Experimental advances have improved the two- (2D) and three-dimensional (3D) spatial resolution that can be extracted from in vivo single-molecule measurements. This enables researchers to quantitatively infer the magnitude and directionality of forces experienced by biomolecules in their native environment. Situations where such force information is relevant range from mitosis to directed transport of protein cargo along cytoskeletal structures. Models commonly applied to quantify single-molecule dynamics assume that effective forces and velocity in the $x,y$ (or $x,y,z$) directions are statistically independent, but this assumption is physically unrealistic in many situations. We present a hypothesis testing approach capable of determining if there is evidence of statistical dependence between positional coordinates in experimentally measured trajectories; if the hypothesis of independence between spatial coordinates is rejected, then a new model accounting for 2D (3D) interactions can and should be considered. Our hypothesis testing technique is robust, meaning it can detect interactions, even if the noise statistics are not well captured by the model. The approach is demonstrated on control simulations and on experimental data (directed transport of intraflagellar transport protein 88 homolog in the primary cilium).

In this paper, we develop an entropy measure for assessing the structural complexity of directed graphs. Although there are many existing alternative measures for quantifying the structural properties of undirected graphs, there are relatively few corresponding measures for directed graphs. To fill this gap in the literature, we explore an alternative technique that is applicable to directed graphs. We commence by using Chung's generalization of the Laplacian of a directed graph to extend the computation of von Neumann entropy from undirected to directed graphs. We provide a simplified form of the entropy which can be expressed in terms of simple node in-degree and out-degree statistics. Moreover, we find approximate forms of the von Neumann entropy that apply to both weakly and strongly directed graphs, and that can be used to characterize network structure. We illustrate the usefulness of these simplified entropy forms defined in this paper on both artificial and real-world data sets, including structures from protein databases and high energy physics theory citation networks.

We develop a biophysical model of neurosensory integration in the model organism Caenorhabditis elegans. Building on experimental findings on the neuron conductances and their resolved connectome, we posit the first full dynamic model of the neural voltage excitations that allows for a characterization of network structures which link input stimuli to neural proxies of behavioral responses. Full connectome simulations of neural responses to prescribed inputs show that robust, low-dimensional bifurcation structures drive neural voltage activity modes. Comparison of these modes with experimental studies allows us to link these network structures to behavioral responses. Thus the underlying bifurcation structures discovered, i.e., induced Hopf bifurcations, are critical in explaining behavioral responses such as swimming and crawling.

Biochemical reactions in a cell can be modeled by a catalytic reaction network (CRN). It has been reported that catalytic chain reactions occur intermittently in the CRN with a homogeneous random-graph topology and its avalanche-size distribution obeys a power law with the exponent $4/3$ [A. Awazu and K. Kaneko, Phys. Rev. E 80, 010902(R) (2009)]. This fact indicates that the catalytic reaction dynamics in homogeneous CRNs exhibits self-organized criticality (SOC). Structures of actual CRNs are, however, known to be highly inhomogeneous. We study the influence of various types of inhomogeneities found in real-world metabolic networks on the universality class of SOC. Our numerical results clarify that SOC keeps its universality class even for networks possessing structural inhomogeneities such as the scale-free property, community structures, and degree correlations. In contrast, if the CRN has inhomogeneous catalytic functionality, the universality class of SOC depends on how widely distributed the number of reaction paths catalyzed by a single chemical species is.

We study the effect of noise on a Josephson junction that, coupled to a linear $RLC$ resonator, can oscillate at two frequencies. To establish the global stability of the attractors, we estimate the position of the separatrix, essential information to establish the stability of the attractor for this multidimensional system, from the analysis of the mean first passage time. We find that the frequency locked to the resonator is most stable at low bias and less stable at high bias, where the resonator exhibits the largest oscillations. The change in the birhythmic region is dramatic for the effective barrier changes of an order of magnitude and the corresponding lifetime of about seven decades.

We study tolerance of dynamic behavior in networks of coupled heterogeneous oscillators to deterioration of the individual oscillator components. As the deterioration proceeds with reduction in dynamic behavior of the oscillators, an order parameter evaluating the level of global oscillation decreases and then vanishes at a certain critical point. We present a method to analytically derive a general formula for this critical point and an approximate formula for the order parameter in the vicinity of the critical point in networks of coupled Stuart-Landau oscillators. Using the critical point as a measure for dynamical robustness of oscillator networks, we show that the more heterogeneous the oscillator components are, the more robust the oscillatory behavior of the network is to the component deterioration. This property is confirmed also in networks of Morris-Lecar neuron models coupled through electrical synapses. Our approach could provide a useful framework for theoretically understanding the role of population heterogeneity in robustness of biological networks.

Formation and interaction of the one-dimensional excitation waves in a reaction-diffusion system with the piecewise linear reaction functions of the Tonnelier-Gerstner type are studied. We show that there exists a parameter region where the established regime of wave propagation depends on initial conditions. Wave phenomena with a complex behavior are found: (i) the reflection of waves at a growing distance (the remote reflection) upon their collision with each other or with no-flux boundaries and (ii) the periodic transformation of waves with the jumping from one regime of wave propagation to another (the periodic trigger wave).

Synchronization transition in networks of nonlocally coupled chaotic oscillators is investigated. It is found that in reaching the state of global synchronization the networks can stay in various states of partial synchronization. The stability of the partial synchronization states is analyzed by the method of eigenvalue analysis, in which the important roles of the network topological symmetry on synchronization transition are identified. Moreover, for networks possessing multiple topological symmetries, it is found that the synchronization transition can be divided into different stages, with each stage characterized by a unique synchronous pattern of the oscillators. Synchronization transitions in networks of nonsymmetric topology and nonidentical oscillators are also investigated, where the partial synchronization states, although unstable, are found to be still playing important roles in the transitions.

Transport in treelike networks has received wide attention in natural systems, oil recovery, microelectronic cooling systems, and textiles. Existing studies are focused on transport behaviors under a constant potential difference (including pressure, temperature, and voltage) in a steady state [B. Yu and B. Li, Phys. Rev. E 73, 066302 (2006); J. Chen, B. Yu, P. Xu, and Y. Li, Phys. Rev. E 75, 056301 (2007)]. However, dynamic (time-dependent) transport in such systems has rarely been concerned. In this work, we theoretically investigate the dynamics of capillary flow in treelike networks and design the distribution of radius and length of local branches for the fastest capillary flow. It is demonstrated that capillary flow in the optimized tree networks is faster than in traditional parallel tube nets under fixed constraints. As well, the flow time of the liquid is found to increase approximately linearly with penetration distance, which differs from Washburn's classic description that flow time increases as the square of penetration distance in a uniform tube.

An analytical expression to evaluate the second-order mean force (acoustic radiation force) on a finite-sized, rigid, spherical particle due to an acoustic wave is presented. The medium in which the particle is situated is taken to be both viscous and compressible. A far-field derivation approach has been used in determining the force, which is a function of the particle size, acoustic wavelength, and viscous boundary-layer thickness. It is assumed that the viscous length scale is negligibly small compared to the acoustic wavelength. The force expression presented here (i) reduces to the correct inviscid behavior (for both small- and finite-sized particles) and (ii) is identical to recent viscous results [M. Settnes and H. Bruus, Phys. Rev. E 85, 016327 (2012)] for small-sized particles. Further, the computed force qualitatively matches the computational fluid dynamics (finite-element) results [D. Foresti, M. Nabavi, and D. Poulikakos, J. Fluid Mech. 709, 581 (2012)] for finite-sized particles. Additionally, the mean force is interpreted in terms of a multipole expansion. Subsequently, considering the fact that the force expansion is an infinite series, the number of terms that are required or adequate to capture the force to a specified accuracy is also provided as a function of the particle size to acoustic wavelength ratio. The dependence of the force on particle density, kinematic viscosity, and bulk viscosity of the fluid is also investigated. Here, both traveling and standing waves are considered.

When a fluid pushes on and accelerates a heavier fluid, small perturbations at their interface grow with time and lead to turbulent mixing. The same instability, known as the Rayleigh-Taylor instability, operates when a heavy fluid is supported by a lighter fluid in a gravitational field. It has a particularly deleterious effect on inertial-confinement-fusion implosions and is known to operate over 18 orders of magnitude in dimension. We propose analytic expressions for the bubble and spike amplitudes and mixing widths in the linear, nonlinear, and turbulent regimes. They cover arbitrary density ratios and accelerations that are constant or changing relatively slowly with time. We discuss their scalings and compare them with simulations and experiments.

We present an approach for the realization of extreme off-Hugoniot states of matter in laser-driven shock experiments. The method is based on the application of impedance-mismatch effect in sandwich targets. In order to verify this model we have realized numerical simulations using the two-dimensional hydrocode multi in three-layer targets (gold-aluminum-gold) with laser intensities ∼10${}^{14}$ W/cm${}^2$ and obtained pressures ∼10 Mbar. Results show the possibility of obtaining high pressures with relatively small temperatures for a low-impedance material sandwiched between layers with high density material.

Based on well-established physical relationships, a semiempirical set of equations dictating the electrical conductivity of dense, strongly coupled, partially ionized copper is presented. With the empirical coefficients, the model is tuned to experimental conductivity data obtained from exploding wire experiments [A. W. DeSilva and J. D. Katsouros, Phys. Rev. E 57, 5945 (1998)]. The result is a wide-range conductivity model, with demonstrated accuracy from room temperature-density conditions to 0.01 g/cm${}^3$ and 30 kK. Using magnetohydrodynamic simulation the ability to utilize the conductivity model for predictive simulations is demonstrated. A complete electrical conductivity dataset for copper has been made available to the public.

Inverse statistical mechanics aims to determine particle interactions from ensemble properties. This article looks at this inverse problem from a Bayesian perspective and discusses several statistical estimators to solve it. In addition, a sequential Monte Carlo algorithm is proposed that draws the interaction parameters from their posterior probability distribution. The posterior probability involves an intractable partition function that is estimated along with the interactions. The method is illustrated for inverse problems of varying complexity, including the estimation of a temperature, the inverse Ising problem, maximum entropy fitting, and the reconstruction of molecular interaction potentials.

By means of coupled molecular dynamics–computational fluid dynamics simulations, we analyze the initiation of avalanches in a granular bed of spherical particles immersed in a viscous fluid and inclined above its angle of repose. In quantitative agreement with experiments, we find that the bed is unstable for a packing fraction below $0.59$ but is stabilized above this packing fraction by negative excess pore pressure induced by the effect of dilatancy. From detailed numerical data, we explore the time evolution of shear strain, packing fraction, excess pore pressures, and granular microstructure in this creeplike pressure redistribution regime, and we show that they scale excellently with a characteristic time extracted from a model based on the balance of granular stresses in the presence of a negative excess pressure and its interplay with dilatancy. The cumulative shear strain at failure is found to be $\simeq$0.2, in close agreement with the experiments, irrespective of the initial packing fraction and inclination angle. Remarkably, the avalanche is triggered when dilatancy vanishes instantly as a result of fluctuations while the average dilatancy is still positive (expanding bed) with a packing fraction that declines with the initial packing fraction. Another nontrivial feature of this creeplike regime is that, in contrast to dry granular materials, the internal friction angle of the bed at failure is independent of dilatancy but depends on the inclination angle, leading therefore to a nonlinear dependence of the excess pore pressure on the inclination angle. We show that this behavior may be described in terms of the contact network anisotropy, which increases with a nearly constant connectivity and levels off at a value (critical state) that increases with the inclination angle. These features suggest that the behavior of immersed granular materials is controlled not only directly by hydrodynamic forces acting on the particles but also by the influence of the fluid on the granular microstructure.

The processes of nucleation, aggregation, annealing, and disintegration of clusters of non-Brownian paramagnetic beads in a vibrofluidized system are experimentally investigated. The interaction among the beads is induced by a magnetic seed composed of two dipoles allocated outside the container cell. We observe a clearly differentiated nucleation stage, whose evolution (nucleation time versus acceleration strength) follows a power law. Thereafter, the beads aggregate forming 2D disordered clusters around the nucleus. Both processes (nucleation and aggregation) are determined by the competition between magnetic forces and the drag produced by a thermal bath created by glass particles. Once the agglomerates reach a final state (shape and length), they are annealed by increasing and decreasing the granular temperature. We found that the fractal dimension and the lacunarity index clearly describe the structural variations of the clusters. Our discussion on this phenomenon is addressed, making a rough analogy with the glass transition in a super-cooled liquid. Finally, we study the disintegration of the clusters as a function of time and the density of the surrounding gas. The question is not if, but how they disintegrate upon removing the external field; we find that the disintegration follows an exponential decay.

We have studied the melting process of a finite-sized two-dimensional colloidal crystal by video microscopy. The local area fraction $\varphi$ and the local hexatic orientational order parameter ${\psi }_6$ have been evaluated for respective Voronoi cells in the crystal. The histogram of $\varphi$ exhibits a peak and the peak $\varphi$ continuously decreases with the time elapsed. The histogram of $|{\psi }_6|$ shows an abrupt broadening for $\varphi <0.65$. This critical value of $\varphi$ is the transition point between the hexatic and dense liquid phases in finite crystal. We have also evaluated $\varphi$ and $|{\psi }_6|$ as a function of the distance from the center of the crystal $r$. $\varphi \left(r\right)$ is almost constant within the crystal and monotonously decreases with the time elapsed. $|{\psi }_6\left(r\right)|$ gradually decreases with $r$ but there is the core with $|{\psi }_6|=1$ at earlier time stage. The temporal change of the average $\varphi$ within the crystal is qualitatively explained by the slow diffusion of the particles situated at the crystal edge. The steric repulsion between the particles within the crystal enhances the expansion rate of the crystal edge. Overall melting behavior is same in the crystals with different sizes. We have also studied the melting of a finite-sized crystal composed of soft-core particles by Brownian dynamics simulation and verified the finite-size effect on the melting process. The simulated behavior is qualitatively in good agreement with the experimental results.

Measures of entropy have been widely used to characterize complexity, particularly in physiological dynamical systems modeled in discrete time. Current approaches associate these measures to finite single values within an observation window, thus not being able to characterize the system evolution at each moment in time. Here, we propose a new definition of approximate and sample entropy based on the inhomogeneous point-process theory. The discrete time series is modeled through probability density functions, which characterize and predict the time until the next event occurs as a function of the past history. Laguerre expansions of the Wiener-Volterra autoregressive terms account for the long-term nonlinear information. As the proposed measures of entropy are instantaneously defined through probability functions, the novel indices are able to provide instantaneous tracking of the system complexity. The new measures are tested on synthetic data, as well as on real data gathered from heartbeat dynamics of healthy subjects and patients with cardiac heart failure and gait recordings from short walks of young and elderly subjects. Results show that instantaneous complexity is able to effectively track the system dynamics and is not affected by statistical noise properties.

We study the origin of mixed-mode oscillations and related bifurcations in a fully molecular laser model that describes ${\mathrm{CO}}_2$ monomode lasers with a slow saturable absorber. Our study indicates that the presence of isolas of periodic mixed-mode oscillations, as the pump parameter and the cavity-frequency detuning change, is inherent to $Q$-switched ${\mathrm{CO}}_2$ monomode lasers. We compare this model, known as the dual four-level model, to the more conventional 3:2 model and to a ${\mathrm{CO}}_2$ laser model for fast saturable absorbers. In these models, we find similarities as well as qualitative differences, such as the different nature of the homoclinic tangency to a relevant unstable periodic orbit, where the Gavrilov-Shilnikov theory and its extensions may hold. We also show that there are isolas of periodic mixed-mode oscillations in a model for ${\mathrm{CO}}_2$ lasers with modulated losses, as the pump parameter varies. The coarse-grained bifurcation diagrams of the periodic mixed-mode oscillations in these models suggest that these oscillations belong to similar classes.