1,713 research outputs found
Lamellar order, microphase structures and glassy phase in a field theoretic model for charged colloids
In this paper we present a detailed analytical study of the phase diagram and
of the structural properties of a field theoretic model with a short-range
attraction and a competing long-range screened repulsion. We provide a full
derivation and expanded discussion and digression on results previously
reported briefly in M. Tarzia and A. Coniglio, Phys. Rev. Lett. 96, 075702
(2006). The model contains the essential features of the effective interaction
potential among charged colloids in polymeric solutions. We employ the
self-consistent Hartree approximation and a replica approach, and we show that
varying the parameters of the repulsive potential and the temperature yields a
phase coexistence, a lamellar and a glassy phase. Our results suggest that the
cluster phase observed in charged colloids might be the signature of an
underlying equilibrium lamellar phase, hidden on experimental time scales, and
emphasize that the formation of microphase structures may play a prominent role
in the process of colloidal gelation.Comment: 16 pages, 7 figure
Explicit solution for a two--phase fractional Stefan problem with a heat flux condition at the fixed face
A generalized Neumann solution for the two-phase fractional
Lam\'e--Clapeyron--Stefan problem for a semi--infinite material with constant
initial temperature and a particular heat flux condition at the fixed face is
obtained, when a restriction on data is satisfied. The fractional derivative in
the Caputo sense of order \al \in (0,1) respect on the temporal variable is
considered in two governing heat equations and in one of the conditions for the
free boundary. Furthermore, we find a relationship between this fractional free
boundary problem and another one with a constant temperature condition at the
fixed face and based on that fact, we obtain an inequality for the coefficient
which characterizes the fractional phase-change interface obtained in
Roscani--Tarzia, Adv. Math. Sci. Appl., 24 (2014), 237-249. We also recover the
restriction on data and the classical Neumann solution, through the error
function, for the classical two-phase Lam\'e-Clapeyron-Stefan problem for the
case \al=1.Comment: 19 pages, 1 figur
One-Phase Stefan-Like Problems with Latent Heat Depending on the Position and Velocity of the Free Boundary and with Neumann or Robin Boundary Conditions at the Fixed Face
A one-phase Stefan-type problem for a semi-infinite material which has as its main feature a variable latent heat that depends on the power of the position and the velocity of the moving boundary is studied. Exact solutions of similarity type are obtained for the cases when Neumann or Robin boundary conditions are imposed at the fixed face. Required relationships between data are presented in order that these problems become equivalent to the problem where a Dirichlet condition at the fixed face is considered. Moreover, in the case where a Robin condition is prescribed, the limit behaviour is studied when the heat transfer coefficient at the fixed face goes to infinity.Fil: Bollati, Julieta. Universidad Austral. Facultad de Ciencias Empresariales. Departamento de Matemáticas; Argentina. Consejo Nacional de Investigaciones CientÃficas y Técnicas. Centro CientÃfico Tecnológico Conicet - Rosario; ArgentinaFil: Tarzia, Domingo Alberto. Universidad Austral. Facultad de Ciencias Empresariales. Departamento de Matemáticas; Argentina. Consejo Nacional de Investigaciones CientÃficas y Técnicas. Centro CientÃfico Tecnológico Conicet - Rosario; Argentin
Exact solution for a two-phase Stefan problem with variable latent heat and a convective boundary condition at the fixed face
Recently it was obtained in [Tarzia, Thermal Sci. 21A (2017) 1-11] for the
classical two-phase Lam\'e-Clapeyron-Stefan problem an equivalence between the
temperature and convective boundary conditions at the fixed face under a
certain restriction. Motivated by this article we study the two-phase Stefan
problem for a semi-infinite material with a latent heat defined as a power
function of the position and a convective boundary condition at the fixed face.
An exact solution is constructed using Kummer functions in case that an
inequality for the convective transfer coefficient is satisfied generalizing
recent works for the corresponding one-phase free boundary problem. We also
consider the limit to our problem when that coefficient goes to infinity
obtaining a new free boundary problem, which has been recently studied in
[Zhou-Shi-Zhou, J. Engng. Math. (2017) DOI 10.1007/s10665-017-9921-y].Comment: 16 pages, 0 figures. arXiv admin note: text overlap with
arXiv:1610.0933
Convergence of optimal control problems governed by second kind parabolic variational inequalities
We consider a family of optimal control problems where the control variable
is given by a boundary condition of Neumann type. This family is governed by
parabolic variational inequalities of the second kind. We prove the strong
convergence of the optimal controls and state systems associated to this family
to a similar optimal control problem. This work solves the open problem left by
the authors in IFIP TC7 CSMO2011
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