The fragmentation of alumina and glass plates due to lateral impact is studied. A few hundred plates have been fragmented at different impact velocities and the produced fragments are analyzed. The method employed in this work allows one to investigate some geometrical properties of the fragments, besides the traditional size distribution usually studied in former experiments. We found that, although both materials exhibit qualitative similar fragment size distribution function, their geometrical properties appear to be quite different. A schematic model for two-dimensional fragmentation is also presented and its predictions are compared to our experimental results. The comparison suggests that the analysis of the fragments’ geometrical properties constitutes a more stringent test of the theoretical models’ assumptions than the size distribution.

We identify the statistical characterizers of congestion and decongestion for message transport in model communication lattices. These turn out to be the travel time distributions, which are Gaussian in the congested phase, and logarithmic normal in the decongested phase. Our results are demonstrated for two-dimensional lattices, such the Waxman graph, and for lattices with local clustering and geographic separations, gradient connections, as well as for a one-dimensional ring lattice with random assortative connections. The behavior of the distribution identifies the congested and decongested phase correctly for these distinct network topologies and decongestion strategies. The waiting time distributions of the systems also show identical signatures of the congested and decongested phases. The distributions are explained using a stochastic differential equation to model the transport.

Nodes in real-world networks are usually organized in local modules. These groups, called communities, are intuitively defined as subgraphs with a larger density of internal connections than of external links. In this work, we define a measure aimed at quantifying the statistical significance of single communities. Extreme and order statistics are used to predict the statistics associated with individual clusters in random graphs. These distributions allows us to define one community significance as the probability that a generic clustering algorithm finds such a group in a random graph. The method is successfully applied in the case of real-world networks for the evaluation of the significance of their communities.

A method is proposed to detect the dynamical structure hiding behind complex chaotic series by comparing prediction performance of trial functions. This method is valid even when the original system is contaminated with noise or only a relatively short data series is recorded. Using this method, the dynamical structure of the Gray-Scott model is detected from its rich spatiotemporal patterns. Finally, this method is successfully applied to the experimental data of Chua’s circuit, which promises its potential of the application to realistic systems.

We study theoretically the stability of “active suspensions,” modeled here as a Stokesian fluid in which are suspended motile particles. The basis of our study is a kinetic model recently posed by Saintillan and Shelley [D. Saintillan and M. J. Shelley, Phys. Rev. Lett. 100, 178103 (2008); D. Saintillan and M. J. Shelley, Phys. Fluids 20, 123304 (2008)] where the motile particles are either “pushers” or “pullers.” General considerations suggest that, in the absence of diffusional processes, perturbations from uniform isotropy will decay for pullers, but grow unboundedly for pushers, suggesting a possible ill-posedness. Hence, we investigate the structure of this system linearized near a state of uniform isotropy. The linearized system is nonnormal and variable coefficient, and not wholly described by an eigenvalue problem, in particular at small length scales. Using a high wave-number asymptotic analysis, we show that while long-wave stability depends on the particular swimming mechanism, short-wave stability does not and that the growth of perturbations for pusher suspensions is associated not with concentration fluctuations, as we show these generally decay, but with a proliferation of oscillations in swimmer orientation. These results are also confirmed through numerical simulation and suggest that the basic model is well-posed, even in the absence of translational and rotational diffusion effects. We also consider the influence of diffusional effects in the case where the rotational and translational diffusion coefficients are proportional and inversely proportional, respectively, to the volume concentration and predict the existence of a critical volume concentration or system size for the onset of the long-wave instability in a pusher suspension. We find reasonable agreement between the predictions of our theory and numerical simulations of rodlike swimmers by Saintillan and Shelley [D. Saintillan and M. J. Shelley, Phys. Rev. Lett. 99, 058102 (2007)].

Electron energy distribution functions (EEDFs) were measured with increasing gas pressure in oxygen capacitively and inductively coupled plasmas. It was found that, in the capacitive discharge, abnormally low-energy electrons became highly populated and the EEDF evolved to a more distinct bi-Maxwellian distribution as the gas pressure was increased. This pressure dependence of the EEDF in the oxygen capacitive discharge is contrary to argon capacitively coupled plasma, where—at high gas pressure—low-energy electrons are significantly reduced due to collisional heating and the EEDF evolves to the Maxwellian. The highly populated low-energy electrons at high gas pressure, which was not observed in inductively coupled oxygen plasma, show that collisional heating is very inefficient in terms of the oxygen capacitive discharge. It appears that this inefficient collisional heating seems to be attributed to a low electric field strength at the center of the oxygen capacitive plasma.

Ultrashort pulse propagation in fibers is affected by intrapulse Raman scattering (IRS) which causes both a linear frequency downshift and a quadratic displacement of the peak pulse, as functions of the propagation distance. This effect has been known and treated by perturbation methods applied to the nonlinear Schrödinger equation since the period of intense research on soliton propagation. Here, we find solutions of the model equation using an accelerating self-similarity variable and study their stability. These solutions have Airy function asymptotics which give them infinite energy. For small IRS, the algebraically decaying tail is negligible and these solutions are a very good approximation of the profiles observed in the full equation simulations. For strong IRS (but beyond the regime in which the evolution equation is valid for silica fibers), the self-similar pulses have noticeable left tails exhibiting Airy oscillations. Whenever their truncated forms are used as initial conditions of the full equation, they experience amplitude decay and show left tails that are consistent with radiation escaping from the central pulse. These observations are interpreted as being the effects of a continuum constitution of the infinite left tail.

This work focuses on the production of both stationary and traveling intrinsic localized modes (ILMs), also known as discrete breathers, in two closely related electrical lattices; we demonstrate experimentally that the interplay between these two ILM types can be utilized for the purpose of spatial control. We describe a novel mechanism that is responsible for the motion of driven ILMs in this system, and quantify this effect by modeling in some detail the electrical components comprising the lattice.

We investigate the escape from a potential well of a test particle driven by fractional Gaussian noise with Hurst exponent $0<H<1$. From a numerical analysis we demonstrate the exponential distribution of escape times from the well and analyze in detail the dependence of the mean escape time on the Hurst exponent $H$ and the particle diffusivity $D$. We observe different behavior for the subdiffusive (antipersistent) and superdiffusive (persistent) domains. In particular, we find that the escape becomes increasingly faster for decreasing values of $H$, consistent with previous findings on the first passage behavior. Approximate analytical calculations are shown to support the numerically observed dependencies.

Monte Carlo simulation has been performed on a classical two-dimensional $XY$ model with a modified form of interaction potential to investigate the role of topological defects on the phase transition exhibited by the model. In simulations in a restricted ensemble without defects, the system appears to remain ordered at all temperatures. Suppression of topological defects on the square plaquettes in the modified $XY$ model leads to complete elimination of the phase transition observed in this model.

Polymer translocation through a nanopore in a thin membrane is studied using a coarse-grained bead-spring model and Langevin dynamics simulation with a particular emphasis to explore out of equilibrium characteristics of the translocating chain. We analyze the out of equilibrium chain conformations both at the cis and the trans side separately either as a function of the time during the translocation process or as as function of the monomer index $m$ inside the pore. A detailed picture of translocation emerges by monitoring the center of mass of the translocating chain, longitudinal and transverse components of the gyration radii and the end to end vector. We observe that polymer configurations at the cis side are distinctly different from those at the trans side. During the translocation and immediately afterwards, the chain is clearly out of equilibrium, as different parts of the chain are characterized by a series of effective Flory exponents. We further notice that immediately after the translocation the last set of beads that have just translocated take a relatively compact structure compared to the first set of beads that translocated earlier and the chain immediately after translocation is described by an effective Flory exponent $0.45\pm 0.01$. The analysis of these results is further strengthened by looking at the conformations of chain segments of equal length as they cross from the cis to the trans side, We discuss implications of these results to the theoretical estimates and numerical simulation studies of the translocation exponent reported by various groups.

We derive a set of effective potentials describing the interaction between pairs of nucleotides that belong to an RNA molecule. Such interaction potentials are then used as the main constituents of a simplified simulation model, which is tested in the description of small secondary structure motifs. Our simulated RNA hairpins are consistent with the experimental structures obtained by NMR.

Signal conduction between endothelial cells along the walls of vessels appears to play an important role in circulatory function. A recently developed approach to calculate analytically the spectrum of propagating compositional waves in models of multicellular architectures is extended to study putative signal conduction dynamics across networks of endothelial cells. Here, compositional waves originate from negative feedback loops, such as between ${\text{Ca}}^{2+}$ and inositol triphosphate $\left({\text{IP}}_3\right)$ in endothelial cells, and are shaped by their connection topologies. We consider models of networks constituted of a main chain of endothelial cells and multiple side chains. The resulting transmission spectra encode information concerning the position and size of the side branches in the form of gaps. This observation suggests that endothelial cell networks may be able to “communicate” information regarding long-range order in their architecture.

We present an experimental and theoretical study of the pattern formation process of standing subharmonic waves in a fluidized quasi-one-dimensional shallow granular bed. The fluidization process is driven by means of a time-periodic air flow, analogous to a tapping type of forcing. Measurements of the amplitude of the critical mode close to the transition are in quite good agreement with those inferred from a universal stochastic amplitude equation. This allows us to determine both the bifurcation point of the deterministic system and the corresponding noise intensity. We also show that the probability density distribution is well described by a generalized Rayleigh distribution, which is the stationary solution of the corresponding Fokker-Planck equation of the universal stochastic amplitude equation that describes our system.

We show that the heat exchange between fluid particles and boundary walls can be achieved by controlling the velocity change rate following the particles’ collision with a wall in discrete kinetic theory, such as the lattice-gas cellular automata and the lattice Boltzmann method. We derive a relation between the velocity change rate and temperature so that we can control the velocity change rate according to a given temperature boundary condition. This relation enables us to deal with the thermal boundary whose temperature varies along a wall in contrast to the previous works of the lattice-gas cellular automata. In addition, we present simulation results to compare our method to the existing and give an example in a microchannel with a high temperature gradient boundary condition by the lattice-gas cellular automata.

Folding of the triangular lattice in a discrete three-dimensional space is investigated by means of the transfer-matrix method. This model was introduced by Bowick and co-workers as a discretized version of the polymerized membrane in thermal equilibrium. The folding rule (constraint) is incompatible with the periodic-boundary condition, and the simulation has been made under the open-boundary condition. In this paper, we propose a modified constraint, which is compatible with the periodic-boundary condition; technically, the restoration of translational invariance leads to a substantial reduction in the transfer-matrix size. Treating the cluster sizes $L\le 7$, we analyze the singularities of the crumpling transitions for a wide range of the bending rigidity $K$. We observe a series of the crumpling transitions at $K=0.206\left(2\right)$, $-0.32\left(1\right)$, and $-0.76\left(10\right)$. At each transition point, we estimate the latent heat as $Q=0.356\left(30\right)$, 0.08(3), and 0.05(5), respectively.

The nonequilibrium work fluctuation theorem provides the way for calculations of (equilibrium) free-energy based on work measurements of nonequilibrium, finite-time processes, and their reversed counterparts by applying Bennett’s acceptance ratio method. A nice property of this method is that each free-energy estimate readily yields an estimate of the asymptotic mean square error. Assuming convergence, it is easy to specify the uncertainty of the results. However, sample sizes have often to be balanced with respect to experimental or computational limitations and the question arises whether available samples of work values are sufficiently large in order to ensure convergence. Here, we propose a convergence measure for the two-sided free-energy estimator and characterize some of its properties, explain how it works, and test its statistical behavior. In total, we derive a convergence criterion for Bennett’s acceptance ratio method.

The six-vertex model is mapped to three-dimensional sphere stacks and different boundary conditions corresponding to different containers. The shape of the container provides a qualitative visualization of the boundary effect. Based on the sphere-stacking picture, we map the phase spaces of the six-vertex models to discrete networks. A node in the network represents a state of the system, and an edge between two nodes represents a zero-energy spin flip, which corresponds to adding or removing a sphere. The network analysis shows that the phase spaces of systems with different boundary conditions share some common features. We derived a few formulas for the number and the sizes of the disconnected phase-space subnetworks under the periodic boundary conditions. The sphere stacking provides new challenges in combinatorics and may cast light on some two-dimensional models.

Nonlinear propagation characteristics are investigated theoretically in a one-dimensional photonic band-gap structure containing indefinite metamaterials. It is found that optical bistability can be achieved at very low threshold values of normalized input intensity in this composite structure when the indefinite metamaterial is a cut-off, anticut-off, and never cut-off medium. It is also found that there exists corresponding bistable lateral shift which is strongly dependent on the parameters of indefinite metamaterials.

The system-plus-reservoir (SPR) model is the most common and effective approach to study quantum dissipative effects. Indeed, it makes quantization possible by considering the whole energy-conserving system, while the reservoir’s degrees of freedom, assumed to be harmonic, can be traced out by the path-integral technique, leading to a formulation that only includes the system of interest. In the standard SPR model the environment is only coupled with the system’s coordinate and turns out to quench its quantum fluctuations. However, there are physical systems coupled with an environment whose “coordinates” and “momenta” can be completely interchangeable (e.g., magnets), so an SPR coupling must symmetrically affect both canonical variables. In this paper such a general environmental coupling is studied in the case of a harmonic oscillator. It is found that quantum fluctuations are generally enhanced by environmental coupling with an unexpected nonmonotonic behavior. This leads one to speculate about the possibility that spin-lattice coupling could drive the two-dimensional Heisenberg antiferromagnet to reach its quantum-critical point.