Molecular dynamics simulations are used to investigate the structure and mechanical properties of a simple two-dimensional model of a cohesive granular material. Intergranular forces involve elasticity, Coulomb friction, and a short-range attraction akin to the van der Waals force in powders. The effects of rolling resistance (RR) at intergranular contacts are also studied. The microstructure of the cohesive packing under low pressure is shown to depend sensitively on the assembling procedure which is applied to the initially isolated particles of a granular gas. While a direct compression produces a final equilibrated configuration with a similar density to that of cohesionless systems, the formation of large aggregates prior to the application of an external pressure results in much looser stable packings. A crucial state variable is the ratio $P^{*}=Pa∕F_0$ of applied pressure $P$, acting on grains of diameter $a$, to maximum tensile contact force $F_0$. At low $P^{*}$ the force-carrying structure and force distribution are sensitive to the level of velocity fluctuations in the early stages of cluster aggregation. The coordination number of packings with RR approaches 2 in the limit of low initial velocities or large rolling friction. In general the force network is composed of hyperstatic clusters, typically comprising four to a few tens of grains, in which forces reach values of the order of $F_0$, joined by barely rigid arms, where contact forces are very small. Under growing $P^{*}$, it quickly rearranges into force chainlike patterns that are more familiar in dense systems. Density correlations are interpreted in terms of a fractal structure, up to a characteristic correlation length $\xi$ of the order of ten particle diameters for the studied solid fractions. The fractal dimension in systems with RR coincides, within measurement uncertainties, with the ballistic aggregation result, in spite of a possibly different connectivity, but is apparently higher without RR. Possible effects of micromechanical and assembling process parameters on mechanical strength of packings are evoked.

We report a high energy-resolution neutron backscattering study to investigate slow motions on nanosecond time scales in highly oriented solid-supported phospholipid bilayers of the model system deuterated 1,2-dimyristoyl-sn-glycero-3-phosphatidylcholine, hydrated with heavy water. Wave-vector-resolved quasielastic neutron scattering is used to determine relaxation times $\tau$, which can be associated with different molecular components, i.e., the lipid acyl chains and the interstitial water molecules in the different phases of the model membrane system. The inelastic data are complemented by both energy-resolved and energy-integrated in situ diffraction. From a combined analysis of the inelastic data in the energy and time domains, the corresponding character of the relaxation, i.e., the exponent of the exponential decay, is also determined. From this analysis we quantify two relaxation processes. We associate the fast relaxation with translational diffusion of lipid and water molecules while the slow process likely stems from collective dynamics.

In this paper we introduce a method to simulate lateral diffusion of inclusions in a fluctuating membrane. The regarded systems are governed by two dynamic processes: the height fluctuations of the membrane and the diffusion of the inclusion along the membrane. While membrane fluctuations can be expressed in terms of a dynamic equation which follows from the Helfrich Hamiltonian, the dynamics of the diffusing particle is described by a Langevin or Smoluchowski equation. In the latter equations, the curvature of the surface needs to be accounted for, which makes particle diffusion a function of membrane fluctuations. In our scheme these coupled dynamic equations, the membrane equation and the Langevin equation for the particle, are numerically integrated to simulate diffusion in a membrane. The simulations are used to study the ratio of the diffusion coefficient projected on a flat plane and the intramembrane diffusion coefficient for the case of free diffusion. We compare our results with recent analytical results that employ a preaveraging approximation and analyze the validity of this approximation. A detailed simulation study of the relevant correlation functions reveals a surprisingly large range where the approximation is applicable.

The effect of magnetic field on lipid bilayers has been a subject of interest to experimentalists in recent years. Here we examine a fluctuation model of reactive bilayer membranes, taking into view the composition-curvature correlation in the presence of a homogeneous magnetic field. We show how the strength of the magnetic field in combination with the intensity of reaction induces instability into the system, at times leading to stationary pattern formation.

A new kind of metamaterial, an array of periodic gold rod pairs standing on gold substrate, is introduced in this paper. A commercial electromagnetic mode solver, the High-Frequency Structure Simulator, is employed to explore the propagation property of electromagnetic waves in this system. When an $S$-polarized electromagnetic (EM) wave propagates along the substrate surface, strong magnetic resonance is produced in the far-infrared regime. Based on the simulated $S$ parameters, effective refraction index is retrieved and negative value is obtained over the wavelength range from $49.2\mu \mathrm{m}$ to $66.7\mu \mathrm{m}$. A wedge made of this metamaterial with an inclined angle 26.6° is designed. An observable negative refraction behavior of EM wave is attained in this structure at wavelength $61.2\mu \mathrm{m}$. The refractive index is calculated by Snell’s law and it is consistent with the retrieved results quite well. This provides direct evidence for the negative refraction property.

We study theoretically the propagation of longitudinal wave in weakly compressible elastic media containing random air bubbles by using a self-consistent method. By inspecting the scattering cross section of an individual bubble and estimating the mean free paths of the elastic wave propagating in the bubbly weakly compressible media, the mode conversion is numerically proved negligible as the longitudinal wave is scattered by the bubbles. On the basis of the bubble dynamic equation, the wave propagation is solved rigorously with the multiple scattering effects incorporated. In a range of frequency slightly above the bubble resonance frequency, the acoustic localization in such a class of media is theoretically identified with even a very small volume fraction of bubbles. We present a method by analyzing the spatial correlation of wave field to identify the phenomenon of localization, which turns out to be effective. The sensibility of the features of localization to the structure parameters is numerically investigated. The spatial distribution of acoustic energy is also studied and the results show that the waves are trapped within a spatial domain adjacent to the source when localization occurs.

The discrete time path integral Monte Carlo with a one-particle density matrix approximation is applied to study the quantum phase transition in the coupled double-well chain. To improve the convergence properties, the exact action for a single particle in a double-well potential is used to construct the many-particle action. The algorithm is applied to the interacting quantum double-well chain for which the zero-temperature phase diagram is determined. The quantum phase transition is studied via finite-size scaling, and the critical exponents are shown to be compatible with the classical two-dimensional Ising universality class—not only in the order-disorder limit (deep potential wells), but also in the displacive regime (shallow potential wells).

We predict the existence of a ring-like localized solutions in wide aperture passive semiconductor quantum well microresonators. These dark ring cavity solitons exist for positive cavity detuning in a frequency range where nonlinear dispersive effects prevail against absorptive ones. As a rule, destabilization of these ring solitons leads to the formation of radial asymmetric rotating solitons in externally driven optical cavities.

We investigate aggregation driven by mass injection. In this stochastic process, mass is added with constant rate $r$ and clusters merge at a constant total rate $1$, so that both the total number of clusters and the total mass steadily grow with time. Analytic results are presented for the three classic aggregation rates $K_{i,j}$ between clusters of size $i$ and $j$. When $K_{i,j}=\mathrm{const}$, the cluster size distribution decays exponentially. When $K_{i,j}\propto i+j$ or $K_{i,j}\propto i\times j$, there are two phases: (i) a condensate phase with a condensate containing a finite fraction of the mass in the system as well as finite clusters and (ii) a cluster phase with finite clusters only. For $K_{i,j}\propto i+j$, the cluster size distribution, $c_k$, has a power-law tail, $c_k\sim k^{-\gamma }$ in either phase. The exponent is a nonmonotonic function of the injection rate $\gamma =r∕(r-1)$ in the condensate phase $r<2$ and $\gamma =r$ in the cluster phase $r>2$.

The dependence on applied shear of the morphological and rheological properties of diffusive binary systems after a quench from the disordered state into the coexistence region is investigated. In particular the behavior of the late-time transversal size of domains $L_y$ and of the maximum of excess viscosity $(\mathrm{\Delta }\eta {)}_M$ is considered. Numerical results show the existence of two regimes corresponding to weak and strong shear separated by a shear rate of the order of ${\gamma }_c\sim 1∕t_D$ where $t_D$ is the diffusive time. $L_y$ and $(\mathrm{\Delta }\eta {)}_M$ behave as $L_y\sim {\gamma }^{-\alpha }$ and $(\mathrm{\Delta }\eta {)}_M\sim {\gamma }^{\nu }$ with $\alpha ={\alpha }_s=0.18\pm 0.02$, $\nu ={\nu }_s=-2.00\pm 0.01$ and $\alpha ={\alpha }_w=0.25\pm 0.01$, $\nu ={\nu }_w=-0.68\pm 0.04$ in the strong- and weak-shear regimes, respectively. Differently from what was found in systems with fluctuating velocity field, it is confirmed that domains continue to grow at all times.

Dynamics in glass-forming liquids in the supercooled regime vary considerably from one point of the sample to another suggesting the existence of regions with different degrees of jamming. In fact, the existence of relatively compact regions with particles with an enhanced propensity for motion has been detected in model glassy systems. In turn, the structural relaxation has been shown to be accomplished by means of a series of fast transitions between metabasins in the potential energy landscape involving the collective motion of a substantial number of particles arranged in relatively compact clusters (democratic clusters or $d$ clusters). In this work we shall complete this picture by identifying the connections between local structural jamming, metabasin confining strength, and $d$ clusters. Thus we shall demonstrate that the degree of jamming of the local structure dictates the confining strength of the local metabasin and that the local high propensity regions and the $d$ clusters are not only similar in nature but that they share a significant amount of particles.

The functional dynamics exhibited by cell collectives are fascinating examples of robust, synchronized, collective behavior in spatially extended biological systems. To investigate the roles of local cellular dynamics and interaction strength in the spatiotemporal dynamics of cell collectives of different sizes, we study a model system consisting of a ring of coupled cells incorporating a three-step biochemical pathway of regulated activator-inhibitor reactions. The isolated individual cells display very complex dynamics as a result of the nonlinear interactions common in cellular processes. On coupling the cells to nearest neighbors, through diffusion of the pathway end product, the ring of cells yields a host of interesting and unusual dynamical features such as, suppression of chaos, phase synchronization, traveling waves, and intermittency, for varying interaction strengths and system sizes. But robust complete synchronization can be induced in these coupled cells with a small degree of random coupling among them even where regular coupling yielded only intermittent synchronization. Our studies indicate that robustness in synchronized functional dynamics in tissues and cell populations in nature can be ensured by a few transient random connections among the cells. Such connections are being discovered only recently in real cellular systems.

We investigate the sensitivity of the time evolution of semiclassical wave packets in two-dimensional chaotic billiards with respect to local perturbations of their boundaries. For this purpose, we address, analytically and numerically, the time decay of the Loschmidt echo (LE). We find the LE to decay exponentially in time, with the rate equal to the classical escape rate from an open billiard obtained from the original one by removing the perturbation-affected region of its boundary. Finally, we propose a principal scheme for the experimental observation of the LE decay.

The learning of signal directions in high-dimensional data through orthogonal decomposition or principal component analysis (PCA) has many important applications in physics and engineering disciplines, e.g., wireless communication, information theory, and econophysics. The accuracy of the orthogonal decomposition can be studied using mean-field theory. Previous analysis of data produced from a model with a single signal direction has predicted a retarded learning phase transition below which learning is not possible, i.e., if the signal is too weak or the data set is too small then it is impossible to learn anything about the signal direction or magnitude. In this contribution we show that the result can be generalized to the case where there are multiple signal directions. Each nondegenerate signal is associated with a retarded learning transition. However, fluctuations around the mean-field solution lead to large finite size effects unless the signal strengths are very well separated. We evaluate the one-loop contribution to the mean-field theory, which shows that signal directions are indistinguishable from one another if their corresponding population eigenvalues are separated by $O\left(N^{-\tau }\right)$ with exponent $\tau >\frac{1}{3}$, where $N$ is the data dimension. Numerical simulations are consistent with the analysis and show that finite size effects can persist even for very large data sets.

Large variety of physical, chemical, and biological systems show excitable behavior, characterized by a nonlinear response under external perturbations: only perturbations exceeding a threshold induce a full system response (firing). It has been reported that in coupled excitable identical systems noise may induce the simultaneous firing of a macroscopic fraction of units. However, a comprehensive understanding of the role of noise and that of natural diversity present in realistic systems is still lacking. Here we develop a theory for the emergence of collective firings in nonidentical excitable systems subject to noise. Three different dynamical regimes arise: subthreshold motion, where all elements remain confined near the fixed point; coherent pulsations, where a macroscopic fraction fire simultaneously; and incoherent pulsations, where units fire in a disordered fashion. We also show that the mechanism for collective firing is generic: it arises from degradation of entrainment originated either by noise or by diversity.

Using numerical simulations we investigate dynamical quantum chaos in isolated nuclear spin systems. We determine the structure of quantum states, investigate the validity of the Curie law for magnetic susceptibility and find the spectrum of magnetic noise. The spectrum is the same for positive and negative temperatures. The study is motivated by recent interest in condensed-matter experiments for searches of fundamental parity- and time-reversal-invariance violations. In these experiments nuclear spins are cooled down to microkelvin temperatures and are completely decoupled from their surroundings. A limitation on statistical sensitivity of the experiments arises from the magnetic noise.

A self-consistent two-dimensional fluid-plasma model coupled to Maxwell’s equations is presented for argon discharges sustained at atmospheric pressure by the propagation of an electromagnetic surface wave. The numerical simulation provides the full axial and radial structure of the surface-wave plasma column and the distribution of the electromagnetic fields for given discharge operating conditions. To describe the contraction phenomenon, a characteristic feature of high-pressure discharges, we consider the kinetics of argon molecular ions in the charged-particle balance. An original feature of the model is to take into account the gas flow by solving self-consistently the mass, momentum, and energy balance equations for neutral particles. Accounting for the gas flow explains reported discrepancies between measured and calculated plasma parameters when assuming the local axial uniformity approximation. In contrast to the low-pressure case, the latter approximation is shown to be of limited validity at atmospheric pressure. The gas temperature is found to be a key parameter in modeling surface-wave discharges sustained at atmospheric pressure. It determines the radial and the axial structure of the plasma column. The calculated plasma parameters and wave propagation characteristics using the present two-dimensional fluid model are in good agreement with our set of experimental data.

For the study of complex synthetic and biological molecular systems by computer simulations one is still restricted to simple model systems or by far too small time scales. To overcome this problem multiscale techniques are being developed. However, in almost all cases, the regions and molecules of different resolution are kept fixed and are not in equilibrium with each other. We here give a basic theoretical framework for an efficient and flexible coupling of the different regimes. The approach leads to a concept, which can be seen as a geometry-induced phase transition, and to a counterpart of the equipartition theorem for fractional degrees of freedom. This represents the initial step in developing a general theoretical framework for computer simulation methods applying simultaneously different levels of resolution.

We investigate the ratchet current that appears in a kicked Hamiltonian system when the period of the kicks corresponds to the regime of quantum resonance. In the classical analog, a spatial-temporal symmetry should be broken to obtain a net directed current. It was recently discovered that in quantum resonance the temporal symmetry can be kept, and we prove that breaking the spatial symmetry is a necessary condition to find this effect. Moreover, we show numerically and analytically how the direction of the motion is dramatically influenced by the strength of the kicking potential and the value of the period. By increasing the strength of the interaction this direction changes periodically, providing us with un-expected source of current reversals in this quantum model. These reversals depend on the kicking period also, though this behavior is theoretically more difficult to analyze. Finally, we generalize the discussion to the case of a nonuniform initial condition.

Polymeric microgels are very interesting systems to study polymer-solvent interactions since they react to changes in the solvent properties by swelling or deswelling to reach a final equilibrium state of minimal free energy. Accordingly, factors such as pH, temperature, or salt concentration can induce size changes. While the volume phase transition undergone by ionic microgels with addition of salt is reasonably well understood in terms of Donnan effects, the origin of these transitions in neutral microgels is devoid of such understanding. In this paper, the effects of electrolytes on the swelling behavior of neutral thermosensitive microgels are interpreted within the Flory-Rehner theory for the swelling of neutral gels, by considering that ionic concentration affects the entropic contribution to the Flory solvency $\chi$ parameter; this manifests macroscopically as particle deswelling. The entropic changes depend on the ability of the electrolyte to disrupt the neighboring water structure and result in increasing values of $\chi$ with salt concentration. In this sense, we find a clear correlation between the deswelling ability of the ions and their chaotropic (structure breaking) or kosmotropic (structure making) nature as classified in the Hofmeister series.