Animal cells can sense chemical gradients without moving and are faced with the challenge of migrating towards a target despite noisy information on the target position. Here we discuss optimal search strategies for a chaser that moves by switching between two phases of motion (“run” and “tumble”), reorienting itself towards the target during tumble phases, and performing persistent migration during run phases. We show that the chaser average run time can be adjusted to minimize the target catching time or the spatial dispersion of the chasers. We obtain analytical results for the catching time and for the spatial dispersion in the limits of small and large ratios of run time to tumble time and scaling laws for the optimal run times. Our findings have implications for optimal chemotactic strategies in animal cell migration.

This paper uses the reliability polynomial, introduced by Moore and Shannon in 1956, to analyze the effect of network structure on diffusive dynamics such as the spread of infectious disease. We exhibit a representation for the reliability polynomial in terms of what we call structural motifs that is well suited for reasoning about the effect of a network's structural properties on diffusion across the network. We illustrate by deriving several general results relating graph structure to dynamical phenomena.

We introduce a method to extract main-stream structures for a given complex network flow by trimming less effective links. As the resulting main streams generally have an almost loopless treelike structure, we can define the stream basin size for each node, which characterizes the importance of the node with regard to the flow. As a real-world example, we apply this method to an interfirm trading network, both for the money flow and its conjugate—the material or service flow—confirming that both basin size distributions follow a similar power law that differs significantly from the basin size distributions of rivers in nature. We theoretically analyze the process of trimming and derive a consistent statistical formulation between the original link number and the basin size.

The classical problem of a semiconductor laser subject to polarized injection is revisited. From the laser rate equations for the transverse electric (TE) and transverse magnetic (TM) modes, we first determine the steady states. We then investigate their linear stability properties and derive analytical expressions for the steady, saddle-node, and Hopf bifurcation points. We highlight conditions for bistability between pure- and mixed-mode steady states for the laser subject to either TE or TM injection. To our knowledge, the first case has not been documented yet. An important parameter is the ratio of the polarization gain coefficients and we explore its effect on the stability and bifurcation diagrams.

We investigate time irreversibility from the point of view of a single particle in Burgers turbulence. Inspired by the recent work for incompressible flows [Xu et al., Proc. Natl. Acad. Sci. USA 111, 7558 (2014)], we analyze the evolution of the kinetic energy for fluid markers and use the fluctuations of the instantaneous power as a measure of time irreversibility. For short times, starting from a uniform distribution of markers, we find the scaling $\langle {[E\left(t\right)-E\left(0\right)]}^n\rangle \propto t$ and $\langle p^n\rangle \propto {\mathrm{Re}}^{n-1}$ for the power as a function of the Reynolds number. Both observations can be explained using the “flight-crash” model, suggested by Xu et al. Furthermore, we use a simple model for shocks that reproduces the moments of the energy difference, including the pre-factor for $\langle E\left(t\right)-E\left(0\right)\rangle$. To complete the single-particle picture for Burgers we compute the moments of the Lagrangian velocity difference and show that they are bifractal. This arises in a similar manner to the bifractality of Eulerian velocity differences. In the above setting, time irreversibility is directly manifest as particles eventually end up in shocks. We additionally investigate time irreversibility in the long-time limit when all particles are located inside shocks and the Lagrangian velocity statistics are stationary. We find the same scalings for the power and energy differences as at short times and argue that this is also a consequence of rare “flight-crash” events related to shock collisions.

We use molecular dynamics simulations to test integral equation theory predictions for the structure of fluids of spherical particles with eight different piecewise-constant pair-interaction forms comprising a hard core and a combination of two shoulders and/or wells. Since model pair potentials like these are of interest for discretized or coarse-grained representations of effective interactions in complex fluids (e.g., for computationally intensive inverse optimization problems), we focus here on assessing how accurately their properties can be predicted by analytical or simple numerical closures including Percus-Yevick, hypernetted-chain, and reference hypernetted-chain closures and first-order mean spherical and modified first-order mean spherical approximations. To make quantitative comparisons between the predicted and simulated radial distribution functions, we introduce a cumulative structural error metric. For equilibrium fluid state points of these models, we find that the reference hypernetted-chain closure is the most accurate of the tested approximations as characterized by this metric or related thermodynamic quantities.

We consider developed turbulence in the two-dimensional Gross-Pitaevskii model, which describes wide classes of phenomena from atomic and optical physics to condensed matter, fluids, and plasma. The well-known difficulty of the problem is that the hypothetical local spectra of both inverse and direct cascades in the weak-turbulence approximation carry fluxes that are either zero or have the wrong sign; Such spectra cannot be realized. We analytically derive the exact flux constancy laws (analogs of Kolmogorov's 4/5 law for incompressible fluid turbulence), expressed via the fourth-order moment and valid for any nonlinearity. We confirm the flux laws in direct numerical simulations. We show that a constant flux is realized by a nonlocal wave interaction in both the direct and inverse cascades. Wave spectra (second-order moments) are close to slightly (logarithmically) distorted thermal equilibrium in both cascades.

We develop the stochastic approach to thermodynamics based on stochastic dynamics, which can be discrete (master equation) and continuous (Fokker-Planck equation), and on two assumptions concerning entropy. The first is the definition of entropy itself and the second the definition of entropy production rate, which is non-negative and vanishes in thermodynamic equilibrium. Based on these assumptions, we study interacting systems with many degrees of freedom in equilibrium or out of thermodynamic equilibrium and how the macroscopic laws are derived from the stochastic dynamics. These studies include the quasiequilibrium processes; the convexity of the equilibrium surface; the monotonic time behavior of thermodynamic potentials, including entropy; the bilinear form of the entropy production rate; the Onsager coefficients and reciprocal relations; and the nonequilibrium steady states of chemical reactions.

We present an analysis of the work performed on a system of interest that is kept thermally isolated during the switching of a control parameter. We show that there exists, for a certain class of systems, a finite-time family of switching protocols for which the work is equal to the quasistatic value. These optimal paths are obtained within linear response for systems initially prepared in a canonical distribution. According to our approach, such protocols are composed of a linear part plus a function which is odd with respect to time reversal. For systems with one degree of freedom, we claim that these optimal paths may also lead to the conservation of the corresponding adiabatic invariant. This points to an interesting connection between work and the conservation of the volume enclosed by the energy shell. To illustrate our findings, we solve analytically the harmonic oscillator and present numerical results for certain anharmonic examples.

In this work we investigate the generic properties of a stochastic linear model in the regime of high dimensionality. We consider in particular the vector autoregressive (VAR) model and the multivariate Hawkes process. We analyze both deterministic and random versions of these models, showing the existence of a stable phase and an unstable phase. We find that along the transition region separating the two regimes the correlations of the process decay slowly, and we characterize the conditions under which these slow correlations are expected to become power laws. We check our findings with numerical simulations showing remarkable agreement with our predictions. We finally argue that real systems with a strong degree of self-interaction are naturally characterized by this type of slow relaxation of the correlations.

Brownian motion, the classical diffusive process, maximizes the Boltzmann-Gibbs entropy. The Tsallis $q$ entropy, which is nonadditive, was developed as an alternative to the classical entropy for systems which are nonergodic. A generalization of Brownian motion is provided that maximizes the Tsallis entropy rather than the Boltzmann-Gibbs entropy. This process is driven by a Brownian measure with a random diffusion coefficient. The distribution of this coefficient is derived as a function of $q$ for $1<q<3$. Applications to transport in porous media are considered.

Experimentally observed electrical breakdown voltages $\left(U_{\mathrm{B}}\right)$ in high-pressure gases and supercritical fluids deviate from classical theories for low-pressure gas discharges, and the underlying breakdown mechanisms for the high-density fluids making the $U_{\mathrm{B}}$ differ from those in the classical discharges are not yet well understood. In this study, we developed an electrical breakdown model for the high-density fluids taking into account the effects of density fluctuations and ion-enhanced field emission (IEFE). The model is based on the concept that a critical anomaly of the $U_{\mathrm{B}}$ (local minimum near the critical point) is caused by long mean free electron path leading to a large first Townsend coefficient in locally low-density spatial domains generated by the density fluctuations. Also, a modified Paschen's curve considering the effect of the IEFE on the second Townsend coefficient was used to reproduce the $U_{\mathrm{B}}$ curve in the high-density fluids. Calculations based on the novel model showed good agreements with the experimentally measured $U_{\mathrm{B}}$ even near the critical point and it also suggested that the critical anomaly of the $U_{\mathrm{B}}$ depends on the gap distance. These results indicate that both the density fluctuations and the IEFE have to be considered to comprehend the plasmas in high-density and density-fluctuating fluids.

We obtain an explicit solution for the island-size distribution described by the rate equations for irreversible growth with the simplified capture rates of the form ${\sigma }_s\left(\mathrm{\Theta }\right)\propto {\mathrm{\Theta }}^p\left(a+s-1\right)$ for all $s\ge 1$, where $s$ is the size and $\mathrm{\Theta }$ is the time-dependent coverage. The intrinsic property of this solution is its scaling form in the continuum limit. The analytic scaling function depends on the two parameters $a$ and $p$ and is capable of describing very dissimilar distribution shapes, both monomodal and monotonically decreasing. The obtained results suggest that the scaling features of the size distributions are closely related to the size linearity of the capture rates. A simple analytic scaling is obtained rigorously here and helps to gain a better theoretical understanding of possible origins of the scaling behavior of the island-size distributions.

Ionizing radiation induces a variety of DNA damages including single-strand breaks (SSBs), double-strand breaks (DSBs), abasic sites, modified sugars, and bases. Most theoretical and experimental studies have been focused on DNA strand scissions, in particular production of DNA double-strand breaks. DSBs have been proven to be a key damage at a molecular level responsible for the formation of chromosomal aberrations, leading often to cell death. We have studied the nature of DNA damage induced directly by the pulsed 46.9-nm (26.5 eV) radiation provided by an extreme ultraviolet (XUV) capillary-discharge Ne-like Ar laser (CDL). Doses up to 45 kGy were delivered with a repetition rate of 3 Hz. We studied the dependence of the yield of SSBs and DSBs of a simple model of DNA molecule (pBR322) on the CDL pulse fluence. Agarose gel electrophoresis method was used for determination of both SSB and DSB yields. The action cross sections of the single- and double-strand breaks of pBR322 plasmid DNA in solid state were determined. We observed an increase in the efficiency of strand-break induction in the supercoiled DNA as a function of laser pulse fluence. Results are compared to those acquired at synchrotron radiation facilities and other sources of extreme-ultraviolet and soft x-ray radiation.

Randomization of binary matrices has become one of the most important quantitative tools in modern computational biology. The equivalent problem of generating random directed networks with fixed degree sequences has also attracted a lot of attention. However, it is very challenging to generate truly unbiased random matrices with fixed row and column sums. Strona et al. [Nat. Commun. 5, 4114 (2014)] introduce the innovative Curveball algorithm and give numerical support for the proposition that it generates truly random matrices. In this paper, we present a rigorous proof of convergence to the uniform distribution. Furthermore, we show the Curveball algorithm must include certain failed trades to ensure uniform sampling.

Power lines, roadways, pipelines, and other physical infrastructure are critical to modern society. These structures may be viewed as spatial networks where geographic distances play a role in the functionality and construction cost of links. Traditionally, studies of network robustness have primarily considered the connectedness of large, random networks. Yet for spatial infrastructure, physical distances must also play a role in network robustness. Understanding the robustness of small spatial networks is particularly important with the increasing interest in microgrids, i.e., small-area distributed power grids that are well suited to using renewable energy resources. We study the random failures of links in small networks where functionality depends on both spatial distance and topological connectedness. By introducing a percolation model where the failure of each link is proportional to its spatial length, we find that when failures depend on spatial distances, networks are more fragile than expected. Accounting for spatial effects in both construction and robustness is important for designing efficient microgrids and other network infrastructure.

In this paper, we investigate the motion of a set of charged particles acted upon by a growing electrostatic wave in the limit when the initial wave amplitude is vanishingly small and when all the particles have the same initial action, $I_0$. We show, both theoretically and numerically, that when all the particles have been trapped in the wave potential, the distribution in action exhibits a very sharp peak about the smallest action. Moreover, as the wave keeps growing, the most probable action tends toward a constant, $I_f$, which we estimate theoretically. In particular, we show that $I_f$ may be calculated very accurately when the particles' motion before trapping is far from adiabatic by making use of a perturbation analysis in the wave amplitude. This fills a gap regarding the computation of the action change, which, in the past, has only been addressed for slowly varying dynamics. Moreover, when the variations of the dynamics are fast enough, we show that the Fourier components of the particles' distribution function can be calculated by connecting estimates from our perturbation analysis with those obtained by assuming that all the particles have the same constant action, $I=I_f$. This result is used to compute theoretically the imaginary part of the electron susceptibility of an electrostatic wave in a plasma. Moreover, using our formula for the electron susceptibility, we can extend the range in ${\epsilon }_a$ (the parameter that quantifies the slowness of the dynamics) for our perturbative estimate of $I_f-I_0$. This range can actually be pushed down to values of ${\epsilon }_a$ allowing the use of neoadiabatic techniques to compute the jump in action. Hence, this paper shows that the action change due to trapping can be calculated theoretically, regardless of the rate of variation of the dynamics, by connecting perturbative results with neoadiabatic ones.

A quantitative comparison of various classes of oscillators (integrate-and-fire, Winfree, and Kuramoto-Daido type) is performed in the weak-coupling limit for a fully connected network of identical units. An almost perfect agreement is found, with only tiny differences among the models. We also show that the regime of self-consistent partial synchronization is rather general and can be observed for arbitrarily small coupling strength in any model class. As a byproduct of our study, we are able to show that an integrate-and-fire model with a generic pulse shape can be always transformed into a similar model with $\delta$ pulses and a suitable phase response curve.

We report on structures in a scale-dependent Lyapunov exponent of an experimental chaotic map that arise due to discontinuities in the map. The chaos is realized in an autonomous Boolean network, which is constructed using asynchronous logic gates to form a map operator that outputs an unclocked pulse-train of varying widths. The map operator executes pulse-width stretching and folding and the operator's output is fed back to its input to continuously iterate the map. Using a simple model, we show that the structured scale-dependence in the system's Lyapunov exponent is the result of the discrete logic elements in the map operator's stretching function.

In this paper, we study the clustering of inertial particles using a periodic kinematic simulation. The systematic Lagrangian tracking of particles makes it possible to identify the particles' clustering patterns for different values of particle inertia and drift velocity. The different cases are characterized by different pairs of Stokes number (St) and Froude number (Fr). For the present study, $0\le \mathrm{St}\le 1$ and $0.4\le \mathrm{Fr}\le 1.4$. The main focus is to identify and then quantify the clustering attractor—when it exists—that is the set of points in the physical space where the particles settle when time goes to infinity. Depending on the gravity effect and inertia values, the Lagrangian attractor can have different dimensions, varying from the initial three-dimensional space to two-dimensional layers and one-dimensional attractors that can be shifted from a horizontal to a vertical position.