The subatomic experimental exploration of physical processes on extremely short time scales has become possible by the generation of high-quality electron bunches and x-ray pulses with subfemtosecond durations. Increasing the photon energy from the x-ray to gamma-ray regime makes probing of extremely small space-time domains accessible. Here, a mechanism for generating attosecond gamma photon and positron bunches with small divergence using laser intensities below ${10}^{23}\mathrm{W}/{\mathrm{cm}}^2$ is proposed. In contrast with previous works, in our scheme a single laser pulse is sufficient instead of two counterpropagating pulses. Numerical simulations are used to formulate the conditions for confined radiation and to characterize the generated photon and positron bunches.

We discuss a resource-competition model, which takes MacArthur's model as a platform, to unveil interesting connections with glassy features and jamming in high dimensions. This model, as first studied by Tikhonov and Monasson, presents two qualitatively different phases: a shielded phase, where a collective, self-sustained behavior emerges, and a vulnerable phase, where a small perturbation can destabilize the system and contribute to population extinction. We first present our perspective based on a strong similarity with continuous constraint satisfaction problems in their convex regime. Then, we discuss the stability analysis in terms of the computation of the leading eigenvalue of the Hessian matrix of the associated Lyapunov function. This computation allows us to efficiently distinguish between the two aforementioned phases and to relate high-dimensional critical ecosystems to glassy phenomena in the low-temperature regime.

Water is ubiquitous, and the surface properties of ice have been studied for some time, due to their importance. A liquidlike layer (LLL) is known to exist on ice, below the melting point. We use surface thermal fluctuation spectroscopy to study the LLL, including its thickness, for pure ice, and for ice with impurities. We find that the properties of the LLL are experimentally those of liquid water, with thickness much smaller than previous results. We also find that impurities cause the LLL to be thicker, and quite inhomogeneous, with properties depending on the dopant.

We investigate the scaling of the interfacial adsorption of the two-dimensional Blume-Capel model using Monte Carlo simulations. In particular, we study the finite-size scaling behavior of the interfacial adsorption of the pure model at both its first- and second-order transition regimes, as well as at the vicinity of the tricritical point. Our analysis benefits from the currently existing quite accurate estimates of the relevant (tri)critical-point locations. In all studied cases, the numerical results verify to a level of high accuracy the expected scenarios derived from analytic free-energy scaling arguments. We also investigate the size dependence of the interfacial adsorption under the presence of quenched bond randomness at the originally first-order transition regime (disorder-induced continuous transition) and the relevant self-averaging properties of the system. For this ex-first-order regime, where strong transient effects are shown to be present, our findings support the scenario of a non-divergent scaling, similar to that found in the original second-order transition regime of the pure model.

We study the heat fluctuation of an overdamped Brownian particle trapped in a harmonic potential and driven by active noise. Employing the phase-space path integral method we derive a general formula for the probability distribution of heat exchange in a generic model of an active bath. The work has been extended by considering two particular models of active noise and computing an exact analytical expression for distribution in Gaussian colored noise and a semianalytical result in the Poissonian bath. We corroborate the fluctuation theorem with our analytical findings by introducing the familiar concept of effective temperature and as a corollary the total entropy production is calculated.

For perturbative scalar field theories, the late-time-limit of the out-of-time-ordered correlation function that measures (quantum) chaos is shown to be equal to a Boltzmann-type kinetic equation that measures the total gross (instead of net) particle exchange between phase-space cells, weighted by a function of energy. This derivation gives a concrete form to numerous attempts to derive chaotic many-body dynamics from ad hoc kinetic equations. A period of exponential growth in the total gross exchange determines the Lyapunov exponent of the chaotic system. Physically, the exponential growth is a front propagating into an unstable state in phase space. As in conventional Boltzmann transport, which follows from the dynamics of the net particle number density exchange, the kernel of this kinetic integral equation for chaos is also set by the 2-to-2 scattering rate. This provides a mathematically precise statement of the known fact that in dilute weakly coupled gases, transport and scrambling (or ergodicity) are controlled by the same physics.

Various types of walks on complex networks have been used in recent years to model search and navigation in several kinds of systems, with particular emphasis on random walks. This gives valuable information on network properties, but self-avoiding walks (SAWs) may be more suitable than unrestricted random walks to study long-distance characteristics of complex systems. Here we study SAWs in clustered scale-free networks, characterized by a degree distribution of the form $P\left(k\right)\sim k^{-\gamma }$ for large $k$. Clustering is introduced in these networks by inserting three-node loops (triangles). The long-distance behavior of SAWs gives us information on asymptotic characteristics of such networks. The number of self-avoiding walks, $a_n$, has been obtained by direct enumeration, allowing us to determine the connective constant $\mu$ of these networks as the large-$n$ limit of the ratio $a_n/a_{n-1}$. An analytical approach is presented to account for the results derived from walk enumeration, and both methods give results agreeing with each other. In general, the average number of SAWs $a_n$ is larger for clustered networks than for unclustered ones with the same degree distribution. The asymptotic limit of the connective constant for large system size $N$ depends on the exponent $\gamma$ of the degree distribution: For $\gamma >3, \mu$ converges to a finite value as $N\to \infty$; for $\gamma =3$, the size-dependent ${\mu }_N$ diverges as $lnN$, and for $\gamma <3$ we have ${\mu }_N\sim N^{(3-\gamma )/2}$.

Mathematical modeling may be an excellent tool to analyze and explain complex biological phenomena. In this paper, we use a mathematical model to reveal various interesting dynamical features of phytoplankton-zooplankton interaction and attempt to explain the reason for contrasting dynamics shown by different laboratory and field experiments. Our study shows that the phytoplankton-zooplankton interaction in a pelagic system is very complex and the plankton dynamics, including the bloom phenomenon, strongly depends on the selective predation of zooplankton and the nutritional value of phytoplankton. The study supports the existing hypothesis that decoupling at the plant-animal interface may occur due to strong fish predation on zooplankton. In addition, we argue that decoupling of the food chain may also occur under low to intermediate nutrient inflow if zooplankton feeds on phytoplankton having lower nutritional value. It is also shown that nutrient enrichment can destabilize an otherwise stable system if zooplankton feeds on highly nutritious prey, but unable to destabilize the system if zooplankton feeds on low-nutritious prey. This may be one possible explanation to the longstanding question: Why do some experiments show the paradox of enrichment and others do not?

We provide analytical formulas for the movement of spherical particles in a corrugated tube, in the approximation of small amplitude of the tube diameter variation. We calculate how the particle is pushed toward the wall at some places and pulled off the wall at others. We show that this effect causes rectification of the particle movement, when the direction of the fluid flow is alternated, thus leading to the hydrodynamic ratchet effect. We propose such scheme as a particle-separation device.

We generalize the particle-conserving dynamics method of de las Heras et al. [J. Phys.: Condens. Matter 28, 244024 (2016)] to binary mixtures and apply this to hard rods in one dimension. Considering the case of one species consisting of only one particle enables us to address the tagged-particle dynamics. The time-evolution of the species-labeled density profiles is compared to exact Brownian dynamics and (grand-canonical) dynamical density functional theory. The particle-conserving dynamics yields improved results over the dynamical density functional theory and well reproduces the simulation data at short and intermediate times. However, the neglect of a strict particle order (due to the fundamental statistical assumption of ergodicity) leads to errors at long times for our one-dimensional setup. The isolated study of that error makes clear the fundamental limitations of (adiabatic) density-based theoretical approaches when applied to systems of any dimension for which particle caging is a dominant physical mechanism.

The evolution of a uniform interface subjected to a perturbed shock wave has been experimentally studied over a range of Atwood numbers $0.22\le A\le 0.68$ and Mach numbers $1.2\le M\le 1.8$ using a vertical shock tube. The perturbed shock wave is produced by diffracting a planar incident shock over a rigid cylinder. The wave patterns of the perturbed shock are captured by high-speed shadowgraphy, while the evolution of the shocked interface is captured by planar Mie scattering. Besides the formations of a cavity and two steps, an apparent counter-rotating vortex pair emerges on the shocked interface due to the baroclinic vorticity deposition, as both the Atwood number and Mach number increase. Quantitatively, it is interesting to note that the amplitude growth rate of the shocked interface decreases with increasing the Atwood number, which is fundamentally different from the results related to the classical RM instability. This notable feature is explained by the approximation of an oblique shock hitting a uniform interface. For weak shock, a suitable time scaling is employed to collapse experimental data irrespective of the Atwood number difference.

The determination of statistical characteristics for particles undergoing Brownian motion in constrained domains has multiple applications in various areas of research. This work presents an attempt to systematically compute globally optimal configurations of traps inside a three-dimensional domain that minimize the average of the mean first passage time (MFPT) for the narrow capture problem, the average time it takes a particle to be captured by any trap. For a given domain, the mean first passage time satisfies a linear Poisson problem with Dirichlet-Neumann boundary conditions. While no closed-form general solution of such problems is known, approximate asymptotic MFPT expressions for small traps in a unit sphere have been found. These solutions explicitly depend on trap parameters, including locations, through a pairwise potential function. After probing the applicability limits of asymptotic formulas through comparisons with numerical and available exact solutions of the narrow capture problem, full three-dimensional global optimization was performed to find optimal trap positions in the unit sphere for $2\le N\le 100$ identical traps. The interaction energy values and geometrical features of the putative optimal trap arrangements are presented.

The following question is the subject of our work: could a two-dimensional (2D) random path pushed by some constraints to an improbable “large-deviation regime” possess extreme statistics with one-dimensional (1D) Kardar-Parisi-Zhang (KPZ) fluctuations? The answer is positive, though nonuniversal, since the fluctuations depend on the underlying geometry. We consider in detail two examples of 2D systems for which imposed external constraints force the underlying stationary stochastic process to stay in an atypical regime with anomalous statistics. The first example deals with the fluctuations of a stretched 2D random walk above a semicircle or a triangle. In the second example we consider a 2D biased random walk along a channel with forbidden voids of circular and triangular shapes. In both cases we are interested in the dependence of a typical span $〈d\left(t\right)〉\sim t^{\gamma }$ of the trajectory of $t$ steps above the top of the semicircle or the triangle. We show that $\gamma =\frac{1}{3}$, i.e., $〈d\left(t\right)〉$ shares the KPZ statistics for the semicircle, while $\gamma =0$ for the triangle. We propose heuristic derivations of scaling exponents $\gamma$ for different geometries, justify them by explicit analytic computations, and compare with numeric simulations. For practical purposes, our results demonstrate that the geometry of voids in a channel might have a crucial impact on the width of the boundary layer and, thus, on the heat transfer in the channel.

Experiments on interacting pinned self-propelled rotators are presented. The rotators are made from paper with camphor infused in its matrix. The ribbons rotate due to Marangoni effect driven forces arising by virtue of surface tension gradients. Two such self-rotating camphor ribbons are observed to experience a repulsive coupling via the camphor layer in the common water medium. Lag synchronization in both corotating (same sense of rotation) and counterrotating (opposite sense of rotation) ribbons is reported for the experiments. This synchronization is found to be dependent on the pivot to pivot distance $l$. For distances less than the span of both the ribbons, $l_c$, the rotators successfully synchronize. Furthermore, it is experimentally perceived that synchronization in the counterrotating ribbons is more robust than in the corotating ribbons. We rationalize the mechanism of this synchronization via a theoretical model involving a Yukawa type interaction which is analyzed numerically.

We examine a model of two interacting populations of phase oscillators labeled “blue” and “red.” To this we apply tempered stable Lévy noise, a generalization of Gaussian noise where the heaviness of the tails parametrized by a power law exponent $\alpha$ can be controlled by a tempering parameter $\lambda$. This system models competitive dynamics, where each population seeks both internal phase synchronization and a phase advantage with respect to the other population, subject to exogenous stochastic shocks. We study the system from an analytic and numerical point of view to understand how the phase lag values and the shape of the noise distribution can lead to steady or noisy behavior. Comparing the analytic and numerical studies shows that the bulk behavior of the system can be effectively described by dynamics in the presence of tilted ratchet potentials. Generally, changes in $\alpha$ away from the Gaussian noise limit $1<\alpha <2$ disrupt the locking between blue and red, while increasing $\lambda$ acts to restore it. However, we observe that with further decreases of $\alpha$ to small values $\alpha \ll 1$, with $\lambda \ne 0$, locking between blue and red may be restored. This is seen analytically in a restoration of metastability through the ratchet mechanism, and numerically in transitions between periodic and noisy regions in a fitness landscape using a measure of noise. This nonmonotonic transition back to an ordered regime is surprising for a linear variation of a parameter such as the power law exponent and provides a mechanism for guiding the collective behavior of such a complex competitive dynamical system.

Nonautonomous driving of an oscillator has been shown to enlarge the Arnold tongue in parameter space, but little is known about the analogous effect for a network of oscillators. To test the hypothesis that deterministic nonautonomous perturbation is a good candidate for stabilizing complex dynamics, we consider a network of identical phase oscillators driven by an oscillator with a slowly time-varying frequency. We investigate both the short- and long-term stability of the synchronous solutions of this nonautonomous system. For attractive couplings we show that the region of stability grows as the amplitude of the frequency modulation is increased, through the birth of an intermittent synchronization regime. For repulsive couplings, we propose a control strategy to stabilize the dynamics by altering very slightly the network topology. We also show how, without changing the topology, time-variability in the driving frequency can itself stabilize the dynamics. As a byproduct of the analysis, we observe chimeralike states. We conclude that time-variability-induced stability phenomena are also present in networks, reinforcing the idea that this is a quite realistic scenario for living systems to use in maintaining their functioning in the face of ongoing perturbations.

We explore the relation between the topological relevance of a node in a complex network and the individual dynamics it exhibits. When the system is weakly coupled, the effect of the coupling strength against the dynamical complexity of the nodes is found to be a function of their topological roles, with nodes of higher degree displaying lower levels of complexity. We provide several examples of theoretical models of chaotic oscillators, pulse-coupled neurons, and experimental networks of nonlinear electronic circuits evidencing such a hierarchical behavior. Importantly, our results imply that it is possible to infer the degree distribution of a network only from individual dynamical measurements.

Networks are often made up of several layers that exhibit diverse degrees of interdependencies. An interdependent network consists of a set of graphs $G$ that are interconnected through a weighted interconnection matrix $B$, where the weight of each intergraph link is a non-negative real number $p$. Various dynamical processes, such as synchronization, cascading failures in power grids, and diffusion processes, are described by the Laplacian matrix $Q$ characterizing the whole system. For the case in which the multilayer graph is a multiplex, where the number of nodes in each layer is the same and the interconnection matrix $B=pI$, $I$ being the identity matrix, it has been shown that there exists a structural transition at some critical coupling $p^{*}$. This transition is such that dynamical processes are separated into two regimes: if $p>p^{*}$, the network acts as a whole; whereas when $p<p^{*}$, the network operates as if the graphs encoding the layers were isolated. In this paper, we extend and generalize the structural transition threshold $p^{*}$ to a regular interconnection matrix $B$ (constant row and column sum). Specifically, we provide upper and lower bounds for the transition threshold $p^{*}$ in interdependent networks with a regular interconnection matrix $B$ and derive the exact transition threshold for special scenarios using the formalism of quotient graphs. Additionally, we discuss the physical meaning of the transition threshold $p^{*}$ in terms of the minimum cut and show, through a counterexample, that the structural transition does not always exist. Our results are one step forward on the characterization of more realistic multilayer networks and might be relevant for systems that deviate from the topological constraints imposed by multiplex networks.

The robustness in real-world complex systems with dependency connectivities differs from that in isolated networks. Although most complex network research has focused on interdependent undirected systems, many real-world networks—such as gene regulatory networks and traffic networks—are directed. We thus develop an analytical framework for examining the robustness of networks made up of directed networks of differing topologies. We use it to predict the phase transitions that occur during node failures and to generate the phase diagrams of a number of different systems, including treelike and random regular (RR) networks of directed Erdős-Rényi (ER) networks and scale-free networks. We find that the the phase transition and phase diagram of networks of directed networks differ from those of networks of undirected networks. For example, the RR networks of directed ER networks show a hybrid phase transition that does not occur in networks of undirected ER networks. In addition, system robustness is affected by network topology in networks of directed networks. As coupling strength $q$ increases, treelike networks of directed ER networks change from a second-order phase transition to a first-order phase transition, and RR networks of directed ER networks change from a second-order phase transition to a hybrid phase transition, then to a first-order phase transition, and finally to a region of collapse. We also find that heterogenous network systems are more robust than homogeneous network systems. We note that there are multiple phase transitions and triple points in the phase diagram of RR networks of directed networks and this helps us understand how to increase network robustness when designing interdependent infrastructure systems.

Neural field models are commonly used to describe wave propagation and bump attractors at a tissue level in the brain. Although motivated by biology, these models are phenomenological in nature. They are built on the assumption that the neural tissue operates in a near synchronous regime, and hence, cannot account for changes in the underlying synchrony of patterns. It is customary to use spiking neural network models when examining within population synchronization. Unfortunately, these high-dimensional models are notoriously hard to obtain insight from. In this paper, we consider a network of $\theta$-neurons, which has recently been shown to admit an exact mean-field description in the absence of a spatial component. We show that the inclusion of space and a realistic synapse model leads to a reduced model that has many of the features of a standard neural field model coupled to a further dynamical equation that describes the evolution of network synchrony. Both Turing instability analysis and numerical continuation software are used to explore the existence and stability of spatiotemporal patterns in the system. In particular, we show that this new model can support states above and beyond those seen in a standard neural field model. These states are typified by structures within bumps and waves showing the dynamic evolution of population synchrony.