Parametric excitation of autoresonant solutions of the nonlinear Schrodinger (NLS) equation by a chirped frequency traveling wave is discussed. Fully nonlinear theory of the process is developed based on Whitham's averaged variational principle and its predictions verified in numerical simulations. The weakly nonlinear limit of the theory is used to find the threshold on the amplitude of the driving wave for entering the autoresonant regime. It is shown that above the threshold, a flat (spatially independent) NLS solution can be fully converted into a traveling wave. A simplified, few spatial harmonics expansion approach is also developed for studying this nonlinear mode conversion process, allowing interpretation as autoresonant interaction within triads of spatial harmonics.

Learning and memory are acquired through long-lasting changes in synapses. In the simplest models, such synaptic potentiation typically leads to runaway excitation, but in reality there must exist processes that robustly preserve overall stability of the neural system dynamics. How is this accomplished? Various approaches to this basic question have been considered. Here we propose a particularly compelling and natural mechanism for preserving stability of learning neural systems. This mechanism is based on the global processes by which metabolic resources are distributed to the neurons by glial cells. Specifically, we introduce and study a model composed of two interacting networks: a model neural network interconnected by synapses that undergo spike-timing-dependent plasticity; and a model glial network interconnected by gap junctions that diffusively transport metabolic resources among the glia and, ultimately, to neural synapses where they are consumed. Our main result is that the biophysical constraints imposed by diffusive transport of metabolic resources through the glial network can prevent runaway growth of synaptic strength, both during ongoing activity and during learning. Our findings suggest a previously unappreciated role for glial transport of metabolites in the feedback control stabilization of neural network dynamics during learning.

In the traditional setup of the public goods game all players are involved in every available group and the mutual benefit is shared among competing cooperator and defector strategies. However, in real life situations the group formation of players could be more sophisticated because not all players are attractive enough for others to participate in a joint venture. What if only those players who are successful enough to the neighbors can initiate a group formation and establish a game? To elaborate this idea we employ a modified protocol and demonstrate that a carefully chosen threshold to establish a joint venture could efficiently improve the cooperation level even if the synergy factor would suggest a full defector state otherwise. The microscopic mechanism that is responsible for this effect is based on the asymmetric consequences of competing strategies: while the success of a cooperator provides a long-time well-being for the neighborhood, the temporary advantage of defection cannot be maintained if the protocol is based on the success of leaders.

The diffusion of a reactant to a binding target plays a key role in many biological processes. The reaction radius at which the reactant and target may interact is often a small parameter relative to the diameter of the domain in which the reactant diffuses. We develop uniform in time asymptotic expansions in the reaction radius of the full solution to the corresponding diffusion equations for two separate reactant-target interaction mechanisms: the Doi or volume reactivity model and the Smoluchowski-Collins-Kimball partial-absorption surface reactivity model. In the former, the reactant and target react with a fixed probability per unit time when within a specified separation. In the latter, upon reaching a fixed separation, they probabilistically react or the reactant reflects away from the target. Expansions of the solution to each model are constructed by projecting out the contribution of the first eigenvalue and eigenfunction to the solution of the diffusion equation and then developing matched asymptotic expansions in Laplace-transform space. Our approach offers an equivalent, but alternative, method to the pseudopotential approach we previously employed [Isaacson and Newby, Phys. Rev. E 88, 012820 (2013)] for the simpler Smoluchowski pure-absorption reaction mechanism. We find that the resulting asymptotic expansions of the diffusion equation solutions are identical with the exception of one parameter: the diffusion-limited reaction rates of the Doi and partial-absorption models. This demonstrates that for biological systems in which the reaction radius is a small parameter, properly calibrated Doi and partial-absorption models may be functionally equivalent.

Bending and Gaussian moduli of a homogenious single-component lipid bilayer are calculated analytically using microscopic model of the lipid hydrocarbon chains. The approach allows for thermodynamic averaging over different chains conformations. Each chain is modeled as a flexible string with finite bending rigidity and an incompressible cross-section area. The interchain steric repulsion is accounted for self-consistently determined single-chain confining parabolic potential. The model provides a simple analytical expression for the membrane bending modulus, which falls within a range of experimental values. An observed dependence of the modulus on hydrocarbon chain length is also reproduced. Correspondence between our microscopic model and the membrane theory of elasticity is established.

In contrast to thermotropic biaxial nematic phases, for which some long sought for experimental realizations have been obtained, no experimental realizations are yet known for their tetrahedratic and cubatic counterparts, involving orientational orders of ranks 3 and 4, respectively, also studied theoretically over the last few decades. In previous studies, cubatic order has been found for hard-core or continuous models consisting of particles possessing cubic or nearly cubic tetragonal or orthorhombic symmetries; in a few cases, hard-core models involving uniaxial ($D_{\infty h}$-symmetric) particles have been claimed to produce cubatic order as well. Here we address by Monte Carlo simulation a lattice model consisting of uniaxial particles coupled by long-range dispersion interactions of the London-De Boer-Heller type; the model was found to produce no second-rank nematic but only fourth-rank cubatic order, in contrast to the nematic behavior long known for its counterpart with interactions truncated at nearest-neighbor separation.

We study the clustering of inertial particles using a periodic kinematic simulation. Particle clustering is observed for different pairs of Stokes number and Froude number and different spectral power laws $\left(1.4\le p\le 2.1\right)$. The main focus is to identify and then quantify the effect of $p$ on the clustering attractor—by attractor we mean the set of points in the physical space where the particles settle when time tends to infinity. It is observed that spectral power laws can have a dramatic effect on the attractor shape. In particular, we observed an attractor type which was not present in previous studies for Kolmogorov spectra ($p=5/3$).

We present a numerical approach for the solution of the dissipative Gross-Pitaevskii equation coupled to the reservoir equation governing the exciton-polaritons Bose-Einstein condensation. It is based on the finite difference method applied to space variables and on the fourth order Range-Kutta algorithm applied to the time variable. Numerical tests illustrate the stability and accuracy of the proposed scheme. Then results on the behavior of the condensate under large Gaussian pumping and around the threshold are presented. We determine the threshold through the particular behavior of the self-energy and characterize it by tracking the establishment time of the steady state.

This paper introduces an analytical description of the probability density function of the dissipated and injected powers $p\left(j_{\mathrm{dis}}\right)$ and $p\left(j_{\mathrm{inj}}\right)$, respectively, in a paradigmatic nonequilibrium damped system in contact with a work reservoir that is analytically represented by telegraph noise and to which one can assign an effective temperature. This approach is able to overcome the well-known impossibility of obtaining closed solutions to steady-state distributions of this system and allows determining a superexponential fluctuation relation of the injected power, which is not even asymptotically exponential as for (shot-noise) Poissonian reservoirs. In the white-noise limit, that relation converges to the exponential formula that is standard in thermal systems; however, the distribution of the injected power remains quite different from that of the latter instance. Surprisingly, it is actually shown that a Gaussian distribution, which is archetypal of thermal systems, for the injected power can be achievable only for athermal reservoirs of this kind.

We investigate thermal transport along a one-dimensional lattice of classical inertial rotators, with attractive couplings that decrease with distance as $r^{-\alpha } \left(\alpha \ge 0\right)$, subject at its ends to Brownian heat reservoirs at different temperatures with average value $T$. By means of numerical integration of the equations of motion, we show the effects of the range of the interactions in the temperature profile and energy transport and determine the domain of validity of Fourier's law in this context. We find that Fourier's law, as signaled by a finite $\kappa$ in the thermodynamic limit, holds only for sufficiently short-range interactions, with $\alpha >{\alpha }_c\left(T\right)$. For $\alpha <{\alpha }_c\left(T\right)$, a kind of insulator behavior emerges at any $T$.

We present a resummed mean-field approximation for inferring the parameters of an Ising or a Potts model from empirical, noisy, one- and two-point correlation functions. Based on a resummation of a class of diagrams of the small correlation expansion of the log-likelihood, the method outperforms standard mean-field inference methods, even when they are regularized. The inference is stable with respect to sampling noise, contrarily to previous works based either on the small correlation expansion, on the Bethe free energy, or on the mean-field and Gaussian models. Because it is mostly analytic, its complexity is still very low, requiring an iterative algorithm to solve for $N$ auxiliary variables, that resorts only to matrix inversions and multiplications. We test our algorithm on the Sherrington-Kirkpatrick model submitted to a random external field and large random couplings, and demonstrate that even without regularization, the inference is stable across the whole phase diagram. In addition, the calculation leads to a consistent estimation of the entropy of the data and allows us to sample form the inferred distribution to obtain artificial data that are consistent with the empirical distribution.

We present a method to derive an analytical expression for the roughness of an eroded surface whose dynamics are ruled by cellular automaton. Starting from the automaton, we obtain the time evolution of the height average and height variance (roughness). We apply this method to the etching model in $1+1$ dimensions, and then we obtain the roughness exponent. Using this in conjunction with the Galilean invariance we obtain the other exponents, which perfectly match the numerical results obtained from simulations. These exponents are exact, and they are the same as those exhibited by the Kardar-Parisi-Zhang (KPZ) model for this dimension. Therefore, our results provide proof for the conjecture that the etching and KPZ models belong to the same universality class. Moreover, the method is general, and it can be applied to other cellular automata models.

Motivated by uncertainty quantification in natural transport systems, we investigate an individual-based transport process involving particles undergoing a random walk along a line of point sinks whose strengths are themselves independent random variables. We assume particles are removed from the system via first-order kinetics. We analyze the system using a hierarchy of approaches when the sinks are sparsely distributed, including a stochastic homogenization approximation that yields explicit predictions for the extrinsic disorder in the stationary state due to sink strength fluctuations. The extrinsic noise induces long-range spatial correlations in the particle concentration, unlike fluctuations due to the intrinsic noise alone. Additionally, the mean concentration profile, averaged over both intrinsic and extrinsic noise, is elevated compared with the corresponding profile from a uniform sink distribution, showing that the classical homogenization approximation can be a biased estimator of the true mean.

We use a nanofluidic system to investigate the emergence of thermally driven collective phenomena along a single polymer chain. In our approach, a single DNA molecule is confined in a nanofluidic slit etched with arrays of embedded nanocavities; the cavity lattice is designed so that a single chain occupies multiple cavities. Fluorescent video-microscopy data shows fluctuations in intensity between cavities, including waves of excess fluorescence that propagate across the cavity-straddling molecule, corresponding to propagating fluctuations of contour overdensity in the cavities. The transfer of DNA between neighboring pits is quantified by examining the correlation in intensity fluctuations between neighboring cavities. Correlations grow from an anticorrelated minimum to a correlated maximum before decaying, corresponding to a transfer of contour between neighboring cavities at a fixed transfer time scale. The observed dynamics can be modeled using Langevin dynamics simulations and a minimal lattice model of coupled diffusion. This study shows how confinement-based sculpting of the polymer equilibrium configuration, by renormalizing the physical system into a series of discrete cavity states, can lead to new types of dynamic collective phenomena.

Colloidal particles were sedimented onto patterned glass slides to grow three-dimensional bicrystals with a controlled structure. Three types of symmetric tilt grain boundaries between close-packed face-centered-cubic crystals were produced: $\mathrm{\Sigma }5\left(100\right),\mathrm{\Sigma }17\left(100\right)$, and $\mathrm{\Sigma }3\left(110\right)$. The structure of the crystals and their defects were visualized by confocal microscopy, and characterized by simple geometric measurements, including image difference, thresholding, and reprojection. This provided a quick and straightforward way to detect the regions in which the atoms are mobile. This atomic mobility was higher at the grain boundaries and close to the solid-liquid interface. This method was compared to the more conventional analysis based on the calculation of the local order parameter of the individual particles to identify the interface. This was used in turn to identify the presence of grooves at the grain-boundary–liquid triple junction for every type of grain boundary, except for the twin $\left[\mathrm{\Sigma }3\right(110\left)\right]$, for which no groove could be detected. Images of these grooves were processed, and the angle linking the grain boundary energy to the solid-liquid interfacial energy was measured. The resulting values of the grain boundary energy were compared to estimates based on the density deficit in the boundary.

The crystallization process of Hertzian spheres is studied by means of molecular dynamics simulations in an NPT ensemble where the total number of particles N, the pressure P, and the temperature T are kept constant. It has been observed that the bond orientational ordering rather than the translational ordering (density) plays a primary role. The crystal polymorphs are determined by the state points. Under the conditions of small supercooling, the system is likely to be nucleated into crystals that have a preference for the metastable bcc structure, which can be regarded as a manifestation of the Alexander-McTague mechanism. In contrast, small nuclei are found to have a preference for fcc symmetry under conditions of a high degree of supercooling. Prestructured precursors that act as seeds and wet on the nuclei during nucleation always have a high degree of bcc-like ordering, despite different state points. The results above may provide a clue to the understanding of the crystallization process in core-softened particles.

A continuum elastic model, describing the wrinkling instability of graphene on substrate-supported silica nanoparticles [M. Yamamoto et al., Phys. Rev. X 2, 041018 (2012)], is analytically studied, and an exact analytical expression of the critical nanoparticle separation or the maximum wrinkle length is derived. Our findings agree with the scaling property of Yamamoto et al. but improve their results. Moreover, from the elastic model we find a pseudomagnetic field as a function of the wrinkling deflection, leading to the conclusion that the middle of the wrinkled graphene may have a zero pseudomagnetic field, in marked contrast with previous results.

The scaling theory of Grossmann and Lohse [J. Fluid Mech. 407, 27 (2000)] for turbulent heat and momentum transfer is extended to the magnetoconvection case in the presence of a (strong) vertical magnetic field. A comparison with existing laboratory experiments and direct numerical simulations in the quasistatic limit allows us to restrict the parameter space to very low Prandtl and magnetic Prandtl numbers and thus to reduce the number of unknown parameters in the model. Also included is the Chandrasekhar limit, for which the outer magnetic induction field $\mathit{B}$ is large enough such that convective motion is suppressed and heat is transported by diffusion. Our theory identifies four distinct regimes of magnetoconvection that are distinguished by the strength of the outer magnetic field and the level of turbulence in the flow, respectively.

Coupled, dynamical spin-lattice models provide a unique test ground for simulations investigating the finite-temperature magnetic properties of materials under the direct influence of the lattice vibrations. These models are constructed by combining a coordinate-dependent interatomic potential with a Heisenberg-like spin Hamiltonian, facilitating the treatment of both the atomic coordinates and the spins as explicit phase variables. Using a model parameterized for bcc iron, we study the magnetic phase transition in these complex systems via the recently introduced, massively parallel replica-exchange Wang-Landau Monte Carlo method. Comparison with the results obtained from rigid lattice (spin-only) simulations shows that the transition temperature as well as the amplitude of the peak in the specific heat curve is marginally affected by the lattice vibrations. Moreover, the results were found to be sensitive to the particular choice of interatomic potential.