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Anomalous large thermal conductivity has been observed numerically and experimentally in one and two dimensional systems. All explicitly solvable microscopic models proposed to date did not explain this phenomenon and there is an open…
In this paper we consider the dynamics of harmonically-confined atomic gases. We present various general results which are independent of particle statistics, interatomic interactions and dimensionality. Of particular interest is the…
Iterative gradient-based algorithms have been increasingly applied for the training of a broad variety of machine learning models including large neural-nets. In particular, momentum-based methods, with accelerated learning guarantees, have…
We consider a Bose-Einstein condensate driven by periodic delta-kicks. In contrast to first-order descriptions, which predict rapid, unbounded growth of the noncondensate in resonant parameter regimes, the consistent treatment of condensate…
A model of clustering dynamics is proposed for a population of spatially distributed active rotators. A transition from excitable to oscillatory dynamics is induced by the increase of the local density of active rotators. It is interpreted…
Predicting diverse object motions from a single static image remains challenging, as current video generation models often entangle object movement with camera motion and other scene changes. While recent methods can predict specific…
A one-dimensional dynamical system with a marginal quasiperiodic gradient is presented as a mathematical extension of a nonuniform oscillator. The system exhibits a nonchaotic stagnant motion, which is reminiscent of intermittent chaos. In…
We introduce a new model of aggregation of particles where in addition to diffusion and aggregation upon contact, a single unit of mass can dissociate from a conglomerate. This dissociation move conserves the total mass and leads to a…
This is a review paper concerned with the global consistency of the quantum dynamics of non-commutative systems. Our point of departure is the theory of constrained systems, since it provides a unified description of the classical and…
Understanding the spontaneous emergence of dislocation patterns during plastic deformation is a long standing challenge in dislocation theory. During the past decades several phenomenological continuum models of dislocation patterning were…
Dynamical systems are found in innumerable forms across the physical and biological sciences, yet all these systems fall naturally into universal equivalence classes: conservative or dissipative, stable or unstable, compressible or…
The mobility of an overdamped particle, in a periodic potential tilted by a constant external field and moving in a medium with periodic friction coefficient is examined. When the potential and the friction coefficient have the same…
The complex behavior of many natural and engineered systems emerges from the interaction of a small number of effective degrees of freedom. Discovering the physical basis of the interactions between these degrees of freedom directly from…
The continuum equations of fluid mechanics are rederived with the intention of keeping certain mechanical and thermodynamic concepts separate. A new "mechanical" mass density is created to be used in computing inertial quantities, whereas…
We describe an experiment involving a mass oscillating in a viscous fluid and analyze viscous damping of harmonic motion. The mechanical oscillator is tracked using a simple webcam and an image processing algorithm records the position of…
The Continuum Dislocation Dynamics (CDD) theory and the Discrete Dislocation Dynamics (DDD) method are compared based on concise mathematical formulations of the coarse graining of discrete data. A numerical tool for converting from a…
We consider a two-dimensional model of double-diffusive convection and its time discretisation using a second-order scheme which treat the nonlinear term explicitly (backward differentiation formula with a one-leg method). Uniform bounds on…
The problem of determining the mathematical model of the dynamics of multi-dimensional control systems in the presence of noise under the condition that the correlation functions cannot be found. Known statistical dynamics of linear systems…
Rotational effects are commonly neglected when considering the dynamics of freely rising or settling isotropic particles. Here, we demonstrate that particle rotations play an important role for rising as well as for settling cylinders in…
Extending our previous work on 2D growth for the Laplace equation we study here {\it multidimensional} growth for {\it arbitrary elliptic} equations, describing inhomogeneous and anisotropic pattern formations processes. We find that these…