Now showing items 96-115 of 240

• #### 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 ﻿

(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 ...
• #### Lorentz estimates for asymptotically regular fully nonlinear parabolic equations ﻿

(2017-06-20)
We prove a global Lorentz estimate of the Hessian of strong solutions to the Cauchy-Dirichlet problem for a class of fully nonlinear parabolic equations with asymptotically regular nonlinearity over a bounded $C^{1,1}$ ...
• #### Lorentz estimates for the gradient of weak solutions to elliptic obstacle problems with partially BMO coefficients ﻿

(2017)
We prove global Lorentz estimates for variable power of the gradient of weak solution to linear elliptic obstacle problems with small partially BMO coefficients over a bounded nonsmooth domain. Here, we assume that the ...
• #### Magnetic domain-twin boundary interactions in Ni-Mn-Ga ﻿

(2020-04)
The stress required for the propagation of twin boundaries in a sample with fine twins increases monotonically with ongoing deformation. In contrast, for samples with a single twin boundary, the stress exhibits a plateau ...
• #### Mathematical problems of nematic liquid crystals: between dynamical and stationary problems ﻿

(2021-05-24)
Mathematical studies of nematic liquid crystals address in general two rather different perspectives: That of fluid mechanics and that of calculus of variations. The former focuses on dynamical problems while the latter ...
• #### Maximal estimates for a generalized spherical mean Radon transform acting on radial functions ﻿

(2020)
We study a generalized spherical means operator, viz.\ generalized spherical mean Radon transform, acting on radial functions. As the main results, we find conditions for the associated maximal operator and its local ...
• #### Maximal operators on the infinite-dimensional torus ﻿

(2022-03-31)
We study maximal operators related to bases on the infinite-dimensional torus $\tom$. {For the normalized Haar measure $dx$ on $\mathbb{T}^\omega$ it is known that $M^{\mathcal{R}_0}$, the maximal operator associated with ...
• #### Mean-field dynamics of the spin-magnetization coupling in ferromagnetic materials: Application to current-driven domain wall motions ﻿

(2015-12-31)
In this paper, we present a mean-field model of the spin-magnetization coupling in ferromagnetic materials. The model includes non-isotropic diffusion for spin dynamics, which is crucial in capturing strong spin-magnetization ...
• #### 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 ...
• #### Mixed norm estimates for the Cesàro means associated with Dunkl-Hermite expansions ﻿

(2017)
Our main goal in this article is to study mixed norm estimates for the Cesàro means associated with Dunkl--Hermite expansions on $\mathbb{R}^d$. These expansions arise when one considers the Dunkl--Hermite operator ...
• #### Mixed weak type estimates: Examples and counterexamples related to a problem of E. Sawyer ﻿

(2016-01-01)
In this paper we study mixed weighted weak-type inequal- ities for families of functions, which can be applied to study classic operators in harmonic analysis. Our main theorem extends the key result from [CMP2].
• #### Modeling cardiac structural heterogeneity via space-fractional differential equations ﻿

(2017)
We discuss here the use of non-local models in space and fractional order operators in the characterisation of structural complexity and the modeling of propagation in heterogeneous biological tissues. In the specific, we ...
• #### 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 ...
• #### Monotonicity and convexity of the ratios of the first kind modified Bessel functions and applications ﻿

(2017-07-18)
Let $I_{v}\left( x\right)$ be modified Bessel functions of the first kind. We prove the monotonicity property of the function \$x\mapsto I_{u}\left( x\right) I_{v}\left( x\right) /I_{\left( u+v\right) /2}\left( x\right) ...
• #### Motion of a rigid body in a compressible fluid with Navier-slip boundary condition ﻿

(2022-11-25)
In this work, we study the motion of a rigid body in a bounded domain which is filled with a compressible isentropic fluid. We consider the Navier-slip boundary condition at the interface as well as at the boundary of the ...
• #### Multilinear operator-valued calderón-zygmund theory ﻿

(2020)
We develop a general theory of multilinear singular integrals with operator- valued kernels, acting on tuples of UMD Banach spaces. This, in particular, involves investigating multilinear variants of the R-boundedness ...
• #### Multilinear singular integrals on non-commutative lp spaces ﻿

(2019)
We prove Lp bounds for the extensions of standard multilinear Calderón- Zygmund operators to tuples of UMD spaces tied by a natural product structure. The product can, for instance, mean the pointwise product in UMD ...
• #### New bounds for bilinear Calderón-Zygmund operators and applications ﻿

(2016-11-25)
In this work we extend Lacey’s domination theorem to prove the pointwise control of bilinear Calderón–Zygmund operators with Dini–continuous kernel by sparse operators. The precise bounds are carefully tracked following ...