An elastic membrane that is forced to reside in a container smaller than its natural size will deform and upon further volume reduction eventually crumple. The crumpled state is characterized by the localization of energy in a complex network of highly deformed crescent-like regions joined by line ridges. In this article we study through a combination of experiments, numerical simulations, and analytic approaches the emergence of localized regions of high stretching when a self-avoiding membrane is subject to a severe geometrical constraint. Based on our experimental observations and numerical results we suggest that at moderate packing fraction interlayer interactions produce a response equivalent to that of a thicker membrane that has the shape of the deformed one. We find that new conical dislocations, coined satellite d-cones, appear as the deformed membrane further compactifies. When these satellite d-cones are born, a substantial relaxation of the mechanical response of the membrane is observed. Evidence is found that friction plays a key role in stabilizing the folded structures.

A fully adaptive methodology is developed for reducing the complexity of large dissipative systems. This represents a significant step toward extracting essential physical knowledge from complex systems, by addressing the challenging problem of a minimal number of variables needed to exactly capture the system dynamics. Accurate reduced description is achieved, by construction of a hierarchy of slow invariant manifolds, with an embarrassingly simple implementation in any dimension. The method is validated with the autoignition of the hydrogen-air mixture where a reduction to a cascade of slow invariant manifolds is observed.

The capability of modeling and simulating complex interfacial dynamics of multiphase flows has been recognized as one of the main advantages of the lattice Boltzmann equation (LBE). A basic feature of two-phase LBE models, i.e., the force balance condition at the discrete lattice level of LBE, is investigated in this work. An explicit force-balance formulation is derived for a flat interface by analyzing the two-dimensional nine-velocity (D2Q9) two-phase LBE model without invoking the Chapman-Enskog expansion. The result suggests that generally the balance between the interaction force and the pressure does not hold exactly on the discrete lattice due to numerical errors. It is also shown that such force imbalance can lead to some artificial velocities in the vicinity of phase interface.

For Brownian motion of a single-particle subject to a tilted periodic potential on a ring, we propose a formula for experimentally determining the cumulant generating function of time-averaged current without measurements of current fluctuations. We first derive this formula phenomenologically on the basis of two key relations: a fluctuation relation associated with Onsager’s principle of the least-energy dissipation in a sufficiently local region and an additivity relation by which spatially inhomogeneous fluctuations can be properly considered. We then derive the formula without any phenomenological assumptions. We also demonstrate its practical advantage by numerical experiments.

We provide an exact analytical solution of the collapse dynamics of self-gravitating Brownian particles and bacterial populations at zero temperature. These systems are described by the Smoluchowski-Poisson system or Keller-Segel model in which the diffusion term is neglected. As a result, the dynamics is purely deterministic. A cold system undergoes a gravitational collapse, leading to a finite-time singularity: The central density increases and becomes infinite in a finite time $t_{\text{coll}}$. The evolution continues in the postcollapse regime. A Dirac peak emerges, grows, and finally captures all the mass in a finite time $t_{\text{end}}$, while the central density excluding the Dirac peak progressively decreases. Close to the collapse time, the pre- and postcollapse evolutions are self-similar. Interestingly, if one starts from a parabolic density profile, one obtains an exact analytical solution that describes the whole collapse dynamics, from the initial time to the end, and accounts for non-self-similar corrections that were neglected in previous works. Our results have possible application in different areas including astrophysics, chemotaxis, colloids, and nanoscience.

The performance of attractor neural networks has been shown to depend crucially on the heterogeneity of the underlying topology. We take this analysis a step further by examining the effect of degree-degree correlations—assortativity—on neural-network behavior. We make use of a method recently put forward for studying correlated networks and dynamics thereon, both analytically and computationally, which is independent of how the topology may have evolved. We show how the robustness to noise is greatly enhanced in assortative (positively correlated) neural networks, especially if it is the hub neurons that store the information.

We show that finite Fermi systems governed by a mean field and a few-body interaction generically possess spectral fluctuations of the Wigner-Dyson type and are, thus, chaotic. Our argument is based on an analogy to the metal-insulator transition. We construct a sparse random-matrix scaffolding ensemble (ScE) that mimics this transition. Our claim then follows from the fact that the generic random-matrix ensemble modeling a fermionic interacting many-body system is much less sparse than ScE.

Many processes in geophysical and industrial settings involve the flow of granular materials down a slope. In order to investigate the granular dynamics, we report a series of laboratory experiments conducted by releasing grains at a steady rate from a localized source on a rough inclined plane. Different types of dense granular flow are observed by varying the flow rate at the source and the slope of the inclined plane. The two cases of steady flow confined by levees and the flow of avalanches down the plane are examined. The width of the steady flow increases linearly with the prescribed flow rate, which does not appreciably affect the characteristic depth or surface velocity of the bulk flow. When the flow rate is just below that required for sustaining the steady flow, avalanches are triggered at regular intervals. The avalanches maintain their shape, size, and speed down the inclined plane. We propose a simple model of steady flow that is consistent with our observations and discuss the challenges associated with the theoretical treatment of avalanche dynamics.

The jamming of bidisperse soft core disks is considered, using a variety of different protocols to produce the jammed state. In agreement with other works, we find that cooling and compression can lead to a broad range of jamming packing fractions ${\varphi }_J$, depending on cooling rate and initial configuration; the larger the degree of big particle clustering in the initial configuration, the larger will be the value of ${\varphi }_J$. In contrast, we find that shearing disrupts particle clustering, leading to a much narrower range of ${\varphi }_J$ as the shear strain rate varies. In the limit of vanishingly small shear strain rate, we find a unique nontrivial value for the jamming density that is independent of the initial system configuration. We conclude that shear driven jamming is a unique and well-defined critical point in the space of shear driven steady states. We clarify the relation between glassy behavior, rigidity, and jamming in such systems and relate our results to recent experiments.

We investigate the rearrangement of the director in thin films of nematic liquid crystals caused by tightly focusing circularly polarized laser beams. We find either target or spiral patterns, depending on the topology of the director configuration at the position of the beam focus. The induced rearrangements of the director are governed by the viscosity of the media, the handedness of circular polarization, and the irradiation power of the laser. Experimental observations are interpreted using a model derived from nematic continuum theory.

We use a lattice Boltzmann based Brownian dynamics simulation to investigate the dependence of DNA thermophoresis on its interaction with dissolved salts. We find the thermal diffusion coefficient $D_T$ depends on the molecule size, in contrast with previous simulations without electrostatics. The measured $S_T$ also depends on the Debye length. This suggests thermophoresis of DNA is influenced by the electrostatic interactions between the polymer beads and the salt ions. However, when electrostatic forces are weak, DNA thermophoresis is not found, suggesting that other repulsive forces such as the excluded volume force prevent thermal migration.

We show that some of the nonlinear conductance properties of electro-osmosis in sweat-duct capillaries may be modeled by a memristive circuit. This includes both the observed phase shift and amplitude modulation of the electrical current response to a simple harmonic driving potential. Memristive sytems may therefore be expected to play a role in modeling the electrical properties of skin, and perhaps also in other systems where nonlinearities are observed in their bioimpedance.

We report experimental observations of sound waves in a granular material during resonant silo discharge called silo music. The grain motion was tracked by high-speed imaging while the resonance of the silo was detected by accelerometers and acoustic methods. The grains do not oscillate in phase at neighboring vertical locations, but information propagates upward in this system in the form of sound waves. We show that the wave velocity is not constant throughout the silo but considerably increases toward the lower end of the system, suggesting increased pressure in this region, where the flow changes from cylindrical to converging flow. In the upper part of the silo the wave velocity matches the sound velocity measured in the same material when standing (in the absence of flow). Grain oscillations show a stick-slip character only in the upper part of the silo.

A penalty method is developed for predicting crystal structures in the presence of hard-core interactions. Applications to binary mixtures of neutral as well as charged disks are in particular investigated. For the case of neutral hard disks, a new stable $A_3{B}_3$ phase is reported. Concerning the charged case (i.e., two-dimensional ionic crystals), the full phase diagram as a function of the size ratio of the constitutive ions is calculated.

In the presence of unstable dimension variability numerical solutions of chaotic systems are valid only for short periods of observation. For this reason, analytical results for systems that exhibit this phenomenon are needed. Aiming to go one step further in obtaining such results, we study the parametric evolution of unstable dimension variability in two coupled bungalow maps. Each of these maps presents intervals of linearity that define Markov partitions, which are recovered for the coupled system in the case of synchronization. Using such partitions we find exact results for the onset of unstable dimension variability and for contrast measure, which quantifies the intensity of the phenomenon in terms of the stability of the periodic orbits embedded in the synchronization subspace.

We report an experimental study of the temperature space-time cross-correlation function, $C_T(r,\tau )$, in the central region of turbulent Rayleigh-Bénard convection. The measured $C_T(r,\tau )$ is found to have the scaling form $C_T(r_E,0)$, where $r_E=[r^2+(V\tau ){}^2]{}^{1/2}$ with $V$ being the rms velocity at the center of the convection cell. The experiment confirms the theory by He et al. [Phys. Rev. E 73, 055303(R) (2006)] and demonstrates its applications to homogenous turbulent flows, where the mean flow velocity is zero and Kraichnan’s random sweeping hypothesis holds approximately.

The heat conductivity of nonperiodic quantum Ising chains whose ends are connected with heat baths at different temperatures are studied numerically by solving the Lindblad master equation. The chains are subjected to a uniform transverse field $h$, while the exchange coupling $J_m$ between the nearest-neighbor spins takes the two values $J_A$ and $J_B$ arranged in Fibonacci, generalized Fibonacci, Thue-Morse, and period-doubling sequences. We calculate the energy-density profile and energy current of the resulting nonequilibrium steady states to study the heat-conducting behavior of finite but large systems. Although these nonperiodic quantum Ising chains are integrable, it is clearly found that energy gradients exist in all chains and the energy currents appear to scale as the system size $\langle Q\rangle ~N^{\alpha }$. By increasing the ratio of couplings, the exponent $\alpha$ can be modulated from $\alpha >-1$ to $\alpha <-1$ corresponding to the nontrivial transition from the abnormal heat transport to the heat insulator. The influences of the temperature gradient and the magnetic field to heat conduction have also been discussed.

Boundary-induced phase transitions in a driven diffusive process can be studied through a phase-plane analysis of the boundary-layer equations. In this paper, we generalize this approach further to show how various shapes including multishocks and downward shocks in the bulk particle density profile can be understood by studying the dependence of the fixed points of the boundary-layer equation on an appropriate parameter. This is done for a particular driven interacting particle system as a prototypical example. The present analysis shows the special role of a specific bifurcation of the fixed points in giving rise to different kinds of shocks.