Related papers: Oriented Active Solids
We study the interplay of Mott localization, geometric frustration, and superfluidity for hard-core bosons with nearest-neighbor repulsion on the triangular lattice. For this model at half-filling, we demonstrate that superfluidity survives…
This paper deals with the stabilization of a coupled system composed by an infinite-dimensional system and an ODE. Moreover, the control, which appears in the dynamics of the ODE, is subject to a general class of nonlinearities. Such a…
Turbulence is most commonly associated with high Reynolds number flow, however the framework of turbulent dynamics has been conceptually extended to many other fields, such as magnetohydrodynamic turbulence, elastic wave turbulence in…
In the present paper, we study a new type of large-scale instability, which arises in obliquely rotating electroconductive fluids with a small-scale external force of zero helicity. This force excites small-scale velocity oscillations with…
In our previous papers we proposed a continuum model for the dynamics of the systems of self-propelling particles with conservative kinematic constraints on the velocities. We have determined a class of stationary solutions of this…
In this letter, we present non linear structures resulting from the saturation of a large scale instability in rotating stratified fluids with small scale forced turbulence which we found in \cite{[1]}. These structures are of helical kinks…
This article is concerned with the existence of traveling wave solutions, including standing waves, to some models based on configurational forces, describing respectively the diffusionless phase transformations of solid materials, e.g.,…
Invariant manifolds are important sets arising in the stability theory of dynamical systems. In this article, we take a brief review of invariant sets. We provide some results regarding the existence of invariant lines and parabolas in…
Designing for rotational stability can dramatically affect the geometry of a space station. If improperly designed, the rotating station could end up catastrophically tumbling end-over-end. Active stabilization can address this problem;…
A wide range of materials can exist in microscopically disordered solid forms, referred to as amorphous solids or glasses. Such materials -- oxide glasses and metallic glasses, to polymer glasses, and soft solids such as colloidal glasses,…
We construct a generic coarse-grained dynamics of a thin inflexible planar layer of polar-ordered suspension of active particles, that is frictionally coupled to an embedding isotropic passive fluid medium with a friction coefficient…
Stability of the zero solution plays an important role in the investigation of positive systems. In this note, we revisit the $\mu$-stability of positive nonlinear systems with unbounded time-varying delays. The system is modelled by…
We investigate the emergence of orientational order among +1/2 disclinations in active nematic liquid crystals. Using a combination of theoretical and experimental methods, we show that +1/2 disclinations have short-range antiferromagnetic…
This paper deals with global asymptotic stability of prolongations of flows induced by specific vector fields and their prolongations. The method used is based on various estimates of the flows.
The well-defined but intricate course of time evolution exhibited by many naturally occurring phenomena suggests some source of dynamic order sustaining it. In spite of its obviousness as a problem, it has remained absent from the…
Local rearrangements are the elements of plastic deformation in an amorphous solid. In oscillatory shear, they can switch reversibly between two distinct configurations. While these repeating relaxations are typically considered in the…
In amorphous solids subject to shear or thermal excitation, so-called structural indicators have been developed that predict locations of future plasticity or particle rearrangements. An open question is whether similar tools can be used in…
Active nematics are conceptually the simplest orientationally ordered phase of self-driven particles, but have proved to be a perennial source of surprises. We show here through numerical solution of coarse-grained equations for order…
By an undirected rigid formation of mobile autonomous agents is meant a formation based on graph rigidity in which each pair of "neighboring" agents is responsible for maintaining a prescribed target distance between them. In a recent paper…
We consider a two-dimensional lattice model for liquid crystals consisting of long rods interacting via purely hard core interactions, with two allowed orientations defined by the underlying lattice. We rigorously prove the existence of a…