Glasses exhibit spatially inhomogeneous elastic properties, which can be investigated by measuring their elastic moduli at a local scale. Various methods to evaluate the local elastic modulus have been proposed in the literature. A first possibility is to measure the local stress-local strain curve and to obtain the local elastic modulus from the slope of the curve or, equivalently, to use a local fluctuation formula. Another possible route is to assume an affine strain and to use the applied global strain instead of the local strain for the calculation of the local modulus. Most recently, a third technique has been introduced, which is easy to be implemented and has the advantage of low computational cost. In this contribution, we compare these three approaches by using the same model glass and reveal the differences among them caused by the nonaffine deformations.

Inspired by the importance of inhibitory and excitatory couplings in the brain, we analyze the largest eigenvalue statistics of random networks incorporating such features. We find that the largest real part of eigenvalues of a network, which accounts for the stability of an underlying system, decreases linearly as a function of inhibitory connection probability up to a particular threshold value, after which it exhibits rich behaviors with the distribution manifesting generalized extreme value statistics. Fluctuations in the largest eigenvalue remain somewhat robust against an increase in system size but reflect a strong dependence on the number of connections, indicating that systems having more interactions among its constituents are likely to be more unstable.

Deterministic nonlinear dynamical processes are ubiquitous in nature. Chaotic sounds generated by such processes may appear irregular and random in waveform, but these sounds are mathematically distinguished from random stochastic sounds in that they contain deterministic short-time predictability in their temporal fine structures. We show that the human brain distinguishes deterministic chaotic sounds from spectrally matched stochastic sounds in neural processing and perception. Deterministic chaotic sounds, even without being attended to, elicited greater cerebral cortical responses than the surrogate control sounds after about 150 ms in latency after sound onset. Listeners also clearly discriminated these sounds in perception. The results support the hypothesis that the human auditory system is sensitive to the subtle short-time predictability embedded in the temporal fine structure of sounds.

Transfer entropy (TE) seems currently to be the most widely used tool to characterize causal influences in ensembles of complex systems from observed time series. In particular, in an elemental case of two systems, nonzero TEs in both directions are usually interpreted as a sign of a bidirectional coupling. However, one often overlooks that both positive TEs may well be encountered for unidirectionally coupled systems so that a false detection of a causal influence on the basis of a nonzero TE is rather possible. This work highlights typical factors leading to such “spurious couplings”: (i) unobserved state variables of the driving system, (ii) low temporal resolution, and (iii) observation errors. All are shown to be particular cases of a general problem: imperfect observations of states of the driving system. Importantly, exact values of TEs, rather than their statistical estimates, are computed here for selected benchmark systems. Conditions for a “spurious” TE to be large and even strongly exceed a “correct” TE are presented and discussed.

A quantum transport model for atomic line radiation in plasmas is developed and analyzed. It is found that the Wigner phase space formulation of QED provides a consistent way to address the wave-particle duality in radiative transfer problems. If the photons’ thermal de Broglie length is much smaller than all of the spatial scales of the problem under consideration (large-spectral-band limit), the radiation is not coherent and radiative transfer can be addressed with the usual treatments. In the general case, the Heisenberg uncertainty relation yields ambiguities in the description of the radiation-matter interaction mechanisms. We examine this issue and show that an accurate description of radiative transfer should involve a model with nonlocal interactions and requires an appropriate coarse-graining procedure. Calculations of transmission factors and absorption spectra in ideal cases are performed and indicate that significant misinterpretations can be made in spectroscopic diagnostics if the radiation coherence is not well accounted for. Applications to laser physics are also discussed.

We study the statistical mechanics of the one-dimensional discrete nonlinear Schrödinger (DNLS) equation with saturable nonlinearity. Our study represents an extension of earlier work [Phys. Rev. Lett. 84, 3740 (2000)] regarding the statistical mechanics of the one-dimensional DNLS equation with a cubic nonlinearity. As in this earlier study, we identify the spontaneous creation of localized excitations with a discontinuity in the partition function. The fact that this phenomenon is retained in the saturable DNLS is nontrivial, since in contrast to the cubic DNLS whose nonlinear character is enhanced as the excitation amplitude increases, the saturable DNLS, in fact, becomes increasingly linear as the excitation amplitude increases. We explore the nonlinear dynamics of this phenomenon by direct numerical simulations.

In this experimental and numerical study, we consider the role of inertial waves in the inverse energy cascade and the transfer of momentum in a rotating fluid. An oscillating torus generates two inertial-wave cones with their energy focusing at their apex. For high wave amplitudes, turbulence is generated locally around the focal point, resulting in angular momentum mixing and the generation of a columnar cyclonic vortex. The results suggest that nonlinear dynamics is essential for the wave induced momentum transport towards columnar vortices in rotating turbulence.

Urban agglomerations exhibit complex emergent features of which Zipf's law, i.e., a power-law size distribution, and fractality may be regarded as the most prominent ones. We propose a simplistic model for the generation of citylike structures which is solely based on the assumption that growth is more likely to take place close to inhabited space. The model involves one parameter which is an exponent determining how strongly the attraction decays with the distance. In addition, the model is run iteratively so that existing clusters can grow (together) and new ones can emerge. The model is capable of reproducing the size distribution and the fractality of the boundary of the largest cluster. Although the power-law distribution depends on both, the imposed exponent and the iteration, the fractality seems to be independent of the former and only depends on the latter. Analyzing land-cover data, we estimate the parameter-value $\gamma \approx 2.5$ for Paris and its surroundings.

Thermally sensitive neurons present bursting activity for certain temperature ranges, characterized by fast repetitive spiking of action potential followed by a short quiescent period. Synchronization of bursting activity is possible in networks of coupled neurons, and it is sometimes an undesirable feature. Control procedures can suppress totally or partially this collective behavior, with potential applications in deep-brain stimulation techniques. We investigate the control of bursting synchronization in small-world networks of Hodgkin-Huxley-type thermally sensitive neurons with chemical synapses through two different strategies. One is the application of an external time-periodic electrical signal and another consists of a time-delayed feedback signal. We consider the effectiveness of both strategies in terms of protocols of applications suitable to be applied by pacemakers.

This paper underscores the conjecture that intrinsic computation is maximal in systems at the “edge of chaos”. We study the relationship between dynamics and computational capability in random Boolean networks (RBN) for reservoir computing (RC). RC is a computational paradigm in which a trained readout layer interprets the dynamics of an excitable component (called the reservoir) that is perturbed by external input. The reservoir is often implemented as a homogeneous recurrent neural network, but there has been little investigation into the properties of reservoirs that are discrete and heterogeneous. Random Boolean networks are generic and heterogeneous dynamical systems and here we use them as the reservoir. A RBN is typically a closed system; to use it as a reservoir we extend it with an input layer. As a consequence of perturbation, the RBN does not necessarily fall into an attractor. Computational capability in RC arises from a tradeoff between separability and fading memory of inputs. We find the balance of these properties predictive of classification power and optimal at critical connectivity. These results are relevant to the construction of devices which exploit the intrinsic dynamics of complex heterogeneous systems, such as biomolecular substrates.

Expressions for the bulk viscosity, shear viscosity, and thermal conductivity of a quantum degenerate Bose gas above the critical temperature for Bose-Einstein condensation are derived using the Uehling-Uhlenbeck kinetic equation. For contact potentials and hard sphere interactions, the eigenvalues (relaxation rates) of the Uehling-Uhlenbeck collision operator have an upper cutoff. This cutoff requires summation over all discrete eigenvalues and eigenvectors of the collision operator when computing transport coefficients. We numerically compute the shear viscosity and thermal conductivity for any boson gas that interacts via a contact potential. We find that the bulk viscosity of the degenerate boson gas remains identically zero, as it is for the classical gas.

We investigate the dynamics of a small long-range interacting system, in contact with a large long-range thermal bath. Our analysis reveals the existence of striking anomalies in the energy flux between the bath and the system. In particular, we find that the evolution of the system is not influenced by the kinetic temperature of the bath, as opposed to what happens for short-range collisional systems. As a consequence, the system may get hotter also when its initial temperature is larger than the bath temperature. This observation is explained quantitatively in the framework of the collisionless Vlasov description of toy models with long-range interactions and shown to be valid whenever the Vlasov picture applies, from cosmology to plasma physics..

The limits for the accuracy of the virial expansion and the problem of its divergence have been investigated using the exact cluster expansion of the configuration integral. In the subcritical temperature regimes the virial equation of state is applicable up to the singularity point of the isothermal compressibility, i.e., to the possible beginning of the condensation process. At supercritical temperatures this equation should be applicable within the region where the cluster expansion is adequate. The problem of the virial series divergence has been found to be irrelevant to the actual behavior of the cluster expansion. Considering the Lennard-Jones fluid as well as the system of hard spheres, the inadequate behavior of the cluster expansion has been discovered in the high density regime. The major reason for this inadequacy should be the basic simplification of the cluster expansion: the integration of irreducible diagrams over the infinite limits.

The explicit thermodynamic functions, in particular, the specific heat of a spin system interacting with a spin bath which exerts finite dissipation on the system are determined. We show that the specific heat is a sum of the products of a thermal equilibration factor that carries the temperature dependence and a dynamical correction factor, characteristic of the dissipative energy flow under steady state from the system. The variation of specific heat with temperature is accompanied by an abrupt transition that depends on these dynamical factors characteristic of the finite system size.

This work presents an approach to evaluate the exact value of the fractal dimension of the cutting path $d_f^{CP}$ on hierarchical structures with finite order of ramification. Our approach is based on a renormalization group treatment of the universality class of watersheds. By making use of the self-similar property, we show that $d_f^{CP}$ depends only on the average cutting path (CP) of the first generation of the structure. For the simplest Wheastone hierarchical lattice (WHL), we present a mathematical proof. For a larger WHL structure, the exact value of $d_f^{CP}$ is derived based on a computer algorithm that identifies the length of all possible CP's of the first generation.

We report on the statistics of bubble size, topology, and shape and on their role in the coarsening dynamics for foams consisting of bubbles compressed between two parallel plates. The design of the sample cell permits control of the liquid content, through a constant pressure condition set by the height of the foam above a liquid reservoir. We find that in the scaling regime, all bubble distributions are independent not only of time, but also of liquid content. For coarsening, the average rate decreases with liquid content due to the blocking of gas diffusion by Plateau borders inflated with liquid; we achieve a factor of 4 reduction from the dry limit. By observing the growth rate of individual bubbles, we find that von Neumann's law becomes progressively violated with increasing wetness and decreasing bubble size. We successfully model this behavior by explicitly incorporating the border-blocking effect into the von Neumann argument. Two dimensionless bubble shape parameters naturally arise, one of which is primarily responsible for the violation of von Neumann's law for foams that are not perfectly dry.

We show that, in the equilibrium phase of glass-forming hard-sphere fluids in three dimensions, the static length scales tentatively associated with the dynamical slowdown and the dynamical length characterizing spatial heterogeneities in the dynamics unambiguously decorrelate. The former grow at a much slower rate than the latter when density increases. This observation is valid for the dynamical range that is accessible to computer simulations, which roughly corresponds to that accessible in colloidal experiments. We also find that, in this same range, no one-to-one correspondence between relaxation time and point-to-set correlation length exists. These results point to the coexistence of several relaxation mechanisms in the dynamically accessible regime of three-dimensional hard-sphere glass formers.

The Kruskal-Segur approach to selection theory in diffusion-limited or Laplacian growth is extended via combination with the Zauderer decomposition scheme. This way nonlinear bulk equations become tractable. To demonstrate the method, we apply it to two-dimensional crystal growth in a potential flow. We omit the simplifying approximations used in a preliminary calculation for the same system [Fischaleck, Kassner, Europhys. Lett. 81, 54004 (2008)], thus exhibiting the capability of the method to extend mathematical rigor to more complex problems than hitherto accessible.

The crystallization of bundles in filament networks interacting via long-range repulsions in confinement is described by a phenomenological model. The model demonstrates the formation of the hexagonal crystalline order via the interplay of the confinement potential and the filament-filament repulsion. Two distinct crystallization mechanisms in the short- and large- screening length regimes are discussed, and the phase diagram is obtained. Simulation of large bundles predicts the existence of topological defects within the bundled filaments. This electrostatic repulsion-driven crystallization model arising from studying filament networks can even find a more general context extending to charged colloidal systems.

An exact description is provided of an almost spherical fluid vesicle with a fixed area and a fixed enclosed volume locally deformed by external normal forces bringing two nearby points on the surface together symmetrically. The conformal invariance of the two-dimensional bending energy is used to identify the distribution of energy as well as the stress established in the vesicle. While these states are local minima of the energy, this energy is degenerate; there is a zero mode in the energy fluctuation spectrum, associated with area- and volume-preserving conformal transformations, which breaks the symmetry between the two points. The volume constraint fixes the distance $S$, measured along the surface, between the two points; if it is relaxed, a second zero mode appears, reflecting the independence of the energy on $S$; in the absence of this constraint a pathway opens for the membrane to slip out of the defect. Logarithmic curvature singularities in the surface geometry at the points of contact signal the presence of external forces. The magnitude of these forces varies inversely with $S$ and so diverges as the points merge; the corresponding torques vanish in these defects. The geometry behaves near each of the singularities as a biharmonic monopole, in the region between them as a surface of constant mean curvature, and in distant regions as a biharmonic quadrupole. Comparison of the distribution of stress with the quadratic approximation in the height functions points to shortcomings of the latter representation. Radial tension is accompanied by lateral compression, both near the singularities and far away, with a crossover from tension to compression occurring in the region between them.