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On a bifurcation problem arising in cholesteric liquid crystal theory

Carlo Greco (2017)

Commentationes Mathematicae Universitatis Carolinae

In a cholesteric liquid crystal the director field n ( x , y , z ) tends to form a right-angle helicoid around a twist axis in order to minimize the internal energy; however, a fixed alignment of the director field at the boundary (strong anchoring) can give rise to distorted configurations of the director field, as oblique helicoid, in order to save energy. The transition to this distorted configurations depend on the boundary conditions and on the geometry of the liquid crystal, and it is known as Freedericksz...

On a mathematical model for the crystallization of polymers

Maria Pia Gualdani (2003)

Bollettino dell'Unione Matematica Italiana

We consider a mathematical model proposed in [1] for the cristallization of polymers, describing the evolution of temperature, crystalline volume fraction, number and average size of crystals. The model includes a constraint W e ⁢ q on the crystal volume fraction. Essentially, the model is a system of both second order and first order evolutionary partial differential equations with nonlinear terms which are Lipschitz continuous, as in [1], or Hölder continuous, as in [3]. The main novelty here is the...

On a model of rotating superfluids

Sylvia Serfaty (2001)

ESAIM: Control, Optimisation and Calculus of Variations

We consider an energy-functional describing rotating superfluids at a rotating velocity ω , and prove similar results as for the Ginzburg-Landau functional of superconductivity: mainly the existence of branches of solutions with vortices, the existence of a critical ω above which energy-minimizers have vortices, evaluations of the minimal energy as a function of ω , and the derivation of a limiting free-boundary problem.

On a model of rotating superfluids

Sylvia Serfaty (2010)

ESAIM: Control, Optimisation and Calculus of Variations

We consider an energy-functional describing rotating superfluids at a rotating velocity ω, and prove similar results as for the Ginzburg-Landau functional of superconductivity: mainly the existence of branches of solutions with vortices, the existence of a critical ω above which energy-minimizers have vortices, evaluations of the minimal energy as a function of ω, and the derivation of a limiting free-boundary problem.

On a nonlocal problem for a confined plasma in a Tokamak

Weilin Zou, Fengquan Li, Boqiang Lv (2013)

Applications of Mathematics

The paper deals with a nonlocal problem related to the equilibrium of a confined plasma in a Tokamak machine. This problem involves terms u * ' ( | u > u ( x ) | ) and | u > u ( x ) | , which are neither local, nor continuous, nor monotone. By using the Galerkin approximate method and establishing some properties of the decreasing rearrangement, we prove the existence of solutions to such problem.

On Cauchy problem for the equations of reactor kinetics.

Jan Kyncl (1989)

Aplikace matematiky

In this paper, the initial value problem for the equations of reactor kinetics is solved and the temperature feedback is taken into account. The space where the problem is solved is chosen in such a way that it may correspond best of all to the mathematical properties of the cross-section models. The local solution is found by the method of iterations, its uniqueness is proved and it is shown also that existence of global solution is ensured in the most cases. Finally, the problem of mild solution...

On the decomposition of particle size distribution in the extraction replica method

Vratislav Horálek (1981)

Aplikace matematiky

This paper deals with the method for evaluating exposures of nickel alloy structures containing both extracted and sectioned particles. The presented stereological model makes it possible to estimate two unknown spatial parameters, the mean value of the particle size distribution and the depth of etching with the use of the information obtained from the combined structure of the exposures.

On the double critical-state model for type-II superconductivity in 3D

Yohei Kashima (2008)

ESAIM: Mathematical Modelling and Numerical Analysis

In this paper we mathematically analyse an evolution variational inequality which formulates the double critical-state model for type-II superconductivity in 3D space and propose a finite element method to discretize the formulation. The double critical-state model originally proposed by Clem and Perez-Gonzalez is formulated as a model in 3D space which characterizes the nonlinear relation between the electric field, the electric current, the perpendicular component of the electric current...

On the Ginzburg-Landau and related equations

Yu N. Ovchinnikov, Israel Michael Sigal (1997/1998)

Séminaire Équations aux dérivées partielles

We describe qualitative behaviour of solutions of the Gross-Pitaevskii equation in 2D in terms of motion of vortices and radiation. To this end we introduce the notion of the intervortex energy. We develop a rather general adiabatic theory of motion of well separated vortices and present the method of effective action which gives a fairly straightforward justification of this theory. Finally we mention briefly two special situations where we are able to obtain rather detailed picture of the vortex...

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