As a model of composite materials, we choose a bundle of fibers with stochastically distributed breaking thresholds for the individual fibers. The fibers are assumed to share the load equally, and to obey Hookean elasticity right up to the breaking point. We study the evolution of the fiber breaking rate at a constant load in excess of the critical load. The analysis shows that the breaking rate reaches a minimum when the system is half-way from its complete collapse.

We consider the switching rate of a metastable reaction scheme, which includes reactions with arbitrary steps, e.g., $kA\leftrightarrow \left(k+r\right)A$ (both forward and reverse reaction steps are allowed to happen). Employing a WKB approximation, controlled by a large system size, we evaluate both the exponent and the preexponential factor for the rate. The results are illustrated on a number of examples.

In this work we concentrate on an experimental validation of the Lifshitz theory for the van der Waals and the Casimir forces in gold-alcohol-glass systems. From this theory weak dispersive forces are predicted when the dielectric properties of the intervening medium become comparable to one of the interacting surfaces. Using inverse colloid probe atomic force microscopy dispersive forces were measured occasionally and under controlled conditions by addition of salt to screen the electrostatic double layer force if present. The dispersive force was found to be attractive and an order of magnitude weaker than that in air. Although the theoretical description of the forces becomes less precise for these systems even with full knowledge of the dielectric properties, we find still our results in reasonable agreement with the Lifshitz theory.

During song production, oscine birds produce large air sac pressure pulses. During those pulses, energy is transferred to labia located at the juncture between the bronchii and the trachea, inducing the high frequency labial oscillations which are responsible for airflow modulations, i.e., the uttered sound. In order to generate diverse syllables, canaries (Serinus canaria) use a set of air sac pressure patterns with characteristic shapes. In this work we show that these different shapes can be approximated by the subharmonic solutions of a forced normal form. This simple model is built from identifying dynamical elements which allow to reproduce the shape of the pressure pattern corresponding to one syllable type. Remarkably, integrating that simple model for other parameters allows to recover the other pressure patterns used during song. Interpreting the diversity of these physiological gestures as subharmonic solutions of a simple nonlinear system allows us to account simultaneously for their morphological features as well as for the syllabic timing and suggests a strategy for the generation of complex motor patterns.

The one-dimensional contact process with weak to intermediate quenched disorder in its transmission rates is investigated via quasistationary Monte Carlo simulation. We address the contested questions of both the nature of dynamical scaling, conventional or activated, as well as of universality of critical exponents by employing a scaling analysis of the distribution of lifetimes and the quasistationary density of infection. We find activated scaling to be the appropriate description for intermediate to strong disorder. Critical exponents taken at face value are disorder dependent and approach the values expected for the limit of strong disorder as predicted by strong-disorder renormalization-group analysis of the process. However, no definitive conclusion about the nature of exponents is possible from this numerical approach on its own.

We consider two-dimensional turbulence driven by a steady prescribed sinusoidal body force working at an average rate $\epsilon$. Energy dissipation is due mainly to drag, which damps all wave number at a rate $\mu$. Simulations at statistical equilibrium reveal a scaling regime in which $\epsilon \propto {\mu }^{1/3}$, with no significant dependence of $\epsilon$ on hyperviscosity, domain size, or numerical resolution. This power-law scaling is explained by a crude closure argument that identifies advection by the energetic large-scale eddies as the crucial process that limits $\epsilon$ by disrupting the phase relation between the body force and fluid velocity. The average input $\epsilon$ is due mainly to spatial regions in which the large-scale velocity is much less than the root-mean-square velocity. We argue that $\epsilon \propto {\mu }^{1/3}$ characterizes energy injection by a steady or slowly changing spectrally confined body force.

It has been claimed that fractal analysis can be applied to unambiguously characterize works of art such as the drip paintings of Jackson Pollock. This academic issue has become of more general interest following the recent discovery of a cache of disputed Pollock paintings. We definitively demonstrate here, by analyzing paintings by Pollock and others, that fractal criteria provide no information about artistic authenticity. This work has led us to a result in fractal analysis of more general scientific significance: we show that the statistics of the “covering staircase” (closely related to the box-counting staircase) provide a way to characterize geometry and distinguish fractals from Euclidean objects. Finally we present a discussion of the composite of two fractals, a problem that was first investigated by Muzy. We show that the composite is not generally scale invariant and that it exhibits complex multifractal scaling in the small distance asymptotic limit.

The shape of the interface and pressure buildup for two-layered steady creeping flow inside a narrow channel of variable topography are examined in this study. The flow is assumed to be induced by the translation of the lower flat plate, similarly to lubrication flow. The interplay between channel topography and viscosity ratio, $R_{\mu }$, is emphasized, in the absence of interfacial tension and gravity. For contracting channel and in the low $R_{\mu }$ range, the pressure increases everywhere in the channel monotonically with $R_{\mu }$, reaching a maximum, and decreases as $R_{\mu }$ is increased further. In contrast, the interface level increases monotonically with $R_{\mu }$. Channel modulation causes considerable pressure buildup. However, unlike the interface, which exhibits modulation, the pressure distribution along the channel remains qualitatively unaffected.

Single-cycle strong terahertz pulses can be generated by irradiating ultrashort intense laser pulses onto a tenuous plasma slab. At the plasma surface, laser ponderomotive force accelerates electrons and induces net currents, which radiate terahertz pulses. Our theoretical model suggests that if ${\tau }_L>2\pi /{\omega }_p$, with ${\tau }_L$ as the laser-pulse duration and ${\omega }_p$ as the plasma frequency, the emission frequency is around ${\tau }_L^{-1}$. On the other hand, the emission frequency is around ${\omega }_p/2\pi$ if ${\tau }_L<2\pi /{\omega }_p$. Our numerical simulations support the theoretical model, showing that such a terahertz source is capable of providing megawatt power, field strengths of MV/cm, and broad frequency tunability.

Brownian dynamics simulations were carried out to study wave spectra of two-dimensional dusty plasma liquids and solids for a wide range of wavelengths. The existence of a longitudinal dust-thermal mode was confirmed in simulations, and a cutoff wave number in the transverse mode was measured. Dispersion relations, resulting from simulations, were compared with those from analytical theories, such as the random-phase approximation (RPA), the quasilocalized charged approximation (QLCA), and the harmonic approximation (HA). An overall good agreement between the QLCA and simulations was found for wide ranges of states and wavelengths after taking into account the direct thermal effect in the QLCA, while for the RPA and HA, good agreement with simulations was found in the high and low-temperature limits, respectively.

We present a method based on a combination of a genetic algorithm and Monte Carlo simulations to predict close-packed crystal structures in hard-core systems. We employ this method to predict the binary crystal structures in a mixture of large and small hard spheres with various stoichiometries and diameter ratios between 0.4 and 0.84. In addition to known binary hard-sphere crystal structures similar to NaCl and ${\text{AlB}}_2$, we predict additional crystal structures with the symmetry of CrB, $\gamma \text{CuTi}$, $\alpha \text{IrV}$, ${\text{HgBr}}_2$, ${\text{AuTe}}_2$, ${\text{Ag}}_2\text{Se}$, and various structures for which an atomic analog was not found. In order to determine the crystal structures at infinite pressures, we calculate the maximum packing density as a function of size ratio for the crystal structures predicted by our GA using a simulated annealing approach.

A nanoscale-sized Stirling engine with an atomistic working fluid has been modeled using molecular dynamics simulation. The design includes heat exchangers based on thermostats, pistons attached to a flywheel under load, and a regenerator. Key aspects of the behavior, including the time-dependent flows, are described. The model is shown to be capable of stable operation while producing net work at a moderate level of efficiency.

Statistical complexity measures are used to detect noise-induced order and to quantify stochastic and coherence resonances. We illustrate the method with two paradigmatic models, one of a Brownian particle in a sinusoidally modulated bistable potential, and the other, the FitzHugh-Nagumo model of excitable systems. The method can be employed for the precise detection of subtle signatures of noise-induced order in real-world complex signals.

By molecular modeling we demonstrate that the nematic long-range order discovered in bent-core liquid-crystal systems should reveal further spatially homogeneous phases. Two of them are identified as a tetrahedratic nematic $\left(N_T\right)$ phase with $D_{2d}$ symmetry and a chiral tetrahedratic nematic $\left(N_T^{\ast }\right)$ phase with $D_2$ symmetry. These phases were found for a lattice model with quadrupolar and octupolar anisotropic interactions using mean-field theory and Monte Carlo simulations. The phase diagrams exhibit tetrahedratic $\left(T\right)$, $N_T$, and $N_T^{\ast }$ phases, in addition to ordinary isotropic $\left(I\right)$, uniaxial nematic $\left(N_U\right)$, and biaxial nematic $\left(N_B\right)$ phases.

The study of brain electrical activities in terms of deterministic nonlinear dynamics has recently received much attention. Forbidden ordinal patterns (FOP) is a recently proposed method to investigate the determinism of a dynamical system through the analysis of intrinsic ordinal properties of a nonstationary time series. The advantages of this method in comparison to others include simplicity and low complexity in computation without further model assumptions. In this paper, the FOP of the EEG series of genetic absence epilepsy rats from Strasbourg was examined to demonstrate evidence of deterministic dynamics during epileptic states. Experiments showed that the number of FOP of the EEG series grew significantly from an interictal to an ictal state via a preictal state. These findings indicated that the deterministic dynamics of neural networks increased significantly in the transition from the interictal to the ictal states and also suggested that the FOP measures of the EEG series could be considered as a predictor of absence seizures.

Semi-Markov processes represent a well-known and widely used class of random processes in classical probability theory. Here, we develop an extension of this type of non-Markovian dynamics to the quantum regime. This extension is demonstrated to yield quantum master equations with memory kernels which allow the formulation of explicit conditions for the complete positivity of the corresponding quantum dynamical maps, thus leading to important insights into the structural characterization of the non-Markovian quantum dynamics of open systems. Explicit examples are analyzed in detail.

Gelation of gelatin was broadly studied by experimental and theoretical methods. Power laws observed on the gel point—mainly obtained by dynamic light scattering (DLS)—are considered to be the signature of some special dynamic phenomena ascribed to the appearance of a percolation cluster. We present here experimental (DLS and rheometric measurements) and Monte Carlo simulation studies showing that the percolation threshold and DLS power-law decay occur on different times. We ascribe the percolation point to the time where the scattering medium mode diverges. This mode is sensitive to the clusters’ growth and diverges when the system attains the percolation threshold. The power-law behavior is obtained only in the postpercolation regime.

Using an improved static and dynamic light-scattering technique, we have observed multiscale relaxation of the pretransitional fluctuations in the isotropic phase of a cromolyn aqueous solution, a lyotropic liquid crystal where rods are formed by aggregates of disklike molecules. We have detected the onset of cromolyn aggregation about $12°\text{C}$ above the transition temperature. The onset is manifested by the emergence of strong scattering due to the fluctuations of local anisotropy and by the split of the diffusion dynamics into two distinctly different modes, one associated with the relatively fast diffusion of monomer-size particles and the other one with the much slower diffusion of the cromolyn aggregates. A third observed dynamic mode is associated with the pretransitional slowing down of fluctuations of the local anisotropy. This mode behaves differently in polarized and depolarized light scattering, due to a coupling between fluctuations of the local-anisotropy and velocity fluctuations.

Circular double-stranded DNA has different topological states which are defined by their linking numbers. Equilibrium distribution of linking numbers can be obtained by closing a linear DNA into a circle by ligase. Using Monte Carlo simulation, we predict the temperature dependence of the linking number distribution of small circular DNAs. Our predictions are based on flexible defect excitations that resulted from local melting or unstacking of DNA base pairs. We found that the reduced bending rigidity alone can lead to measurable changes of the variance of linking number distribution of short circular DNAs. If the defect is accompanied by local unwinding, the effect becomes much more prominent. The predictions can be easily investigated in experiments, providing a new method to study the micromechanics of sharply bent DNAs and the thermal stability of specific DNA sequences. Furthermore, the predictions are directly applicable to the studies of binding of DNA-distorting proteins that can locally reduce DNA rigidity, form DNA kinks, or introduce local unwinding.