Molecular-dynamics simulations of the Lennard-Jones fluid (up to 10${}^7$ atoms) are used to analyze the collapse of a nanoscopic bubble. The collapse is triggered by a traveling sound wave that forms a shock wave at the interface. The peak temperature $T_{\max }$ in the focal point of the collapse is approximately $\Sigma R_0^a$, where $\Sigma$ is the surface density of energy injected at the boundary of the container of radius $R_0$ and $\alpha$ ≈ 0.4–0.45. For $\Sigma$ $=$ 1.6 J/m${}^2$ and $R_0$ $=$ 51 nm, the shock wave velocity, which is proportional to$\sqrt{\Sigma }$, reaches 3400 m/s (4 times the speed of sound in the liquid); the pressure at the interface, which is proportional to $\Sigma$, reaches 10 GPa; and $T_{\max }$ reaches 40 000 K. The Rayleigh-Plesset equation together with the time of the collapse can be used to estimate the pressure at the front of the shock wave.

The spatial structure of dusty plasma confined in a spherical microcavity has been investigated by use of the density functional theory for classical fluids, in which all particles undergo an isotropic harmonic potential and the interparticle interaction is described by the hard-core Yukawa potential. The fundamental measure theory of Rosenfeld and its modified versions have been used in the energy functional to incorporate hard-core interactions between particles. Based on the variational principle, the equilibrium density profile can be obtained by use of an iteration calculation with the average density of particles as an input. In terms of density profiles presented under various conditions, the roles of the trapped parameter, coupling parameter, screening parameter, and the average number density of particles are discussed, and significant influences of these factors on the structure of confined dusty plasma are found.

We consider two-dimensional bright matter-wave solitons in two-dimensional Bose-Einstein condensates. From the asymptotic form of their wave function, we derive an analytic expression for the force of interaction between solitons in the large separation limit, which turns out to decay with solitons separation $\Delta$ as $F\left(\Delta \right)\propto \exp (-\Delta )/\sqrt{\Delta }$. Simulating the dynamics of two solitons using the relevant Gross-Pitaevskii equation, we obtain the force of the interaction for the full range of $\Delta$, which turns out to be of molecular type. We show that many-soliton molecules can exist as a result of such a molecular-type of interaction. These include string-shaped, ring-shaped, or regular-lattice-shaped soliton molecules. By calculating their binding energy, we investigate the stability of these structures. Contrary to one-dimensional soliton molecules, which have no binding energy, two-dimensional molecules of a lattice of solitons with alternating phases are robust and have a negative binding energy. Lattices of size larger than $2\times 2$ solitons have many discrete equilibrium values of the separation between two neighboring solitons.

Special localized wave modes show up in several physical scenarios including BEC in optical lattices, nonlinear photonic crystals, and systems with strong electron-phonon interaction. These result from an underlying nonlinear contribution to the wave equation that is usually assumed to be instantaneous. Here we demonstrate that the relaxation process of the nonlinearity has a profound impact in the wave-packet dynamics and in the formation of localized modes. We illustrate this phenomenology by considering the one-electron wave packet spreading in a $C60$ buckball structure whose dynamics is governed by a discrete nonlinear Schrödinger equation with a Debye relaxation of the nonlinearity. We report the full phase diagram related to the spacial extension of the asymptotic wave packet and unveil a complex wave-packet dynamical behavior.

In the general case of a many-body Hamiltonian system described by an autonomous Hamiltonian $H$ and with $K⩾0$ independent conserved quantities, we derive the microcanonical thermodynamics. Using simple approach, based on differential geometry, we derive the microcanonical entropy and the derivatives of the entropy with respect to the conserved quantities. In such a way, we show that all the thermodynamical quantities, such as the temperature, the chemical potential, and the specific heat, are measured as a microcanonical average of the appropriate microscopic dynamical functions that we have explicitly derived. Our method applies also in the case of nonseparable Hamiltonians, where the usual definition of kinetic temperature, derived by the virial theorem, does not apply.

We establish that equally spaced smectic configurations enjoy an infinite-dimensional conformal symmetry and show that there is a natural map between them and null hypersurfaces in maximally symmetric spacetimes. By choosing the appropriate conformal factor it is possible to restore additional symmetries of focal structures only found before for smectics on flat substrates.

We extend Jarzynski's work relation and the second law of thermodynamics to a heat conducting system, which is operated by an external agent. These extensions contain a nonequilibrium contribution expressed as the violation of the (linear) response relation caused by the operation. We find that a natural extension of the minimum work principle involves information about the time-reversed operation, and is far from straightforward. Our work relation may be tested experimentally especially when the temperature gradient is small.

We study the optimal packing of hard spheres in an infinitely long cylinder, using simulated annealing, and compare our results with the analogous problem of packing disks on the unrolled surface of a cylinder. The densest structures are described and tabulated in detail up to $D/d=2.873$ (ratio of cylinder and sphere diameters). This extends previous computations into the range of structures which include internal spheres that are not in contact with the cylinder.

The propagation of the primary pulse through an uncompressed granular chain subject to external on-site perturbation is studied. An analytical procedure predicting the evolution of the primary pulse is devised for the general form of the on-site perturbation applied on the chain. The validity of the analytical model is confirmed with several specific granular setups, such as chains mounted on the nonlinear elastic foundation, chains perturbed by the dissipative forces, as well as randomly perturbed chains. An additional interesting finding made in the present paper corresponds to the chains subject to a special type of perturbation, including the terms leading to dissipation and those acting as an energy source. In the paper, it is shown that an application of such a perturbation may lead to the formation of stable stationary primary pulses propagating with constant amplitudes and acting as attractors for the initially unperturbed Nesterenko solitary waves. Interestingly enough, the developed analytical procedure provides an extremely close estimation for the amplitudes of these stationary primary pulses as well as predicts zones of their stability. In conclusion, we would like to stress that the developed analytical model has demonstrated spectacular agreement with the results of the direct numerical simulations, and this is for various configurations considered in the current paper.

Grand canonical Monte Carlo and histogram reweighting techniques are used to study the fluid-phase behavior of an athermal system of colloids and nonadsorbing polymers on a fine lattice in the “protein limit,” where polymer dimensions exceed those of the colloids. The main parameters are the chains' radius of gyration, $R_g$, the diameter of the colloids, ${\sigma }_c$, and the monomer diameter, ${\sigma }_s$. The phase behavior is controlled by the macroscopic size ratio, $q_r=2R_g/{\sigma }_c$, and the microscopic size ratio, $d={\sigma }_s/{\sigma }_c$. The latter ratio is found to play a significant role in determining the critical monomer concentration for $q_r\lesssim 4$ and the critical colloid density for all chain lengths. However, the critical (osmotic) pressure is independent of the microscopic size ratio at all macroscopic size ratios studied. Quantitative agreement is observed between our simulation results and experimental data. We scale our results based on the polymer correlation length, which has previously been suggested to universally collapse these binodals [Bolhuis et al., Phys. Rev. Lett. 90, 068304 (2003); Fleer and Tuinier, Phys. Rev. E 76, 041802 (2007)]. While the density binodals exhibit universal characteristics along the low-colloid-density branch, such features are not present in the corresponding high-density phase. However, pressure binodals do collapse nicely under such a scaling, even far from the critical point, which allows us to produce a binodal curve whose shape is independent of either size ratio.

Droplet motion on solid substrates has been widely studied not only because of its importance in fundamental research but also because of its promising potentials in droplet-based devices developed for various applications in chemistry, biology, and industry. In this paper, we investigate the motion of an evaporating droplet in one-component fluids on a solid substrate with a wettability gradient. As is well known, there are two major difficulties in the continuum description of fluid flows and heat fluxes near the contact line of droplets on solid substrates, namely, the hydrodynamic (stress) singularity and thermal singularity. To model the droplet motion, we use the dynamic van der Waals theory [Phys. Rev. E 75, 036304 (2007)] for the hydrodynamic equations in the bulk region, supplemented with the boundary conditions at the fluid-solid interface. In this continuum hydrodynamic model, various physical processes involved in the droplet motion can be taken into account simultaneously, e.g., phase transitions (evaporation or condensation), capillary flows, fluid velocity slip, and substrate cooling or heating. Due to the use of the phase field method (diffuse interface method), the hydrodynamic and thermal singularities are resolved automatically. Furthermore, in the dynamic van der Waals theory, the evaporation or condensation rate at the liquid-gas interface is an outcome of the calculation rather than a prerequisite as in most of the other models proposed for evaporating droplets. Numerical results show that the droplet migrates in the direction of increasing wettability on the solid substrates. The migration velocity of the droplet is found to be proportional to the wettability gradients as predicted by Brochard [Langmuir 5, 432 (1989)]. The proportionality coefficient is found to be linearly dependent on the ratio of slip length to initial droplet radius. These results indicate that the steady migration of the droplets results from the balance between the (conservative) driving force due to the wettability gradient and the (dissipative) viscous drag force. In addition, we study the motion of droplets on cooled or heated solid substrates with wettability gradients. The fast temperature variations from the solid to the fluid can be accurately described in the present approach. It is observed that accompanying the droplet migration, the contact lines move through phase transition and boundary velocity slip with their relative contributions mostly determined by the slip length. The results presented in this paper may lead to a more complete understanding of the droplet motion driven by wettability gradients with a detailed picture of the fluid flows and phase transitions in the vicinity of the moving contact line.

We report direct measurement of surface deformation in soft solids due to their surface tension. Gel replicas of poly(dimethysiloxane) masters with rippled surfaces are found to have amplitudes that decrease with decreasing gel modulus. Surface undulations of a thin elastomeric film are attenuated when it is oxidized by brief exposure to oxygen plasma. Surface deformation in both cases is modeled successfully as driven by surface tension and resisted by elasticity. Our results show that surface tension of soft solids drives significant deformation, and that the latter can be used to determine the former.

Can synchronization properties of a network of identical oscillators in the presence of noise be improved through appropriate rewiring of its connections? What are the optimal network architectures for a given total number of connections? We address these questions by running the optimization process, using the stochastic Markov Chain Monte Carlo method with replica exchange, to design networks of phase oscillators with increased tolerance against noise. As we find, the synchronization of a network, characterized by the Kuramoto order parameter, can be increased up to 40%, as compared to that of the randomly generated networks, when the optimization is applied. Large ensembles of optimized networks are obtained, and their statistical properties are investigated.

The analytical two- and three-dimensional vortex solitons with arbitrary values of vorticity are constructed in the cubic defocusing media with spatially inhomogeneous nonlinearity. The values of the nonlinearity coefficients are zero near the center and increase rapidly toward the periphery. In addition to the analytical ones, a number of vortex solitons are found numerically. It is shown that analytical vortex solitons are stable. Also, the stability region of the numerically constructed vortex solitons are given.

Several earlier studies have shown signatures of crossover in various static and dynamics properties of a confined fluid when the confining dimension decreases to about a nanometer. The density fluctuations govern the majority of such properties of a fluid. Here, we illustrate the crossover in density fluctuation in a confined fluid, to provide a generic understanding of confinement-induced crossover of fluid properties, using computer simulations. The crossover can be understood as a manifestation of changes in the long-wavelength behavior of fluctuation in density due to geometrical constraints. We further show that the confining potential significantly affects the crossover behavior.

We introduce antiferromagnetic quantum fluctuations into quantum annealing in addition to the conventional transverse-field term. We apply this method to the infinite-range ferromagnetic $p$-spin model, for which the conventional quantum annealing has been shown to have difficulties in finding the ground state efficiently due to a first-order transition. We study the phase diagram of this system both analytically and numerically. Using the static approximation, we find that there exists a quantum path to reach the final ground state from the trivial initial state that avoids first-order transitions for intermediate values of $p$. We also study numerically the energy gap between the ground state and the first excited state and find evidence for intermediate values of $p$ for which the time complexity scales polynomially with the system size at a second-order transition point along the quantum path that avoids first-order transitions. These results suggest that quantum annealing would be able to solve this problem with intermediate values of $p$ efficiently, in contrast to the case with only simple transverse-field fluctuations.

Total entropy production and its three constituent components are described both as fluctuating trajectory-dependent quantities and as averaged contributions in the context of the continuous Markovian dynamics, described by stochastic differential equations with multiplicative noise, of systems with both odd and even coordinates with respect to time reversal, such as dynamics in full phase space. Two of these constituent quantities obey integral fluctuation theorems and are thus rigorously positive in the mean due to Jensen's inequality. The third, however, is not and furthermore cannot be uniquely associated with irreversibility arising from relaxation, nor with the breakage of detailed balance brought about by nonequilibrium constraints. The properties of the various contributions to total entropy production are explored through the consideration of two examples: steady-state heat conduction due to a temperature gradient, and transitions between stationary states of drift diffusion on a ring, both in the context of the full phase space dynamics of a single Brownian particle.

Four stroke Otto refrigerator cycles with no classical analog are studied. Extremely short cycle times with respect to the internal timescale of the working medium characterize these refrigerators. Therefore, these cycles are termed sudden. The sudden cycles are characterized by the stable limit cycle, which is the invariant of the global cycle propagator. During their operation the states of the working medium possess significant coherence which is not erased in the equilibration segments due to the very short time allocated. This characteristic is reflected in a difference between the energy entropy and the Von Neumann entropy of the working medium. A classification scheme for sudden refrigerators is developed allowing simple approximations for the cooling power and coefficient of performance.

Although the presence of hydrogen bonds determines most properties of associated materials, their role in relaxation dynamics of liquids remains unclear. Very recently Nakanishi and Nozaki [M. Nakanishi and R. Nozaki, Phys. Rev. E 84, 011503 (2011)] proposed a simplified model for the description of the molecular dynamics of H-bonding network and tested its validity for several polyols. The authors concluded that relaxation dynamics is controlled mainly by the number of hydroxyl groups, whereas the role of molecular architecture can be neglected. This conclusion, as demonstrated herein, fails in the case of pentiols. When we take into account the role of molecular architecture for development of H-bonded structures, it is still possible to satisfactorily describe molecular dynamics in polyols with the use of the Nakanishi and Nozaki model.

Many intriguing properties of driven nonlinear resonators, including the appearance of chaos, are very important for understanding the universal features of nonlinear dynamical systems and can have great practical significance. We consider a cylindrical cavity resonator driven by an alternating voltage and filled with a nonlinear nondispersive medium. It is assumed that the medium lacks a center of inversion and the dependence of the electric displacement on the electric field can be approximated by an exponential function. We show that the Maxwell equations are integrated exactly in this case and the field components in the cavity are represented in terms of implicit functions of special form. The driven electromagnetic oscillations in the cavity are found to display very interesting temporal behavior and their Fourier spectra contain singular continuous components. This is a demonstration of the existence of a singular continuous (fractal) spectrum in an exactly integrable system.