6,535 research outputs found
Optimal boundary control of a simplified Ericksen--Leslie system for nematic liquid crystal flows in
In this paper, we investigate an optimal boundary control problem for a two
dimensional simplified Ericksen--Leslie system modelling the incompressible
nematic liquid crystal flows. The hydrodynamic system consists of the
Navier--Stokes equations for the fluid velocity coupled with a convective
Ginzburg--Landau type equation for the averaged molecular orientation. The
fluid velocity is assumed to satisfy a no-slip boundary condition, while the
molecular orientation is subject to a time-dependent Dirichlet boundary
condition that corresponds to the strong anchoring condition for liquid
crystals. We first establish the existence of optimal boundary controls. Then
we show that the control-to-state operator is Fr\'echet differentiable between
appropriate Banach spaces and derive first-order necessary optimality
conditions in terms of a variational inequality involving the adjoint state
variables
Analysis and simulations of multifrequency induction hardening
We study a model for induction hardening of steel. The related differential
system consists of a time domain vector potential formulation of the Maxwell's
equations coupled with an internal energy balance and an ODE for the volume
fraction of {\sl austenite}, the high temperature phase in steel. We first
solve the initial boundary value problem associated by means of a Schauder
fixed point argument coupled with suitable a-priori estimates and regularity
results. Moreover, we prove a stability estimate entailing, in particular,
uniqueness of solutions for our Cauchy problem. We conclude with some finite
element simulations for the coupled system
A temperature-dependent phase-field model for phase separation and damage
In this paper we study a model for phase separation and damage in
thermoviscoelastic materials. The main novelty of the paper consists in the
fact that, in contrast with previous works in the literature (cf., e.g., [C.
Heinemann, C. Kraus: Existence results of weak solutions for Cahn-Hilliard
systems coupled with elasticity and damage. Adv. Math. Sci. Appl. 21 (2011),
321--359] and [C. Heinemann, C. Kraus: Existence results for diffuse interface
models describing phase separation and damage. European J. Appl. Math. 24
(2013), 179--211]), we encompass in the model thermal processes, nonlinearly
coupled with the damage, concentration and displacement evolutions. More in
particular, we prove the existence of "entropic weak solutions", resorting to a
solvability concept first introduced in [E. Feireisl: Mathematical theory of
compressible, viscous, and heat conducting fluids. Comput. Math. Appl. 53
(2007), 461--490] in the framework of Fourier-Navier-Stokes systems and then
recently employed in [E. Feireisl, H. Petzeltov\'a, E. Rocca: Existence of
solutions to a phase transition model with microscopic movements. Math. Methods
Appl. Sci. 32 (2009), 1345--1369], [E. Rocca, R. Rossi: "Entropic" solutions to
a thermodynamically consistent PDE system for phase transitions and damage.
SIAM J. Math. Anal., 47 (2015), 2519--2586] for the study of PDE systems for
phase transition and damage. Our global-in-time existence result is obtained by
passing to the limit in a carefully devised time-discretization scheme
Canonical quantization of non-local field equations
We consistently quantize a class of relativistic non-local field equations
characterized by a non-local kinetic term in the lagrangian. We solve the
classical non-local equations of motion for a scalar field and evaluate the
on-shell hamiltonian. The quantization is realized by imposing Heisenberg's
equation which leads to the commutator algebra obeyed by the Fourier components
of the field. We show that the field operator carries, in general, a reducible
representation of the Poincare group. We also consider the Gupta-Bleuler
quantization of a non-local gauge field and analyze the propagators and the
physical states of the theory.Comment: 18 p., LaTe
A Family of unitary higher order equations
A scalar field obeying a Lorentz invariant higher order wave equation, is
minimally coupled to the electromagnetic field. The propagator and vertex
factors for the Feynman diagrams, are determined. As an example we write down
the matrix element for the Compton effect. This matrix element is algebraically
reduced to the usual one for a charged Klein-Gordon particle. It is proved that
the order theory is equivalent to n independent second order
theories. It is also shown that the higher order theory is both renormalizable
and unitary for arbitrary n.Comment: 17 pages, LaTex, no figure
The influence of persuasion in opinion formation and polarization
We present a model that explores the influence of persuasion in a population
of agents with positive and negative opinion orientations. The opinion of each
agent is represented by an integer number that expresses its level of
agreement on a given issue, from totally against to totally in favor
. Same-orientation agents persuade each other with probability ,
becoming more extreme, while opposite-orientation agents become more moderate
as they reach a compromise with probability . The population initially
evolves to (a) a polarized state for , where opinions' distribution is
peaked at the extreme values , or (b) a centralized state for ,
with most opinions around . When , polarization lasts for a
time that diverges as , where is the population's size. Finally,
an extremist consensus ( or ) is reached in a time that scales as
for
Competition between surface relaxation and ballistic deposition models in scale free networks
In this paper we study the scaling behavior of the fluctuations in the steady
state with the system size for a surface growth process given by the
competition between the surface relaxation (SRM) and the Ballistic Deposition
(BD) models on degree uncorrelated Scale Free networks (SF), characterized by a
degree distribution , where is the degree of a node.
It is known that the fluctuations of the SRM model above the critical dimension
() scales logarithmically with on euclidean lattices. However,
Pastore y Piontti {\it et. al.} [A. L. Pastore y Piontti {\it et. al.}, Phys.
Rev. E {\bf 76}, 046117 (2007)] found that the fluctuations of the SRM model in
SF networks scale logarithmically with for and as a constant
for . In this letter we found that for a pure ballistic
deposition model on SF networks scales as a power law with an exponent
that depends on . On the other hand when both processes are in
competition, we find that there is a continuous crossover between a SRM
behavior and a power law behavior due to the BD model that depends on the
occurrence probability of each process and the system size. Interestingly, we
find that a relaxation process contaminated by any small contribution of
ballistic deposition will behave, for increasing system sizes, as a pure
ballistic one. Our findings could be relevant when surface relaxation
mechanisms are used to synchronize processes that evolve on top of complex
networks.Comment: 8 pages, 6 figure
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