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A gap in understanding the link between continuum theories of ion transport in ionic liquids and the underlying microscopic dynamics has hindered the development of frameworks for transport phenomena in these concentrated electrolytes. Here, we construct a continuum theory for ion transport in ionic liquids by coarse graining a simple exclusion process of interacting particles on a lattice. The resulting dynamical equations can be written as a gradient flow with a mobility matrix that vanishes at high densities. This form of the mobility matrix gives rise to a charging behaviour that is different to the one known for electrolytic solutions, but which agrees qualitatively with the phenomenology observed in experiments and simulations., Comment: To appear in PRL

We apply a recently developed method for the analysis of spatiotemporal data to extract the dynamical equations that describe an experiment on traveling-wave convection in a binary fluid. The technique is based on nonlinear regression analysis and allows the nonparametric estimation of the functions involved in these equations. We find that the system is well described by a pair of coupled complex Ginzburg-Landau equations, and the coefficient of the term that describes the interaction between the two oppositely propagating waves can be determined.

Brittle failures of materials and earthquakes generate acoustic/seismic waves which lead to radiation damping feedbacks that should be introduced in the dynamical equations of crack motion. We present direct experimental evidence of the importance of this feedback on the acoustic noise spectrum of well-controlled spring-block sliding experiments performed on a variety of smooth surfaces. The full noise spectrum is quantitatively explained by a simple noisy harmonic oscillator equation with a radiation damping force proportional to the derivative of the acceleration, added to a standard viscous term., Comment: 4 pages including 3 figures. Replaced with version accepted in PRL

We propose a new continuum description of the dynamics of sandpile surfaces, which involves two populations of grains: immobile and rolling. The latter move down the slope with a constant mean velocity and a certain dispersion constant. We introduce a simple bilinear form for the interconversion processes of ``sticking'' (below the angle of repose) and ``dislodgment'' (for greater slopes). We find a ``spinodal'' angle, larger than the angle of repose, at which the surface of a tilted immobile sandpile first becomes unstable to an infinitesimal perturbation. The effect of noise on our dynamical equations is briefly outlined.

A simulation scheme for performing first-principles molecular dynamics at a constant electrode potential is presented, opening the way for a more realistic modeling of voltage-driven devices. The system is allowed to exchange electrons with a reservoir at fixed potential, and dynamical equations for the total electronic charge are derived by using the potential energy of the extended system. In combination with a thermostat, this potentiostat scheme reproduces thermal fluctuations of the charge with the correct statistics, implying a realistic treatment of the potential as a control variable. Practically, the dynamics of the charge are decoupled from the electronic structure calculations, making the scheme easily implementable in existing first-principles molecular dynamics codes. Our approach is demonstrated on a test system by considering various test cases.

We investigate chaos synchronization of small-scale motions in the three-dimensional turbulent energy cascade, via pseudo-spectral simulations of the incompressible Navier-Stokes equations. The modes of the turbulent velocity field below about 20 Kolmogorov dissipation lengths are found to be slaved to the chaotic dynamics of larger-scale modes. The dynamics of all dissipation-range modes can be recovered to full numerical precision by solving small-scale dynamical equations with the given large-scale solution as an input, regardless of initial condition. The synchronization rate exponent scales with the Kolmogorov dissipation time-scale, with possible weak corrections due to intermittency. Our results suggest that all sub-Kolmogorov length modes should be fully recoverable from numerical simulations with standard, Kolmogorov-length grid resolutions., Comment: 4 pages, two-column, 4 figures

If a long-standing selection problem in brittle fracture is to be resolved, one must begin with dynamical equations suited to comparison with experiment. Such an equation is derived here in closed form by finding the energy flux to the tip of a slowly accelerating crack in a brittle strip

Results of direct numerical simulation of isotropic turbulence of surface gravity waves in the framework of Hamiltonian equations are presented. For the first time simultaneous formation of both direct and inverse cascades was observed in the framework of primordial dynamical equations. At the same time, strong long waves background was developed. It was shown, that obtained Kolmogorov spectra are very sensitive to the presence of this condensate. Such situation has to be typical for experimental wave tanks, flumes, and small lakes., 6 pages, 6 figures

The opening motion of a bileaflet valve driven by a pulsed stream is studied in the limiting condition of rigid massless leaflets closing a two-dimensional channel. This simple arrangement allows us to write simple dynamical equations for the solid that are solved numerically with the Navier-Stokes equation for the fluid. The analysis is focused on the influence of asymmetry on the coupled fluid-valve dynamics when parameters are taken with references to cardiac valves. Results show that the wake generation from the leaflet's trailing edge can be partly inhibited; the primary vortex downstream does not occur in an intermediate range of asymmetry. The potential emergence of such a phenomenon in realistic cases would present implications in development of diagnostic schemes.

We propose a practically accessible non-mean-field ground state of Bose-Einstein condensation (BEC), which occurs in an interspecies two-particle entangled state, and is thus described by an entangled order parameter. A suitably defined entanglement entropy is used as the characterization of the non-mean-field nature, and is found to persist in a wide parameter regime. The interspecies entanglement leads to novel interference terms in the dynamical equations governing the single particle orbital wavefunctions. Experimental feasibility and several methods of probe are discussed. We urge the study of multi-channel scattering between different species of atoms., Comment: V1: 5 pages, 4 figures. Accepted by Phys. Rev. Lett.; V2: A couple of very minor typos corrected, published

The dynamical behavior of the surface tension of two initially immiscible phases on raising the temperature to a value greater than or equal to the critical temperature is studied using analytic techniques, mean field dynamical equations, Monte Carlo simulations, and molecular dynamics simulations. Distinct behavior is predicted in situations with a conserved order parameter and when no conservation law is operative. A novel scaling form is obtained for a system evolving to equilibrium at its critical temperature

Recently formulated techniques for controlling chaotic dynamics face a fundamental problem when the system is high dimensional, and this problem is present even when the chaotic attractor is low dimensional. Here we introduce a procedure for controlling a chaotic time signal of an arbitrarily high dimensional system, without assuming any knowledge of the underlying dynamical equations. Specifically, we formulate a feedback control that requires modeling the local dynamics of only a single or a few of the possibly infinite number of phase-space variables.

By means of an asymptotic analysis, two distinct approaches to incompressibility are found for a low-Mach-number ideal fluid, distinguished according to the relative magnitudes of temperature, density, and pressure fluctuations. For heat-conduction-dominated-fluids, temperature and density fluctuations are predicted to be anticorrelated, and the classical passive scalar equation for temperature is recovered, whereas a generalized ``pseudosound'' relationship for the fluctuations is found for heat-conduction-modified fluids, together with a modified thermal equation. The full set of nearly incompressible dynamical equations is described.

The Pauli principle is introduced into the theory of the optical potential in a consistent manner. This is facilitated by an appropriate choice of off-shell extension for the two-fragment transition operators. Dynamical equations for the optical potential are derived and low-order approximations are discussed.

For quantum bound systems whose classical versions are nonintegrable, coupled dynamical equations for both energy levels and eigenfunctions with a nonintegrability parameter $t$ taken as "time" are shown to be a completely integrable Calogero-Moser system in 1 + 1 dimensions with internal complex vector space. Lax forms and their complete algebraic solutions are given which, in place of statistical mechanics procedures, determine possible energy spectrum and wave-function patterns at an arbitrary value of $t$.

International audience; We develop an inverse geometric optimization technique that allows the derivation of optimal and robust exact solutions of low-dimension quantum control problems driven by external fields: we determine in the dynamical variable space optimal trajectories constrained to robust solutions by Euler-Lagrange optimization; the control fields are then derived from the obtained robust geodesics and the inverted dynamical equations. We apply this method, referred to as robust inverse optimization (RIO), to design optimal control fields producing a complete or half population transfer and a NOT quantum gate robust with respect to the pulse inhomogeneities. The method is versatile and can be applied to numerous quantum control problems, e.g. other gates, other types of imperfections, Raman processes, or dynamical decoupling of undesirable e↵ects.