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A Wigner crystal structure of the electronic ground state is induced by strong Coulomb interactions at low temperature in clean or disordered two-dimensional (2d) samples. For fermions on a mesoscopic disordered 2d lattice, being closed to…
The study of granular crystals, metamaterials that consist of closely packed arrays of particles that interact elastically, is a vibrant area of research that combines ideas from disciplines such as materials science, nonlinear dynamics,…
A systematic method is proposed for the determination of the statistical properties of a field consisting of a coherent structure interacting with turbulent linear waves. The explicit expression of the generating functional of the…
In the framework of the theory of partially fluidized granular flows we study the formation of longitudinal structures observed experimentally by Forterre and Pouliquen in a flow down a rough inclined plane. We show that the formation of…
This essay summarizes the state of the art on some aspects of the dynamics of polynomial diffeomorphsms in complex dimension two, and it presents a number of open questions.
Biological tissues exhibit complex behaviors with their dynamics often resembling inert soft matter such as liquids, polymers, colloids, and liquid crystals. These analogies enable physics-based approaches for investigations of emergent…
A quantitative model of the mobility of functionalized particles at the interface is pivotal to understanding important systems in biology and nanotechnology. In this work, we investigate the emerging dynamics of particles anchored through…
We model Lagrangian lateral mixing and transport of passive scalars in meandering oceanic jet currents by two-dimensional advection equations with a kinematic stream function with a time-dependent amplitude of a meander imposed. The…
We consider a mixture of one neutral and two oppositely charged types of molecules confined to a surface. Using analytical techniques and molecular dynamics simulations, we construct the phase diagram of the system and exhibit the…
We consider a spinless fermionic $p\pm ip$ superfluid living on a two-dimensional sphere. Using superfluid hydrodynamics we show that the ground state necessarily exhibits topological defects: either a pair of elementary vortices or a…
We study the transport properties of a one-dimensional hard-core boson lattice gas coupled to two particle reservoirs at different chemical potentials generating a current flow through the system. In particular, the influence of random…
Each of the existing types of the electric charges come forwards in the system as the source of a kind of the dipole moment. Therefore, to investigate these regularities, we have established the compound structures of Dirac and Pauli form…
Using molecular dynamics simulations, we study particle-transport in a system of interacting colloidal particles on a ring, where the system is driven by a time-dependent external potential, moving along the ring. We consider two driving…
Spiral waves are striking self-organized coherent structures that organize spatio-temporal dynamics in dissipative, spatially extended systems. In this paper, we provide a conceptual approach to various properties of spiral waves. Rather…
Longitudinal non-dissipative current states in bilayer electron-hole systems in the presence of potential barriers that divide the system into left and right sides was investigated. The consideration is performed both for the case of weak…
We study the dynamics of active nematic films on a substrate driven by active flows with or without the incompressible constraint.Through simulations and theoretical analysis, we show that arch patterns are stable in the compressible case,…
The atomic structure and elastic properties of silicon carbide nanowires of different shapes and effective sizes were studied using density functional theory and classical molecular dynamics. The surface relaxation led to surface…
We present initial results regarding the existence, stability and interaction of linear and nonlinear vibrational modes in a system of two coupled, one dimensional lattices with unequal numbers of masses. The effects on these nonlinear…
In this paper, we extend the discrete-to-continuum procedure we developed in our previous work to derive a continuum variational model for a hexagonal twisted bilayer material in which one layer is fixed. We use a discrete energy containing…
The longitudinal transport problem (the current is applied parallel to some bias magnetic field) in type-II superconductors is analyzed theoretically. Based on analytical results for simplified configurations, and relying on numerical…