We study various time series of surface-layer wind velocity at different locations and provide evidences for the intermittent nature of the wind fluctuations in mesoscale to large-scale range. By means of the magnitude covariance analysis, which is shown to be a more efficient tool to study intermittency than classical scaling analysis, we find that all wind series exhibit similar features than those observed for laboratory turbulence. Our findings suggest the existence of a “universal” cascade mechanism associated with the energy transfer between synoptic motions and turbulent microscales in the atmospheric boundary layer.

The linear stability of the flows induced in a fluid layer by buoyant convection (due to an applied horizontal temperature gradient) and by acoustic streaming (due to an applied horizontal ultrasound beam) is studied. The vertical profiles of the basic flows are determined analytically, and the eigenvalue problem resulting from the temporal stability analysis is solved by a spectral Tau Chebyshev method. Pure acoustic streaming flows are found to be sensitive to a shear instability developing in the plane of the flow (two-dimensional instability), and the thresholds for this oscillatory instability depend on the normalized width $H_b$ of the ultrasound beam with a minimum for $H_b=0.32$. Acoustic streaming also affects the stability of the buoyant convection. For a centered beam, effects of stabilization are obtained at small Prandtl number Pr for large beam widths $H_b$ (two-dimensional shear instability) and for moderate Pr (three-dimensional oscillatory instability), but destabilization is also effective at small Pr for small beam widths $H_b$ and at large Pr with a spectacular decrease of the thresholds of the three-dimensional steady instability. An adequate decentring of the ultrasound beam can enhance the stabilization. Insight into the stabilizing and destabilizing mechanisms is gained from the analysis of the fluctuating energy budget associated with the disturbances at threshold. The modifications affecting the two-dimensional shear instability thresholds are strongly connected to modifications of the velocity fluctuations when acoustic streaming is applied. Concerning the three-dimensional steady instability, the spectacular decrease of the thresholds is explained by the extension of the zone with inverse stratification in the lower half of the layer.

In a random spin system, the cooperation of randomness and frustration will lead to a spin-glass phase. However, in geometrically frustrated spin systems, quenched nonmagnetic impurities lift frustration locally. This makes randomness and frustration in these systems as competitors rather than cooperators. By mapping the dilute triangular Ising antiferromagnetic system to elastic array of noncrossing strings, we find that the nonmagnetic impurities in the spin system play roles of pinning centers in the string system. Calculation shows that in the ground state of this system, the spin-glass correlation is power-law decayed, quite different from the standard behavior of spin glass in which spin-glass correlation between two spins at infinite distance tends to a finite value. This indicates that triangular Ising antiferromagnets with quenched nonmagnetic impurities cannot be a spin glass. Instead, in the ground states, they present properties of vortex glass.

By means of numerical simulations, we investigate the geometric properties of loops on hypercubic lattice graphs in dimensions $d=2$ through 7, where edge weights are drawn from a distribution that allows for positive and negative weights. We are interested in the appearance of system-spanning loops of total negative weight. The resulting negative-weight percolation (NWP) problem is fundamentally different from conventional percolation, as we have seen in previous studies of this model for the two-dimensional case. Here, we characterize the transition for hypercubic systems, where the aim of the present study is to get a grip on the upper critical dimension $d_u$ of the NWP problem. For the numerical simulations, we employ a mapping of the NWP model to a combinatorial optimization problem that can be solved exactly by using sophisticated matching algorithms. We characterize the loops via observables similar to those in percolation theory and perform finite-size scaling analyses, e.g., three-dimensional hypercubic systems with side length up to $L=56$ sites, in order to estimate the critical properties of the NWP phenomenon. We find our numerical results consistent with an upper critical dimension $d_u=6$ for the NWP problem.

We report the application of a far-from-equilibrium statistical-mechanical theory to a nontrivial system with Newtonian interactions in continuous boundary-driven flow. By numerically time stepping the force-balance equations of a one-dimensional model fluid we measure occupancies and transition rates in simulation. The high-shear-rate simulation data reproduce the predicted invariant quantities, thus supporting the theory that a class of nonequilibrium steady states of matter, namely, sheared complex fluids, is amenable to statistical treatment from first principles.

The Langevin equation with a multiplicative Lévy white noise is solved. The noise amplitude and the drift coefficient have a power-law form. A validity of ordinary rules of the calculus for the Stratonovich interpretation is discussed. The solution has the algebraic asymptotic form and the variance may assume a finite value for the case of the Stratonovich interpretation. The problem of escaping from a potential well is analyzed numerically; predictions of different interpretations of the stochastic integral are compared.

This paper addresses the relative viscosity of concentrated suspensions loaded with unimodal hard particles. So far, exact equations have only been put forward in the dilute limit, e.g., by Einstein [A. Einstein, Ann. Phys. 19, 289 (1906) (in German); Ann. Phys. 34, 591 (1911) (in German)] for spheres. For larger concentrations, a number of phenomenological models for the relative viscosity was presented, which depend on particle concentration only. Here, an original and exact closed form expression is derived based on geometrical considerations that predicts the viscosity of a concentrated suspension of monosized particles. This master curve for the suspension viscosity is governed by the relative viscosity-concentration gradient in the dilute limit (for spheres the Einstein limit) and by random close packing of the unimodal particles in the concentrated limit. The analytical expression of the relative viscosity is thoroughly compared with experiments and simulations reported in the literature, concerning both dilute and concentrated suspensions of spheres, and good agreement is found.

We characterize both analytically and numerically short-range forces between spatially diffuse interfaces in multi-phase-field models of polycrystalline materials. During late-stage solidification, crystal-melt interfaces may attract or repel each other depending on the degree of misorientation between impinging grains, temperature, composition, and stress. To characterize this interaction, we map the multiphase-field equations for stationary interfaces to a multidimensional classical mechanical scattering problem. From the solution of this problem, we derive asymptotic forms for short-range forces between interfaces for distances larger than the interface thickness. The results show that forces are always attractive for traditional models where each phase-field represents the phase fraction of a given grain. Those predictions are validated by numerical computations of forces for all distances. Based on insights from the scattering problem, we propose a multi-phase-field formulation that can describe both attractive and repulsive forces in real systems. This model is then used to investigate the influence of solute addition and a uniaxial stress perpendicular to the interface. Solute addition leads to bistability of different interfacial equilibrium states, with the temperature range of bistability increasing with strength of partitioning. Stress in turn, is shown to be equivalent to a temperature change through a standard Clausius-Clapeyron relation. The implications of those results for understanding grain boundary premelting are discussed.

Using the discrete phenomenological model with interlayer anticlinic and chiral interaction, the unwinding of the antiferroelectric helix in external electric field was studied. The dependence of the helical pitch on the electric field differs essentially in antiferroelectric and ferroelectric phases. It was found that in antiferroelectric the critical electric field $E_h$ of the transition into the unwound structure is proportional to the value of chiral interaction and does not depend on the anticlinic interaction between nearest layers. This behavior differs significantly from the case of ferroelectric in which $E_h$ increases as the square of the chiral interaction and is inversely related to the synclinic interaction between layers. Peculiarities of the unwinding process and the dependence of the critical field $E_h$ on model parameters are discussed. Based on our calculations, we propose an analytical equation for the critical unwinding field in the antiferroelectric.

The thermodynamical properties of heterogeneous DNA sequences are computed by path-integral techniques applied to a nonlinear model Hamiltonian. The base pairs relative displacements are interpreted as time-dependent paths whose amplitudes are consistent with the model potential for the hydrogen bonds between complementary strands. The portion of configuration space contributing to the partition function is determined, at any temperature, by selecting the ensemble of paths which fulfill the second law of thermodynamics. For a short DNA fragment, the denaturation is signaled by a succession of peaks in the specific-heat plots while the entropy grows continuously versus $T$. Thus, the opening of the double strand with bubble formation appears as a smooth crossover due to base pair fluctuation effects which are accounted for by the path-integral method. The multistep transition is driven by the adenine-thymine- (AT) rich regions of the DNA fragment. The base pairs path ensemble shows an enhanced degree of cooperativity at about the same temperatures for which the specific-heat peaks occur. These findings establish a link between microscopic and macroscopic signatures of the transition. The fractions of mean base pair stretchings are computed by varying the AT base pairs content and taking some threshold values for the occurrence of the molecule denaturation.

A simple model is presented for the effective extensional rheology of a dilute suspension of active particles, such as self-propelled microswimmers, extending previous classical studies on suspensions of passive rodlike particles. Neglecting particle-particle hydrodynamic interactions, we characterize the configuration of the suspension by an orientation distribution, which satisfies a Fokker-Planck equation including the effects of an external flow field and of rotary diffusion. Knowledge of this orientation distribution then allows the determination of the particle extra stress as a configurational average of the force dipoles exerted by the particles on the fluid, which involve contributions from the imposed flow, rotary diffusion, and the permanent dipoles resulting from activity. Analytical expressions are obtained for the stress tensor in uniaxial extensional and compressional flows, as well as in planar extensional flow. In all types of flows, the effective viscosity is found to increase as a result of activity in suspensions of head-actuated swimmers (pullers) and to decrease in suspensions of tail-actuated swimmers (pushers). In the latter case, a negative particle viscosity is found to occur in weak flows. In planar extensional flow, we also characterize normal stresses, which are enhanced by activity in suspensions of pullers but reduced in suspensions of pushers. Finally, an energetic interpretation of the seemingly unphysical decrease in viscosity predicted in suspensions of pushers is proposed, where the decrease is explained as a consequence of the active power input generated by the swimming particles and is shown not to be directly related to viscous dissipative processes.

Game theory formalizes certain interactions between physical particles or between living beings in biology, sociology, and economics and quantifies the outcomes by payoffs. The prisoner’s dilemma (PD) describes situations in which it is profitable if everybody cooperates rather than defects (free rides or cheats), but as cooperation is risky and defection is tempting, the expected outcome is defection. Nevertheless, some biological and social mechanisms can support cooperation by effectively transforming the payoffs. Here, we study the related phase transitions, which can be of first order (discontinuous) or of second order (continuous), implying a variety of different routes to cooperation. After classifying the transitions into cases of equilibrium displacement, equilibrium selection, and equilibrium creation, we show that a transition to cooperation may take place even if the stationary states and the eigenvalues of the replicator equation for the PD stay unchanged. Our example is based on adaptive group pressure, which makes the payoffs dependent on the endogenous dynamics in the population. The resulting bistability can invert the expected outcome in favor of cooperation.

The critical phase of bond percolation on the random growing tree is examined. It is shown that the root cluster grows with the system size $N$ as $N^{\psi }$ and the mean number of clusters with size $s$ per node follows a power function $n_s\propto s^{-\tau }$ in the whole range of open bond probability $p$. The exponent $\tau$ and the fractal exponent $\psi$ are also derived as a function of $p$ and the degree exponent $\gamma$ and are found to satisfy the scaling relation $\tau =1+{\psi }^{-1}$. Numerical results with several network sizes are quite well fitted by a finite-size scaling for a wide range of $p$ and $\gamma$, which gives a clear evidence for the existence of a critical phase.

The random diffusion model is a continuum model for a conserved scalar density field $\varphi$ driven by diffusive dynamics where the bare diffusion coefficient is density dependent. We generalize the model from one with a sharp wave-number cutoff to one with a more natural large wave-number cutoff. We investigate whether the features seen previously—namely, a slowing down of the system and the development of a prepeak in the dynamic structure factor at a wave number below the first structure peak—survive in this model. A method for extracting information about a hidden prepeak in experimental data is presented.

Bilayer lipid membranes (BLMs) are an essential component of all biological systems, forming a functional barrier for cells and organelles from the surrounding environment. The lipid molecules that form membranes contain both permanent and induced dipoles, and an electric field can induce the formation of pores when the transverse field is sufficiently strong (electroporation). Here, a phenomenological free energy is constructed to model the response of a BLM to a transverse static electric field. The model contains a continuum description of the membrane dipoles and a coupling between the headgroup dipoles and the membrane tilt. The membrane is found to become unstable through buckling modes, which are weakly coupled to thickness fluctuations in the membrane. The thickness fluctuations, along with the increase in interfacial area produced by membrane buckling, increase the probability of localized membrane breakdown, which may lead to pore formation. The instability is found to depend strongly on the strength of the coupling between the dipolar headgroups and the membrane tilt as well as the degree of dipolar ordering in the membrane.

Metadynamics is a powerful sampling technique that uses a nonequilibrium history-dependent process to reconstruct the free-energy surface as a function of the relevant collective variables $\mathbf{s}$. In Bussi et al. [Phys. Rev. Lett. 96, 090601 (2006)] it is proved that, in a Langevin process, metadynamics provides an unbiased estimate of the free energy $F\left(\mathbf{s}\right)$. We here study the convergence properties of this approach in a multidimensional system, with a Hamiltonian depending on several variables. Specifically, we show that in a Monte Carlo metadynamics simulation of an Ising model the time average of the history-dependent potential converge to $F\left(\mathbf{s}\right)$ with the same law of an umbrella sampling performed in optimal conditions (i.e., with a bias exactly equal to the negative of the free energy). Remarkably, after a short transient, the error becomes approximately independent on the filling speed, showing that even in out-of-equilibrium conditions metadynamics allows recovering an accurate estimate of $F\left(\mathbf{s}\right)$. These results have been obtained introducing a functional form of the history-dependent potential that avoids the onset of systematic errors near the boundaries of the free-energy landscape.

The problem of soliton-soliton force is revisited. From the exact two-soliton solution of a nonautonomous Gross-Pitaevskii equation, we derive a generalized formula for the mutual force between two solitons. The force is given for arbitrary soliton amplitude difference, relative speed, phase, and separation. The latter allows for the investigation of soliton molecule formation, dynamics, and stability. We reveal the role of the time-dependent relative phase between the solitons in binding them in a soliton molecule. We derive its equilibrium bond length, spring constant, frequency, effective mass, and binding energy of the molecule. We investigate the molecule’s stability against perturbations such as reflection from surfaces, scattering by barriers, and collisions with other solitons.

We revisit the Kibble-Zurek mechanism by analyzing the dynamics of phase ordering systems during an infinitely slow annealing across a second-order phase transition. We elucidate the time and cooling rate dependence of the typical growing length, and we use it to predict the number of topological defects left over in the symmetry broken phase as a function of time, both close and far from the critical region. Our results extend the Kibble-Zurek mechanism and reveal its limitations.

We consider a system of particles interacting via a screened Newtonian potential and study phase transitions between homogeneous and inhomogeneous states in the microcanonical and canonical ensembles. For small screenings, the interaction is long range. Like for other systems with long-range interactions, we obtain a great diversity of microcanonical and canonical phase transitions depending on the dimension of space and on the importance of the screening length. We also consider a system of particles in Newtonian interaction (without screening) in the presence of a “neutralizing background.” By a proper interpretation of the parameters, our study describes (i) self-gravitating systems in a cosmological setting, and (ii) chemotaxis of bacterial populations in the original Keller-Segel model.

A lattice-gas model with two types of particles, a particle-dependent short-range coupling and a long-range repulsive Coulombic interaction, is introduced. The phase diagram of an isolated finite system of 129 particles is constructed using the bimodality properties of the observables’ distribution. We show that this generic Hamiltonian, with couplings optimized on the properties of the atomic nucleus, exhibits a specific phase diagram including, together with the well-known liquid-gas phase transition, a segregation phase that can be assimilated to nuclear fission.