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

Buckling and longterm dynamics of a nonlinear model for the extensible beam

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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 $p$, 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

Heat transfer at nanoscale and boundary conditions

A model of nonlocal heat transfer at nanoscale in rigid bodies is considered. Depending on the relevance of the particular interaction’s mechanism between the heat carriers and the lateral walls, three different strategies for the setting-up of the boundary conditions are analyzed, and the consequent forms of the basic fields have been obtained, as well. From the physical point of view, the possible influence of those interactions on the unknown fields is pointed out. From the mathematical point of view, instead, the well-posedness of the problem is shown

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