Browsing Applied Analysis by Title
Now showing items 1-20 of 53
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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 ... -
Cavity Volume and Free Energy in Many-Body Systems
Taylor, J.M.
; Fai, T.G.; Virga, E.G.; Zheng, X.; Palffy-Muhoray, P. (2021-10-01)
Within this work, we derive and analyse an expression for the free energy of a single-species system in the thermodynamic limit in terms of a generalised cavity volume, that is exact in general, and in principle applicable ... -
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 ... -
Cubic microlattices embedded in nematic liquid crystals: A Landau-de Gennes study
Ceuca, R.D. (2021-01-01)
We consider a Landau-de Gennes model for a connected cubic lattice scaffold in a nematic host, in a dilute regime. We analyse the homogenised limit for both cases in which the lattice of embedded particles presents or not ... -
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
Canevari, G.; Zarnescu, A. (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
Hao, W.; Xiang, X.; Zarnescu, A. (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 ... -
Entire Minimizers of Allen–Cahn Systems with Sub-Quadratic Potentials
Alikakos, N.; Gazoulis, D.; Zarnescu, A. (2021-01-01)
We study entire minimizers of the Allen–Cahn systems. The specific feature of our systems are potentials having a finite number of global minima, with sub-quadratic behaviour locally near their minima. The corresponding ... -
Entire vortex solutions of negative degree for the anisotropic Ginzburg-Landau system
Kowalczyk, M.; Lamy, X.; Smyrnelis, P.A. (2022)
The anisotropic Ginzburg-Landau system $\Delta u+\delta \nabla (div u) +\delta curl^*(curl u)=(|u|^2-1) u$, for $u\colon\mathbb R^2\to\mathbb R^2$ and $\delta\in (-1,1)$, models the formation of vortices in liquid crystals. ... -
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 ... -
Existence of a weak solution to a nonlinear fluid-structure interaction problem with heat exchange
(2022-01-01)In this paper, we study a nonlinear interaction problem between a thermoelastic shell and a heat-conducting fluid. The shell is governed by linear thermoelasticity equations and encompasses a time-dependent domain which ... -
Global well-posedness and twist-wave solutions for the inertial Qian-Sheng model of liquid crystals
De Anna, F.; Zarnescu, A. (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 ... -
Hölder regularity and convergence for a non-local model of nematic liquid crystals in the large-domain limit
Canevari, G.; Taylor, J.M. (2022-02-01)
We consider a non-local free energy functional, modelling a competition between entropy and pairwise interactions reminiscent of the second order virial expansion, with applications to nematic liquid crystals as a particular ...