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Recently, it has been proposed that a mechanism for the appearance of non-equilibrium superconductivity in a resonantly driven semiconductor with repulsive interband interactions exists.~\cite{Goldstein_PRB15} The underlying microscopic…
The present research is devoted to the problem of stability of the fluid flow moving in a channel with flexible walls and interacting with the walls, which are subject to traveling waves. Experimental data shows that the energy of the…
Soft-walled microchannels arise in many applications, ranging from organ-on-a-chip platforms to soft-robotic actuators. However, despite extensive research on their static and dynamic response, the potential failure of these devices has not…
We will present qualitative and numerical results on a partial differential equation (PDE) system which models a certain fluid-structure dynamics. The wellposedness of this PDE model is established by means of constructing for it a…
In this paper we construct a novel technique for eliminating and recovering the pressure for a fluid-structure interaction model. This pressure elimination methodology is valid for general bounded Lipschitz domains. The specific…
We introduce a class of continuum mechanical models aimed at describing the behaviour of viscoelastic fluids by incorporating concepts originated in the theory of solid plasticity. Within this class, even a simple model with constant…
Local phonon motion underneath a surface interacting with a flow may cause the flow to passively stabilize, or destabilize, as desired within the region adjacent to the subsurface motion. This mechanism has been extensively analyzed over…
In this paper, we address the well-posedness theory of F. John's problem for freely floating objects in a two-dimensional framework. This problem is a linear description of the interactions between an incompressible, irrotational…
A finite one-dimensional microscopic model of a superfulid is presented. The model consists of interacting Bose particles with an additional impurity particle confined to a ring. Both semiclassical and exact quantum calculations reveal…
In a series of papers, Avalos and Triggiani established the fluid-elastic semigroup for the coupled Stokes-Lam\'e system modelling the coupled dynamics of a linearly elastic structure immersed in a viscous Newtonian fluid. They analyzed the…
Instabilities driven by strong gradients appear in a wide variety of physical systems, including plasmas, neutral fluids, and self-gravitating systems. This work develops an analytic formulation to describe the transport structure and…
In this article we study a class of hyperbolic partial differential equations of order one on the semi-axis. The so-called port-Hamiltonian systems cover for instance the wave equation and the transport equation, but also networks of the…
We determine the hydrodynamic modes of the superfluid analog of a smectic-A phase in liquid crystals, i.e., a state in which both gauge invariance and translational invariance along a single direction are spontaneously broken. Such a…
Ordered, collective motions commonly arise spontaneously in systems of many interacting, active units, ranging from cellular tissues and bacterial colonies to self-propelled colloids and animal flocks. Active phases are especially rich when…
We outline a general theory for the analysis of flow-distributed standing and travelling wave patterns in one-dimensional, open plug-flows of oscillatory chemical media. We treat both the amplitude and phase dynamics of small and…
We propose a scenario for superconductivity at strong electron-electron attractive interaction, in the case when the increase of the interaction strength promotes the nucleation of the local Cooper pairs and forms a state with a spatially…
We map out the phase diagram of strongly interacting fermions in a potential trap with mass and population imbalance between the two spin components. As a unique feature distinctively different from the equal-mass case, we show that the…
The complicated dynamics of the contact line of a moving droplet on a solid substrate often hamper the efficient modeling of microfluidic systems. In particular, the selection of the effective boundary conditions, specifying the contact…
Superfluidity is a fascinating phenomenon that, at the macroscopic scale, leads to dissipationless flow and the emergence of vortices. While these macroscopic manifestations of superfluidity are well described by theories that have their…
We explore the regime of ``superfast'' reactivity that has been predicted to occur in turbulent flow in the presence of potential disorder. Computer simulation studies confirm qualitative features of the previous renormalization group…