We suggest a general approach to parameter estimation using autosynchronization with some restrictions on system dynamics. This parameter identification method can be extended to estimate parameters from a scalar time series. Furthermore, we propose an average filter method to suppress the influence of noise on parameter estimation. Some limits and extensions of the autosynchronization method are given as well. Several examples are presented to illustrate all methods suggested.

Random migrations of non-Brownian neutrally buoyant particles in the flow of a dilute suspension in a periodic Couette cell is simulated on the basis of a dipole model. A diffusivity is due to far-field collective hydrodynamic interactions. Large-scale fluctuations of particle concentration induce fluid velocity disturbances with a length scale comparable to the cell size. The calculated self-diffusivity coefficient is linear in particle volume content and agrees well with the experimental data.

The one-dimensional expansion of a plasma slab is studied using a kinetic description of the electrons based on an adiabatic invariant. The distribution function of the electrons is determined at any time and any position. Solution of the Poisson equation then enables us to determine the electric potential and the ion acceleration. Special attention is devoted to the disassembly time of the plasma slab which appears shorter than expected, due to the distortion of the electron distribution function. The spatial structures of the ion and electron densities and velocities are presented, together with a prediction of the maximum ion velocity. The model is compared to particle-in-cell simulations and excellent agreement is found.

A two-dimensional map is derived from the model of a curved Fermi-Pasta-Ulam (FPU) chain which supports exact discrete breather (DB) solutions with frequencies lying outside the linear spectrum or phonon band. The stability of the equilibrium points of the two-dimensional map is examined and the nature of the trajectories is numerically studied. The map displays regular orbits and commensurate states in the phase space for different choices of curvature strength of the FPU chain. The homoclinic map orbits are attributed to the stationary DB solutions of the lattice system.

We analyze order-disorder phase transitions driven by noise that occur in two kinds of network models closely related to the self-propelled model proposed by Vicsek et al. [Phys. Rev. Lett. 75, 1226 (1995)] to describe the collective motion of groups of organisms. Two different types of noise, which we call intrinsic and extrinsic, are considered. The intrinsic noise, the one used by Vicsek et al. in their original work, is related to the decision mechanism through which the particles update their positions. In contrast, the extrinsic noise, later introduced by Grégoire and Chaté [Phys. Rev. Lett. 92, 025702 (2004)], affects the signal that the particles receive from the environment. The network models presented here can be considered as mean-field representations of the self-propelled model. We show analytically and numerically that, for these two network models, the phase transitions driven by the intrinsic noise are continuous, whereas the extrinsic noise produces discontinuous phase transitions. This is true even for the small-world topology, which induces strong spatial correlations between the network elements. We also analyze the case where both types of noise are present simultaneously. In this situation, the phase transition can be continuous or discontinuous depending upon the amplitude of each type of noise.

We study the diluted Ising ferromagnet on the Bethe lattice as a case study for the application of the cavity method to problems with Griffiths-McCoy singularities. Specifically, we are able to make much progress at infinite coupling where we compute, from the cavity method, the density of Lee-Yang zeros in the paramagnetic Griffiths region as well as the properties of the phase transition to the ferromagnet. This phase transition is itself of a Griffiths-McCoy character albeit with a power law distribution of cluster sizes.

The origin of stress dip under the apex of a standard sandpile has stimulated significant debate within the scientific community. On the other hand, it could be argued that a semipile built against a vertical wall is of more practical interest since it serves as a model of dams, dykes, and embankments. There is surprisingly little information available for the stress distribution in this case. Here we show clear experimental evidence that the presence of the wall enhances the dip under a granular pile significantly. Our investigation provides insight into the influence of walls on the orientation of force chains and this appears to be key in enhancing the dip. Moreover, numerical simulations and experiments with different kinds of particles show that the vertical wall induces an alignment of isotropic particles.

The network of forces between contacts in a granular material determines the response of the material to an external perturbation. As the shear stress is increased, a static, rigid material can start to yield and flow as it becomes unjammed. The time- and ensemble-averaged distribution of forces shows a marked change in character at this jamming-unjamming transition. Here, we investigate the temporal fluctuations of the forces between individual particles and the external boundary in a dense, slowly sheared system. We find that the fluctuations occur over a very broad range of time scales, resulting in power spectra characterized by a $1/f$-type shape and a rollover to $1/f^2$ behavior above a turnover frequency $f^{\ast }$. At very low frequencies additional enhancements over the $1/f$ contributions are observed in regions of significant in-plane shear. Moreover, the magnitude of the force fluctuation spectra produced by one particle is different from those produced by its neighbors. Such heterogeneities persist over periods of time exceeding our measurement interval (60 h). In this respect they are reminiscent of the dynamic heterogeneities that occur in liquids supercooled toward the glass transition temperature.

The effect of glottal aerodynamics in producing the nonlinear characteristics of voice is investigated by comparing the outputs of the asymmetric composite model and the two-mass model. The two-mass model assumes the glottal airflow to be laminar, nonviscous, and incompressible. In this model, when the asymmetric factor is decreased from 0.65 to 0.35, only 1:1 and 1:2 modes are detectable. However, with the same parameters, four vibratory modes (1:1, 1:2, 2:4, 2:6) are found in the asymmetric composite model using the Navier-Stokes equations to describe the complex aerodynamics in the glottis. Moreover, the amplitude of the waveform is modulated by a small-amplitude noiselike series. The nonlinear detection method reveals that this noiselike modulation is not random, but rather it is deterministic chaos. This result agrees with the phenomenon often seen in voice, in which the voice signal is strongly periodic but modulated by a small-amplitude chaotic component. The only difference between the two-mass model and the composite model is in their descriptions of glottal airflow. Therefore, the complex aerodynamic characteristics of glottal airflow could be important in generating the nonlinear dynamic behavior of voice production, including bifurcation and a small-amplitude chaotic component obscured by strong periodicity.

In the crowded environment of the eukaryotic nucleus, the presence of intrinsic structural defects is shown to predispose chromatin fiber to spontaneously form rosettelike structures. These multilooped patterns self-organize through entropy-driven clustering of sequence-induced fiber defects by depletive forces prior to any external factors coming into play. They provide an attractive description of replication foci that are observed in interphase mammalian nuclei as stable chromatin domains of autonomous DNA replication and gene expression. Experimental perspectives for in vivo visualization of rosettelike organization of the chromatin fiber via the clustering of recently identified putative replication initiation zones are discussed.

A bifurcation criterion for the transition from straight to oscillatory quasistatic crack propagation in an isotropic material is derived from the requirement of pure mode I stress fields at the crack tip $\left(K_{\text{II}}=0\right)$ on the entire crack path, henceforth called global bifurcation criterion. For a small-amplitude sine-shaped crack path which is observed in experiments at the transition, it is shown to be sufficient to postulate $K_{\text{II}}=0$ only for two phases of the crack path instead, which simplifies calculations. By using the measured temperature fields to solve the thermoelastic problem of dipping a hot thin glass slab into cold water, critical wavelengths of the oscillating crack growth obtained with the derived global bifurcation criterion agree remarkably well with those observed in experiments by Ronsin and Perrin. It is also shown that local bifurcation criteria, which do not take into account $K_{\text{II}}=0$ on the entire crack path, lead to incorrect results for the oscillatory crack path instability.

We investigate the bifurcation cascades of a linear librational orbit in a generalized class of Hénon-Heiles potentials. The stability traces of the new orbits created at its bifurcations are found numerically to intersect linearly at the saddle energy $\left(e=1\right)$, forming what we term the “Hénon-Heiles fans.” In the limit close to the saddle energy $\left(e\to 1\right)$, where the dynamics is nearly chaotic, we derive analytical asymptotic expressions for the stability traces of both types of orbits and confirm the numerically determined properties of the generalized Hénon-Heiles fans. As a bonus of our results, we obtain analytical approximations for the bifurcation energies $e_n$ which become asymptotically exact for $e_n\to 1$.

The influence of time-delayed feedback on pattern formation in subexcitable media represented by a net of FitzHugh-Nagumo elements, a minimal model of neuronal dynamics, is studied. Without feedback, wave fronts die out after a short propagation length (subexcitable net dynamics). Applying time-delayed feedback with appropriate feedback parameters, pattern formation is sustained and the wave fronts may propagate through the whole net (signature of excitable behavior). The coherence of noise-induced patterns is significantly enhanced if feedback with appropriately chosen parameters is applied, and shows a resonancelike dependency on the delay time. In a next step, the transition to the excitable regime is investigated in dependence on the quota of elements, which get the feedback signal. It is sufficient to control approximately half of the elements to achieve excitable behavior. Regarding a medical application, where the external control of a neural tissue would affect not single neurons but clusters of neurons, the spatial correlation of the controlled elements is of importance. The selection of the elements, which get the feedback signal, is based on a spatially correlated random distribution. It is shown that the correlation length of this distribution affects the pattern formation.

Spontaneous imbibition phenomenon was modeled using the lattice Boltzmann method (LBM). The model was validated using silicon-etched micromodel and sandpack visualization experiments. The strongly water-wet model saturated with oil (kerosene or mineral oil) was exposed to distilled water in order for a capillary interaction to take place under static conditions. These experiments mimic the transfer between rock matrix and fracture during any wetting phase flow in fractures while the matrix contains a nonwetting phase as encountered in oil, gas, and geothermal reservoirs as well as during the application of subsurface ${\mathrm{CO}}_2$ sequestration or waste disposal reservoirs. Despite the vast amount of research work on this common process, pore-scale investigations and modeling are limited especially at small time scales. The results showed that the LBM captures the physics of the process at pore scale for low viscosity values of nonwetting phase for any type of (cocurrent or countercurrent imbibition) interaction.

We consider the deterministic escape dynamics of a chain of coupled oscillators under microcanonical conditions from a metastable state over a cubic potential barrier. The underlying dynamics is conservative and noise free. We introduce a two-dimensional chain model and assume that neighboring units are coupled by Morse springs. It is found that, starting from a homogeneous lattice state, due to the nonlinearity of the external potential the system self-promotes an instability of its initial preparation and initiates complex lattice dynamics leading to the formation of localized large amplitude breathers, evolving in the direction of barrier crossing, accompanied by global oscillations of the chain transverse to the barrier. A few chain units accumulate locally sufficient energy to cross the barrier. Eventually the metastable state is left and either these particles dissociate or pull the remaining chain over the barrier. We show this escape for both linear rodlike and coil-like configurations of the chain in two dimensions.

Microscopic theory of Brownian motion of a particle of mass $M$ in a bath of molecules of mass $m⪡M$ is considered beyond lowest order in the mass ratio $m∕M$. The corresponding Langevin equation contains nonlinear corrections to the dissipative force, and the generalized Fokker-Planck equation involves derivatives of order higher than 2. These equations are derived from first principles with coefficients expressed in terms of correlation functions of microscopic force on the particle. The coefficients are evaluated explicitly for a generalized Rayleigh model with a finite time of molecule-particle collisions. In the limit of a low-density bath, we recover the results obtained previously for a model with instantaneous binary collisions. In the general case, the equations contain additional corrections, quadratic in bath density, originating from a finite collision time. These corrections survive to order $(m∕M{)}^2$ and are found to make the stationary distribution non-Maxwellian. Some relevant numerical simulations are also presented.

We study the linear response in a soft potential, the Landau-type temperature dependence of which is responsible for the monostable-to-bistable transformation. The system can be considered as a model of a sample with internal noise, where a second-order phase transition takes place in the bulk limit. The intensity of noise influencing the order parameter is supposed to be a function of the volume. We demonstrate that the anomaly of susceptibility at the phase transition point described by the Landau phase transition theory transforms into the maximal response caused by stochastic resonance if the volume of the system decreases. The phenomenon can be treated also as an increase in the diffuseness of a phase transition with lowering of the critical temperature. We suggest that it is this crossover that contributes to the mechanism of dielectric peculiarities in ceramic and relaxor ferroelectrics.

We analyze the stability of sessile filaments (ridges) of nonvolatile liquids versus pearling in the case of externally driven flow along a chemical stripe within the framework of the thin-film approximation. The ridges can be stable with respect to pearling even if the contact line is not completely pinned. A generalized stability criterion for moving contact lines is provided. For large wavelengths and no driving force, within perturbation theory, an analytical expression of the growth rate of pearling instabilities is derived. A numerical analysis shows that a body force along the ridge further stabilizes the ridge by reducing the growth rate of unstable perturbations, even though there is no complete stabilization. Hence the stability criteria established in the absence of driven flow ensure overall stability.

We show that a generalized Landau theory for the smectic-$\mathit{A}$–smectic-$\mathit{C}$ (Sm-$\mathit{A}$–Sm-$\mathit{C}$) phases exhibits a biaxiality induced Sm-$\mathit{A}$–Sm-$\mathit{C}$ tricritical point. Proximity to this tricritical point depends on the degree of orientational order in the system; for sufficiently large orientational order the Sm-$\mathit{A}$–Sm-$\mathit{C}$ transition is three-dimensional $XY$-like, while for sufficiently small orientational order, it is either tricritical or first order. We investigate each of the three types of Sm-$\mathit{A}$–Sm-$\mathit{C}$ transitions near tricriticality and show that for each type of transition, small orientational order implies de Vries behavior in the layer spacing, an unusually small layer contraction. This result is consistent with, and can be understood in terms of, the “diffuse cone” model of de Vries. Additionally, we show that birefringence grows upon entry to the Sm-$\mathit{C}$ phase. For a continuous transition, this growth is more rapid the closer the transition is to tricriticality. Our model also predicts the possibility of a nonmontonic temperature dependence of birefringence.