We consider a nonlinear system and show the unexpected and surprising result that, even for high dissipation, the mean energy of a particle can attain higher values than when there is no dissipation in the system. We reconsider the time-dependent annular billiard in the presence of inelastic collisions with the boundaries. For some magnitudes of dissipation, we observe the phenomenon of boundary crisis, which drives the particles to an asymptotic attractive fixed point located at a value of energy that is higher than the mean energy of the nondissipative case and so much higher than the mean energy just before the crisis. We should emphasize that the unexpected results presented here reveal the importance of a nonlinear dynamics analysis to explain the paradoxical strategy of introducing dissipation in the system in order to gain energy.

Parametrically driven spatially extended systems exhibit uniform oscillations which are modulationally unstable. The resulting periodic state evolves to the creation of a gas of dissipative solitons. Driven by the interaction of dissipative solitons, the multisoliton state undergoes a cascade of coalescence processes, where the average soliton separation distance obeys a temporal self-similar law. Starting from the soliton pair interaction law, we have derived analytically and characterized the law of this multisoliton coarsening process. A comparison of numerical results obtained with different models such as the parametrically driven damped nonlinear Schrödinger equation, a vertically driven chain of pendula, and a parametrically forced magnetic wire, shows remarkable agreement. Both phenomena, the pair interaction law and the coarsening process, are also observed experimentally in a quasi-one-dimensional layer of Newtonian fluid which is oscillated vertically.

We study the relaxation process in a two-dimensional lattice gas model, based on the concept of geometrical frustration. In this model the particles are $k$-mers that can both randomly translate and rotate on the planar triangular lattice. In the absence of rotation, the diffusion of hard-core particles in crossed single-file systems is investigated. We monitor, for different densities, several quantities: mean-square displacement, the self-part of the van Hove correlation function, and the self-intermediate scattering function. We observe a considerable slowing of diffusion on a long-time scale when suppressing the rotational motion of $k$-mers; our system is subdiffusive at intermediate times between the initial transient and the long-time diffusive regime. We show that the self-part of the van Hove correlation function exhibits, as a function of particle displacement, a stretched exponential decay at intermediate times. The self-intermediate scattering function (SISF), displaying slower than exponential relaxation, suggests the existence of heterogeneous dynamics. For each value of density, the SISF is well described by the Kohlrausch-Williams-Watts law; the characteristic timescale $\tau \left(q_n\right)$ is found to decrease with the wave vector $q_n$ according to a simple power law. Furthermore, the slowing of the dynamics with density ${\rho }_0$ is consistent with the scaling law $1/\tau (q_n;{\rho }_0)\propto {({\rho }_c-{\rho }_0)}^{\varkappa }$, with the same exponent $\varkappa =3.34\pm 0.12$ for all wave vectors $q_n$. The density ${\rho }_c$ is approximately equal to the closest packing limit, ${\theta }_{\text{CPL}}⪅1$, for dimers on the two-dimensional triangular lattice. The self-diffusion coefficient $D_s$ scales with the same power-law exponent and critical density.

We consider a quantum system linearly coupled to a reservoir of harmonic oscillators. For finite coupling strengths, the stationary distribution of the damped system deviates from the predictions of standard thermodynamics. With the help of the quantum Hamiltonian of mean force, we quantify this deviation exactly for a harmonic oscillator and provide approximations in the limit of high and low temperatures and weak and strong couplings. Moreover, in the semiclassical regime, we use the quantum Smoluchowski equation to obtain results valid for any potential. We finally give a physical interpretation of the deviation in terms of the initial system-reservoir coupling.

This work focuses on the mechanical response of dry granular materials under steady, simple shear conditions. In particular, the goal is to obtain a complete rheology able to describe the material behavior within the entire range of concentrations for which the flow can be considered dense. The total stress is assumed to be the linear sum of a frictional and a kinetic component. The frictional and the kinetic contributions are modeled in the context of the critical state theory and the kinetic theory of dense granular gases, respectively; in the latter, the correlated motion among the particles, which is likely to occur at high concentration, is also included. In accordance with recent findings on disordered granular packings, the frictional component of stresses is assumed to vanish when the concentration is below the random loose packing. According to this approach, four nondimensional quantities govern steady, simple shear flows: the concentration, the shear to normal stress ratio, the ratio of the time scales associated with the motion perpendicular and parallel to the flow, and the ratio between the particle stiffness and the normal stress. The present theory allows us to reproduce, in a notable way, both numerical simulations on simple shear flows of disks and physical experiments on incline flows of glass spheres taken from the literature.

The local cooling rates of the components of a vibrated binary granular mixture in a steady state are investigated. The accuracy of the expression obtained by assuming a local homogeneous cooling state distribution of the gas is analyzed by comparing it with molecular dynamics simulation results. A good agreement is observed. Also, the profiles of the partial temperatures are compared with the theoretical prediction following from the application of the Chapman-Enskog method to solve the kinetic Enskog equations of the mixture. In this case, the agreement is satisfactory if the boundary layers near the walls are excluded. The implications of the results are discussed.

The anisotropy of magnetic emulsions induced by simultaneously acting electric and magnetic fields is theoretically and experimentally investigated. Due to the anisotropy, the electric conductivity and magnetic permeability of a magnetic emulsion are no longer scalar coefficients, but are tensors. The electric conductivity and magnetic permeability tensors of sufficiently diluted emulsions in sufficiently weak electric and magnetic fields are found as functions of the electric and magnetic intensity vectors. The theoretically predicted induced anisotropy was verified experimentally. The experimental data are fitted in order to calculate the dimensions of the ellipsoidal drops of the emulsion distorted by the electric and magnetic fields. The dependence of the calculated fitting parameter on the intensity of the magnetic field is compared with the theoretical one. The results of the analysis of the experimental data are discussed.

Agent-based stochastic models for finite populations have recently received much attention in the game theory of evolutionary dynamics. Both the ultimate fixation and the pre-fixation transient behavior are important to a full understanding of the dynamics. In this paper, we study the transient dynamics of the well-mixed Moran process through constructing a landscape function. It is shown that the landscape playing a central theoretical “device” that integrates several lines of inquiries: the stable behavior of the replicator dynamics, the long-time fixation, and continuous diffusion approximation associated with asymptotically large population. Several issues relating to the transient dynamics are discussed: (i) multiple time scales phenomenon associated with intra- and inter-attractoral dynamics; (ii) discontinuous transition in stochastically stationary process akin to Maxwell construction in equilibrium statistical physics; and (iii) the dilemma diffusion approximation facing as a continuous approximation of the discrete evolutionary dynamics. It is found that rare events with exponentially small probabilities, corresponding to the uphill movements and barrier crossing in the landscape with multiple wells that are made possible by strong nonlinear dynamics, plays an important role in understanding the origin of the complexity in evolutionary, nonlinear biological systems.

We consider a fully connected network of leaky integrate-and-fire neurons with spike-timing-dependent plasticity. The plasticity is controlled by a parameter representing the expected weight of a synapse between neurons that are firing randomly with the same mean frequency. For low values of the plasticity parameter, the activities of the system are dominated by noise, while large values of the plasticity parameter lead to self-sustaining activity in the network. We perform event-driven simulations on finite-size networks with up to 128 neurons to find the stationary synaptic weight conformations for different values of the plasticity parameter. In both the low- and high-activity regimes, the synaptic weights are narrowly distributed around the plasticity parameter value consistent with the predictions of mean-field theory. However, the distribution broadens in the transition region between the two regimes, representing emergent network structures. Using a pseudophysical approach for visualization, we show that the emergent structures are of “path” or “hub” type, observed at different values of the plasticity parameter in the transition region.

We show that the simple analytical model proposed by Zhang and Marko [Phys. Rev. E 77, 031916 (2008)] to illustrate Maxwell relations for single-DNA experiments can be improved by including the zero-force entropy of a Gaussian chain. The resulting model is in excellent agreement with the discrete persistent-chain model and is in a form convenient for analyzing experimental data.

In this paper we propose a scaling argument to quantify the role of added electrolyte salt in affecting the stability and the morphology of preformed surface nanobubbles on hydrophobic substrates like the water-OTS-silicon or the water-HOPG interfaces. The added salt controls the electric double layer formation as well as affects the zeta ($\zeta$) potential at the air-water and solid-water interfaces. The resulting electrostatic wetting tension acts in conjunction with the air-water surface tension (analogous to electrowetting scenarios), thereby affecting the nanobubble morphologies. Weak $\zeta$ potential of the water-HOPG interface or the water-OTS-silicon interface at acidic pH ensures that the added salt will have imperceptible effect on the corresponding preformed surface nanobubbles, validating the experimental observations. However, at alkaline buffer pH for the OTS-silicon substrate, under certain system conditions, salt-induced $\zeta$ potential can be substantially high so that the properties of preformed surface nanobubbles will be affected. This paper will thus readdress the long-held universal notion that added salt, no matter in what concentration, will not influence the properties of preformed surface nanobubbles.

Magnetorotational instability (MRI) triggers turbulence and enables outward transport of angular momentum in hydrodynamically stable accretion discs. By using the WKB approximation and methods of singular function theory, we resolve two different paradoxes of MRI that appear in the limits of infinite and vanishing magnetic Prandtl number. For the latter case, we derive a strict limit of the critical Rossby number. This limit of ${\mathrm{Ro}}_{\mathrm{c}}=-0.802$, which appears for a finite Lundquist number of $\mathit{S}=0.618$, extends the formerly known inductionless Liu limit of ${\mathrm{Ro}}_{\mathrm{c}}=-0.828$ valid at $\mathit{S}=0$.

The one-dimensional collisionless expansion into a vacuum of a plasma with a bi-Maxwellian electron distribution function and a single ion species is studied both theoretically and numerically. A shock wave occurs when the ratio of the temperatures between the hot and the cold electrons is larger than $5+\sqrt{24}$ [B. Bezzerides, D. W. Forslund, and E. L. Lindman, Phys. Fluids 21, 2179 (1978)]. The theoretical model presented here gives a coherent and complete description of the rarefaction shock and its effects on the ion acceleration process. Analytical expressions of the characteristics of the shock are given. The analytical findings are compared to the results of a hybrid code describing the plasma expansion, and an excellent agreement is obtained.

The process of heat conduction has recently found application in personalized recommendation [Zhou et al., Proc. Natl. Acad. Sci. USA 107, 4511 (2010)], which is of high diversity but low accuracy. By decreasing the temperatures of small-degree objects, we present an improved algorithm, called biased heat conduction, which could simultaneously enhance the accuracy and diversity. Extensive experimental analyses demonstrate that the accuracy on MovieLens, Netflix, and Delicious datasets could be improved by 43.5$\%$, 55.4$\%$ and 19.2$\%$, respectively, compared with the standard heat conduction algorithm and also the diversity is increased or approximately unchanged. Further statistical analyses suggest that the present algorithm could simultaneously identify users' mainstream and special tastes, resulting in better performance than the standard heat conduction algorithm. This work provides a creditable way for highly efficient information filtering.

In this paper we study the influence of localized or widespread nonhomogeneous temperature profiles on the stability and intensity of vertical vortices generated in a cylindrical annulus by a convective instability. Localized profiles lead to more stable vortices while widespread inhomogeneities intensify the spin motion around the inner cylinder.

Motivated by the phenomenology of transport through the Golgi apparatus of cells, we study a multispecies model with boundary injection of one species of particle, interconversion between the different species of particle, and driven diffusive movement of particles through the system by chipping of a single particle from a site. The model is analyzed in one dimension using equations for particle currents. It is found that, depending on the rates of various processes and the asymmetry in the hopping, the system may exist either in a steady phase, in which the average mass at each site attains a time-independent value, or in a “growing” phase, in which the total mass grows indefinitely in time, even in a finite system. The growing phases have interesting spatial structure. In particular, we find phases in which some spatial regions of the system have a constant average mass, while other regions show unbounded growth.

We consider strips of Ising spins at criticality. For strips of width $N$ sites, subdominant (additive) finite-size corrections to scaling are assumed to be of the form $a_k/N^k$ for the free energy, and $b_k/N^k$ for inverse correlation length, with integer values of $k$. We investigate the set $\{a_k,b_k\}$ ($k\ge 2$) by exact evaluation and numerical transfer-matrix diagonalization techniques, and their changes upon varying anisotropy of couplings, spin quantum number $S$, and (finite) interaction range, in all cases for both periodic (PBCs) and free (FBCs) boundary conditions across the strip. We find that the coefficient ratios $b_k/a_k$ remain constant upon varying coupling anisotropy for $S=1/2$ and first-neighbor couplings, for both PBCs and FBCs (albeit at distinct values in either case). Such apparently universal behavior is not maintained upon changes in $S$ or interaction range.

It is known that for a particle held in an optical trap the interaction of thermal fluctuations with a nonconservative scattering force can cause a persistent nonequilibrium probability flux in the particle position. We investigate position fluctuations associated with this nonequilibrium flux analytically and through simulation. We introduce a model which reproduces the nonequilibrium effects, and in which the magnitude of additional position fluctuations can be calculated in closed form. The ratio of additional nonconservative fluctuations to direct thermal fluctuations scales inversely with the square root of trap power, and is small for typical experimental parameters. In a simulated biophysical experiment the nonconservative scattering force does not significantly increase the observed fluctuations in the length of a double-stranded DNA tether.

We use a simple nonlinear scaler displacement model to calculate the distribution of effects created by a shear stress on a double-stranded DNA (dsDNA) molecule and the value of shear force $F_c$ that is required to separate the two strands of a molecule at a given temperature. It is shown that for molecules of base pairs fewer than than 21, the entire single strand moves in the direction of applied force, whereas for molecules having base pairs more than 21, part of the strand moves in the opposite direction under the influence of force acting on the other strand. This result as well as the calculated values of $F_c$ as a function of length of dsDNA molecules are in very good agreement with the experimental values of Hatch et al. [Phys. Rev. E 78, 011920 (2008)].

We studied the effects of surface hydrophobicity on the conformational changes of different length polypeptides by calculating the free energy difference between peptide structures using the bias-potential Monte Carlo technique and the probability ratio method. It was found that the hydrophobic surface plays an important role in the stability of secondary structures of the polypeptides with hydrophobic side chains. For short GAAAAG peptides, the hydrophobic surface destabilizes the α helix but stabilizes the β hairpin in the entire temperature region considered in our study. Interestingly, when the surface hydrophobic strength ε${}_{hpsf}\ge \epsilon {}_{hp}$, the most stable structure in the low temperature region changes from α helix to β hairpin, and the corresponding phase transition temperature increases slightly. For longer GAAAAAAAAAAG peptides, the effects of the relatively weak hydrophobic surface (ε${}_{hpsf}$ < ε${}_{hp}$) on α-helical structures may be neglected, while the relatively strongly hydrophobic surface (ε${}_{hpsf}\ge \epsilon {}_{hp}$) leads to the obvious partial helicity loss. In contrast, the stability of β structures can be enhanced significantly by the hydrophobic surface, especially by the strongly hydrophobic surface, at low and intermediate temperatures. At high temperatures, in addition to thermal fluctuations, the strongly hydrophobic surface (ε${}_{hpsf}>\epsilon {}_{hp}$) may further disturb the formation of both α-helical and β structures. Moreover, the phase transition temperature between α-helical structures and random coils significantly decreases due to the helicity loss when ε${}_{hpsf}>\epsilon {}_{hp}$. Our findings provide a basic and quantitative picture for understanding the effects of a hydrophobic surface on the conformational changes of the polypeptides with hydrophobic side chains. From an application viewpoint, the present study is helpful in developing alternative strategies of producing high-quality biological fibrillar materials and functional nanoscale devices by the self-assembly of the polypeptides on hydrophobic surfaces.