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This article introduces the class of periodic trawl processes, which are continuous-time, infinitely divisible, stationary stochastic processes, that allow for periodicity and flexible forms of their serial correlation, including both…
We study chiral models in one spatial dimension, both static and periodically driven. We demonstrate that their topological properties may be read out through the long time limit of a bulk observable, the mean chiral displacement. The…
In microfluidic devices, inertia drives particles to focus on a finite number of inertial focusing streamlines. Particles on the same streamline interact to form one-dimensional microfluidic crystals (or "particle trains"). Here we develop…
Topological edge states are known to emerge in certain quasicrystals. We investigate a topological quasicrystal in the presence of nonlinearity by generalizing the Toda lattice to include modulated periodic hoppings, where the period is…
The similarity in mechanical properties of dense active matter and sheared amorphous solids has been noted in recent years without a rigorous examination of the underlying mechanism. We develop a mean-field model that predicts that their…
In this article it is proved that the dynamical properties of a broad class of semilinear parabolic problems are sensitive to arbitrarily small but smooth perturbations of the nonlinear term, when the spatial dimension is either equal to…
We study the excitation and damping of tides in close binary systems, accounting for the leading order nonlinear corrections to linear tidal theory. These nonlinear corrections include two distinct effects: three-mode nonlinear interactions…
Due to studies in nonequilibrium (periodically-driven) topological matter, it is now understood that some topological invariants used to classify equilibrium states of matter do not suffice to describe their nonequilibrium counterparts.…
Oscillons are spatially stationary, quasi-periodic solutions of nonlinear field theories seen in settings ranging from granular systems, low temperature condensates and early universe cosmology. We describe a new class of oscillon in which…
The dynamical behavior of the column that made up binary granular beads is investigated systematically by tracking the displacement of particles in the collapse process. An experimental setup is first devised to control the quasi-static…
In the following we consider a 2-dimensional system of ODE's containing quasiperiodic terms. The system is proposed as an extension of Mathieu-type equations to higher dimensions, with emphasis on how resonance between the internal…
We show that a scaling approach successfully characterizes clustering and intermittency in space and time, in systems of noninteracting particles driven by fluctuating surfaces. We study both the steady state and the approach to it, for…
Active hydrodynamic theories are a powerful tool to study the emergent ordered phases of internally driven particles such as bird flocks, bacterial suspension and their artificial analogues. While theories of orientationally ordered phases…
Driven systems offer the potential to realize a wide range of non-equilibrium phenomena that are inaccessible in static systems, such as the discrete time crystals. Time rondeau crystals with a partial temporal order have been proposed as a…
Discrete time crystals are novel phases of matter that break the discrete time translational symmetry of a periodically driven system. In this work, we propose a classical system of weakly-nonlinear parametrically-driven coupled oscillators…
A model demonstrating existence of a thermodynamically stable quantum time-space crystal has been proposed and studied. This state is characterized by an order parameter periodic in both real and imaginary times. The average of the order…
A new class of critical points, termed as perpetual points, where acceleration becomes zero but the velocity remains non-zero, are observed in dynamical systems. The velocity at these points is either maximum or minimum or of inflection…
We construct, to leading orders in the momentum expansion, an effective theory of a chiral $p_x + ip_y$ two-dimensional fermionic superfluid at zero temperature that is consistent with nonrelativistic general coordinate invariance. This…
We present a numerical study of spatially quasi-periodic traveling waves on the surface of an ideal fluid of infinite depth. This is a generalization of the classic Wilton ripple problem to the case when the ratio of wave numbers satisfying…
In the last two years we have witnessed the exciting experimental discovery of soft matter with nontrivial quasiperiodic long-range order - a new form of matter termed a soft quasicrystal. Two groups have independently discovered such order…