In the present paper we propose a van der Waals–like model that allows a purely analytical study of fluid properties including the equation of state, phase behavior, and supercritical fluctuations. We take a square-well system as an example and calculate its liquid-gas transition line and supercritical fluctuations. Employing this model allows us to calculate not only the thermodynamic response functions (isothermal compressibility ${\beta }_T$, isobaric heat capacity $C_P$, density fluctuations ${\zeta }_T$, and thermal expansion coefficient ${\alpha }_T$), but also the correlation length in the fluid $\xi$. It is shown that the bunch of extrema widens rapidly upon departure from the critical point. It seems that the Widom line defined in this way cannot be considered as a real boundary that divides the supercritical region into gaslike and liquidlike regions. As it has been shown recently, a dynamic line on the phase diagram in the supercritical region, namely, the Frenkel line, can be used for this purpose.

We present numerical results of the effect that the driving force has on the clogging probability of inert particles passing through a bottleneck. When the driving force is increased by four orders of magnitude, the mean avalanche size remains almost unaltered (increases $1.6$ times) while the flow rate and the avalanche duration display strong dependence on this magnitude. This indicates that in order to characterize the ability of a system to clog, the right variable to consider is the number of particles that pass through the outlet. The weak dependence of this magnitude on the driving force is explained in terms of the average kinetic energy of the flowing grains that has to be dissipated in order to get an arch stabilized.

We analyze numerically the problem of spontaneous symmetry breaking and migration of a three-dimensional vesicle [a model for red blood cells (RBCs)] in axisymmetric Poiseuille flow. We explore the three relevant dimensionless parameters: (i) capillary number, $C_a$, measuring the ratio between the flow strength over the membrane bending mode, (ii) the ratio of viscosities of internal and external liquids, $\lambda$, and (iii) the reduced volume, $\nu =[V/(4/3)\pi ]/{(A/4\pi )}^{3/2}$ ($A$ and $V$ are the area and volume of the vesicle). The overall picture turns out to be quite complex. We find that the parachute shape undergoes spontaneous symmetry-breaking bifurcations into a croissant shape and then into slipper shape. Regarding migration, we find complex scenarios depending on parameters: The vesicles either migrate towards the center, or migrate indefinitely away from it, or stop at some intermediate position. We also find coexisting solutions, in which the migration is inwards or outwards depending on the initial position. The revealed complexity can be exploited in the problem of cell sorting out and can help understanding the evolution of RBCs' in vivo circulation.

Growing network models with both heterogeneity of the nodes and topological constraints can give rise to a rich phase structure. We present a simple model based on preferential attachment with rewiring of the links. Rewiring probabilities are modulated by the negative fitness of the nodes and by the constraint for the network to be a simple graph. At low temperatures and high rewiring rates, this constraint induces a Bose-Einstein condensation of paths of length 2, i.e., a new phase transition with an extended condensate of links. The phase space of the model includes further transitions in the size of the connected component and the degeneracy of the network.

An approach to obtaining a parsimonious polynomial model from time series is proposed. An optimal minimal nonuniform time series embedding schema is used to obtain a time delay kernel. This scheme recursively optimizes an objective functional that eliminates a maximum number of false nearest neighbors between successive state space reconstruction cycles. A polynomial basis is then constructed from this time delay kernel. A sparse model from this polynomial basis is obtained by solving a regularized least squares problem. The constraint satisfaction problem is made computationally tractable by keeping the ratio between the number of constraints to the number of variables small by using fewer samples spanning all regions of the reconstructed state space. This helps the structure selection process from an exponentially large combinatorial search space. A forward stagewise algorithm is then used for fast discovery of the optimization path. Results are presented for the Mackey-Glass system.

We investigate the mobility of nonlinear localized modes in a generalized discrete Ginzburg-Landau-type model, describing a one-dimensional waveguide array in an active Kerr medium with intrinsic, saturable gain and damping. It is shown that exponentially localized, traveling discrete dissipative breather-solitons may exist as stable attractors supported only by intrinsic properties of the medium, i.e., in the absence of any external field or symmetry-breaking perturbations. Through an interplay by the gain and damping effects, the moving soliton may overcome the Peierls-Nabarro barrier, present in the corresponding conservative system, by self-induced time-periodic oscillations of its power (norm) and energy (Hamiltonian), yielding exponential decays to zero with different rates in the forward and backward directions. In certain parameter windows, bistability appears between fast modes with small oscillations and slower, large-oscillation modes. The velocities and the oscillation periods are typically related by lattice commensurability and exhibit period-doubling bifurcations to chaotically “walking” modes under parameter variations. If the model is augmented by intersite Kerr nonlinearity, thereby reducing the Peierls-Nabarro barrier of the conservative system, the existence regime for moving solitons increases considerably, and a richer scenario appears including Hopf bifurcations to incommensurately moving solutions and phase-locking intervals. Stable moving breathers also survive in the presence of weak disorder.

The instabilities and transitions of flow in an annular container with a heated bottom, a cooled top, and insulated sidewalls are studied numerically. The instabilities of the static diffusive state and of axisymmetric flows are investigated by linear stability analysis. The onset of convection is independent of the Prandtl number but determined by the geometry of the annulus, i.e., the aspect ratio $\Gamma$ (outer radius to height) and radius ratio $\delta$ (inner radius to outer radius). The stability curves for onset of convection are presented for $0.001\le \delta \le 0.8$ at six fixed aspect ratios: $\Gamma =1$, 1.2, 1.6, 1.75, 2.5, and 3.2. The instability of convective flow (secondary instability), which depends on both the annular geometry and the Prandtl number, is studied for axisymmetric convection. Two pairs of geometric control parameters are chosen to perform the secondary instability analysis—$\Gamma =1.2$, $\delta =0.08$ and $\Gamma =1.6$, $\delta =0.2$—and the Prandtl number ranges from 0.02 to 6.7. The secondary instability exhibits some similarities to that for convection in a cylinder. A hysteresis stability loop is found for $\Gamma =1.2$, $\delta =0.08$ and frequent changes of critical mode with Prandtl number are found for $\Gamma =1.6$, $\delta =0.2$. The three-dimensional flows beyond the axisymmetry-breaking bifurcations are obtained by direct numerical simulation for $\Gamma =1.2$, $\delta =0.08$.

In this paper we consider the surfatron acceleration of relativistic charged particles by a strong electrostatic wave propagating in a transverse direction relative to the background magnetic field. We investigate how high-frequency fluctuations of the background magnetic field affect the process of the resonant acceleration. We show that the presence of fluctuations leads to particle escape from the surfatron resonance and illustrate that fluctuations of different components of the magnetic field have quite a distinct effect on the energy gained by particles. In the case of the same power density, the strongest effect corresponds to fluctuations of the component directed along the background magnetic field, while the effect of the component along the wave front is substantially weaker. This is more important for particles with a large velocity component along the background magnetic field. We demonstrate that the dynamics of particles can statistically be described in terms of the adiabatic invariant diffusion. We derive the corresponding diffusion equation and compare solutions of that equation with results obtained by the explicit particle tracing.

We report a combined dynamic light scattering and neutron spin-echo (NSE) study on vesicles composed of the phospholipid 1,2-dimyristoyl-sn-glycero-3-phosphatidylcholine under the influence of varying amounts of perfluorooctanoic acid. We study local lipid bilayer undulations using NSE on time scales up to 200 ns. Similar to the effect evoked by cholesterol, we attribute the observed lipid bilayer stiffening to a condensing effect of the perfluorinated compound on the membrane.

We derive an exact equation governing two-particle backwards mean-squared dispersion for both deterministic and stochastic tracer particles in turbulent flows. For the deterministic trajectories, we probe the consequences of our formula for short times and arrive at approximate expressions for the mean-squared dispersion which involve second order structure functions of the velocity and acceleration fields. For the stochastic trajectories, we analytically compute an exact $t^3$ contribution to the squared separation of stochastic paths. We argue that this contribution appears also for deterministic paths at long times and present direct numerical simulation results for incompressible Navier-Stokes flows to support this claim. We also numerically compute the probability distribution of particle separations for the deterministic paths and the stochastic paths and show their strong self-similar nature.

We present a statistical physics framework for the description of nonlinear nonequilibrium stochastic processes, modeled via a chemical master equation, in the weak-noise limit. Using the Poisson-representation approach and applying the large-deviation principle, we first solve the master equation. Then we use the notion of the nonequilibrium free energy to derive an integral fluctuation relation for nonlinear nonequilibrium systems under feedback control. We point out that the free energy as well as some functionals can serve as a nonequilibrium Lyapunov function which has an important property to decay monotonously to its minimal value at all times. The Poisson-representation technique is illustrated via exact stochastic treatment of biophysical processes, such as bacterial chemosensing and molecular evolution.

We present a mean-field model for abnormal grain growth processes described by competition of both deterministic and stochastic mechanisms with the grain mobility depending on the grain size. The derived approach is applied to study delayed dynamics of grain growth in system of point defects subjected to irradiation according to the swelling rate theory for irradiated materials. We have shown that with the irradiation dose increase, the corresponding grain growth dynamics is slowed down and growth processes with power-law time asymptotics are realized. We discuss behavior of grain size distributions with competing regular and fluctuation mechanisms.

We investigated local layer structures of the three smectic-$C$ phases (Sm$C$, Sm$C^{\prime }$, and Sm$C^{″}$) in a liquid crystal with the terminal hydroxyl group using high resolution and microbeam x-ray diffraction. It is found that Sm$C$ is the conventional Sm$C_1$ phase and Sm$C^{″}$ is the bilayer Sm$C_2$ phase. The Sm$C^{\prime }$ phase forms an in-plane modulation structure, so that this phase is the smectic-$C$ antiphase. From the Fourier transform infrared spectroscopy, it is suggested that the intermolecular hydrogen bonding is important to induce the Sm$C^{\prime }$ and Sm$C^{″}$ phases.

A near-infrared optical tomography approach for detection, three-dimensional localization, and cross-section imaging of fluorescent targets in a turbid medium is introduced. The approach uses multisource probing of targets, multidetector acquisition of diffusely transmitted fluorescence signal, and a non-negative matrix factorization based blind source separation scheme to obtain three-dimensional location of the targets. A Fourier transform back-projection algorithm provides an estimate of target cross section. The efficacy of the approach is demonstrated in an experiment involving two laterally separated small fluorescent targets embedded in a human breast tissue-simulating sample of thickness 60 times the transport mean free path. The approach could locate the targets within ∼1 mm of their known positions, and provide estimates of their cross sections. The high spatial resolution, fast reconstruction speed, noise tolerance, and ability to detect small targets are indicative of the potential of the approach for detecting and locating fluorescence contrast-enhanced breast tumors in early growth stages, when they are more amenable to treatment.

The fractality and self-similarity of complex networks have been widely investigated by evaluating the fractal dimension, the crux of which is how to locate the optimal solution or how to tile the network with the fewest boxes. The results yielded by the box-covering method with separated boxes possess great randomness or large errors. In this paper, we adopt the overlapping box to tile the entire network, called the overlapping-box-covering method. In such a case, for verifying its validity, we propose an overlapping-box-covering algorithm; we first apply it to three deterministic networks, then to four real-world fractal networks. It produces optimums or more accurate fractal dimension for the former; the quantities of boxes finally obtained for the latter are fewer and more deterministic, with the redundant box reaching up to 33.3%. The experimental results show that the overlapping-box-covering method is available and that the overlapping box outperforms the previous case, rendering the errors smaller. Moreover, we conclude that the overlapping box is an important determinant to acquire the fewest boxes for complex networks.

The effects of a periodic forcing on chaotic scattering are relevant in certain situations of physical interest. We investigate the effects of the forcing amplitude and the external frequency in both the survival probability of the particles in the scattering region and the exit basins associated to phase space. We have found an exponential decay law for the survival probability of the particles in the scattering region. A resonant-like behavior is uncovered where the critical values of the frequencies $\omega \simeq 1$ and $\omega \simeq 2$ permit the particles to escape faster than for other different values. On the other hand, the computation of the exit basins in phase space reveals the existence of Wada basins depending of the frequency values. We provide some heuristic arguments that are in good agreement with the numerical results. Our results are expected to be relevant for physical phenomena such as the effect of companion galaxies, among others.

Information processing with an excitable chemical medium, like the Belousov-Zhabotinsky (BZ) reaction, is typically based on information coding in the presence or absence of excitation pulses. Here we present a new concept of Boolean coding that can be applied to an oscillatory medium. A medium represents the logical TRUE state if a selected region oscillates with a high frequency. If the frequency fails below a specified value, it represents the logical FALSE state. We consider a medium composed of disks encapsulating an oscillatory mixture of reagents, as related to our recent experiments with lipid-coated BZ droplets. We demonstrate that by using specific geometrical arrangements of disks containing the oscillatory medium one can perform logical operations on variables coded in oscillation frequency. Realizations of a chemical signal diode and of a single-bit memory with oscillatory disks are also discussed.

Based on the properties of exponential distribution families we analyze the Fisher information of the Gibbs canonical ensemble to construct a new state function for simple systems with no mechanical work. This function possesses nice symmetry properties with respect to Legendre transform and provides a connection with previous alternative formulations of thermodynamics, most notably the work by Biot, Serrin, and Frieden and collaborators. Logical extensions to systems with mechanical work may similarly consider generalized Gibbs ensembles.

It is well known that heat pumps, while being all limited by the same basic thermodynamic laws, may find realization on systems as “small” and “quantum” as a three-level maser. In order to quantitatively assess how the performance of these devices scales with their size, we design generalized $N$-dimensional ideal heat pumps by merging $N-2$ elementary three-level stages. We set them to operate in the absorption chiller mode between given hot and cold baths and study their maximum achievable cooling power and the corresponding efficiency as a function of $N$. While the efficiency at maximum power is roughly size-independent, the power itself slightly increases with the dimension, quickly saturating to a constant. Thus, interestingly, scaling up autonomous quantum heat pumps does not render a significant enhancement beyond the optimal double-stage configuration.

We study a two-dimensional tight-binding lattice for excitons with on-site disorder, coupled to a thermal environment at infinite temperature. The disorder acts to localize an exciton spatially, while the environment generates dynamics which enable exploration of the lattice. Although the steady state of the system is trivially uniform, we observe a rich dynamics and uncover a dynamical phase transition in the space of temporal trajectories. This transition is identified as a localization in the dynamics generated by the bath. We explore spatial features in the dynamics and employ a generalization of the inverse participation ratio to deduce an ergodic timescale for the lattice.