In a nanoscale system out of thermodynamic equilibrium, it is important to account for thermal fluctuations. Typically, the thermal noise contributes fluctuations, e.g., of distances that are substantial in comparison to the size of the system and typical distances measured. If the thermal fluctuations are ignored, misinterpretation of measured quantities such as interaction forces, potentials, and constants may result. Here, we consider a particle moving in a time-dependent landscape, as, e.g., in an optical tweezers or atomic force nanoscopic measurement. Based on the Kramers equation [H. A. Kramers, Physica 7, 284 (1940)], we propose an approximate but quantitative way of dealing with such an out-of-equilibrium system. The limits of this approximate description of the escape process are determined through optical tweezers experiments and comparison to simulations. Also, this serves as a recipe for how to use the proposed method to obtain knowledge about the underlying energy landscape from a set of experimental measurements. Finally, we perform estimates of the error made if thermal fluctuations are ignored.

We present a multiscale simulation algorithm for amorphous materials, which we illustrate and validate in a canonical case of dense granular flow. Our algorithm is based on the recently proposed spot model, where particles in a dense random packing undergo chainlike collective displacements in response to diffusing “spots” of influence, carrying a slight excess of interstitial free volume. We reconstruct the microscopic dynamics of particles from the “coarse grained” dynamics of spots by introducing a localized particle relaxation step after each spot-induced block displacement, simply to enforce packing constraints with a (fairly arbitrary) soft-core repulsion. To test the model, we study to what extent it can describe the dynamics of up to 135 000 frictional, viscoelastic spheres in granular drainage simulated by the discrete-element method (DEM). With only five fitting parameters (the radius, volume, diffusivity, drift velocity, and injection rate of spots), we find that the spot simulations are able to largely reproduce not only the mean flow and diffusion, but also some subtle statistics of the flowing packings, such as spatial velocity correlations and many-body structural correlations. The spot simulations run over 100 times faster than the DEM and demonstrate the possibility of multiscale modeling for amorphous materials, whenever a suitable model can be devised for the coarse-grained spot dynamics.

Flexible spontaneously magnetized filaments exist in the living world (magnetotactic bacteria) and arise in magnetic colloids with large magnetodipolar interaction parameter. We demonstrate that these filaments possess variety of novel nonlinear phenomena in an ac magnetic field: orientation of the filament in the direction perpendicular to the field and the development of the oscillating U-like shapes, which presumably can lead to the formation of rings of magnetic filaments. It is found that these phenomena are determined by the development of the localized boundary modes of the filament deformation. We have illustrated by qualitative estimates that the phenomena found may be useful for insight into the complex pattern formation phenomena in ensembles of magnetic particles under the action of an ac magnetic field.

Experimentally grown ice crystals from ultrapure supercooled water are imaged by means of Mach-Zehnder interferometry. By analyzing the fringe patterns the phase information and thus the three-dimensional shape of the ice crystals is recovered quantitatively. The integral parameters height of the basal plane, volume, and surface of the crystals are measured as a function of time and supercooling. It is found that all measured parameters follow a power law as a function of time and the exponents are found to be independent of the supercooling. The shape transition from the prismatic to the basal face along the main growth direction of the ice dendrites as a function of the distance from the tip is found to be a power law as well. Our findings support the validity of universal growth laws in pattern forming systems.

We present a quantitative theory and experiments for the expansion dynamics of domains in stratifying foam films. Foam films containing micelles, colloidal particles or polymer-surfactant complexes often form layered structures and thin in a stepwise fashion: circular domains of lower thickness are formed and expand following a $R\left(t\right)\propto t^{1∕2}$ law. In the present paper the film is modeled by an incompressible three-dimensional fluid with incompressible surfaces. The film tension difference between the film and domains results in the formation of a rim at the domain boundary and a gradient in film thickness and pressure in the surrounding film. The material transport due to this gradient lets the domains grow. We present experiments utilizing the thin balance method to qualitatively confirm the thinning mechanism and to determine material parameters including local film viscosity of a film composed of $4400\mathrm{ppm}$ acrylamide/acrylamidomethylpropanesulfonate-copolymer and $0.06\mathrm{mmol}∕\mathrm{l}$ dodecyltrimethylammonium bromide solution. We found a film viscosity of about 60 times the bulk viscosity, consistent with previous measurement in the same system but using another method.

Langmuir monolayers of stearic acid on Co ions in the aqueous subphase have been deposited at different stages of constant pressure collapse, on hydrophilic Si(001) using a modified version of the inverse Langmuir-Schaefer method of horizontal deposition. The electron density profiles (EDPs) along the depth of the deposited films, extracted from the x-ray reflectivity data, show that a monolayer to bi-molecular layer transformation takes place after collapse. The molecules in the lower monolayer have asymmetric configurations with head groups touching water and tails in air, whereas molecules in the upper layer are in symmetric configurations with tails on both sides of the heads. Atomic force microscopy images of the deposited films after collapse, however, show nearly circular islands of height more than that of the bimolecular layer observed in the EDP. As pressure increases, ridges are seen to coexist with these islands. Although the coverage of such islands and ridges is low, they play an important role in determining the growth mode. The growth of the wetting and island layers, taken together, has a striking similarity with the Stranski-Krastanow mode, observed usually for heteroepitaxial growth.

We use the empirical mode decomposition method to decompose experimental respiratory signals into a set of intrinsic mode functions (IMFs), and consider one of these IMFs as a respiratory rhythm. We then use the Hilbert spectral analysis to calculate the instantaneous phase of the IMF. Heartbeat data are finally incorporated to construct the cardiorespiratory synchrogram, which is a visual tool for inspecting synchronization. We perform analysis on 20 data sets collected by the Harvard medical school from ten young ($21–34\text{years}$ old) and ten elderly ($68–81\text{years}$ old) rigorously screened healthy subjects. Our results support the existence of cardiorespiratory synchronization. We also investigate the origin of the cardiorespiratory synchronization by addressing the problem of correlations between regularities of respiratory and cardiac signals. Our analysis shows that regularity of respiratory signals plays a dominant role in the cardiorespiratory synchronization.

Physiological systems generate complex fluctuations in their output signals that reflect the underlying dynamics. The base-scale entropy method was proposed as a complexity measure to investigate the complexity of time series. The advantages of this method are simplicity and extremely fast calculation for very short data sets. This method enables analyzing very short, nonstationary, and noisy data sets. We employed this method for short-term physiological time series for analysis of heart-rate variability signals. The results show that the simple and easily calculated measure can effectively detect the complexity dissimilarity of physiological time series in different physiological or pathological states, which is convenient for clinical applications.

We investigate the dynamics of a semiconductor laser subject to coherent delayed filtered optical feedback. A systematic bifurcation analysis reveals that this system supports two fundamentally different types of oscillations, namely relaxation oscillations and external roundtrip oscillations. Both occur stably in large domains under variation of the feedback conditions, where the feedback phase is identified as a key quantity for controlling this dynamical complexity. We identify two separate parameter regions of stable roundtrip oscillations, which occur throughout in the form of pure frequency oscillations.

An elliptic model for space-time correlations in turbulent shear flows is proposed based on a second order approximation to the iso-correlation contours, while Taylor’s hypothesis implies a first-order approximation. It is shown that the space-time correlations are mainly determined by their space correlations and the convection and sweeping velocities. This model accommodates two extreme cases: Taylor’s hypothesis at vanishing sweeping velocity and the sweeping hypothesis at vanishing convection velocity. The result is supported by the data from the direct numerical simulation of turbulent channel flows.

We analyze a model that interpolates between scale-free and Erdos-Rényi networks. The model introduced generates a one-parameter family of networks and allows one to analyze the role of structural heterogeneity. Analytical calculations are compared with extensive numerical simulations in order to describe the transition between these two important classes of networks. Finally, an application of the proposed model to the study of the percolation transition is presented.

Periodic spatiotemporal two-dimensional (2D) asymptotic patterns in an excitable two-variable thermochemical (reaction-diffusion) system are shown. In a one-dimensional system the traveling impulse which reflects from impermeable boundaries is a stable asymptotic solution if the diffusion coefficient of the reactant is greater than the thermal diffusivity of the system. Periodic patterns of two symmetries are presented in the 2D system: the impulse of excitation propagating along the diagonal of a square spatial domain and a structure consisting of curved impulses which propagate in the direction perpendicular to one side of a rectangular domain.

Fine particles agglomerate in the fluidized state due to the strength of interparticle attractive forces as compared to particle weight. Interparticle adhesion can be largely increased by consolidation stresses applied during powder handling. As a consequence, fragments of the consolidated powder may persist when the powder is fluidized, which gives rise to large agglomerates of strongly adhered particles in fluidization. This history-dependent effect can be minimized by coating the particles with surface additives such as silica nanoparticles. In this paper, we investigate the effect of high consolidation stresses ${\sigma }_c$ previously applied to samples of silica-coated fine particles on their fluidization behavior. Our experimental measurements show that, even though homogeneous fluidization is still observed, the average agglomerate size and fractal dimension of the agglomerates increase as ${\sigma }_c$ is increased. Bed expansion in the fluidized state is hindered by previously applied high consolidations, which we attribute to an increase of the largest stable size of mesoscopic fluid pockets. As a consequence, we observe that the initiation of macroscopic bubbling is delayed up to larger values of the fluid velocity.

The mean electromotive force caused by turbulence of an electrically conducting fluid, which plays a central part in mean-field electrodynamics, is calculated for a rotating fluid. Going beyond most of the investigations on this topic, an additional mean motion in the rotating frame is taken into account. One motivation for our investigation originates from a planned laboratory experiment with a Ponomarenko-type dynamo. In view of this application the second-order correlation approximation is used. The investigation is of high interest in astrophysical context, too. Some contributions to the mean electromotive are revealed which have not been considered so far, in particular contributions to the $\alpha$ effect and related effects due to the gradient of the mean velocity. Their relevance for dynamo processes is discussed. In a forthcoming paper the results reported here will be specified to the situation in the laboratory and partially compared with experimental findings.

Shift and broadening of isolated neutral helium lines $7281\mathrm{\AA }$ $(2^{1}P-3^{1}S)$, $7065\mathrm{\AA }$ $(2^{3}P-3^{3}S)$, $6678\mathrm{\AA }$ $(2^{1}P-3^{1}D)$, $5048\mathrm{\AA }$ $(2^{1}P-4^{1}S)$, $4922\mathrm{\AA }$ $(2^{1}P-4^{1}D)$, and $4713\mathrm{\AA }$ $(2^{3}P-4^{3}S)$ in a dense plasma are investigated. Based on a quantum statistical theory, the electronic contributions to the shift and width are considered, using the method of thermodynamic Green functions. Dynamic screening of the electron-atom interaction is included. Compared to the width, the electronic shift is more affected by dynamical screening. This effect increases at high density. A cut-off procedure for strong collisions is used. The contribution of the ions is taken into account in a quasi-static approximation, with both the quadratic Stark effect and the quadrupole interaction included. The results for shift and width agree well with the available experimental and theoretical data.

The electromagnetic energy flux vector in a dispersive linear medium is derived from energy conservation and microscopic quantum electrodynamics and is found to be of the Umov form as the product of an electromagnetic energy density and a velocity vector.

We study statistical properties of excited levels of the $\mathrm{E}\otimes (b_1+b_2)$ Jahn-Teller model. The multitude of avoided crossings of energy levels is generally claimed to be a testimony of quantum chaos. We found that apart from two limiting cases ($E\otimes e$ and Holstein model) the distribution of nearest-neighbor spacings is rather stable as to the change of parameters and different from the Wigner one. This limiting distribution assumably shows scaling $\sim \sqrt{S}$ at small $S$ and resembles the semi-Poisson law $P\left(S\right)=4S\exp (-2S)$ at $S\ge 1$. The latter is believed to be universal and characteristic, e.g., at the transition between metal and insulator phases.

Anti-phase synchronization (AS) in coupled chaotic oscillators is investigated. The necessary condition for AS is given and the stability of AS is studied. Results are demonstrated with numerical simulations and electronic circuits.

Avalanche experiments on an erodible substrate are analyzed using the “partial fluidization” model of dense granular flows. The model identifies a family of propagating solitonlike avalanches with shape and velocity controlled by the inclination angle and the depth of the substrate. At high inclination angles, the solitons display a transverse instability, followed by coarsening and fingering similar to recent experimental observation. A primary cause for the transverse instability is directly related to the dependence of the soliton velocity on the granular mass trapped in the avalanche.

According to a recently developed density functional theory, athermal polymer solutions, in which the solvent particles are smaller than the monomers, may undergo a bulk fluid-fluid phase separation, driven by excluded volume effects. In recent work, we showed that an inert surface immersed in the dilute polymer phase can, in principle, be wetted by the condensed phase. However, we show here that the “prewetting transition” we assumed in our earlier studies is in fact a different type of surface transition. Rather than completely wet the surface at coexistence, the condensed phase layer which forms in the presence of the dilute bulk remains globally stable (and is finite in width) even as the bulk coexistence conditions are approached. Hence, the adsorbed phase inhibits complete wetting of the surface by the dilute phase. The surface transition is first order for the systems we study here and, for longer polymers, the surface phase coexistence line meets the bulk coexistence curve nontangentially to give rise to a lower transition point. For short polymers, we find that the surface transition can occur for a supercritical bulk. We develop a simple one-component thermal model, which displays analogous behavior at an adsorbing surface and provides us with some insight into the qualitative mechanisms responsible.