322 research outputs found
Phase separation in quasi incompressible fluids: Cahn-Hilliard model in the Cattaneo-Maxwell framework
In this paper we propose a mathematical model of phase separation for a
quasi-incompressible binary mixture where the spinodal decomposition is induced
by an heat flux governed by the Cattaneo-Maxwell equation. As usual, the phase
separation is considered in the framework of phase field modeling so that the
transition is described by an additional field, the concentration c. The
evolution of concentration is described by the Cahn-Hilliard equation and in
our model is coupled with the Navier-Stokes equation. Since thermal effect are
included, the whole set of evolution equations is set up for the velocity, the
concentration, the temperature and the heat flux. The model is compatible with
thermodynamics and a maximum theorem holds.Comment: Submitted to ZAM
Chiral symmetry in the 2-flavour lattice Schwinger model
We study the 2-flavour lattice Schwinger model: QED in D=2 with two fermion
species of identical mass. In the simulation we are using Wilson fermions where
chiral symmetry is explicitly broken. Since there is no known simple order
parameter it is non-trivial to identify the critical line of the chiral phase
transition. We therefore need to find observables which allow an identification
of a possible restoration of chiral symmetry. We utilize the PCAC-relations in
order to identify the critical coupling, where chiral symmetry is restored.Comment: 3 pages (LaTeX), 4 figures (EPS
Exact beta function from the holographic loop equation of large-N QCD_4
We construct and study a previously defined quantum holographic effective
action whose critical equation implies the holographic loop equation of large-N
QCD_4 for planar self-avoiding loops in a certain regularization scheme. We
extract from the effective action the exact beta function in the given scheme.
For the Wilsonean coupling constant the beta function is exacly one loop and
the first coefficient agrees with its value in perturbation theory. For the
canonical coupling constant the exact beta function has a NSVZ form and the
first two coefficients agree with their value in perturbation theory.Comment: 42 pages, latex. The exponent of the Vandermonde determinant in the
quantum effective action has been changed, because it has been employed a
holomorphic rather than a hermitean resolution of identity in the functional
integral. Beta function unchanged. New explanations and references added,
typos correcte
Asymptotic dynamics of nonlinear coupled suspension bridge equations
In this paper we study the long-term dynamics of a doubly nonlinear abstract system which involves a single differential operator to different powers. For a special choice of the nonlinear terms, the system describes the motion of a suspension bridge where the road bed and the main cable are modeled as a nonlinear beam and a vibrating string, respectively, and their coupling is carried out by nonlinear springs. The set of stationary solutions turns out to be nonempty and bounded. As the external loads vanish, the null solution of the system is proved to be exponentially stable provided that the axial load does not exceed some critical value. Finally, we prove the existence of a bounded global attractor of optimal regularity in connection with an arbitrary axial load and quite general nonlinear terms
Steady states analysis and exponential stability of an extensible thermoelastic system
In this work we consider a nonlinear model for the vibrations of a thermoelastic beam with fixed ends resting on an elastic foundation. The behavior of the related dissipative system accounts for both the midplane stretching of the beam and the Fourier heat conduction. The nonlinear term enters the motion equation, only, while the dissipation is entirely contributed by the heat equation. Under stationary axial load and uniform external temperature the problem uncouples and the bending equilibria of the beam satisfy a semilinear equation. For a general axial load , the existence of a finite/infinite set of steady states is proved and buckling occurrence is discussed. Finally, long-term dynamics of solutions and exponential stability of the straight position are scrutinized
On some nonlinear models for suspension bridges
In this paper we discuss some mathematical models describing the nonlinear vibrations of different kinds of single-span simply supported suspension bridges and we summarize some results about the longtime behavior of solutions to the related evolution problems. Finally, in connection with the static counterpart of a general string-beam nonlinear model, we present some original results concerning the existence of multiple buckled solutions
A Lemaitre-Tolman-Bondi cosmological wormhole
We present a new analytical solution of the Einstein field equations
describing a wormhole shell of zero thickness joining two
Lema{\i}tre-Tolman-Bondi universes, with no radial accretion. The material on
the shell satisfies the energy conditions and, at late times, the shell becomes
comoving with the dust-dominated cosmic substratum.Comment: 5 pages, latex, no figures, to appear in Phys. Rev.
Digital media inhibit self-regulatory private speech use in preschool children: The “digital bubble effect”
Preschoolers spend much time with digital media and some are concerned about impacts on language development. Private speech (PS) is self-talk children use during play, representing a necessary form of self-regulation. This study examined whether modality (material vs. digital) matters for children's PS. Twenty-nine White 5-yr-olds (52% female) completed the Tower of London task twice - once as a material version and once on a tablet. Children used more PS on the material than digital version of the task (d=0.46). During the material task, the typical pattern of increased PS as difficulty increased appeared. However, during the digital task, PS declined as difficulty increased. Digital games may inhibit children's use of PS for self-regulation, having implications for executive function development
Asymptotic behavior and numerical approximation of a double-suspended bridge system
This paper is devoted to introduce and analyze a new non linear problem describing the vibrations of a double suspended bridge system. The road bed is modeled as a double beam of Woinowsky-Krieger type and the two cables, each connected to a single beam by a distributed system of elastic springs, are modeled as one-sided elastic strings. We achieve the existence and uniqueness of solutions by using the semigroup theory and the exponential decay property is also proved. Then, the model is numerically analyzed, through a variational formulation, by using the finite element method and a first-order time integration scheme. A priori error estimates are obtained and the linear convergence is derived under some suitable additional regularity conditions. Finally, some numerical experiments are performed to verify the behavior of the numerical method.Universidade Vigo/CISU
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