Browsing Applied Analysis by Title
Now showing items 1-20 of 40
-
Asymptotic models for free boundary flow in porous media
(2019)We provide rigorous asymptotic models for the free boundary Darcy and Forchheimer problem under the assumption of weak nonlinear interaction, in a regime in which the steepness parameter of the interface is considered to ... -
A comparison principle for vector valued minimizers of semilinear elliptic energy, with application to dead cores
Smyrnelis, P.A.
(2021)
We establish a comparison principle providing accurate upper bounds for the modulus of vector valued minimizers of an energy functional, associated when the potential is smooth, to elliptic gradient systems. Our assumptions ... -
Convex Integration Arising in the Modelling of Shape-Memory Alloys: Some Remarks on Rigidity, Flexibility and Some Numerical Implementations
Rüland, A.; Taylor, J.M.; Zillinger, C. (2019-03-30)
We study convex integration solutions in the context of the modelling of shape-memory alloys. The purpose of the article is twofold, treating both rigidity and flexibility prop- erties: Firstly, we relate the maximal ... -
Defects in Nematic Shells: a Gamma-convergence discrete-to-continuum approach
(2018-07)In this paper we rigorously investigate the emergence of defects on Nematic Shells with a genus different from one. This phenomenon is related to a non-trivial interplay between the topology of the shell and the alignment ... -
Derivation of limit equation for a singular perturbation of a 3D periodic Boussinesq system
(2017-07-15)We consider a system describing the dynamics of an hydrodynamical, density-dependent flow under the effects of gravitational forces. We prove that if the Froude number is sufficiently small such system is globally well ... -
Design of effective bulk potentials for nematic liquid crystals via colloidal homogenisation
(2020-02-01)We consider a Landau–de Gennes model for a suspension of small colloidal inclusions in a nematic host. We impose suitable anchoring conditions at the boundary of the inclusions, and we work in the dilute regime — i.e. the ... -
Dimension reduction for the micromagnetic energy functional on curved thin films
(2016-12-14)Micromagnetic con gurations of the vortex and onion type have beenwidely studied in the context of planar structures. Recently a signi cant interest to micromagnetic curved thin lms has appeared. In particular, thin ... -
Dispersive effects of weakly compressible and fast rotating inviscid fluids
(2017-08)We consider a system describing the motion of an isentropic, inviscid, weakly compressible, fast rotating fluid in the whole space $\mathbb{R}^3$, with initial data belonging to $ H^s \left( \mathbb{R}^3 \right), s>5/2 $. ... -
Double layered solutions to the extended Fisher–Kolmogorov P.D.E.
Smyrnelis, P.A. (2021-06-22)
We construct double layered solutions to the extended Fisher–Kolmogorov P.D.E., under the assumption that the set of minimal heteroclinics of the corresponding O.D.E. satisfies a separation condition. The aim of our work ... -
Dynamics and flow effects in the Beris-Edwards system modeling nematic liquid crystals
(2018-08-10)We consider the Beris-Edwards system modelling incompressible liquid crystal flows of nematic type. This couples a Navier-Stokes system for the fluid velocity with a parabolic reaction-convection-diffusion equation for the ... -
The excluded volume of two-dimensional convex bodies: shape reconstruction and non-uniqueness
Taylor, J.M. (2019-02-05)
In the Onsager model of one-component hard-particle systems, the entire phase behaviour is dictated by a function of relative orientation, which represents the amount of space excluded to one particle by another at this ... -
Global well-posedness and twist-wave solutions for the inertial Qian-Sheng model of liquid crystals
(2017-10-02)We consider the inertial Qian-Sheng model of liquid crystals which couples a hyperbolic-type equation involving a second-order material derivative with a forced incompressible Navier-Stokes system. We study the energy law ... -
A Global well-posedness result for the Rosensweig system of ferrofluids
(2019)In this Paper we study a Bloch-Torrey regularization of the Rosensweig system for ferrofluids. The scope of this paper is twofold. First of all, we investigate the existence and uniqueness of Leray-Hopf solutions of this ... -
Highly rotating fluids with vertical stratification for periodic data and vanishing vertical viscosity
(2017-07)We prove that the three-dimensional, periodic primitive equations with zero vertical diffusivity are globally well posed if the Rossby and Froude number are sufficiently small. The initial data is considered to be of zero ... -
Landau-de Gennes Corrections to the Oseen-Frank Theory of Nematic Liquid Crystals
(2020-01-03)We study the asymptotic behavior of the minimisers of the Landau-de Gennes model for nematic liquid crystals in a two-dimensional domain in the regime of small elastic constant. At leading order in the elasticity constant, ... -
Leaky Cell Model of Hard Spheres
Fai, Tomas G.; Taylor, J.M.; Virga, Epifanio G.; Zheng, Xiaoyu; Palffy-Muhoray, Peter (9-03-20)
We study packings of hard spheres on lattices. The partition function, and therefore the pressure, may be written solely in terms of the accessible free volume, i.e., the volume of space that a sphere can explore without ... -
Liquid crystal defects in the Landau–de Gennes theory in two dimensions — Beyond the one-constant approximation
(2016-12-31)We consider the two-dimensional Landau-de Gennes energy with several elastic constants, subject to general $k$-radially symmetric boundary conditions. We show that for generic elastic constants the critical points consistent ... -
Minimizers of a Landau-de Gennes energy with a subquadratic elastic energy
(2019)We study a modified Landau-de Gennes model for nematic liq- uid crystals, where the elastic term is assumed to be of subquadratic growth in the gradient. We analyze the behaviour of global minimizers in two- and three-dimensional ... -
Models for damped water waves
(2019)In this paper we derive some new weakly nonlinear asymptotic models describing viscous waves in deep water with or without surface tension effects. These asymptotic models take into account several different dissipative ... -
Nondegeneracy of heteroclinic orbits for a class of potentials on the plane
Jendrej, J.; Smyrnelis, P.A. (2021)
In the scalar case, the nondegeneracy of heteroclinic orbits is a well-known property, commonly used in problems involving nonlinear elliptic, parabolic or hyperbolic P.D.E. On the other hand, Schatzman proved that in the ...