Related papers: The weirdest martensite: Smectic liquid crystal mi…
The Landau-de Gennes model of liquid crystals is a functional acting on wave functions (order parameters) and vector fields (director fields). In a specific asymptotic limit of the physical parameters, we construct critical points such that…
We prove that symplectic ball packing stability holds for every compact, connected symplectic $4$-manifold with smooth boundary. This follows from a stronger result: the full volume of any such manifold can be filled by a single symplectic…
We study spatial optical solitons in a one-dimensional nonlinear photonic crystal created by an array of thin-film nonlinear waveguides, the so-called Dirac-comb nonlinear lattice. We analyze modulational instability of the extended…
We present an x-ray study of freely suspended hexatic films of the liquid crystal 3(10)OBC. Our results reveal spatial inhomogeneities of the bond-orientational (BO) order in the vicinity of the hexatic-smectic phase transition and the…
We present simulations of flux-gradient-driven superconducting rigid vortices interacting with square and triangular arrays of columnar pinning sites in an increasing external magnetic field. These simulations allow us to quantitatively…
Motivated by the paraxial narrow-angle approximation of the Helmholtz equation in domains of variable topography that appears as an important application in Underwater Acoustics, we analyze a general Schr\"odinger-type equation posed on…
We study the topology of smectic defects in two and three dimensions. We give a topological classification of smectic point defects and disclination lines in three dimensions. In addition we describe the combination rules for smectic point…
Consider the scattering of a time-harmonic acoustic incident wave by a bounded, penetrable, and isotropic elastic solid, which is immersed in a homogeneous compressible air or fluid. The paper concerns the numerical solution for such an…
Conventional wisdom presumes that low-coordinated crystal ground states require directional interactions. Using our recently introduced optimization procedure to achieve self-assembly of targeted structures (Phys. Rev. Lett. 95, 228301…
The Weyl relations, the harmonic oscillator, the hydrogen atom, the Dirac equation on the lattice are presented with the help of the difference equations and the orthogonal polynomials of discrete variable. This area of research is…
The isothermal, isobaric spontaneous crystallization of a supercooled polymer melt is investigated by MD simulation of an ensemble of fully-flexible linear chains. Frustration is introduced via two incommensurate length scales set by the…
We consider here an elliptic coupled system describing the dynamics of liquid crystals flows. This system is posed on the whole n-dimensional space. We introduce first the notion of very weak solutions for this system. Then, within the…
In this paper, we address a way to reduce the total computational cost of meshless approximation by reducing the required stencil size through spatial variation of computational node regularity. Rather than covering the entire domain with…
Maxwell-Stefan systems describing the dynamics of the molar concentrations of a gas mixture with an arbitrary number of components are analyzed in a bounded domain under isobaric, isothermal conditions. The systems consist of mass balance…
By the simple finite element method, we study the symplectic, multisymplectic structures and relevant preserving properties in some semi-linear elliptic boundary value problem in one-dimensional and two-dimensional spaces respectively. We…
Elastomers are artificial polymeric materials created for industrial and commercial applications. Depending on their purpose, they are performing in different species and structure modifications. Our studies focus on the systems of…
The known ground state of ultrathin smectic films confined to the surface of a sphere is described by four +1/2 defects assembled on a great circle and a director which follows geodesic lines. Using a simple perturbative approach we show…
In this article we consider systems of parallel hard {\it superellipsoids}, which can be viewed as a possible interpolation between ellipsoids of revolution and cylinders. Superellipsoids are characterized by an aspect ratio and an exponent…
A spin-1 atomic gas in an optical lattice, in the unit-filling Mott Insulator (MI) phase and in the presence of disordered spin-dependent interaction, is considered. In this regime, at zero temperature, the system is well described by a…
Aiming at the study of critical phenomena in the presence of boundaries with a non-trivial shape we discuss how lattices with an adaptive lattice spacing can be implemented. Since the parameters of the Hamiltonian transform non-trivially…