Relationships between general long-range interacting classical systems on a lattice and the corresponding mean-field models (infinitely long-range interacting models) are investigated. We study systems in arbitrary dimension $d$ for periodic boundary conditions and focus on the free energy for fixed value of the total magnetization. As a result, it is shown that the equilibrium free energy of the long-range interacting systems are exactly the same as that of the corresponding mean-field models (exactness of the mean-field theory). Moreover, the mean-field metastable states can be also preserved in general long-range interacting systems. It is found that in the case that the magnetization is conserved, the mean-field theory does not give correct property in some parameter region.

Heat transport over large distances is classically performed with gravity or capillarity driven heat pipes. We investigate here whether the “piston effect,” a thermalization process that is very efficient in weightlessness in compressible fluids, could also be used to perform long-distance heat transfer. Experiments are performed in a modeling heat pipe (16.5 mm long, 3 mm inner diameter closed cylinder), with nearly adiabatic polymethylmethacrylate walls and two copper base plates. The cell is filled with ${\text{H}}_2$ near its gas-liquid critical point (critical temperature: 33 K). Weightlessness is achieved by submitting the fluid to a magnetic force that compensates gravity. Initially the fluid is isothermal. Then heat is sent to one of the bases with an electrical resistance. The instantaneous amount of heat transported by the fluid is measured at the other end. The data are analyzed and compared with a two-dimensional numerical simulation that allows an extrapolation to be made to other fluids (e.g., ${\text{CO}}_2$, with critical temperature of 300 K). The major result is concerned with the existence of a very fast response at early times that is only limited by the thermal properties of the cell materials. The yield in terms of ratio, injected or transported heat power, does not exceed $10–30\mathrm{\%}$ and is limited by the heat capacity of the pipe. These results are valid in a large temperature domain around the critical temperature.

Spontaneous symmetry breaking occurs in a system when its Hamiltonian possesses a certain symmetry, whereas the ground-state wave functions do not preserve it. This provides such a scenario that a bifurcation, which breaks the symmetry, occurs when some control parameter crosses its critical value. It is unveiled that the ground-state fidelity per lattice site exhibits such a bifurcation for quantum lattice systems undergoing quantum phase transitions. The significance of this result lies in the fact that the ground-state fidelity per lattice site is universal, in the sense that it is model independent, in contrast to (model-dependent) order parameters. This fundamental quantity may be computed by exploiting the developed tensor network algorithms on infinite-size lattices. We illustrate the scheme in terms of the quantum Ising model in a transverse magnetic field and the spin-$\frac{1}{2}$ $XYX$ model in an external magnetic field on an infinite-size lattice in one spatial dimension.

The mechanism of plastic flow in amorphous solids involves nucleation-controlled shear transformations, triggered under stress from fertile sites. However, the origin of these sites is still a matter of debate. In this paper, we show that the connection between local plastic activity and coordination defects in amorphous systems depends on the nature of the interatomic interactions. In particular, the directionality of the bonds, as quantified by the three-body term in Stillinger-Weber-like interactions, affects not only the role of local defects, but also the size of the plastic rearrangements, and the global stress-strain behavior. We study the effect of structure changes due to different quenching rates as well. We conclude the paper by a comparison between amorphous plasticity and the Peierls-Nabarro theory of plasticity in crystals.

We have studied the kinetics of cluster formation for dynamical systems of dimensions up to $n=8$ interacting through elastic collisions or coalescence. These systems could serve as possible models for gas kinetics, polymerization, and self-assembly. In the case of elastic collisions, we found that the cluster size probability distribution undergoes a phase transition at a critical time which can be predicted from the average time between collisions. This enables forecasting of rare events based on limited statistical sampling of the collision dynamics over short time windows. The analysis was extended to $L^p$-normed spaces $\left(p=1,\dots ,\infty \right)$ to allow for some amount of interpenetration or volume exclusion. The results for the elastic collisions are consistent with previously published low-dimensional results in that a power law is observed for the empirical cluster size distribution at the critical time. We found that the same power law also exists for all dimensions $n=2,\dots ,8$, two-dimensional $L^p$ norms, and even for coalescing collisions in two dimensions. This broad universality in behavior may be indicative of a more fundamental process governing the growth of clusters.

This paper develops an adaptive synchronization strategy to identify both discrete and distributed time delays in nonlinear dynamical models. In contrast with adaptive techniques for parameter estimation in the literature, the adaptive strategy developed here for time-delay identification invites more precise results that have physical and dynamical importance. It is analytically and numerically found that distributed time delays in a model with an asymptotically stable steady state can be adaptively identified, and which is different from the case of discrete time-delays identification. Other aspects of the strategy developed here, for time-delay identification, are illustrated by several representative dynamical models. Aside from illustrations for toy models and their generated data, the strategy developed is used with experimental data, to identify a time delay, called transcriptional delay, in a model describing the transcription of messenger RNAs (mRNAs) for Notch signaling molecules.

The feed-forward relationship naturally observed in time-dependent processes and in a diverse number of real systems—such as some food webs and electronic and neural wiring—can be described in terms of the so-called directed acyclic graphs (DAGs). An important ingredient of the analysis of such networks is a proper comparison of their observed architecture against an ensemble of randomized graphs, thereby quantifying the randomness of the real systems with respect to suitable null models. This approximation is particularly relevant when the finite size and/or large connectivity of real systems make inadequate a comparison with the predictions obtained from the so-called configuration model. In this paper we analyze two methods of DAG randomization as defined by the desired combination of two topological invariants (directed degree sequence and component distributions) aimed to be preserved. A highly ordered DAG, called snake graph, and an Erdös-Rényi DAG were used to validate the performance of the algorithms. Finally, three real case studies, namely, the C. elegans cell lineage network, a Ph.D. student-supervisor network, and the Milgram’s citation network, were analyzed using each randomization method. Results show how the interpretation of degree-degree relations in DAGs with respect to their randomized ensembles depends on the topological invariants imposed.

A system of $n$ spherical-cap drops, coupled by a network of conduits, coarsens due to surface tension forces. The total interfacial energy drives the fluid through the conduits such that, with time, the volume becomes increasingly localized into fewer large drops. The coarsening rate is predicted heuristically for drops coupled by orthogonal networks, a porous medium, and fractal networks of various dimensions. The predicted coarsening law as it depends upon the type and dimension of network, total number of drops, and initial drop volume is compared against numerical simulations of large $n$. Additionally, distributions of large drop volumes are obtained using a Lifshitz-Slyozov-Wagner (LSW) model. The predicted distributions are independent of network topology; in contrast, simulation results depend weakly on the network dimension. The heuristic coarsening rate laws are recovered using the LSW model for all but a square network topology.

Small amounts of a wetting liquid render sand a stiff and moldable material. The cohesive forces between the sand grains are caused by capillary bridges at the points of contact. Due to the finite strength of these bridges wet sand undergoes a transition from an arrested (i.e., solidified) to a fluidized state under an externally applied shear force. The transition between these two dynamic states is studied in a MD-type simulation of a two-dimensional assembly of bidisperse frictionless disks under the action of a cosine force profile. In addition to soft core repulsion the disks interact through a hysteretic and short ranged attractive force modeling the effect of the capillary bridges. In this model the transition between the fluidized and the arrested state is discontinuous and hysteretic. The parameter dependence of the critical force for solidification is modeled by combining theoretical arguments with a detailed numerical exploration of the transition. We address a range of densities from slightly below close packing until slightly above densities where the system approaches a shear-banded state. Differences and similarities of the transition in wet granulates to the jamming transition are also addressed.

We measure the fractal dimension of loop-erased random walk (LERW) in three dimensions and estimate that it is $1.62400\pm 0.00005$. LERW is closely related to the uniform spanning tree and the Abelian sandpile model. We simulated LERW on both the cubic and face-centered-cubic lattices; the corrections to scaling are slightly smaller for the face-centered-cubic lattice.

The evolution of human cooperation has been the subject of much research, especially within the framework of evolutionary public goods games, where several mechanisms have been proposed to account for persistent cooperation. Yet, in addressing this issue, little attention has been given to games of a more adversarial nature, in which defecting players, rather than simply free riding, actively seek to harm others. Here, we develop an adversarial evolutionary game using the specific example of criminal activity, recasting the familiar public goods strategies of punishers, cooperators, and defectors in this light. We then introduce a strategy—the informant—with no clear analog in public goods games and show that individuals employing this strategy are a key to the emergence of systems where cooperation dominates. We also find that a defection-dominated regime may be transitioned to one that is cooperation-dominated by converting an optimal number of players into informants. We discuss these findings, the role of informants, and possible intervention strategies in extreme adversarial societies, such as those marred by wars and insurgencies.

We study, theoretically and experimentally, the dynamical response of macroscopic Turing patterns to a mechanical periodic forcing which implies a sinusoidal modulation of gravity. Theoretical predictions indicate that the extra energy, due to the forcing, modifies the diffusion coefficient at a microscopic level, producing changes in the Turing domain and in the pattern characteristics, in particular its wavelength. To check the theoretical analysis, we perform numerical simulations with standard models. Experiments were also performed in the closed Belousov-Zhabotinsky reaction confined in AOT microemulsion (BZ-AOT system). Experiments as well as numerical and theoretical results show good agreement.

Time-reversibility measured by the deviation of perturbed time-reversed motion from the unperturbed motion is examined for normal quantum diffusion exhibited by four classes of quantum maps with contrasting physical nature. Irrespective of the system, there exists a universal minimal quantum threshold above which the system completely loses memory of the past. The time-reversed dynamics as well as the time-reversal characteristics are asymptotically universal curves independent of the details of the systems.

Motivated by the relation between particle shape and packing, we measure the volume fraction $\varphi$ occupied by the Platonic solids which are a class of polyhedrons with congruent sides, vertices, and dihedral angles. Tetrahedron-, cube-, octahedron-, dodecahedron-, and icosahedron-shaped plastic dice were fluidized or mechanically vibrated to find stable random loose packing ${\varphi }_{rlp}=0.51,0.54,0.52,0.51,0.50$ and densest packing ${\varphi }_{rcp}=0.64,0.67,0.64,0.63,0.59$, respectively, with standard deviation of $\simeq \pm 0.01$. We find that $\varphi$ obtained by all protocols peak at the cube, which is the only Platonic solid that can tessellate space, and then monotonically decrease with number of sides. This overall trend is similar but systematically lower than the maximum $\varphi$ reported for frictionless Platonic solids and below ${\varphi }_{rlp}$ of spheres for the loose packings. Experiments with ceramic tetrahedron were also conducted, and higher friction was observed to lead to lower $\varphi$.

The effect of intrinsic channel noise is investigated for the dynamic response of a neuronal cell with a delayed feedback loop. The loop is based on the so-called autapse phenomenon in which dendrites establish connections not only to neighboring cells but also to its own axon. The biophysical modeling is achieved in terms of a stochastic Hodgkin-Huxley model containing such a built in delayed feedback. The fluctuations stem from intrinsic channel noise, being caused by the stochastic nature of the gating dynamics of ion channels. The influence of the delayed stimulus is systematically analyzed with respect to the coupling parameter and the delay time in terms of the interspike interval histograms and the average interspike interval. The delayed feedback manifests itself in the occurrence of bursting and a rich multimodal interspike interval distribution, exhibiting a delay-induced reduction in the spontaneous spiking activity at characteristic frequencies. Moreover, a specific frequency-locking mechanism is detected for the mean interspike interval.

The motion of swimming microorganisms is strongly influenced by the presence of boundaries. Attraction of bacteria and sperm cells to surfaces is a well-known phenomenon which has been observed in experiments and confirmed by numerical simulations. This effect is studied in this work from a viewpoint of dynamical systems theory by analyzing a swimmer model which is a variant of the classical Purcell’s three-link swimmer near an infinite plane wall. The underlying geometric structure of the swimmer’s dynamics and its relation to stability are elucidated. It is found that a swimmer which breaks its fore-aft symmetry has a preferred swimming direction in which its motion is passively stable and converges to a fixed separation distance from the wall.

We demonstrate the dynamics of arrays of transient cavitation bubbles exposed to a sound field in a planar geometry. Single, double, and complex configurations of cavitation bubbles are obtained by shaping a pulsed laser beam with a digital hologram and focusing it into a thin gap of liquid. The liquid is driven with an oscillating pressure field of variable phase and amplitude. We compare the dynamics of a single bubble recorded with high-speed photography with a two-dimensional Rayleigh model. For multibubble configurations we observe bubble-bubble interaction and coalescence which depends on the phase of the acoustic field. Larger clusters demonstrate drastically enhanced collapse for high-amplitude driving, enabling the study of artificial cavitation clusters under strong driving.

We use theory and simulations to investigate the existence of amorphous glassy states in ultrasoft colloids. We combine the hypernetted chain approximation with mode-coupling theory to study the dynamic phase diagram of soft repulsive spheres interacting with a Hertzian potential, focusing on low temperatures and large densities. At constant temperature, we find that an amorphous glassy state is entered upon compression, as in colloidal hard spheres, but the glass unexpectedly melts when density increases further. We attribute this reentrant fluid-glass transition to particle softness and correlate this behavior to previously reported anomalies in soft systems, thus emphasizing its generality. The predicted fluid-glass-fluid sequence is confirmed numerically.

We derive a renormalization method to calculate the spectral dimension $\overline{d}$ of deterministic self-similar networks with arbitrary base units and branching constants. The generality of the method allows the affect of a multitude of microstructural details to be quantitatively investigated. In addition to providing models for physical networks, the results allow precise tests of theories of diffusive transport. For example, the properties of a class of nonrecurrent trees $\left(\overline{d}>2\right)$ with asymmetric elements and branching violate the Alexander-Orbach scaling law.

We study the dynamics of the infection of a two mobile species reaction from a single infected agent in a population of healthy agents. Historically, the main focus for infection propagation has been through spreading phenomena, where a random location of the system is initially infected and then propagates by successfully infecting its neighbor sites. Here both the infected and healthy agents are mobile, performing classical random walks. This may be a more realistic picture to such epidemiological models, such as the spread of a virus in communication networks of routers, where data travel in packets, the communication time of stations in ad hoc mobile networks, information spreading (such as rumor spreading) in social networks, etc. We monitor the density of healthy particles $\rho \left(t\right)$, which we find in all cases to be an exponential function in the long-time limit in two-dimensional and three-dimensional lattices and Erdős-Rényi (ER) and scale-free (SF) networks. We also investigate the scaling of the crossover time $t_c$ from short- to long-time exponential behavior, which we find to be a power law in lattices and ER networks. This crossover is shown to be absent in SF networks, where we reveal the role of the connectivity of the network in the infection process. We compare this behavior to ER networks and lattices and highlight the significance of various connectivity patterns, as well as the important differences of this process in the various underlying geometries, revealing a more complex behavior of $\rho \left(t\right)$.