We present experimental results for the friction of a flat surface against a hexagonally patterned surface, both being made of PolyDiMethylSiloxane. We simultaneously measure forces of range $10\text{m}\text{N}$ and observe the contact under sliding velocities of about $100\mu \text{m}/\text{s}$. We observe adhesive friction on three different pattern heights (80, 310, and 2100 nm). Two kinds of contacts have been observed: the flat surface is in close contact with the patterned one (called intimate contact, observed for 80 nm) or only suspended on the tops on the asperities (called laid contact, observed for 2100 nm). In the range of velocities used, the contact during friction is similar to the static one. Furthermore, our experimental system presents a contact transition during friction for $h=310\text{nm}$.

We develop and analyze a scheme to achieve both spatial and energetic focusing of an ensemble of neutral particles which is based on an oscillating billiard with frictional forces. The interplay of two competing mechanisms, acceleration due to collisions with the oscillating billiard walls and deceleration caused by friction, leads to the emergence of attractors in phase space. Their specific properties, i.e., spatial localization and energy spread, can be controlled and tuned by varying, e.g., the frequency of the time-dependent billiard.

Nonlinear time series analysis is an active field of research that studies the structure of complex signals in order to derive information of the process that generated those series, for understanding, modeling and forecasting purposes. In the last years, some methods mapping time series to network representations have been proposed. The purpose is to investigate on the properties of the series through graph theoretical tools recently developed in the core of the celebrated complex network theory. Among some other methods, the so-called visibility algorithm has received much attention, since it has been shown that series correlations are captured by the algorithm and translated in the associated graph, opening the possibility of building fruitful connections between time series analysis, nonlinear dynamics, and graph theory. Here we use the horizontal visibility algorithm to characterize and distinguish between correlated stochastic, uncorrelated and chaotic processes. We show that in every case the series maps into a graph with exponential degree distribution $P\left(k\right)\sim \text{exp}\left(-\lambda k\right)$, where the value of $\lambda$ characterizes the specific process. The frontier between chaotic and correlated stochastic processes, $\lambda =\text{ln}\left(3/2\right)$, can be calculated exactly, and some other analytical developments confirm the results provided by extensive numerical simulations and (short) experimental time series.

In the early days of stable single-bubble sonoluminescence, it was strongly debated whether the emission was blackbody radiation or whether the bubble was transparent to its own radiation (volume emission). Presently, the volume emission picture is nearly universally accepted. We present new measurements of spectra with apparent color temperatures ranging from 6000 to 21 000 K. We show through data collapse that within experimental uncertainty, apart from a constant, the spectra of strongly driven stable single-bubble sonoluminescence in water can be written as the product between a universal function of wavelength and a functional form that only depends on wavelength and apparent temperature but has no reference to any other parameter specific to the experimental situation. This remarkable result does question our theoretical understanding of the state of the plasma in the interior of strongly driven stable sonoluminescent bubbles.

In this paper we predict and simulate a peculiar type of compressive shock in a real gas modeled by the van der Waals constitutive equation. This shock produces a phase transition from the gas to the liquid phase and, under some special circumstances, back to the gas phase. This shock has a quite unusual property that when the perturbed pressure (the pressure after a shock) increases, the perturbed density decreases and tends to a limit value from above, in contrast with the ordinary well-known compressive shock in which the density tends to the limit value from below. To achieve such a compressive upper shock, it is necessary to choose the unperturbed state (the state before the shock) in a very thin region in the $\rho p$ plane, characterized by low values of density and pressure, near the gas-liquid coexistence curve. This region, which depends on the internal degrees of freedom of a constituent molecule, is completely identified.

We observe that the fully nonlinear evolution equations of Rosenau and Hymann, often abbreviated as $K\left(n,m\right)$ equations, can be reduced to Hamiltonian form only on a zero-energy hypersurface belonging to some potential function associated with the equations. We treat the resulting Hamiltonian equations by the dynamical systems theory and present a phase-space analysis of their stable points. The results of our study demonstrate that the equations can, in general, support both compacton and soliton solutions. For the $K\left(2,2\right)$ and $K\left(3,3\right)$ cases one type of solutions can be obtained from the other by continuously varying a parameter of the equations. This is not true for the $K\left(3,2\right)$ equation for which the parameter can take only negative values. The $K\left(2,3\right)$ equation does not have any stable point and, in the language of mechanics, represents a particle moving with constant acceleration.

We extend our earlier study about the fractional exclusion statistics to higher dimensions in full physical range and in the nonrelativistic and ultrarelativistic limits. Also, two other fractional statistics, namely, Gentile and Polychronakos fractional statistics, will be considered and similarities and differences between these statistics will be explored. Thermodynamic geometry suggests that a two dimensional Haldane fractional exclusion gas is more stable than higher dimensional gases. Also, a complete picture of attractive and repulsive statistical interaction of fractional statistics is given. For a special kind of fractional statistics, by considering the singular points of thermodynamic curvature, we find a condensation for a nonpure bosonic system which is similar to the Bose-Einstein condensation and the phase transition temperature will be worked out.

An evolution of $\text{Sm-}{C}_A^{\ast }$, biaxial intermediate phases, and $\text{Sm-}{C}^{\ast }$ in the electric field is investigated in a framework of molecular-statistical approach [A. V. Emelyanenko et al.., Phys. Rev. E 74, 011705 (2006); A. V. Emelyanenko, Eur. Phys. J. E 28, 441 (2009)]. The “electric field–temperature” phase diagrams including the possibility of existence of various tilted smectic phases are plotted and compared with the experimental ones. Permanent transverse molecular dipole moments (without electric field participating only in the spontaneous polarization) were also found to generate the induced polarization in the presence of electric field and to produce very strong dielectriclike effect. This effect is positive in $\text{Sm-}{C}^{\ast }$ (tilt planes have a tendency of orienting along or against the electric field) and is negative in $\text{Sm-}{C}_A^{\ast }$ and in biaxial intermediate phases (tilt planes have a tendency of orienting perpendicular to the electric field). In the ferrielectric intermediate phases both spontaneous and induced polarizations favor similar tendencies and provide the helix unwinding at very low electric field. At the same time, the tendencies provided by spontaneous and induced polarizations are opposite in $\text{Sm-}{C}^{\ast }$, and therefore the unwinding threshold is larger. It was shown that interplay between spontaneous and induced polarizations can lead to the formation of complex bidomain smectic structures. A single parameter regulating an evolution of structure of $\text{Sm-}{C}^{\ast }$, $\text{Sm-}{C}_A^{\ast }$, and biaxial intermediate phases in the electric field was found. We suppose that bidomain helical structure is the same as additional ferrielectric phase FiLC existing in some materials just below $\text{Sm-}{C}^{\ast }$. The numerical calculations are done with help of AFLC phase diagram plotter software developed by the author and available at his webpage.

The droplet coalescence process was investigated in immiscible polymer blends when subjected to a step electric field. We present sequential three-dimensional images captured during the process with a confocal scanning laser microscope. Characteristic lengths parallel and perpendicular to the electric field were obtained from the spatial correlation functions of the images. It was found that the droplet growth rate increased with both the electric field and the volume fraction of droplets. A function describing the droplet growth rate was derived from theory using the “hierarchical model” and was found to be in good agreement with the experimental results.

We have examined the temperature dependence of noise-induced escape rate of Brownian particles between two distinct regions in a two-dimensional enclosure through a narrow bottleneck. Varying cross section of the confinement results in an effective entropic barrier in reduced dimension. The strong non-Arrhenius dependence of the escape rate is observed, which can be explained in terms of a crossover between entropy-dominated regime and energy-dominated regime in presence of an interplay of gravitational bias and thermal motion.

At the mesoscale friction occurs through the breaking and formation of local contacts. This is often described by the earthquakelike model which requires numerical studies. We show that this phenomenon can also be described by a master equation, which can be solved analytically in some cases and provides an efficient numerical solution for more general cases. We examine the effect of temperature and aging of the contacts and discuss the statistical properties of the contacts for different situations of friction and their implications, particularly regarding the existence of stick-slip.

The origin of economic crises is a key problem for economics. We present a model of long-run competitive markets to show that the multiplicity of behaviors in an economic system, over a long time scale, emerge as statistical regularities (perfectly competitive markets obey Bose-Einstein statistics and purely monopolistic-competitive markets obey Boltzmann statistics) and that how interaction among firms influences the evolutionary of competitive markets. It has been widely accepted that perfect competition is most efficient. Our study shows that the perfectly competitive system, as an extreme case of competitive markets, is most efficient but not stable, and gives rise to economic crises as society reaches full employment. In the economic crisis revealed by our model, many firms condense (collapse) into the lowest supply level (zero supply, namely, bankruptcy status), in analogy to Bose-Einstein condensation. This curious phenomenon arises because perfect competition (homogeneous competitions) equals symmetric (indistinguishable) investment direction, a fact abhorred by nature. Therefore, we urge the promotion of monopolistic competition (heterogeneous competitions) rather than perfect competition. To provide early warning of economic crises, we introduce a resolving index of investment, which approaches zero in the run-up to an economic crisis. On the other hand, our model discloses, as a profound conclusion, that the technological level for a long-run social or economic system is proportional to the freedom (disorder) of this system; in other words, technology equals the entropy of system. As an application of this concept, we give a possible answer to the Needham question: “Why was it that despite the immense achievements of traditional China it had been in Europe and not in China that the scientific and industrial revolutions occurred?”

We propose a protocol optimization technique that is applicable to both weighted and unweighted graphs. Our aim is to explore by how much a small variation around the shortest-path or optimal-path protocols can enhance protocol performance. Such an optimization strategy can be necessary because even though some protocols can achieve very high traffic tolerance levels, this is commonly done by enlarging the path lengths, which may jeopardize scalability. We use ideas borrowed from extremal optimization to guide our algorithm, which proves to be an effective technique. Our method exploits the degeneracy of the paths or their close-weight alternatives, which significantly improves the scalability of the protocols in comparison to shortest-path or optimal-path protocols, keeping at the same time almost intact the length or weight of the paths. This characteristic ensures that the optimized routing protocols are composed of paths that are quick to traverse, avoiding negative effects in data communication due to path-length increases that can become specially relevant when information losses are present.

The optimal amplifications of small coherent perturbations within turbulent pipe flow are computed for Reynolds numbers up to one million. Three standard frameworks are considered: the optimal growth of an initial condition, the response to harmonic forcing and the Karhunen-Loève (proper orthogonal decomposition) analysis of the response to stochastic forcing. Similar to analyses of the turbulent plane channel flow and boundary layer, it is found that streaks elongated in the streamwise direction can be greatly amplified from quasistreamwise vortices, despite linear stability of the mean flow profile. The most responsive perturbations are streamwise uniform and, for sufficiently large Reynolds number, the most responsive azimuthal mode is of wave number $m=1$. The response of this mode increases with the Reynolds number. A secondary peak, where $m$ corresponds to azimuthal wavelengths ${\lambda }_{\theta }^{+}\approx 70–90$ in wall units, also exists in the amplification of initial conditions and in premultiplied response curves for the forced problems. Direct numerical simulations at $\text{Re}=5300$ confirm that the forcing of $m=1,2$ and $m=4$ optimal structures results in the large response of coherent large-scale streaks. For moderate amplitudes of the forcing, low-speed streaks become narrower and more energetic, whereas high-speed streaks become more spread. It is further shown that drag reduction can be achieved by forcing steady large-scale structures, as anticipated from earlier investigations. Here the energy balance is calculated. At $\text{Re}=5300$ it is shown that, due to the small power required by the forcing of optimal structures, a net power saving of the order of 10% can be achieved following this approach, which could be relevant for practical applications.

We validate experimentally the Kapitsa-Shkadov model utilized in the theoretical studies by Demekhin et al. [Phys. Fluids 19, 114103 (2007); Phys. Fluids 19, 114104 (2007)] of surface turbulence on a thin liquid film flowing down a vertical planar wall. For water at $15°$, surface turbulence typically occurs at an inlet Reynolds number of $\simeq 40$. Of particular interest is to assess experimentally the predictions of the model for three-dimensional nonlinear localized coherent structures, which represent elementary processes of surface turbulence. For this purpose we devise simple experiments to investigate the instabilities and transitions leading to such structures. Our experimental results are in good agreement with the theoretical predictions of the model. We also perform time-dependent computations for the formation of coherent structures and their interaction with localized structures of smaller amplitude on the surface of the film.

We present a generalized nonlinear susceptibility retrieval method for metamaterials based on transfer matrices and valid in the nondepleted pump approximation. We construct a general formalism to describe the transfer matrix method for nonlinear media and apply it to the processes of three- and four-wave mixing. The accuracy of this approach is verified via finite element simulations. The method is then reversed to give a set of equations for retrieving the nonlinear susceptibility. Finally, we apply the proposed retrieval operation to a three-wave mixing transmission experiment performed on a varactor loaded split ring resonator metamaterial sample and find quantitative agreement with an analytical effective medium theory model.

Here, we use molecular simulation to consider the behavior of a thin nematic film confined between two identical nanopatterned substrates. Using patterns involving alternating stripes of homeotropic-favoring and homogeneous-favoring substrates, we investigate the influence of the relative stripe width and the film thickness. From this, we show that the polar anchoring angle can be varied continuously from planar to homeotropic by appropriate tuning of these parameters. For very thin films with equal stripe widths, we observe orientational bridging, the surface patterning being written in domains which traverse the nematic film. This dual-bridging-domain arrangement breaks down with increase in film thickness, however, being replaced by a single tilted monodomain. Strong azimuthal anchoring in the plane of the stripe boundaries is observed for all systems.

We study the thermal and mechanical behaviors of DNA denaturation in the frame of the mesoscopic Peyrard-Bishop-Dauxois model with the inclusion of solvent interaction. By analyzing the melting transition of a homogeneous A-T sequence, we are able to set suitable values of the parameters of the model and study the formation and stability of bubbles in the system. Then, we focus on the case of the P5 promoter sequence and use the principal component analysis of the trajectories to extract the main information on the dynamical behavior of the system. We find that this analysis method gives an excellent agreement with previous biological results.

In the Comment by Choi et al. [Phys. Rev. E 82, 013901 (2010)] on two our articles [Phys. Rev. E 72, 061907 (2005); Phys. Rev. E 79, 021910 (2009)], it is claimed that (a) there is more than one natural frequency associated with the quadruple mode and (b) the quadruple mode shows resonance more closely at the characteristic frequency ${\omega }_{\text{T}}/2\pi$ than at ${\omega }_{\text{K}}/2\pi$. In this Reply we would like to provide evidence supporting the conclusions made in our original articles.