The mixture of isobutyric acid and water has a consolute point at a temperature of 25.75 °C and mole fraction 0.1148 isobutyric acid. When charcoal is added to this mixture, the concentration of isobutyric acid is reduced by adsorption. We have measured the action of charcoal on solutions of isobutyric acid and water as a function of isobutyric acid mole fraction at temperatures of 25.85 and 32.50 °C. At the higher temperature, the specific adsorption density $(y_2^{\alpha }/m)$ satisfies the Freundlich equation $(y_2^{\alpha }/m)={\mathit{KX}}_2^{1/n}$, where $y_2^{\alpha }$ is the mass of isobutyric acid adsorbed, $m$ is the mass of charcoal, $X_2$ is the equilibrium mole fraction of isobutyric acid, $n$ is the Freundlich index, and $K=K(T)$ is an amplitude that depends upon the temperature $T$. At 25.85 °C, a critical endpoint is located at an isobutyric acid mole fraction $X_2^{\mathit{ce}}=0.09$. When compared with the Freundlich equation at this temperature, a plot of the specific adsorption density as a function of $X_2$ in the vicinity of the critical-endpoint composition assumes a shape which is reminiscent of the derivative of a Dirac delta function. Using critical-point scaling theory, we show that this divergent pattern is consistent with the principle of critical point universality.

The second self-diffusion and viscosity virial coefficients of the Lennard-Jones (LJ) fluid were calculated by a detailed evaluation of the velocity and shear-stress autocorrelation functions using equilibrium molecular dynamics simulations at low and moderate densities. Accurate calculation of these coefficients requires corresponding transport coefficient values with low degrees of uncertainty. These were obtained via very long simulations by increasing the number of particles and by using the knowledge of correlation functions in the Green-Kubo method in conjunction with their corresponding generalized Einstein relations. The values of the self-diffusion and shear viscosity coefficients have been evaluated for systems with reduced densities between 0.0005 and 0.05 and reduced temperatures from 0.7 to 30.0. This provides a new insight into the transport coefficients beyond what can be offered by the Rainwater-Friend theory, which has not been developed for the self-diffusion coefficient.

We report on real-time observations of the aggregation of gold nanoparticles using a custom-made liquid cell that allows for in situ electron microscopy. Process kinetics and fractal dimension of the aggregates are consistent with three-dimensional cluster-cluster diffusion-limited aggregation, even for large aggregates, for which confinement effects are expected. This apparent paradox was resolved through in situ observations of the interactions between individual particles as well as clusters at various stages of the aggregation process that yielded the large aggregates. The liquid cell described herein facilitates real-time observations of various processes in liquid media with the high resolution of the electron microscope.

We present a detailed experimental study of the aggregation of particles of permanent magnetic moment in an external magnetic field. The experiments are performed with millimeter-sized particles floating on the surface of water. Due to the large size of the particles, thermal noise does not have any relevance in the system; the particles undergo deterministic motion. Experiments are carried out varying the concentration which also controls the relative importance of the dipole-external field and the dipole-dipole interactions. We determined the exponents characterizing the aggregation process and found that the attraction driven aggregation of dipolar particles obeys the Vicsek-Family dynamic scaling. The exponents are found to have a concentration dependence which can be attributed to the change of mobility of clusters and their interaction at higher concentrations.

Through molecular simulations we investigate the dynamics of crystallization of hard spheres of uniform size from dense amorphous states and the role that hidden structures in an otherwise disordered medium might have on it. It is shown that short-range order in the form of sites with fivefold symmetry acts as a powerful inhibitor to crystal growth. Fivefold sites not only retard crystallization, but can self-assemble into organized structures that arrest crystallization at high densities or lead to the formation of defects in a crystal. The latter effect can be understood in terms of a random polyhedral model.

Broadband dielectric measurements were performed in a wide range of temperatures on glucose, maltose, and their acetyl derivatives. We have indicated that molecular dynamics above and below the glass transition temperature differ considerably for the hydrogen-bonded and van der Waals systems. We have shown that structural relaxation dispersions of D-glucose and maltose are broader than those obtained for peracetyl carbohydrates. Moreover, glass transition temperatures of the former systems are much higher than for the latter ones. In the glassy state of both glucose and its acetyl derivatives only one well-separated secondary relaxation process was identified. In the case of maltose and peracetyl maltose a completely different situation was observed. In the former carbohydrate two secondary modes were detected, whereas in the latter one only a faster relaxation process was visible in the glassy state. This finding is discussed in greater detail on the basis of density functional theory calculations.

We revisit a theoretical approach based on the discrete Landau model of polar smectic liquid crystals. Treating equilibrium structures on many length scales, we have analyzed different periodically modulated polar smectic phases. Besides already known smectic structures, we have obtained a number of other phases which are stable in a narrow range (that is why the phases can be termed as microphases) of model parameters and thermodynamic conditions. The sequence of microphases represents a so-called “harmless staircase” of structures with oscillating periods. We anticipate that the range of stabilities for various microphases can be extended (and therefore the microphases can be easier to detect experimentally) by applying external electric fields or/and investigating freestanding smectic films.

We propose a simple dynamic model of polymers under shear with an anisotropic mobility tensor. We calculate the shear viscosity, the rheo-dielectric response function, and the parallel relaxation modulus under shear flow deduced from our model. We utilize recently developed linear response theories for nonequilibrium systems to calculate linear response functions. Our results are qualitatively consistent with experimental results. We show that our anisotropic mobility model can reproduce essential dynamical nature of polymers under shear qualitatively. We compare our model with other models or theories such as the convective constraint release model or nonequilibrium linear response theories.

The transportation of water across a cell membrane facilitated by water channel proteins is fundamental to the normal water metabolism in all forms of life. It is understood that the narrow region in a water channel is responsible for gating or selectivity. However, the influence of the position of the narrow region on water transportation is still not thoroughly understood. By choosing a single-walled carbon nanotube (SWNT) as a simplified model and using molecular dynamics simulation, we have found that the water flux through the nanotube would change significantly if the narrow location moves away from the middle region along the tube. Simulation results show that the flux reaches the maximum when the deformation occurs in the middle part of nanotube and decreases as the deformation location moves toward the ends of the nanotube. However, the decrease of water flux is not monotonic and the flux gets the minimum near the ends. These interesting phenomena can be explained in terms of water-water interactions and water-SWNT interactions. It can be concluded that the regulation of water transportation through nanopores depends sensitively on the location of the narrow region, and these findings are helpful in devising high flux nanochannels and nanofiltration as well.

A cluster of $N$ ligand-receptor pairs between two parallel surfaces under an applied force $F=\Gamma t$ with a constant loading rate $\Gamma$ is considered. Our theoretical and numerical studies show that there is a characteristic force $f_c$ and a characteristic loading rate ${\Gamma }_c$. At $\Gamma <{\Gamma }_c$, the mean rupture force $F_r$ of the cluster is close to but lower than $N{f}_c$. In this regime, cluster dissociation can be modeled as a one-dimensional barrier crossing process and $F_r$ scales like $N{f}_c-F_r~N^{1/3}[\ln ({\Gamma }_c/\Gamma )]{}^{2/3}$. At $\Gamma ={\Gamma }_c$, the cluster dissociation occurs at $F_r=N{f}_c$. At $\Gamma >{\Gamma }_c$, $F_r$ for clusters with large $N$ is well predicted by the rate equation because the fluctuations of the number of closed bonds are unimportant. Our study shows that $f_c$ and ${\Gamma }_c$ are important emergent properties for understanding the mechanical response of adhesion clusters.

It is known that in the regime of superlinear diffusion, characterized by zero integral friction (vanishing integral of the memory function), the generalized Langevin equation may have nonergodic solutions that do not relax to equilibrium values. It is shown that the equation may have nonergodic (nonstationary) solutions even if the integral of the memory function is finite and diffusion is normal.

We introduce the temperature-dependent autocatalytic coefficient into the Merkin-Needham-Scott version of the Selkov system and consider the resulting equations as a model for temperature-controlled, self-sustained glycolytic oscillations in a closed reactor. It has been shown that this simple model reproduces key features observed in the experiments with temperature growth: (i) exponentially decreasing period of oscillations; (ii) reversal of relative duration leading and tail fronts. The applied model also reproduces the modulations of oscillations induced by the periodic temperature change.

We investigate the effect of thermal fluctuations on the critical stress and the microstructure of damage preceding macroscopic fracture of Lennard-Jones solids under a constant external load. Based on molecular dynamics simulations of notched specimens at finite temperatures, we show that the crystalline structure gets distorted ahead of the crack in the secondary creep regime. The damage profile characterizing the spatial distribution of lattice distortions is well described by an exponential form. The characteristic length of the exponential form provides the scale of damage, which is found to be an increasing function of the temperature: At low temperatures, damage is strongly localized to the crack tip, while at high temperatures, damage extends to a broader range, leading to more efficient relaxation of overloads. As a consequence, the stress intensity factor decreases with increasing temperature. The final macroscopic failure of the system occurs suddenly and is initiated by the creation of vacancies and voids. The creep strength exhibits inverse square root scaling with the notch size corrected by the extension of the process zone.

Developing an effective coarse-grained (CG) approach is a promising way for studying dynamics on large size networks. In the present work, we have proposed a strength-based CG ($s$-CG) method to study critical phenomena of the Potts model on weighted complex networks. By merging nodes with close strengths together, the original network is reduced to a CG network with much smaller size, on which the CG Hamiltonian can be well defined. In particular, we make an error analysis and show that our $s$-CG approach satisfies the condition of statistical consistency, which demands that the equilibrium probability distribution of the CG model matches that of the microscopic counterpart. Extensive numerical simulations are performed on scale-free networks and random networks, without or with strength correlation, showing that this $s$-CG approach works very well in reproducing the phase diagrams, fluctuations, and finite-size effects of the microscopic model, while the $d$-CG approach proposed in our recent work [Phys. Rev. E 82, 011107 (2010)] does not.

We propose a hierarchical model of social development composed of two associated hierarchies, each of which describes economic and noneconomic activities in society, respectively. The model is designed to explain the development of wealth distribution and social structure over 50 years in a premodern Japanese local society. Data analysis shows that the wealth distribution has a well-known universal power-law tail throughout the observed period, while the Pareto index gradually decreases with time. We further show that the noneconomic social properties, such as the household number, average family size, and number of collaterals in a household, of the local society, also have decreasing or increasing trends throughout the observed period. We show that the hierarchical model consistently demonstrates the correlations of these economic and noneconomic properties.

The statistical equilibria of the (conservative) dynamics of the Gross-Pitaevskii equation (GPE) with a finite range of spatial Fourier modes are characterized using a new algorithm, based on a stochastically forced Ginzburg-Landau equation (SGLE), that directly generates grand-canonical distributions. The SGLE-generated distributions are validated against finite-temperature GPE-thermalized states and exact (low-temperature) results obtained by steepest descent on the (grand-canonical) partition function. A standard finite-temperature second-order $\lambda$ transition is exhibited. A mechanism of GPE thermalization through a direct cascade of energy is found using initial conditions with mass and energy distributed at large scales. A long transient with partial thermalization at small scales is observed before the system reaches equilibrium. Vortices are shown to disappear as a prelude to final thermalization and their annihilation is related to the contraction of vortex rings due to mutual friction. Increasing the amount of dispersion at the truncation wave number is shown to slow thermalization and vortex annihilation. A bottleneck that produces spontaneous effective self-truncation with partial thermalization is characterized in the limit of large dispersive effects. Metastable counterflow states, with nonzero values of momentum, are generated using the SGLE algorithm. Spontaneous nucleation of the vortex ring is observed and the corresponding Arrhenius law is characterized. Dynamical counterflow effects on vortex evolution are investigated using two exact solutions of the GPE: traveling vortex rings and a motionless crystal-like lattice of vortex lines. Longitudinal effects are produced and measured on the crystal lattice. A dilatation of vortex rings is obtained for counterflows larger than their translational velocity. The vortex ring translational velocity has a dependence on temperature that is an order of magnitude above that of the crystal lattice, an effect that is related to the presence of finite-amplitude Kelvin waves. This anomalous vortex ring velocity is quantitatively reproduced by assuming equipartition of energy of the Kelvin waves. Orders of magnitude are given for the predicted effects in weakly interacting Bose-Einstein condensates and superfluid ${}^4\mathrm{He}$.

The propagation of a nonlinear low-frequency mode in a strongly coupled dusty plasma is investigated using a generalized hydrodynamical model. For the well-known longitudinal dust acoustic mode a standard perturbative approach leads to a Korteweg-de Vries (KdV) soliton. The strong viscoelastic effect, however, introduced a nonlinear forcing and a linear damping in the KdV equation. This novel equation is solved analytically to show a competition between nonlinear forcing and dissipative damping. The physical consequence of such a solution is also sketched.

The problem of designing electromagnetic metamaterials is complicated by the pseudo-infinite parameter space governing such materials. We present a general solution based on group theory for the design and optimization of the electromagnetic properties of metamaterials. Using this framework, the fundamental properties of a metamaterial design, such as anisotropy or magnetic or electrical resonances, can be elucidated based on the symmetry class into which the unit cell falls. This provides a methodology for the inverse problem of design of the electromagnetic properties of a metamaterial. We also present simulations of a zia metamaterial that provides greater design flexibility for tuning the resonant properties of the device than a structure based on a simple split-ring resonator. The power of this zia element is demonstrated by creating bianisotropic, chiral, and biaxial designs using the inverse group-theory procedure outlined in this paper.

This paper reports the lattice Boltzmann method (LBM) based formulation for viscoelastic fluids with both volumetric and shear viscoelasticity. The relaxation limit of the viscoelastic fluid formulation yields the LBM for elastic solids with both volumetric or pressure ($p$) and shear ($s$) wave propagation modes. The reflection of a two-dimensional $p$ wave from an obstacle (wedge) inclined to the propagation direction of the $p$ wave is studied together with the convergence and stability behavior of the LBM as the lattice size and lattice time step decrease. The model is capable of accurately predicting the mode change ($p$ to $s$) due to the reflection. The model provides a unique unified approach capable of simulating fluids, viscoelastic fluids, and solids within a single LBM framework, thus avoiding interface problems between different simulation methods. The paper concentrates on the wave propagation part of the model, in the quasielastic regime.

A radiation model is developed to obtain evolution of band intensities according to the state-to-state (STS) approach by considering vibration-translation and vibration-electronic jumps and dissociation. Investigation of the behavior of a nonequilibrium ${\mathrm{N}}_2$ gas flow behind a shock shows that the radiation intensity remains weak and the flow is far from radiative equilibrium. Similar intensities are predicted by pure STS and hybrid approaches based on existing radiation models. However, the coupling between physicochemical and radiative processes increases with radiation intensity.