We apply connectedness percolation theory to fractal liquids of hard particles, and make use of a Percus-Yevick liquid state theory combined with a geometric connectivity criterion. We find that in fractal dimensions the percolation threshold interpolates continuously between integer-dimensional values, and that it decreases monotonically with increasing (fractal) dimension. The influence of hard-core interactions is significant only for dimensions below three. Finally, our theory incorrectly suggests that a percolation threshold is absent below about two dimensions, which we attribute to the breakdown of the connectedness Percus-Yevick closure.

A combined experimental and numerical investigation of the roughness of intergranular cracks in two-dimensional disordered solids is presented. We focus on brittle materials for which the characteristic length scale of damage is much smaller than the grain size. Surprisingly, brittle cracks do not follow a persistent path with a roughness exponent $\zeta \approx 0.6–0.7$ as reported for a large range of materials. Instead, we show that they exhibit monoaffine scaling properties characterized by a roughness exponent $\zeta =0.50\pm 0.05$, which we explain theoretically from linear elastic fracture mechanics. Our findings support the description of the roughening process in two-dimensional brittle disordered solids by a random walk. Furthermore, they shed light on the failure mechanism at the origin of the persistent behavior with $\zeta \approx 0.6–0.7$ observed for fractures in other materials, suggesting a unified scenario for the geometry of crack paths in two-dimensional disordered solids.

The coupling boundary condition to be imposed at the evaporative surface of a porous medium is studied from pore network simulations considering the capillary regime. This paper highlights the formation of a thin edge effect region of smaller saturation along the evaporative surface. It is shown that this thin region forms in the breakthrough period at the very beginning of the drying process. The size of this region is studied and shown to be not network size dependent. This region is shown to be the locus of a nonlocal equilibrium effect. The features lead to the consideration of a coupling boundary condition involving an interfacial mass transfer resistance and an external mass transfer resistance. Contrary to previous considerations, it is shown that both resistances depend on the variation of the saturation, i.e., the fluid topology, and the size of the external mass transfer layer, i.e., the mass transfer rate. This is explained by the evolution of the vapor partial pressure distribution at the surface which becomes increasingly heterogeneous during evaporation and depends on both the evolving fluid distribution in the interfacial region and the mass transfer rate. However, the geometric effects due to the configuration of the fluids can be separated from rate effects that arise due to the nonequilibrium mass transport.

Soft cellular systems, such as foams or biological tissues, exhibit highly complex rheological properties, even in the quasistatic regime, that numerical modeling can help to apprehend. We present a numerical implementation of quasistatic strain within the widely used cellular Potts model (CPM). The accuracy of the method is tested by simulating the quasistatic strain of two-dimensional dry foams, both ordered and disordered. The implementation of quasistatic strain in CPM allows the investigation of sophisticated interplays between stress-strain relationship and structural changes that take place in cellular systems.

We perform a finite-time scaling analysis over the detrapping point of a three-state quantum walk on the line. The coin operator is parametrized by $\rho$ that controls the wave packet spreading velocity. The input state prepared at the origin is set as a symmetric linear combination of two eigenstates of the coin operator with a characteristic mixing angle $\theta$, one of them being the component that results in full spreading occurring at ${\theta }_c\left(\rho \right)$ for which no fraction of the wave packet remains trapped near the initial position. We show that relevant quantities, such as the survival probability and the participation ratio assume single parameter scaling forms at the vicinity of the detrapping angle ${\theta }_c$. In particular, we show that the participation ratio grows linearly in time with a logarithmic correction, thus, shedding light on previous reports of sublinear behavior.

We consider the additional entropy production (EP) incurred by a fixed quantum or classical process on some initial state $\rho$, above the minimum EP incurred by the same process on any initial state. We show that this additional EP, which we term the “mismatch cost of $\rho$,” has a universal information-theoretic form: it is given by the contraction of the relative entropy between $\rho$ and the least-dissipative initial state $\phi$ over time. We derive versions of this result for integrated EP incurred over the course of a process, for trajectory-level fluctuating EP, and for instantaneous EP rate. We also show that mismatch cost for fluctuating EP obeys an integral fluctuation theorem. Our results demonstrate a fundamental relationship between thermodynamic irreversibility (generation of EP) and logical irreversibility (inability to know the initial state corresponding to a given final state). We use this relationship to derive quantitative bounds on the thermodynamics of quantum error correction and to propose a thermodynamically operationalized measure of the logical irreversibility of a quantum channel. Our results hold for both finite- and infinite-dimensional systems, and generalize beyond EP to many other thermodynamic costs, including nonadiabatic EP, free-energy loss, and entropy gain.

We show that the number of solitons produced from an arbitrary initial pulse of the simple wave type can be calculated analytically if its evolution is governed by a generalized nonlinear Schrödinger (NLS) equation provided this number is large enough. The final result generalizes the asymptotic formula derived for completely integrable nonlinear wave equations such as the standard NLS equation with the use of the inverse scattering transform method.

We unravel the collective dynamics exhibited by two coupled nonlinearly damped Liénard oscillators exhibiting parity and time symmetry, which is a classical example of the position-dependent damped systems. The coupled system facilitates the onset of limit-cycle and aperiodic oscillations in addition to large-amplitude oscillations. In particular, a nontrivial amplitude death state emerges as a consequence of balanced linear loss and gain of the coupled PT-symmetric systems, where gain in the amplitude of oscillation in one oscillator is exactly balanced by the loss in the other. Further, quasiperiodic attractors exist in the parameter space of a neutrally stable trivial steady state. We deduce analytical critical curves enclosing the stable regions of a nontrivial fixed point, leading to the manifestation of nontrivial amplitude death state, and neutrally stable trivial steady state. The latter loses its stability leading to the emergence of the former. The analytical critical curves exactly match with the simulation boundaries. There is also a reemergence of dynamical states as a function of the coupling strength and multistability among the observed dynamical states. The basin of attraction provides an explanation for the observed probability of dynamical states.

The long-term behavior of a modulationally unstable conservative nonintegrable system is known to be characterized by the soliton turbulence self-organization process. We consider this problem in the presence of a long-range interaction in the framework of the Schrödinger-Poisson (or Newton-Schrödinger) equation accounting for the gravitational interaction. By increasing the amount of nonlinearity, the system self-organizes into a large-scale incoherent localized structure that contains “hidden” coherent soliton states: The solitons can hardly be identified in the usual spatial or spectral domains, but their existence can be unveiled in the phase-space representation (spectrogram). We develop a theoretical approach that provides the coupled description of the coherent soliton component [governed by the Schrödinger-Poisson equation (SPE)] and of the incoherent structure [governed by a wave turbulence Vlasov-Poisson equation (WT-VPE)]. We demonstrate theoretically and numerically that the incoherent structure introduces an effective trapping potential that stabilizes the hidden coherent soliton and we show that the incoherent structure belongs to a family of stationary solutions of the WT-VPE. The analysis reveals that the incoherent structure evolves in the strongly nonlinear regime and that it is characterized by a compactly supported spectral shape. By relating the analytical properties of the hidden soliton to those of the stationary incoherent structure, we clarify the quantum-to-classical (i.e., SPE-to-VPE) correspondence in the limit $\hslash /m\to 0$: The hidden soliton appears as the latest residual quantum correction preceding the classical limit described by the VPE. This study is of potential interest for self-gravitating Boson models of fuzzy dark matter. Although we focus our paper on the Schrödinger-Poisson equation, we show that the regime of hidden solitons stabilized by an incoherent structure is general for long-range wave systems featured by an algebraic decay of the interacting potential. This work should stimulate nonlinear optics experiments in highly nonlocal nonlinear (thermal) media that mimic the long-range nature of gravitational interactions.

From social interactions to the human brain, higher-order networks are key to describe the underlying network geometry and topology of many complex systems. While it is well known that network structure strongly affects its function, the role that network topology and geometry has on the emerging dynamical properties of higher-order networks is yet to be clarified. In this perspective, the spectral dimension plays a key role since it determines the effective dimension for diffusion processes on a network. Despite its relevance, a theoretical understanding of which mechanisms lead to a finite spectral dimension, and how this can be controlled, still represents a challenge and is the object of intense research. Here, we introduce two nonequilibrium models of hyperbolic higher-order networks and we characterize their network topology and geometry by investigating the intertwined appearance of small-world behavior, $\delta$-hyperbolicity, and community structure. We show that different topological moves, determining the nonequilibrium growth of the higher-order hyperbolic network models, induce tuneable values of the spectral dimension, showing a rich phenomenology which is not displayed in random graph ensembles. In particular, we observe that, if the topological moves used to construct the higher-order network increase the area/volume ratio, then the spectral dimension continuously decreases, while the opposite effect is observed if the topological moves decrease the area/volume ratio. Our work reveals a new link between the geometry of a network and its diffusion properties, contributing to a better understanding of the complex interplay between network structure and dynamics.

By using Monte Carlo numerical simulation, this work investigates the phase behavior of systems of hard infinitesimally thin circular arcs, from an aperture angle $\theta \to 0$ to an aperture angle $\theta \to 2\pi$, in the two-dimensional Euclidean space. Except in the isotropic phase at lower density and in the (quasi)nematic phase, in the other phases that form, including the isotropic phase at higher density, hard infinitesimally thin circular arcs autoassemble to form clusters. These clusters are either filamentous, for smaller values of $\theta$, or roundish, for larger values of $\theta$. Provided the density is sufficiently high, the filaments lengthen, merge, and straighten to finally produce a filamentary phase while the roundels compact and dispose themselves with their centers of mass at the sites of a triangular lattice to finally produce a cluster hexagonal phase.

Statically indeterminate systems are experimentally demonstrated to be in fact dynamical. Take the classic problems of a beam with three supporting points, granules in a silo, and a ladder leaning against a wall, for instance; their reaction forces are found to vary logarithmically for over ${10}^4\mathrm{s}$ with an increment or decrement of more than $10\%$. This seemingly contradictory mixture of dynamics for a static system is shown to derive from the evolution of microcontact area with the ground and/or wall due to the aging effect.

The symmetry breaking that is induced by initial imperfection (e.g., geometry or material inhomogeneity and out-of-plane disturbance) is a necessary condition for film buckling. However, the effect of initial imperfection on the buckling behavior is still not clear cut. Herein, given an elastic substrate-free circular film subjected to in-plane compressive stress and arbitrary initial imperfection, evolution of the deflection morphology is numerically studied and theoretically analyzed. Specifically, a two-dimensional spatial spectrum analysis is adopted to acquire the deflection morphology's dominant wavelength, which is combined with the maximum absolute deflection to characterize the deflection patterns. Before the so-called critical instability, the film under compression is found to go through a transition stage. Overall, the deflection increment in this stage is negligible except approaching the critical state. However, the dominant wavelength is found to be continuously growing (or decreasing) rather than suddenly appears upon reaching the so-called critical state, and, interestingly, such growth is found to be independent of the intensity and pattern of the initial imperfection if the same initial dominant wavelength is guaranteed. In the discussion, for both the transition and buckling stages, evolution laws of the deflection amplitude and wavelength are established analytically and found to agree well with the numerical results. This research clearly presents the actual evolution process of wrinkling morphology from linear in-plane deformation with small stable deflection to out-of-plane instability with large deflection, which deepens the cognition of instability behavior of films and provides a basis for related applications such as high-precision mechanical characterization.

The effect of rapid wedge rotation on the transition from regular (RR) to Mach reflection (MR) is investigated. This unsteady shock reflection transition is compared with the steady-state transition. The dependence of various flow features such as the unsteady Mach stem height, position of the reflection point, and shock angle at the reflection or triple point on the wedge angle for a fixed Mach number is compared at various rotation rates. The study is further extended to compare the dynamic effects for various Mach numbers in the strong shock reflection domain at higher wedge speeds. Transition lines corresponding to different rotation speeds are obtained similar to the detachment transition line in steady cases. It is found that the pivot point has only marginal effect on the transition point, but it substantially affects the Mach stem growth and the movement of the reflection point, specifically at higher Mach numbers. The location of the transition from the inlet also depends on the pivot point and the rate of rotation.

Energy conservation is a basic physics principle, the breakdown of which often implies new physics. This paper presents a method for data-driven “new physics” discovery. Specifically, given a trajectory governed by unknown forces, our neural new-physics detector (NNPhD) aims to detect new physics by decomposing the force field into conservative and nonconservative components, which are represented by a Lagrangian neural network (LNN) and an unconstrained neural network, respectively, trained to minimize the force recovery error plus a constant $\lambda$ times the magnitude of the predicted nonconservative force. We show that a phase transition occurs at $\lambda =1$, universally for arbitrary forces. We demonstrate that NNPhD successfully discovers new physics in toy numerical experiments, rediscovering friction (1493) from a damped double pendulum, Neptune from Uranus' orbit (1846), and gravitational waves (2017) from an inspiraling orbit. We also show how NNPhD coupled with an integrator outperforms both an LNN and an unconstrained neural network for predicting the future of a damped double pendulum.

The behavior of a system of two-dimensional elongated particles (discorectangles) packed in a slit between the two parallel walls was analyzed using a simulation approach. The packings were produced using the random sequential adsorption model with continuous positional and orientational degrees of freedom. The aspect ratio (length-to-width ratio, $\varepsilon =l/d$) of the particles was varied within the range $\varepsilon \in [1;32]$ while the distance between the walls was varied within the range $h/d\in [1;80]$. The properties of deposits in jammed state [the coverage, the order parameter, and the long-range (percolation) connectivity between particles] were studied numerically. The values of $\varepsilon$ and $h$ significantly affected the structure of the packings and the percolation connectivity. Particularly, the observed nontrivial dependencies of the jamming coverage $\phi \left(\varepsilon \right)$ or $\phi \left(h\right)$ were explained by the interplay of the different geometrical factors related to confinement, particle orientation degrees of freedom and excluded volume effects.

We analyze a one-dimensional XXZ spin chain in a disordered magnetic field. As the main probes of the system's behavior, we use the sensitivity of eigenstates to adiabatic transformations, as expressed through the fidelity susceptibility, in conjunction with the low-frequency asymptotes of the spectral function. We identify a region of maximal chaos—with exponentially enhanced susceptibility—which separates the many-body localized phase from the diffusive ergodic phase. This regime is characterized by slow transport, and we argue that the presence of such slow dynamics highly constrains any possible localization transition in the thermodynamic limit. Rather, the results are more consistent with absence of the localized phase.

Antipredator behavior is present in many biological systems where individuals collectively react to an imminent attack. The antipredator response may influence spatial pattern formation and ecosystem stability but requires an organism's cost to contribute to the collective effort. We investigate a nonhierarchical tritrophic system, whose predator-prey interactions are described by the rock-paper-scissors game rules. In our spatial stochastic simulations, the radius of antipredator response defines the maximum prey group size that disturbs the predator's action, determining the individual cost to participate in antipredator strategies. We consider that each organism contributes equally to the collective effort, having its mobility limited by the proportion of energy devoted to the antipredator reaction. Our outcomes show that the antipredator response leads to spiral patterns, with the segregation of organisms of the same species occupying departed spatial domains. We found that a less localized antipredator response increases the average size of the single-species patches, improving the protection of individuals against predation. Finally, our findings show that although the increase of the predation risk for a more localized antipredator response, the high mobility constraining benefits species coexistence. Our results may help ecologists understand the mechanisms leading to the stability of biological systems where locality is crucial to behavioral interactions among species.

Remote synchronization implies that oscillators interacting not directly but via an additional unit (hub) adjust their frequencies and exhibit frequency locking while the hub remains asynchronous. In this paper, we analyze the mechanisms of remote synchrony in a small network of three coupled Stuart-Landau oscillators using recent results on higher-order phase reduction. We analytically demonstrate the role of two factors promoting remote synchrony. These factors are the nonisochronicity of oscillators and the coupling terms appearing in the second-order phase approximation. We show a good correspondence between our theory and numerical results for small and moderate coupling strengths.

The spatial critical shelter sizes above which populations would survive are investigated for the infection of hantavirus among rodent populations surrounded by a deadly environment. We show that the critical shelter sizes for the infected population and the susceptible population are different due to symmetry breaking in the reproduction and the transmission processes. Therefore, there exists a shelter size gap within which the infected population becomes extinct while only the susceptible population survives. With the field data reported in the literature, we estimate that, if one confines the rodent population within a stripe region surrounded by a deadly environment with the shorter dimension between $335.5\pm 27.2\text{m}$ and $547.9\pm 78.3\text{m}$, the infected population would become extinct. In addition, we introduce two factors that influence the movement of rodents, namely, the spatial asymmetry of the landscape and the sociality of rodents, to study their effects on the shelter size gap. The effects on the critical size due to environmental bias are twofold: it enhances the overall competition among rodents which increases the critical size, but on the other hand it promotes the spread of the hantavirus which reduces the critical size for the infected population. On the contrary, the sociality of rodents gives rise to a more localized population profile which promotes the spread of the hantavirus and reduces the shelter size gap. The results shed light on a possible strategy of eliminating hantavirus while preserving the integrity of food webs in ecosystems.