We present both the experimental and computational methods and results of phase-separating experiments performed with sulfur hexafluoride $\left({\text{SF}}_6\right)$ close to its critical density. These experiments were performed in microgravity to suppress buoyancy and convection-driven effects. Phase separation under reduced gravity is analyzed for both 0.3 mK and 3.6 mK temperature quenches in order to derive the early-stage growth law. We found a 1/3 growth law for early stages of phase separation for a volume fraction of minority domains of 50%. Our findings support the hypothesis of a crossover between Brownian motion and hydrodynamic effects in the early stages of phase separation. The temperature inside the bulk of the pure fluid was estimated using a proposed histogram method. Our histogram method allowed temperature estimation below thermistors’ sensitivity and detected small temperature variations inside the bulk of the pure fluid.

We consider continuous-time random walks (CTRW) for open systems that exchange energy and matter with multiple reservoirs. Each waiting time distribution (WTD) for times between steps is characterized by a positive parameter $\alpha$, which is set to $\alpha =1$ if it decays at least as fast as $t^{-2}$ at long times and therefore has a finite first moment. A WTD with $\alpha <1$ decays as $t^{-\alpha -1}$. A fluctuation theorem for the trajectory quantity $R$, defined as the logarithm of the ratio of the probability of a trajectory and the probability of the time reversed trajectory, holds for any CTRW. However, $R$ can be identified as a trajectory entropy change only if the WTDs have $\alpha =1$ and satisfy separability (also called “direction time independence”). For nonseparable WTDs with $\alpha =1$, $R$ can only be identified as a trajectory entropy change at long times, and a fluctuation theorem for the entropy change then only holds at long times. For WTDs with $0<\alpha <1$ no meaningful fluctuation theorem can be derived. We also show that the (experimentally accessible) $n\text{th}$ moments of the energy and matter transfers between the system and a given reservoir grow as $t^{n\alpha }$ at long times.

We study the work fluctuations of two types of finite quantum spin chains under the application of a time-dependent magnetic field in the context of the fluctuation relation and Jarzynski equality. The two types of quantum chains correspond to the integrable Ising quantum chain and the nonintegrable $XX$ quantum chain in a longitudinal magnetic field. For several magnetic field protocols, the quantum Crooks and Jarzynski relations are numerically tested and fulfilled. As a more interesting situation, we consider the forcing regime where a periodic magnetic field is applied. In the Ising case we give an exact solution in terms of double-confluent Heun functions. We show that the fluctuations of the work performed by the external periodic drift are maximum at a frequency proportional to the amplitude of the field. In the nonintegrable case, we show that depending on the field frequency a sharp transition is observed between a Poisson-limit work distribution at high frequencies toward a normal work distribution at low frequencies.

We have reconsidered the Bell-Lavis model of liquid water and investigated its relation to its isotropic version, the antiferromagnetic Blume-Emery-Griffiths model on the triangular lattice. Our study was carried out by means of an exact solution on the sequential Husimi cactus. We show that the ground states of both models share the same topology and that fluid phases (gas and low- and high-density liquids) can be mapped onto magnetic phases (paramagnetic, antiferromagnetic, and dense paramagnetic, respectively). Both models present liquid-liquid coexistence and several thermodynamic anomalies. This result suggests that anisotropy introduced through orientational variables play no specific role in producing the density anomaly, in agreement with a similar conclusion discussed previously following results for continuous soft core models. We propose that the presence of liquid anomalies may be related to energetic frustration, a feature common to both models.

We obtain a fundamental-measure density functional for mixtures of parallel hard cylinders. For this purpose we first generalize to multicomponent mixtures the fundamental-measure functional proposed by Tarazona and Rosenfeld for a one-component hard disk fluid, through a method alternative to the cavity formalism of those authors. We show the equivalence of both methods when applied to two-dimensional fluids. The density functional so obtained reduces to the exact density functional for one-dimensional mixtures of hard rods when applied to one-dimensional profiles. In a second step, we apply an idea put forward some time ago by two of us, based again on a dimensional reduction of the system, and derive a density functional for mixtures of parallel hard cylinders. We explore some features of this functional by determining the fluid-fluid demixing spinodals for a binary mixture of cylinders with the same volume, and by calculating the direct correlation functions.

We introduce a model of attractive penetrable spheres by adding a short-range attractive square well outside a penetrable core, and we provide a detailed analysis of structural and thermodynamical properties in one dimension using the exact impenetrable counterpart as a starting point. The model is expected to describe star polymers in regimes of good and moderate solvent under dilute conditions. We derive the exact coefficients of a low-density expansion up to second order for the radial distribution function and up to fourth order in the virial expansion. These exact results are used as a benchmark to test the reliability of approximate theories (Percus-Yevick and hypernetted chain). Notwithstanding the lack of an exact solution for arbitrary densities, our results are expected to be rather precise within a wide range of temperatures and densities. A detailed analysis of some limiting cases is carried out. In particular, we provide a complete solution of the sticky penetrable-sphere model in one dimension up to the same order in density. The issue of Ruelle’s thermodynamics stability is analyzed and the region of a well-defined thermodynamic limit is identified.

We present results from simulations of regular pentagons arranged in a rectangular box. The particles are subjected to vertical tapping. We study the packing fraction, number of contacts, and arch size distribution as a function of the tapping amplitude. Compared with disks, pentagons show peculiar features. As a general rule, pentagons tend to form fewer arches than do disks. Nevertheless, as the tapping amplitude is decreased, the typical size of the pentagon arches grows significantly. As a consequence, a pentagon packing reduces its packing fraction when tapped gently, in contrast with the behavior found in rounded particle deposits.

We generalize Berreman’s model to the case $qA\ge 1$, where $q$ is the wave vector of the surface structure and $A$ its amplitude, to describe the alignment induced by a solid surface on a nematic liquid crystal. We show that, by taking into account correctly the elastic contribution to the surface energy connected with the surface topography, the effective surface energy is smaller than the one determined by Berreman, where the limiting surface is assumed flat and $qA⪡1$. The analysis is performed by assuming that the anchoring energy on the surface is strong, i.e., nematic molecules in contact with the limiting surface are tangent to it, for any bulk distortion. The generalization to the weak anchoring case is also presented.

The limit cycles of brain activity are studied using a compact continuum model that reproduces the main features of electroencephalographic signals, including bifurcations of fixed points and limit cycles in seizures. Frequencies and amplitudes are predicted analytically and related to physiology. Gaussian stimuli yield two distinct evoked responses in the linearly stable zone, consistent with experiment. Limit cycles can be initiated or suppressed by control signals or stimuli.

One of the important features of human locomotion is its instant adaptability to various unpredictable changes of physical and environmental conditions. This property is known as flexibility. Modeling the bipedal locomotion system, we show that initial-state coordination by a global variable which encodes the attractor basins of the system can yield flexibility. This model is based on the following hypotheses: (i) the walking velocity is a global variable, and (ii) the leg posture at the beginning of the stance phase is the initial state of the gait. Moreover, we confirm these hypotheses. We investigate the regions near the neutral states between walking and falling phases using numerical experiments and demonstrate that global variables can be defined as the dominant unstable directions of the system dynamics near the neutral states. We propose the concept of an “instability-induced hierarchy.” In this hierarchy, global variables govern other variables near neutral states; i.e., they become elements of a higher level.

Cytoplasmic dyneins transport cellular organelles by moving on a microtubule filament. It has been found recently that depending on the applied force and the concentration of the adenosine triphosphate molecules, dynein’s step size varies. Based on these studies, we propose a simple model for dynein’s unidirectional motion taking into account the variations in its step size. We study how the average velocity and the relative dispersion in the displacement vary with the applied load. The model is amenable to further extensions by inclusion of details associated with the structure and the processivity of the molecule.

We study theoretically a family of localized states which asymptotically connect a uniform oscillatory state in the magnetization of an easy-plane ferromagnetic spin chain when an oscillatory magnetic field is applied and in a parametrically driven damped pendula chain. The conventional approach to these systems, the parametrically driven damped nonlinear Schrödinger equation, does not account for these states. Adding higher order terms to this model we were able to obtain these localized structures.

We introduce a model combining basic elements of conservative systems which give rise to gap solitons, i.e., a periodic potential and self-defocusing cubic nonlinearity, and dissipative terms corresponding to the complex Ginzburg-Landau (CGL) equation of the cubic-quintic type. The model may be realized in optical cavities with a periodic transverse modulation of the refractive index, self-defocusing nonlinearity, linear gain, and saturable absorption. By means of systematic simulations and analytical approximations, we find three species of stable dissipative gap solitons (DGSs), and also dark solitons. They are located in the first finite band gap, very close to the border of the Bloch band separating the finite and the semi-infinite gaps. Two species represent loosely and tightly bound solitons, in cases when the underlying Bloch band is, respectively, relatively broad or very narrow. These two families of stationary solitons are separated by a region of breathers. The loosely bound DGSs are accurately described by means of two approximations, which rely on the product of a carrier Bloch function and a slowly varying envelope, or reduce the model to CGL-Bragg equations. The former approximation also applies to dark solitons. Another method, based on the variational approximation, accurately describes tightly bound solitons. The loosely bound DGSs, as well as dark solitons, are mobile, and their collisions are quasielastic.

The mean size of unordered binary avalanches on infinite directed random networks may be determined using the damage propagation function introduced by [B. Samuelsson and J. E. S. Socolar, Phys. Rev. E 74, 036113 (2006)]. The derivation of Samuelsson and Socolar explicitly assumes a Poisson distribution of out-degrees. It is shown here that the damage propagation function method may be used whenever the in-degree and out-degree of network nodes are independently distributed; in particular, it is not necessary that the out-degree distribution be Poisson. The general case of correlated in- and out-degrees is discussed and numerical simulations (on large finite networks) are compared with the theoretical predictions (for infinite networks).

It is shown that the conventional theory based on the integral equations for the correlation functions of fluid allows for a reasonable scaling analysis of the critical phenomena. The calculated critical exponents are in rather good agreement with the experimental data for real media, but some of the exponents (first of all, Fisher’s exponent $\eta$) differ from the values predicted by the three-dimensional Ising model. The possibility to obtain Ising-like criticality from the statistical theory of fluids means that the latter does not disagree with the Kadanoff-Wilson-Fisher renormalization group approach.

Analysis of x-ray and neutron reflectivity is usually performed by modeling the density profile of the sample and performing a least square fit to the measured (phaseless) reflectivity data. Here we address the uniqueness of the reflectivity problem as well as its numerical reconstruction. In particular, we derive conditions for uniqueness, which are applicable in the kinematic limit (Born approximation), and for the most relevant case of box model profiles with Gaussian roughness. At the same time we present an iterative method to reconstruct the profile based on regularization methods. The method is successfully implemented and tested both on simulated and real experimental data.

Actin filament networks enable the cytoskeleton to adjust to internal and external forcing. These dynamic networks can adapt to changes by dynamically adjusting their cross-links. Here, we model actin filaments as cross-linked elastic fibers of finite dimensions, with the cross-links being approximately $1\mu \text{m}$ apart, and employ a full three-dimensional model to study their elastic properties by computer simulations. The results show compelling evidence that dense actin networks are characterized by (a) strain hardening without entropic elasticity, (b) avalanches of cross-link slippage leading to strain softening in the case of breakable cross-links, and (c) spontaneous formation of stress fibers in the case of dynamic cross-link formation and destruction.

Weighted scale-free networks exhibit two types of degree-strength relationship: linear and nonlinear relationships between them. To understand the mechanism underlying such empirical relationships, theoretical evolution models for weighted scale-free networks have been introduced for each case. However, those models have not yet been tested with empirical data. In this study, we collect temporal records of several online bulletin board systems and a movie actor network. We measure the growth rates of degree and strength of each vertex and weight of each edge within the framework of preferential attachment (PA). We also measure the probability of creating new edges between unconnected pairs of vertices. Then, based on the measured rates, linear and nonlinear growth models are constructed. We find that indeed the dynamics of creating new edges and adding weight to existing edges in a nonlocal manner is essential to reproduce the nonlinear degree-strength relationship. We also find that the degree-driven PA rule is more appropriate to real systems rather than the strength-driven one used for the linear model.

Recent studies have shown that the synchronizability of complex networks can be significantly improved by gradient or asymmetric couplings, and increase of the gradient strength could enhance the network synchronizability monotonically. Here we argue and demonstrate that, for a typical complex network, there could be an optimal gradient where the maximum network synchronizability is achieved. That is, large gradient may deteriorate synchronization. We attribute the suppressing effect of gradient coupling to the phenomenon of network breaking and show that, comparing with sparse homogeneous networks, dense heterogeneous networks suffer less from network breaking and, consequently, benefit more from large gradient in improving synchronization. The findings are supported by indirect simulations of eigenvalue analysis and direct simulations of coupled nonidentical oscillators.

Evaporation from porous media involves mass and energy transport including phase change, vapor diffusion, and liquid flow, resulting in complex displacement patterns affecting drying rates. Force balance considering media properties yields characteristic lengths affecting the transition in the evaporation rate from a liquid-flow-based first stage limited only by vapor exchange with air to a second stage controlled by vapor diffusion through the medium. The characteristic lengths determine the extent of the hydraulically connected region between the receding drying front and evaporating surface (film region) and the onset of flow rate limitations through this film region. Water is displaced from large pores at the receding drying front to supply evaporation from hydraulically connected finer pores at the surface. Liquid flow is driven by a capillary pressure gradient spanned by the width of the pore size distribution and is sustained as long as the capillary gradient remains larger than gravitational forces and viscous dissipation. The maximum extent of the film region sustaining liquid flow is determined by a characteristic length $L_C$ combining the gravity characteristic length $L_G$ and viscous dissipation characteristic length $L_V$. We used two sands with particle sizes 0.1–0.5 mm (“fine”) and 0.3–0.9 mm (“coarse”) to measure the evaporation from columns of different lengths under various atmospheric evaporative demands. The value of $L_G$ determined from capillary pressure-saturation relationships was 90 mm for the coarse sand and 140 mm for the fine sand. A significant decrease in drying rate occurred when the drying front reached the predicted $L_G$ value (viscous dissipation was negligibly small in sand and $L_C\approx L_G$). The approach enables a prediction of the duration of first-stage evaporation with the highest water losses from soil to the atmosphere.