The existence of dense clusters has been shown to be a transient phenomenon for realistic models of granular collisions, where the coefficient of restitution depends on the impact velocity. We report direct numerical simulations that elucidate the conditions for the disappearance of structures. We find that upon cluster formation the granular temperature and the convective kinetic energy couple and both follow Haff's law. Furthermore, we show that clusters will eventually dissolve in all finite-size systems. We find the strong power law $t^{\prime }\propto L^{12}$ for the dependency of the declustering time on system size. Our results imply that only in systems close to the initial critical system size both clustering and declustering transitions are observable.

The existence of surface elastic waves at a mechanically free surface of granular phononic crystals is studied. The granular phononic crystals are made of spherical particles distributed periodically on a simple cubic lattice. It is assumed that the particles are interacting by means of normal, shear, and bending contact rigidities. First, Rayleigh-type surface acoustic waves, where the displacement of the particles takes place in the sagittal plane while the particles possess one rotational and two translational degrees of freedom, are analyzed. Second, shear-horizontal-type waves, where the displacement of the particles is normal to the sagittal plane while the particles possess one translational and two rotational degrees of freedom are studied. The existence of zero-group-velocity surface acoustic waves of Rayleigh type is theoretically predicted and interpreted. A comparison with surface waves predicted by the reduced Cosserat theory is performed, and some limitations of the latter are established.

The onset of dynamo action is investigated within the context of a newly developed low Rossby, low magnetic Prandtl number, convection-driven dynamo model. This multiscale model represents an asymptotically exact form of an ${\alpha }^2$ mean field dynamo model in which the small-scale convection is represented explicitly by finite amplitude, single mode solutions. Both steady and oscillatory convection are considered for a variety of horizontal planforms. The kinetic helicity is observed to be a monotonically increasing function of the Rayleigh number. As a result, very small magnetic Prandtl number dynamos can be found for sufficiently large Rayleigh numbers. All dynamos are found to be oscillatory with an oscillation frequency that increases as the strength of the convection is increased and the magnetic Prandtl number is reduced. Kinematic dynamo action is strongly controlled by the profile of the helicity; single mode solutions which exhibit boundary layer behavior in the helicity show a decrease in the efficiency of dynamo action due to the enhancement of magnetic diffusion in the boundary layer regions. For a given value of the Rayleigh number, lower magnetic Prandtl number dynamos are excited for the case of oscillatory convection in comparison to steady convection. With regard to planetary dynamos, these results suggest that the low magnetic Prandtl number dynamos typical of liquid metals are more easily driven by thermal convection than by compositional convection.

Fluid flowing through a deformable porous medium imparts viscous drag on the solid matrix, causing it to deform. This effect is investigated theoretically and experimentally in a one-dimensional configuration. The experiments consist of the downwards flow of water through a saturated pack of small, soft, hydrogel spheres, driven by a pressure head that can be increased or decreased. As the pressure head is increased, the effective permeability of the medium decreases and, in contrast to flow through a rigid medium, the flux of water is found to increase towards a finite upper bound such that it becomes insensitive to changes in the pressure head. Measurements of the internal deformation, extracted by particle tracking, show that the medium compacts differentially, with the porosity being lower at the base than at the upper free surface. A general theoretical model is derived, and the predictions of the model give good agreement with experimental measurements from a series of experiments in which the applied pressure head is sequentially increased. However, contrary to theory, all the experimental results display a distinct and repeatable hysteresis: the flux through the material for a particular applied pressure drop is appreciably lower when the pressure has been decreased to that value compared to when it has been increased to the same value.

Various approaches of defining and determining work performed on a quantum system are compared. Any operational definition of work, however, must allow for two facts: first, that work characterizes a process rather than an instantaneous state of a system and, second, that quantum systems are sensitive to the interactions with a measurement apparatus. We compare different measurement scenarios on the basis of the resulting postmeasurement states and the according probabilities for finding a particular work value. In particular, we analyze a recently proposed work meter for the case of a Gaussian pointer state and compare it with the results obtained by two projective and, alternatively, two Gaussian measurements. In the limit of a strong effective measurement strength the work distribution of projective two energy measurements can be recovered. In the opposite limit the average of work becomes independent of any measurement. Yet the fluctuations about this value diverge. The performance of the work meter is illustrated by the example of a spin in a suddenly changing magnetic field.

Irreversible processes of weakly coupled one-dimensional quantum perfect Lorentz gas are studied on the basis of the fundamental laws of physics in terms of the complex spectral analysis associated with the resonance state of the Liouville–von Neumann operator. Without any phenomenological operations, such as a coarse-graining of space-time, or a truncation of the higher order correlation, we obtained irreversible processes in a purely dynamical basis in all space and time scale including the microscopic atomic interaction range that is much smaller than the mean-free length. Based on this solution, a limitation of the usual phenomenological Boltzmann equation, as well as an extension of the Boltzmann equation to entire space-time scale, is discussed.

In this paper we study Markov processes and related first-passage problems on a class of weighted, modular graphs which generalize the Dyson hierarchical model. In these networks, the coupling strength between two nodes depends on their distance and is modulated by a parameter $\sigma$. We find that, in the thermodynamic limit, ergodicity is lost and the “distant” nodes cannot be reached. Moreover, for finite-sized systems, there exists a threshold value for $\sigma$ such that, when $\sigma$ is relatively large, the inhomogeneity of the coupling pattern prevails and “distant” nodes are hardly reached. The same analysis is carried on also for generic hierarchical graphs, where interactions are meant to involve $p$-plets $(p>2)$ of nodes, finding that ergodicity is still broken in the thermodynamic limit, but no threshold value for $\sigma$ is evidenced, ultimately due to a slow growth of the network diameter with the size.

We study the functioning of a three-level thermal machine when acting on a many-qubit system, the entire system being placed in an electromagnetic field in a stationary out-of-thermal-equilibrium configuration. This realistic setup stands between the two so-far-explored cases of single-qubit and macroscopic object targets, providing information on the scaling with system size of purely quantum properties in thermodynamic contexts. We show that, thanks to the presence of robust correlations among the qubits induced by the field, thermodynamic tasks can be delivered by the machine both locally to each qubit and collectively to the many-qubit system: This allows a task to be delivered also on systems much bigger than the machine size.

We model the hierarchical evolution of an organized criminal network via antagonistic recruitment and pursuit processes. Within the recruitment phase, a criminal kingpin enlists new members into the network, who in turn seek out other affiliates. New recruits are linked to established criminals according to a probability distribution that depends on the current network structure. At the same time, law enforcement agents attempt to dismantle the growing organization using pursuit strategies that initiate on the lower level nodes and that unfold as self-avoiding random walks. The global details of the organization are unknown to law enforcement, who must explore the hierarchy node by node. We halt the pursuit when certain local criteria of the network are uncovered, encoding if and when an arrest is made; the criminal network is assumed to be eradicated if the kingpin is arrested. We first analyze recruitment and study the large scale properties of the growing network; later we add pursuit and use numerical simulations to study the eradication probability in the case of three pursuit strategies, the time to first eradication, and related costs. Within the context of this model, we find that eradication becomes increasingly costly as the network increases in size and that the optimal way of arresting the kingpin is to intervene at the early stages of network formation. We discuss our results in the context of dark network disruption and their implications on possible law enforcement strategies.

We study the effect of disorder on spectral properties of tubular chlorosomes in green sulfur bacteria Cf. aurantiacus. Employing a Frenkel-exciton Hamiltonian with diagonal and off-diagonal disorder consistent with spectral and structural studies, we analyze excitonic localization and spectral statistics of the chlorosomes. A size-dependent localization-delocalization crossover is found to occur as a function of the excitonic energy. The crossover energy region coincides with the more optically active states with maximized superradiance and is, consequently, more conducive for energy transfer.

We study self-excited oscillations (SEOs) in an on-fiber optomechanical cavity. While the phase of SEOs randomly diffuses in time when the laser power injected into the cavity is kept constant, phase locking may occur when the laser power is periodically modulated in time. We investigate the dependence of phase locking on the amplitude and frequency of the laser-power modulation. We find that phase locking can be induced with a relatively low modulation amplitude provided that the ratio between the modulation frequency and the frequency of SEOs is tuned close to a rational number of relatively low hierarchy in the Farey tree. To account for the experimental results, a one-dimensional map, which allows evaluating the time evolution of the phase of SEOs, is theoretically derived. By calculating the winding number of the one-dimensional map, the regions of phase locking can be mapped in the plane of modulation amplitude and modulation frequency. Comparison between the theoretical predictions and the experimental findings yields a partial agreement.

When a fluid is heated by the absorption of a continuous laser wave, the fluid density decreases in the heated area. This induces a pressure gradient that generates internal motion of the fluid. Due to mass conservation, convection eddies emerge in the sample. To investigate these laser-driven bulk flows at the microscopic scale, we built a setup to perform temperature measurements with a fluorescent-sensitive dye on the one hand, and measured the flow pattern at different beam powers, using a particle image velocimetry technique on the other hand. Temperature measurements were also used in numerical simulations in order to compare predictions to the experimental velocity profiles. The combination of our numerical and experimental approaches allows a detailed description of the convection flows induced by the absorption of light, which reveals a transition between a thin and a thick liquid layer regime. This supports the basis of optothermal approaches for microfluidic applications.

Transient elasticity (TE) is a concept useful for a systematic generalization of viscoelasticity. Due to its thermodynamic consistency, it naturally leads to a simple description of non-Newtonian effects displayed by polymeric fluids, granular media, and other soft matter. We employ a continuum-mechanical theory that is derived from TE and tailored to polymeric fluids, showing how it captures a surprisingly large number of phenomena in shear and elongational flows, including stationary, oscillatory, and transient ones, as well as the flow down an inclined channel. Even the Weissenberg effect is well accounted for. This theory is applicable for small- as well as large-amplitude deformations. We concentrate on the former in the present article, leaving the latter to a companion article.

Transient elasticity is a systematic generalization of viscoelasticity. Its purpose is to give a coherent description of non-Newtonian effects displayed by soft-matter systems, especially polymer melts and solutions. Using the concept of transient elasticity we describe here a hydrodynamic model for polymeric fluids, which is applicable for large amplitude deformations. We present an energy density with only two independent parameters, which is compatible with all thermodynamic requirements and which reduces for small deformations to models studied previously. The expression discussed is simple enough to allow full analytic treatment and shows semiquantitative agreement with experimental data. This model is used to capture many of the interesting effects thought to be characteristic of polymer rheology for large deformations including viscosity overshoot near the onset of shear flow, the onset of elongational flows in situations for which there is no stationary solution as well as shear thinning and normal stress differences for a large range of shear rates. In addition, we analyze how well our model accounts for empirical relations including the Cox-Merz rule, the Yamamoto relation, and Gleißle's mirror relations.

Employing efficient diagonalization techniques, we perform a detailed quantitative study of the regular and chaotic regions in phase space in the simplest nonintegrable atom-field system, the Dicke model. A close correlation between the classical Lyapunov exponents and the quantum Participation Ratio of coherent states on the eigenenergy basis is exhibited for different points in the phase space. It is also shown that the Participation Ratio scales linearly with the number of atoms in chaotic regions and with its square root in the regular ones.

On high-dimensional and complex potential energy surfaces, the identification of the most likely mechanism for the transition between local minima is a challenging task. Usually the steepest-descent path is used interchangeably with the minimum-energy path and is associated with the most likely path. Here we compare the meaning of the steepest-descent path in complex energy landscapes to the path integral formulation of a trajectory that minimizes the action functional for Brownian dynamics. In particular, for energy landscapes with bifurcation points and multiple minima and saddle points, there can be several steepest-descent paths associated with specific saddles that connect two predetermined states but largely differ from the path of maximum likelihood. The minimum-action path, however, additionally takes into account the scalar work along the trajectory. Minimizing the scalar work can be less ambiguous in the identification of the most likely path in different gradient systems. It can also be used to distinguish between multiple steepest-descent paths that connect reactant and product states. We illustrate that in systems with complex energy landscapes a careful assessment of the steepest-descent path is thus advisable. Here the evaluation of the action can provide valuable information on the analysis and description of the most likely path.

A recent conceptual model of tumor-driven angiogenesis including branching, elongation, and anastomosis of blood vessels captures some of the intrinsic multiscale structures of this complex system, yet allowing one to extract a deterministic integro-partial-differential description of the vessel tip density [Phys. Rev. E 90, 062716 (2014)]. Here we solve the stochastic model, show that ensemble averages over many realizations correspond to the deterministic equations, and fit the anastomosis rate coefficient so that the total number of vessel tips evolves similarly in the deterministic and ensemble-averaged stochastic descriptions.

We studied the magnetic interaction between circular Janus magnetic particles suspended in a Newtonian fluid under the influence of an externally applied uniform magnetic field. The particles are equally compartmentalized into paramagnetic and nonmagnetic sides. A direct numerical scheme is employed to solve the magnetic particulate flow in the Stokes flow regime. Upon applying the magnetic field, contrary to isotropic paramagnetic particles, a single Janus particle can rotate due to the magnetic torque created by the magnetic anisotropy of the particle. In a two-particle problem, the orientation of each particle is found to be an additional factor that affects the critical angle separating the nature of magnetic interaction. Using multiparticle problems, we show that the orientation of the particles has a significant influence on the dynamics of the particles, the fluid flow induced by the actuated particles, and the final conformation of the particles. Straight and staggered chain structures observed experimentally can be reproduced numerically in a multiple particle problem.

This paper concerns the instability behavior of a nematic liquid crystal in the region of dielectric inversion frequency for different waveforms of the exciting electric field. The critical frequency separating the regimes of dielectric and electroconvective primary bifurcation states shows a notable dependence on the waveform. In particular, it is found to undergo a large downshift for square-wave and sawtooth-wave fields as compared to sine-wave and triangle-wave fields. This seems to underscore the significance of harmonics in nonsinusoidal fields for the evolution of patterned electroconvective states. The study also deals with the flow pattern associated with the periodic state and the sequence of secondary instabilities occurring at higher fields to emphasize the role of the Carr-Helfrich mechanism for the instabilities in this region. The relevance of dielectric heating to the formation of transient structures is also pointed out.

The gas-liquid interfacial dynamics of bubble breakup in a T junction was investigated. Four regimes were observed for a bubble passing through the T junction. It was identified by the stop flow that a critical width of the bubble neck existed: if the minimum width of the bubble neck was less than the critical value, the breakup was irreversible and fast; while if the minimum width of the bubble neck was larger than the critical value, the breakup was reversible and slow. The fast breakup was driven by the surface tension and liquid inertia and is independent of the operating conditions. The minimum width of the bubble neck could be scaled with the remaining time as a power law with an exponent of 0.22 in the beginning and of 0.5 approaching the final fast pinch-off. The slow breakup was driven by the continuous phase and the gas-liquid interface was in the equilibrium stage. Before the appearance of the tunnel, the width of the depression region could be scaled with the time as a power law with an exponent of 0.75; while after that, the width of the depression was a logarithmic function with the time.