in the presence of time varying gate charge, and examine the nonequilibrium work done by the charge control in the framework of fluctuation theorems. Assuming first a high quality junction with negligible Ohmic current, we obtain the probability distribution functions of the work and confirm the Crooks relation to give the estimation of the free energy changes $\Delta F=0$. The reliability of $\Delta F$ estimated from the Jarzynksi equality is crucially dependent on protocol parameters, while the Bennett's acceptance ratio method yields consistently $\Delta F=0$. We examine the behaviors of the work average and point out its relation to heat and entropy production associated with the circuit control. Finally considering finite tunnel resistance we discuss dissipation effects on the work statistics.

We show that states of macroscopic systems with purported absolute negative temperatures are not stable under small, yet arbitrary, perturbations. We prove the previous statement using the fact that, in equilibrium, the entropy takes its maximum value. We discuss that, while Ramsey theoretical reformulation of the second law for systems with negative temperatures is logically correct, it must be a priori assumed that those states are in thermodynamic equilibrium. Since we argue that those states cannot occur, reversible processes are impossible, and, thus, Ramsey identification of absolute negative temperatures is untenable.

We study statistics of records in a sequence of random variables. These identical and independently distributed variables are drawn from the parent distribution $\rho$. The running record equals the maximum of all elements in the sequence up to a given point. We define a superior sequence as one where all running records are above the average record expected for the parent distribution $\rho$. We find that the fraction of superior sequences $S_N$ decays algebraically with sequence length $N$, $S_N\sim N^{-\beta }$ in the limit $N\to \infty$. Interestingly, the decay exponent $\beta$ is nontrivial, being the root of an integral equation. For example, when $\rho$ is a uniform distribution with compact support, we find $\beta =0.450265$. In general, the tail of the parent distribution governs the exponent $\beta$. We also consider the dual problem of inferior sequences, where all records are below average, and find that the fraction of inferior sequences $I_N$ decays algebraically, albeit with a different decay exponent, $I_N\sim N^{-\alpha }$. We use the above statistical measures to analyze earthquake data.

Solid-liquid interfaces are central to nanoscale science and technology and control processes as diverse as self-assembly, heterogeneous catalysis, wetting, electrochemistry, or protein function. Experimentally, measuring the structure and dynamics of solid-liquid interfaces with molecular resolution remains a challenge. This task can, in principle, be achieved with atomic force microscopy (AFM), which functions locally, and with nanometer precision. When operated dynamically and at small amplitudes, AFM can provide molecular-level images of the liquid solvation layers at the interfaces. At larger amplitudes, results in the field of multifrequency AFM have shown that anharmonicities in the tip motion can provide quantitative information about the solid's mechanical properties. The two approaches probe opposite aspects of the interface and are generally seen as distinct. Here it is shown that, for amplitudes $A<d$, the thickness of the solvation region, the tip mainly probes the interfacial liquid, and subnanometer resolution can be achieved through solvation forces. For $A>d$, the tip trajectory becomes rapidly anharmonic due to the tip tapping the solid, and the resolution decreases. A nonlinear transition between the two regimes occurs for $A\sim d$ and can be quantified with the second harmonic of the tip oscillation. These results, confirmed by computer simulations, remain valid in most experimental conditions. Significantly, they provide an objective criterion to enhance resolution and to decide whether the results are dominated by the properties of the solid or of the liquid.

Multiscale entropy (MSE) has been widely and successfully used in analyzing the complexity of physiological time series. We reinterpret the averaging process in MSE as filtering a time series by a filter of a piecewise constant type. From this viewpoint, we introduce filter-based multiscale entropy (FME), which filters a time series to generate multiple frequency components, and then we compute the blockwise entropy of the resulting components. By choosing filters adapted to the feature of a given time series, FME is able to better capture its multiscale information and to provide more flexibility for studying its complexity. Motivated by the heart rate turbulence theory, which suggests that the human heartbeat interval time series can be described in piecewise linear patterns, we propose piecewise linear filter multiscale entropy (PLFME) for the complexity analysis of the time series. Numerical results from PLFME are more robust to data of various lengths than those from MSE. The numerical performance of the adaptive piecewise constant filter multiscale entropy without prior information is comparable to that of PLFME, whose design takes prior information into account.

Analytical and numerical calculations are presented for the mechanical response of fiber networks in a state of axisymmetric prestress, in the limit where geometric nonlinearities such as fiber rotation are negligible. This allows us to focus on the anisotropy deriving purely from the nonlinear force-extension curves of individual fibers. The number of independent elastic coefficients for isotropic, axisymmetric, and fully anisotropic networks are enumerated before deriving expressions for the response to a locally applied force that can be tested against, e.g., microrheology experiments. Localized forces can generate anisotropy away from the point of application, so numerical integration of nonlinear continuum equations is employed to determine the stress field, and induced mechanical anisotropy, at points located directly behind and in front of a force monopole. Results are presented for the wormlike chain model in normalized forms, allowing them to be easily mapped to a range of systems. Finally, the relevance of these findings to naturally occurring systems and directions for future investigation are discussed.

We study binary state dynamics on a network where each node acts in response to the average state of its neighborhood. By allowing varying amounts of stochasticity in both the network and node responses, we find different outcomes in random and deterministic versions of the model. In the limit of a large, dense network, however, we show that these dynamics coincide. We construct a general mean-field theory for random networks and show this predicts that the dynamics on the network is a smoothed version of the average response function dynamics. Thus, the behavior of the system can range from steady state to chaotic depending on the response functions, network connectivity, and update synchronicity. As a specific example, we model the competing tendencies of imitation and nonconformity by incorporating an off-threshold into standard threshold models of social contagion. In this way, we attempt to capture important aspects of fashions and societal trends. We compare our theory to extensive simulations of this “limited imitation contagion” model on Poisson random graphs, finding agreement between the mean-field theory and stochastic simulations.

Suppressing harmful synchronization in complex networked systems is receiving increasing interest in various contexts including epileptic seizure and the Internet and traffic congestion. It is traditionally believed that by disrupting the most important nodes (i.e., those nodes of high degrees) synchronization can be effectively mitigated. However, this approach can perform poorly in more general situations such as homogeneous (random) or small world networks. In this article, we investigate how topological properties, such as the heterogeneity of the network can have an impact on its desynchronization. In particular, we propose a topology-aware scheme that chooses topologically sufficiently diversified contrarian nodes by taking into account the patterns of connectivity among them. Hence, a maximal number of nodes in the network can be influenced, leading to a more global impact and greater disruption to synchronization. Our scheme demonstrates significantly improved performance on various networked systems including homogeneous networks, small world, and even scale-free networks.

Exponential energy growth in a rectangular billiard with an oscillating bar has been clearly demonstrated earlier. Using the log-normal approximation, analytical estimates for the energy growth rate have also been provided. However, these analytical estimates are valid only when the amplitude of oscillation of the bar is small. In this paper, for larger oscillation amplitude, the log-normal approximation is numerically shown to be invalid and analytical estimates are obtained for the true energy growth rate in the case of very large particle velocities or small bar length. It is also shown that when everything else remains constant, the length of the bar which gives rise to maximum energy growth rate decreases as the oscillation amplitude increases and the true value of this maximizing length is also smaller than what is predicted by the log-normal approximation. Thus, the rectangular Fermi accelerator forms a very good example of a contemporary research problem where the limitations of the log-normal approximation can be easily appreciated.

The modified reduced Ostrovsky equation is a reduction of the modified Korteweg–de Vries equation, in which the usual linear dispersive term with a third-order derivative is replaced by a linear nonlocal integral term, representing the effect of background rotation. Here we study the case when the cubic nonlinear term has the same polarity as the rotation term. This equation is integrable provided certain slope constraints are satisfied. We demonstrate, through theoretical analysis and numerical simulations, that when this constraint is not satisfied at the initial time, wave breaking inevitably occurs.