We present a generalized optical theorem for surface waves. The theorem also applies to body waves since under many circumstances body waves can be written in terms of surface-wave modal summations. This theorem therefore extends the domain of applicability of the optical theorem from homogeneous background media to a general class of body and surface-wave propagation regimes within layered elastic media.

Hydrostatically pressurized circular rings confined to two dimensions (or cylinders constrained to have only $z$-independent deformations) undergo Euler-type buckling when the outside pressure exceeds a critical value. We perform a stability analysis of rings with arclength-dependent bending moduli and determine how weakened bending modulus segments affect the buckling critical pressure. Rings with a fourfold symmetric modulation are particularly susceptible to collapse. In addition we study the initial postbuckling stages of the pressurized rings to determine possible ring folding patterns.

We have shown that the nonlinearity of the chemical reaction may induce instability on a homogenous stable steady state of a one-component reaction-diffusion system characterized by a cubic polynomial source term. This results in a growth of an asymptotically approaching inhomogeneous spatial profile of secant-hyperbolic form reminiscent of a solitary wave.

We study the minimum-energy configuration of a $d$-dimensional elastic interface in a random potential tied to a harmonic spring. As a function of the spring position, the center of mass of the interface changes in discrete jumps, also called shocks or “static avalanches.” We obtain analytically the distribution of avalanche sizes and its cumulants within an $ϵ=4-d$ expansion from a tree and one-loop resummation using functional renormalization. This is compared with exact numerical minimizations of interface energies for random-field disorder in $d=2,3$. Connections to dynamic avalanches are mentioned.

Here we report a first-order all-or-none transition from an expanded coil to a compact crystallite for a flexible polymer chain. Wang-Landau sampling is used to construct the complete density of states for square-well chains up to length 256. Analysis within both the microcanonical and canonical ensembles shows a direct freezing transition for finite length chains with sufficiently short-range interactions. This type of transition is a distinctive feature of “one-step” protein folding and our findings demonstrate that a simple homopolymer model can exhibit protein-folding thermodynamics.

We review how the renormalized force correlator $\Delta \left(u\right)$, the function computed in the functional renormalization-group (RG) field theory, can be measured directly in numerics and experiments on the dynamics of elastic manifolds in the presence of pinning disorder. We show how this function can be computed analytically for a particle dragged through a one-dimensional random-force landscape. The limit of small velocity allows one to access the critical behavior at the depinning transition. For uncorrelated forces one finds three universality classes, corresponding to the three extreme value statistics, Gumbel, Weibull, and Fréchet. For each class we obtain analytically the universal function $\Delta \left(u\right)$, the corrections to the critical force, and the joint probability distribution of avalanche sizes $s$ and waiting times $w$. We find $P\left(s\right)=P\left(w\right)$ for all three cases. All results are checked numerically. For a Brownian force landscape, known as the Alessandro, Beatrice, Bertotti, and Montorsi (ABBM) model, avalanche distributions and $\Delta \left(u\right)$ can be computed for any velocity. For two-dimensional disorder, we perform large-scale numerical simulations to calculate the renormalized force correlator tensor ${\Delta }_{ij}\left(\vec{u}\right)$, and to extract the anisotropic scaling exponents ${\zeta }_x>{\zeta }_y$. We also show how the Middleton theorem is violated. Our results are relevant for the record statistics of random sequences with linear trends, as encountered, e.g., in some models of global warming. We give the joint distribution of the time $s$ between two successive records and their difference in value $w$.

Interfaces pinned by quenched disorder are often used to model jerky self-organized critical motion. We study static avalanches, or shocks, defined here as jumps between distinct global minima upon changing an external field. We show how the full statistics of these jumps is encoded in the functional-renormalization-group fixed-point functions. This allows us to obtain the size distribution $P\left(S\right)$ of static avalanches in an expansion in the internal dimension $d$ of the interface. Near and above $d=4$ this yields the mean-field distribution $P\left(S\right)\sim S^{-3∕2}{e}^{-S∕4S_m}$, where $S_m$ is a large-scale cutoff, in some cases calculable. Resumming all one-loop contributions, we find $P\left(S\right)\sim S^{-\tau }\exp \mathbf{(}C{(S∕S_m)}^{1∕2}-\frac{B}{4}{(S∕S_m)}^{\delta }\mathbf{)}$, where $B$, $C$, $\delta$, and $\tau$ are obtained to first order in $ϵ=4-d$. Our result is consistent to $O\left(ϵ\right)$ with the relation $\tau ={\tau }_{\zeta }≔2-\frac{2}{d+\zeta }$, where $\zeta$ is the static roughness exponent, often conjectured to hold at depinning. Our calculation applies to all static universality classes, including random-bond, random-field, and random-periodic disorders. Extended to long-range elastic systems, it yields a different size distribution for the case of contact-line elasticity, with an exponent compatible with $\tau =2-\frac{1}{d+\zeta }$ to $O(ϵ=2-d)$. We discuss consequences for avalanches at depinning and for sandpile models, relations to Burgers turbulence and the possibility that the relation $\tau ={\tau }_{\zeta }$ be violated to higher loop order. Finally, we show that the avalanche-size distribution on a hyperplane of codimension one is in mean field (valid close to and above $d=4$) given by $P\left(S\right)\sim K_{1∕3}\left(S\right)∕S$, where $K$ is the Bessel-$K$ function, thus ${\tau }_{\text{hyper}\text{plane}}=\frac{4}{3}$.

We rely on the lattice element method to simulate and analyze the stress fields at subparticle scales in two-dimensional granular solids composed of particles of variable stiffness together with an interstitial matrix of variable volume fraction. We find that the contact force distributions as approached from the subscale stresses are similar to those obtained from a particle-scale discrete element approach. This means that the well-known properties of force distributions in model granular media, with hard particles and without an interstitial phase, can be extended to materials such as concrete and sandstone involving a jammed particle phase. Interestingly, the stress distributions are exponential at the contact zones and they are mainly guided by the particle phase in compression and by the matrix in tension. We also show that the distributions are increasingly broader for a decreasing matrix volume fraction in tension whereas in compression they depend only on the particle stiffness.

We consider the dynamics of a thin liquid film in the attractive substrate potential and under the action of a longitudinal or a tilted vibration. Using a multiscale technique we split the film motion into the oscillatory and the averaged parts. The frequency of the vibration is assumed high enough for the inertial effects to become essential for the oscillatory motion. Applying the lubrication approximation for the averaged motion we obtain the amplitude equation, which includes contributions from gravity, van der Waals attraction, surface tension, and the vibration. We show that the longitudinal vibration leads to destabilization of the initially planar film. Stable solutions corresponding to the deflected free surface are possible in this case. Linear analysis in the case of tilted vibration shows that either stabilization or destabilization is possible. Stabilization of the dewetting film by mechanical action (i.e., the vibration) was first reported by us [Phys. Rev. E 77, 036320 (2008)]. This effect may be important for applications. Also, it is shown that the tilted vibration causes the averaged longitudinal fluid flow, which can be used to transport microparticles.

We formulate a technique for the detection of functional clusters in discrete event data. The advantage of this algorithm is that no prior knowledge of the number of functional groups is needed, as our procedure progressively combines data traces and derives the optimal clustering cutoff in a simple and intuitive manner through the use of surrogate data sets. In order to demonstrate the power of this algorithm to detect changes in network dynamics and connectivity, we apply it to both simulated neural spike train data and real neural data obtained from the mouse hippocampus during exploration and slow-wave sleep. Using the simulated data, we show that our algorithm performs better than existing methods. In the experimental data, we observe state-dependent clustering patterns consistent with known neurophysiological processes involved in memory consolidation.

The spin-1/2 Ising-Heisenberg model with the pair $XYZ$ Heisenberg interaction and quartic Ising interactions is exactly solved by establishing a precise mapping relationship with the corresponding zero-field (symmetric) eight-vertex model. It is shown that the Ising-Heisenberg model with the ferromagnetic Heisenberg interaction exhibits a striking critical behavior, which manifests itself through re-entrant phase transitions as well as continuously varying critical exponents. The changes in critical exponents are in accordance with the weak universality hypothesis in spite of a peculiar singular behavior that emerges at a quantum critical point of the infinite order, which occurs at the isotropic limit of the Heisenberg interaction. On the other hand, the Ising-Heisenberg model with the antiferromagnetic Heisenberg interaction surprisingly exhibits less significant changes in both critical temperatures and critical exponents upon varying the strength of the exchange anisotropy in the Heisenberg interaction.

Based on recent work [C. J. Tessone, C. R. Mirasso, R. Toral, and J. D. Gunton, Phys. Rev. Lett. 97, 194101 (2006)], the study of coupled bistable oscillators with different sources of diversity is extended. Effects of the correlation between the diversity on the resonant response of the system are discussed. It is found that the diversity of the coupled system, in the form of quenched noise, can induce a resonant effect in response to external signals. The resonance is reduced and even disappears as the correlation length between the diversity increases, while the spatial synchronization is enhanced due to the correlation between the diversity.

We present a numerical study of the effect of interstitial air on a vertically vibrated granular bed within one period of oscillation. We use a three-dimensional molecular-dynamics simulation including air phenomenologically. The simulations are validated with experiments made with spherical glass beads in a rectangular container. After validation, results are reported for a granular column of 9000 grains and $\approx 50$ layers deep (at rest), agitated with a sinusoidal excitation with maximal acceleration $4.7g$ at 11.7 Hz. We report the evolution of density, granular temperature, and coordination number within a vibration cycle, and the effect of interstitial air on those parameters. In three-dimensional computer simulations we found that the presence of interstitial air can promote the collective motion of the granular material as a whole.

We report an experimental study of the intermittent dynamics of a gas flowing through a column of a non-Newtonian fluid. In a given range of the imposed constant flow rate, the system spontaneously alternates between two regimes: bubbles emitted at the bottom either rise independently one from the other or merge to create a winding flue which then connects the bottom air entrance to the free surface. The observations are reminiscent of the spontaneous changes in the degassing regime observed on volcanoes and suggest that, in the nature, such a phenomenon is likely to be governed by the non-Newtonian properties of the magma. We focus on the statistical distribution of the lifespans of the bubbling and flue regimes in the intermittent steady state. The bubbling regime exhibits a characteristic time whereas, interestingly, the flue lifespan displays a decaying power-law distribution. The associated exponent, which is significantly smaller than the value 1.5 often reported experimentally and predicted in some standard intermittency scenarios, depends on the fluid properties and can be interpreted as the ratio of two characteristic times of the system.

The collective behavior of an ensemble of multimode stochastic oscillators is investigated. The oscillators are pulse coupled; they are able to emit pulses and to detect the pulses emitted by the others. As a function of the output intensity in the system they can operate in different modes having different pulsing periods. The system is designed to optimize the output intensity around a fixed $f^{\ast }$ output threshold. In order to do so a simple dynamics is considered. Whenever the total output intensity in the system is lower than $f^{\ast }$, a mode with a higher interpulse period is chosen. If the light intensity in the system is higher than $f^{\ast }$, a mode with a lower interpulse period is selected. As a side effect of this simple optimization rule, for a given $f^{\ast }$ interval a nontrivial synchronization of the oscillators is observed. The synchronization level is studied by computer simulations, investigating the influence of model parameters (number of modes, stochasticity of the oscillators, the $f^{\ast }$ threshold value, and interaction topology). An experimental realization of this system is also considered; an ensemble of electronic oscillators communicating with light pulses was constructed and studied. The experimental system behaves in many ways similar to the theoretically considered multimode stochastic oscillator ensemble.

A method to synchronize two chaotic systems with anticipation or lag, coupled in the drive response mode, is proposed. The coupling involves variable delay with three time scales. The method has the advantage that synchronization is realized with intermittent information about the driving system at intervals fixed by a reset time. The stability of the synchronization manifold is analyzed with the resulting discrete error dynamics. The numerical calculations in standard systems such as the Rössler and Lorenz systems are used to demonstrate the method and the results of the analysis.

The dynamics of the truncated Euler equations with helical initial conditions are studied. Transient energy and helicity cascades leading to Kraichnan helical absolute equilibrium at small scales, including a linear scaling of the relative helicity spectrum are obtained. Strong helicity effects are found using initial data concentrated at high wave numbers. Using low-wave-number initial conditions, the results of Cichowlas et al. [Phys. Rev. Lett. 95, 264502 (2005)] are extended to helical flows. Similarities between the turbulent transient evolution of the ideal (time-reversible) system and viscous helical flows are found. Using an argument in the manner of Frisch et al. [Phys. Rev. Lett. 101, 144501 (2008)], the excess of relative helicity found at small scales in the viscous run is related to the thermalization of the ideal flow. The observed differences in the behavior of truncated Euler and (constant viscosity) Navier-Stokes are qualitatively understood using the concept of eddy viscosity. The large scales of truncated Euler equations are then shown to follow quantitatively an effective Navier-Stokes dynamics based on a variable (scale dependent) eddy viscosity.

The nonlinear wave modulation of planar and nonplanar (cylindrical and spherical) ion-acoustic envelope solitons in a collisionless unmagnetized electron-positron-ion plasma with two-electron temperature distributions has been studied. The reductive perturbative technique is used to obtain a modified nonlinear Schrödinger equation, which includes a damping term that accounts for the geometrical effect. The critical wave number threshold $K_c$, which indicates where the modulational instability sets in, has been determined for various regimes. It is found that an increase in the positron concentration $\left(\alpha \right)$ leads to a decrease in the critical wave number $\left(K_c\right)$ until $\alpha$ approaches certain value ${\alpha }_c$ (critical positron concentration), then further increase in $\alpha$ beyond ${\alpha }_c$ increases the value of $K_c$. Also, it is found that there is a modulation instability period for the cylindrical and spherical wave modulation, which does not exist in the one-dimensional case.

The one-dimensional Frenkel-Kontorova (FK) model, well known from the theory of dislocations in crystal materials, is applied to the simulation of the process of nonelastic stress propagation along transform faults. Dynamic parameters of plate boundary earthquakes as well as slow earthquakes and afterslip are quantitatively described, including propagation velocity along the strike, plate boundary velocity during and after the strike, stress drop, displacement, extent of the rupture zone, and spatiotemporal distribution of stress and strain. The three fundamental speeds of plate movement, earthquake migration, and seismic waves are shown to be connected in framework of the continuum FK model. The magnitude of the strain wave velocity is a strong (almost exponential) function of accumulated stress or strain. It changes from a few km/s during earthquakes to a few dozen km per day, month, or year during afterslip and interearthquake periods. Results of the earthquake parameter calculation based on real data are in reasonable agreement with measured values. The distributions of aftershocks in this model are consistent with the Omori law for temporal distribution and a $1/r$ for the spatial distributions.

A Darboux transformation for the generalized Hirota-Satsuma coupled Korteweg–de Vries (KdV) equation is derived with the aid of the gauge transformation between the corresponding $4\times 4$ matrix spectral problems with three potentials, by which some explicit solutions of the generalized Hirota-Satsuma coupled KdV equation are constructed. As a reduction, a Darboux transformation of the complex coupled KdV equation and its explicit solutions are obtained.