I consider branches of replica-symmetry-breaking (RSB) solutions in glassy systems that display a dynamical transition at a temperature $T_d$ characterized by a mode-coupling-theory dynamical behavior. Below $T_d$ these branches of solutions are considered to be relevant to the system complexity and to off-equilibrium dynamics. Under general assumptions I argue that near $T_d$ it is not possible to stabilize the one-step (1RSB) solution beyond the marginal point by making a full RSB (FRSB) ansatz. However, depending on the model, there may exist a temperature $T_{*}$ strictly lower than $T_d$ below which the 1RSB branch can be continued to a FRSB branch. Such a temperature certainly exists for models that display the so-called Gardner transition and in this case $T_G<T_{*}<T_d$. An analytical study in the context of the truncated model reveals that the FRSB branch of solutions below $T_{*}$ is characterized by a two-plateau structure and it ends where the first plateau disappears. These general features are confirmed in the context of the Ising $p$-spin model with $p=3$ by means of a numerical solution of the FRSB equations. The results are discussed in connection with off-equilibrium dynamics within Cugliandolo-Kurchan theory. In this context I assume that the RSB solution relevant for off-equilibrium dynamics is the 1RSB marginal solution in the whole range $(T_{*},T_d)$ and it is the end point of the FRSB branch for $T<T_{*}$. Remarkably, under these assumptions it can be argued that $T_{*}$ marks a qualitative change in off-equilibrium dynamics in the sense that the decay of various dynamical quantities changes from power law to logarithmic.

We propose a simply computable formula for the excluded volume of convex, axially symmetric bodies, based on the classical Brunn-Minkoski theory for convex bodies, which is briefly outlined in an Appendix written in a modern mathematical language. This formula is applied to cones and spherocones, which are regularized cones; a shape-reconstruction algorithm is able to generate the region in space inaccessible to them and to compute their excluded volume, which is found to be in good agreement with our approximate analytical formula. Finally, for spherocones with an appropriately tuned amplitude, we predict the occurrence of a relative deep minimum of the excluded volume in a configuration lying between the parallel alignment (where the excluded volume is maximum) and the antiparallel alignment (where the excluded volume is minimum).

This work focuses on the dynamics of globally coupled phase oscillators with three-body interaction and time delay. Analytic estimates regarding the stability of the incoherent solution are presented. Expressions for the phase synchronization frequencies and their stability are also derived. These theoretical results are supplemented with appropriate numerical computations. Numerical results regarding the fluctuations observed in the synchronization order parameter are then discussed. Some comparative results for phase synchronization in two-body, three-body, and mixed-coupled systems for different coupling combinations are also presented.

Amplitude death (AD) is an emergent phenomenon whereby two or more autonomously oscillating systems completely lose their oscillations due to coupling. In this work, we study AD in nonlinear oscillators with mixed time-delayed coupling, which is a combination of instantaneous and time-delayed couplings. We find that the mixed time-delayed coupling favors the onset of AD for a larger set of parameters than in the limiting cases of purely instantaneous or completely time-delayed coupling. Coupled identical oscillators experience AD under instantaneous coupling mixed with a small proportion of time-delayed coupling. Our work gives a deeper understanding of delay-induced AD in coupled nonlinear oscillators.

Spatial periodic forcing can entrain a pattern-forming system in the same way as temporal periodic forcing can entrain an oscillator. The forcing can lock the pattern's wave number to a fraction of the forcing wave number within tonguelike domains in the forcing parameter plane, it can increase the pattern's amplitude, and it can also create patterns below their onset. We derive these results using a multiple-scale analysis of a spatially forced Swift-Hohenberg equation in one spatial dimension. In two spatial dimensions the one-dimensional forcing can induce a symmetry-breaking instability that leads to two-dimensional (2D) patterns, rectangular or oblique. These patterns resonate with the forcing by locking their wave-vector component in the forcing direction to half the forcing wave number. The range of this type of 2:1 resonance overlaps with the 1:1 resonance tongue of stripe patterns. Using a multiple-scale analysis in the overlap region we show that the 2D patterns can destabilize the 1:1 resonant stripes even at exact resonance. This result sheds new light on the use of spatial periodic forcing for controlling patterns.

To simulate the motion of neutrophils and their morphodynamics in response to chemical cues, we construct a model based on the phase-field method utilizing a description with a free-energy functional and associated dynamics which captures the basic features of the phenomenon. We additionally incorporate spatial sensing by introducing an auxiliary field which depicts the polymerization of the region of the cell facing the highest concentration of the chemical attractant.

We consider the classical problem of kinematic dynamo action in simple steady flows. Due to the adjointness of the induction operator, we show that the growth rate of the dynamo will be exactly the same for two types of magnetic boundary conditions: the magnetic field can be normal (infinite magnetic permeability, also called pseudovacuum) or tangent (perfect electrical conductor) to the boundaries of the domain. These boundary conditions correspond to well-defined physical limits often used in numerical models and relevant to laboratory experiments. The only constraint is for the velocity field $\mathit{u}$ to be reversible, meaning there exists a transformation changing $\mathit{u}$ into $-\mathit{u}$. We illustrate this surprising property using $S_2{T}_2$ type of flows in spherical geometry inspired by [Dudley and James, Proc. R. Soc. London A 425, 407 (1989)]. Using both types of boundary conditions, it is shown that the growth rates of the dynamos are identical, although the corresponding magnetic eigenmodes are drastically different.

We simulate the conductivity of quasi-two-dimensional mono- and polydisperse rod networks having rods of various aspect ratios (L/D $=$ 25–800) and rod densities up to 100 times the critical density and assuming contact-resistance dominated transport. We report the rod-size dependence of the percolation threshold and the density dependence of the conductivity exponent over the entire L/D range studied. Our findings clarify the range of applicability for the popular widthless-stick description for physical networks of rodlike objects with modest aspect ratios and confirm predictions for the high-density dependence of the conductivity exponent obtained from modest-density systems. We also propose a heuristic extension to the finite-width excluded area percolation model to account for arbitrary distributions in rod length and validate this solution with numerical results from our simulations. These results are relevant to nanowire films that are among the most promising candidates for high performance flexible transparent electrodes.

Interesting collective motion emerges when several heavy intruder disks fall in a loose packed, quasi-two-dimensional granular bed of extremely light grains [F. Pacheco-Vázquez and J. C. Ruiz-Suárez, Nat. Commun. 1, 123 (2010)]. In particular, when two disks impact side by side, they initially repel and then they attract each other until they finally stop. Here we perform experiments and discrete-element soft-particle simulations to determine the range of action and the origin of these attractive and repulsive flow-mediated forces. We find that (1) the drag force on the disks fluctuate with a characteristic length linked to force chains that build up and break; (2) the repulsive force is present when the separation of the intruder disks is less than 6 times the size of the grains of the granular bed, which is the size of an aperture that allows a continuous discharge flow from a container; (3) the attractive force has a range of action between 5 and 6 times the size of the intruder disks; and (4) attraction exists only when intruders move faster than 1 m/s. These results suggest that repulsion originates from jamming of grains between intruders, and it supports the idea that attraction could be due to a “granular pressure” drop in the region between intruders caused by a high flow velocity of grains: a Bernoulli-like effect. However, our results do not rule out other mechanisms of interaction, like fluctuation-induced forces.

We study, by means of Brownian dynamics simulations, heterogeneous dynamics in a dense columnar phase of monodisperse hard filamentous particles, and find that in a background of barely moving particles, some particles occasionally engage in a fast coherent string-type motion similar to what is observed in glassy states of isometric particles. This fast motion is triggered by the exchange of particles between two or more columns at different positions in the columns, which leads to sudden displacement of particles between these positions. The distribution of particle displacements shows a pronounced peak at one particle length. We perform our simulations with particles of different persistence lengths and find that for more flexible particles, the number of jump events increases. As the number of particles in the columns increases with system size for a given linear fraction of particles in the columns, the peak in the distribution becomes wider and, for sufficiently large systems, the peak disappears completely. This is associated with the increase in the magnitude of fluctuations in the motion of particles as the system size increases. Our simulation results explain recent experimental observations on single-particle motion in dense columnar phases in aqueous dispersions of filamentous virus particles.

Liquid addition is common in industrial fluidization-based processes. A detailed understanding of collision mechanics of particles with liquid layers is helpful to optimize these processes. The normal impact with liquid has been studied extensively; however, the studies on oblique impact with liquid are scarce. In this work, experiments are conducted to trace Al${}_2$O${}_3$ spheres obliquely impacting on a surface covered by liquid layers, in which the free-fall spheres are disturbed initially by a horizontal gas flow. The oblique impact exhibits different rebound behaviors from normal collision due to the occurrence of strong rotation. The normal and tangential restitution coefficients ($e_n$ and $e_t$) and liquid bridge rupture time ($t_{\mathrm{rup}}$) are analyzed. With increase in liquid layer thickness and viscosity, $e_n$ and $e_t$ decline, and $t_{\mathrm{rup}}$ increases. With increase in tangential velocity, $e_t$ decreases first and then increases, whereas $e_n$ remains nearly unchanged, and $t_{\mathrm{rup}}$ decreases constantly. A modified Stokes number is proposed to further explore the relation between restitution coefficients and the impact parameters. Finally, an analysis of energy dissipation shows that the contact deformation and liquid phase are the two main sources of total energy dissipation. Unexpectedly, the dissipative energy caused by the liquid phase is independent of tangential velocity.

When a high voltage is applied between two beakers filled with deionized water, a floating bridge of water is formed in between exceeding the length of 2 cm when the beakers are pulled apart. Currently two theories regarding the stability of the floating water bridge exist, one suggesting that the tension caused by electric field in the dielectric medium is holding the bridge and the other suggesting surface tension to be responsible for the vertical equilibrium. We construct experiments in which the electric field and the geometry of the bridge are measured and compared with predictions of theories of the floating water bridge stability. We use a numerical simulation for estimation of the electric field. Our results indicate that the two forces of dielectric and surface tensions hold the bridge against gravity simultaneously and, having the same order of magnitude, neither of the two forces are negligible. In bridges with larger diameters, the effect of dielectric tension is slightly more in the vertical equilibrium than surface tension. Results show that the stability can be explained by macroscopic forces, regardless of the microscopic changes in the water structure.

It is generally acknowledged that the direction of the thermophoretic force acting on microparticles is largely determined by the imposed temperature gradient, and the shape of the microparticle has little influence on its direction. We show that one type of thermophoretic force, emerged due to the advent of microfabrication techniques, is highly sensitive to object shape, and it is feasible to tune force orientation via proper shape design. We reveal the underlying mechanism by an asymptotic analysis of the Boltzmann equation and point out the reason why the classical thermophoretic force is insensitive to the particle shape, but the force in microsystems is. The discovered phenomenon could find its applications in methods for microparticle manipulation and separation.

We formulate and analyze the third-frequency-moment sum rules for the two-dimensional (point) dipole system (2DDS) and the mass-symmetric electron-hole bilayer (EHB) in their strongly coupled liquid phases. The former, characterized by the repulsive interaction potential ${\phi }_D\left(r\right)={\mu }^2/r^3$ ($\mu$ is the electric dipole moment), reasonably well approximates the latter in the $d\to 0$ limit ($d$ is the interlayer spacing), a conjecture that is further supported by the findings of the present work. We explore the extent to which the in-phase sum rule for the closely spaced EHB may or may not reconcile with its 2DDS sum-rule counterpart. This is the main emphasis of the present work.

A restricted solid-on-solid growth model is studied for various restriction parameters $N$ in $d=4+1$ dimensions. The interface width $W$ grows as $t^{\beta }$ with $\beta =0.158\pm 0.006$ and $W$ follows $W\sim L^{\alpha }$ at saturation with $\alpha =0.273\pm 0.009$, where $L$ is the system size. The dynamic exponent $z\approx 1.73$ is obtained from the relation $z=\frac{\alpha }{\beta }$. The estimated exponents satisfy the scaling relation $\alpha +z=2$ very well. Our results indicate that the upper critical dimension of the Kardar-Parisi-Zhang equation is larger than $d=4+1$ dimensions. With a proper choice of the restriction parameter $N$, we can reduce the discrete effect of the height to the width and obtain the values of the exponents accurately.

In the paper [Phys. Rev. E 76, 061122 (2007)], the authors presented a way of playing $2\times 2$ games so that players were able to exploit nonfactorizable joint probabilities respecting the nonsignaling principle (i.e., relativistic causality). We are going to prove, however, that the scheme does not generalize the games studied in the commented paper. Moreover, it allows the players to obtain nonclassical results even if the factorizable joint probabilities are used.

A surprising observation in dusty plasma experiments is that the dust thermal energy density, $P_d\propto n_d{T}_d$, is typically much greater than $n_d{T}_n$ (where $n_d$ and $T_d$ are the dust density and temperature, and $T_n$ is the neutral temperature), even though the dust particles would be expected to be in thermal equilibrium with the neutrals. We show here, theoretically and experimentally, that the anomalously high dust thermal energy density can be accounted for if electrostatic interactions between the dust particles and the background plasma are taken into account. Thus, the dust pressure in dusty plasma is mostly of electrostatic origin.

Self-sustained spin clusters are analytically linked to ergodicity breaking in fully connected Ising and Sherrington-Kirkpatick (SK) models, relating the less understood spin space to the well understood state space. This correspondence is established through the absence of clusters in the paramagnetic phase, the presence of one dominant cluster in the Ising ferromagnet, and the formation of nontrivial clusters in SK spin glass. Yet unobserved phenomena are also revealed such as a first order phase transition in cluster sizes in the SK ferromagnet. The method could be adapted to investigate other spin models.

We derive analytical results for various quantities related to the excited-state quantum phase transitions in a class of Dicke superradiance models in the semiclassical limit. Based on a calculation of a partition sum restricted to Dicke states, we discuss the singular behavior of the derivative of the density of states and find observables such as the mean (atomic) inversion and the boson (photon) number and its fluctuations at arbitrary energies. Criticality depends on energy and a parameter that quantifies the relative weight of rotating versus counterrotating terms, and we find a close analogy to the logarithmic and jump-type nonanalyticities known from the Lipkin-Meshkov-Glick model.

Liquid may give strong cohesion properties to a granular medium, and confer a solidlike behavior. We study the erosion of a fixed circular aggregate of wet granular matter subjected to a flow of dry grains inside a half-filled rotating drum. During the rotation, the dry grains flow around the fixed obstacle. We show that its diameter decreases linearly with time for low liquid content, as wet grains are pulled out of the aggregate. This erosion phenomenon is governed by the properties of the liquids. The erosion rate decreases exponentially with the surface tension while it depends on the viscosity to the power $-1$. We propose a model based on the force fluctuations arising inside the flow, explaining both dependencies: The capillary force acts as a threshold and the viscosity controls the erosion time scale. We also provide experiments using different flowing grains, confirming our model.