Related papers: A Novel Landau-de Gennes Model with Quartic Elasti…
In a previous paper we have discussed how the Landau potential (entering in Landau theory of phase transitions) can be simplified using the Poincar\'e normalization procedure. Here we apply this approach to the Landau-deGennes functional…
We study a system of semi-linear elliptic partial differential equations with a lower order cubic nonlinear term, and inhomogeneous Dirichlet boundary conditions, relevant for two-dimensional bistable liquid crystal devices, within a…
We consider a class of non-quasiconvex frame indifferent energy densities which includes Ogden-type energy densities for nematic elastomers. For the corresponding geometrically linear problem we provide an explicit minimizer of the energy…
In the Landau-de Gennes theoretical framework of a $Q -tensor description of nematic liquid crystals, we consider a radial hedgehog defect with strong anchoring conditions in a ball $B \subset \mathbb{R}^3$ . We show that the scalar order…
We consider the relationship between three continuum liquid crystal theories: Oseen-Frank, Ericksen and Landau-de Gennes. It is known that the function space is an important part of the mathematical model and by considering various function…
We suggest an alternative mathematical model for the massless neutrino. Consider an elastic continuum in 3-dimensional Euclidean space and assume that points of this continuum can experience no displacements, only rotations. This framework…
Chromonic liquid crystals (CLCs) are lyotropic materials which are attracting growing interest for their adaptability to living systems. A considerable body of works has been devoted to exploring their properties and applications. In this…
A Noether-enhanced Legendre transformation from Lagrange densities to energy-momentum tensors is developed into an alternative framework for formulating classical field equations. This approach offers direct access to the Hamiltonian while…
In the mathematical modeling of nematic liquid crystals, a practical and physically reliable $\mathbf{Q}$-tensor model can be derived from Onsager's molecular model with the Bingham closure. However, this procedure leads to a singular…
Quantum Electrodynamics (QED) has been so successful a theory that it is taken as a model for the production of further quantum theories. However, when the prescription for quantising electromagnetic interactions that so successfully…
Linearized elasticity models are derived, via Gamma-convergence, from suitably rescaled nonlinear energies when the corresponding energy densities have a multiwell structure and satisfy a weak coercivity condition, in the sense that the…
We construct a general metric-tensor framework for treating inhomogenous adiabatic deformations applied to crystalline insulators, by deriving an effective time-dependent Schr\"odinger equation in the undistorted frame. The response can be…
We study the transitions between neighboring energy levels in a quasi-one-dimensional semiconductor quantum dot with two interacting electrons in it, when it is subject to a linearly time-dependent electric field. We analyze the…
We study the hydrodynamics of compressible flows of active liquid crystals in the Beris-Edwards hydrodynamics framework, using the Landau-de Gennes $Q$-tensor order parameter to describe liquid crystalline ordering. We prove the existence…
The quantum null energy condition (QNEC) is a conjectured bound on components $(T_{kk} = T_{ab} k^a k^b$) of the stress tensor along a null vector $k^a$ at a point $p$ in terms of a second $k$-derivative of the von Neumann entropy $S$ on…
A comprehensive theory of the Landau-Zener transition in quadratic nonlinear two-state systems is developed. A compact analytic formula involving elementary functions only is derived for the final transition probability. The formula…
We propose Landau phenomenology for describing the phase transition from the conventional nematic into the conical helical orientationally non-uniform structure recently identified in liquid crystals formed by "banana"-shaped molecules. The…
We consider the simplest one-constant model, put forward by J. Ericksen, for nematic liquid crystals with variable degree of orientation. The equilibrium state is described by a director field $\mathbf{n}$ and its degree of orientation $s$,…
We investigate the asymptotic behaviour of a correlation function associated with a nematic liquid crystal system undergoing an isotropic-nematic phase transition following an instantaneous change of temperature. Within the setting of…
On a two-dimensional Riemannian manifold without boundary we consider the variational limit of a family of functionals given by the sum of two terms: a Ginzburg-Landau and a perimeter term. Our scaling allows low-energy states to be…