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We study the topological properties of one dimensional systems undergoing unitary time evolution. We show that symmetries possessed both by the initial wavefunction and by the Hamiltonian at all times may not be present in the…
The possibility of production of pulses with scale-invariant properties at presence of fluctuations of parameters of self-oscillatory system with three-dimensional phase space is shown. The system of equations of inertial nonlinearity…
Meso-scale turbulence was originally observed experimentally in various suspensions of swimming bacteria, as well as in the collective motion of active colloids. The corresponding large-scale dynamical patterns were reproduced in a simple…
From cytoskeletal networks to tissues, many biological systems behave as active materials. Their composition and stress-generation is affected by chemical reaction networks. In such systems, the coupling between mechanics and chemistry…
We predict the conditions under which two oppositely charged membranes show a dynamic, attractive instability. Two layers with unequal charges of opposite sign can repel or be stable when in close proximity. However, dynamic charge density…
Increasing evidence suggests that active matter exhibits instances of mixed symmetry that cannot be fully described by either polar or nematic formalism. Here, we introduce a minimal model that integrates self-propulsion into the active…
Induced by proteins within the cell membrane or by differential growth, heating, or swelling, spontaneous curvatures can drastically affect the morphology of thin bodies and induce mechanical instabilities. Yet, the interaction of…
The dynamics of membrane undulations inside a viscous solvent is governed by distinctive, anomalous, power laws. Inside a viscoelastic continuous medium these universal behaviors are modified by the specific bulk viscoelastic spectrum. Yet,…
We consider the failure of localized control in a nonlinear spatially extended system caused by extremely small amounts of noise. It is shown that this failure occurs as a result of a nonlinear instability. Nonlinear instabilities can occur…
Micron-size charged particles can be easily levitated in low-density plasma environments. At low pressures, suspended particles have been observed to spontaneously oscillate around an equilibrium position. In systems of many particles,…
We construct a coarse-grained effective two-dimensional (2d) hydrodynamic theory as a theoretical model for a coupled system of a fluid membrane and a thin layer of a polar active fluid in its ordered state that is anchored to the membrane.…
We study the dynamics of systems consisting of two spatially segregated ODE compartments coupled through a one-dimensional bulk diffusion field. For this coupled PDE-ODE system, we first employ a multi-scale asymptotic expansion to derive…
We consider a model where a population of diffusively coupled limit-cycle oscillators, described by the complex Ginzburg-Landau equation, interacts nonlocally via an inertial field. For sufficiently high intensity of nonlocal inertial…
We explore the dynamical consequences of switching the coupling form in a system of coupled oscillators. We consider two types of switching, one where the coupling function changes periodically and one where it changes probabilistically. We…
In this article I investigate the novel synchronization behaviors of evolving pulse-coupled oscillator networks. Unlike previous models, the time-varying mechanism is inspired by neural network development, where seldom used links die out…
Spontaneous emergence of periodic oscillations due to self-organization is ubiquitous in turbulent flows. The emergence of such oscillatory instabilities in turbulent fluid mechanical systems is often studied in different system-specific…
In this paper we examine the stability of scalar perturbations in nonsingular models which emerge from an interacting vacuum component. The analysis developed in this paper relies on two phenomenological choices for the energy exchange…
Active motions of a biological membrane can be induced by non-thermal fluctuations that occur in the outer environment of the membrane. We discuss the dynamics of a membrane interacting hydrodynamically with an active wall that exerts…
Many physical, chemical and biological processes rely on intrinsic oscillations to employ resonance responses to external stimuli of certain frequency. Such resonance phenomena in biological systems are typically explained by one of two…
We study the synchronization phenomena in a system of globally coupled oscillators with time delay in the coupling. The self-consistency equations for the order parameter are derived, which depend explicitly on the amount of delay. Analysis…