Cahn-Hilliard equations with memory and dynamic boundary conditions

We consider a modified Cahn\u2013Hiliard equation where the velocity of the order parameter u depends on the past history of \u394\u3bc, \u3bc being the chemical potential with an additional viscous term \u3b1ut, \u3b1 650. This type of equation has been proposed by P. Galenko et al. to model phase separation phenomena in special materials (e.g., glasses). In addition, the usual no-flux boundary condition for u is replaced by a nonlinear dynamic boundary condition which accounts for possible interactions with the boundary. The resulting boundary value problem is subject to suitable initial conditions and is reformulated in the so-called past history space. Existence of a variational solution is obtained. Then, in the case \u3b1>0, we can also prove uniqueness and construct a strongly continuous semigroup acting on a suitable phase space. We show that the corresponding dynamical system has a (smooth) global attractor as well as an exponential attractor. In the case \u3b1=0, we only establish the existence of a trajectory attractor

Variability of Symmetric Dimethylarginine in apparently healthy dogs

Background: Symmetric dimethylarginine (SDMA) is a screening tool for early kidney dysfunction and monitoring treatment in cases of chronic kidney disease (CKD). There are no current studies describing the suitability of this test for use with published populationbased reference intervals. Hypothesis/Objectives: To determine the components of biological variability, the index of individuality (IOI), the critical difference between sequential measurements (CD) and the number of measurements required to assess the homeostatic set point (HSP), for both SDMA and serum creatinine (sCr), in apparently healthy dogs. Animals: Twenty apparently healthy adult dogs owned by clients or staff at a veterinary teaching hospital. Methods: Prospective, observational study. Blood was collected from each dog on 9 occasions, and SDMA and sCr were measured in duplicate using commercially available assays. Results: SDMA and sCr had intermediate and low IOI values of 0.87 and 0.28, respectively. The CD of SDMA and sCr, was 1.34 mg/dL and 0.89 mmol/L, respectively. The sample numbers required for estimation of an individual’s HSP (with 90 and 95% CI) for SDMA and sCr were 8 and 45, and 2 and 12 sequential measurements, respectively. Conclusions and Clinical Importance: Based on our findings, in comparison to sCr, SDMA is better suited for use with population based reference intervals. False-negative test results could occur when comparing a single test result from an individual to such intervals. Ideally CD should be used with sequential measurements

On a diffuse interface model for tumour growth with non-local interactions and degenerate mobilities

We study a non-local variant of a diffuse interface model proposed by Hawkins--Darrud et al. (2012) for tumour growth in the presence of a chemical species acting as nutrient. The system consists of a Cahn--Hilliard equation coupled to a reaction-diffusion equation. For non-degenerate mobilities and smooth potentials, we derive well-posedness results, which are the non-local analogue of those obtained in Frigeri et al. (European J. Appl. Math. 2015). Furthermore, we establish existence of weak solutions for the case of degenerate mobilities and singular potentials, which serves to confine the order parameter to its physically relevant interval. Due to the non-local nature of the equations, under additional assumptions continuous dependence on initial data can also be shown.Comment: 28 page

Kaon properties in (proto)neutron stars

The modification on kaon and antikaon properties of in the interior of (proto-)neutron stars is investigated using a chiral SU(3) model. The parameters of the model are fitted to nuclear matter saturation properties, baryon octet vacuum masses, hyperon optical potentials and low energy a kaon-nucleon scattering lengths. We study the kaon/antikaon medium modification and explore the possibility of antikaon condensation in (proto-)neutron star matter at zero as well as finite temperature/entropy and neutrino content. The effect of hyperons on kaon and antikaon optical potentials is also investigated at different stages of the neutron star evolution.Comment: 17 pages including 4 figure

CAHN-HILLIARD-NAVIER-STOKES SYSTEMS WITH MOVING CONTACT LINES

We consider a well-known model for the study of the evolution of an incompressible binary fluid flow in a two or three-dimensional bounded domain, through the fluid velocity u and an order parameter φ. This model consists of a system of two evolution equations, namely, the incompressible Navier-Stokes equations coupled with a convective Cahn-Hilliard equation. The novelty is that the system is endowed with boundary conditions which account for moving contact line slip velocity. The existence of a suitable global energy solution is proven and the convergence of any such solution to a single equilibrium is also established

Pa-las. Diccionario enciclopédico manual en cinco idiomas : español, francés, inglés, alemán e italiano

Na port.: "250,000 artíulos = 4,000 grabados contiene el caudal de voces del Diccionario de la Academia Española ... "Data tomada da 18ª ed. (1932) e de non ter D.

The non-autonomous wave equation with general Wentzell boundary conditions

We study the problem of the well-posedness for the abstract Cauchy problem associated to the non-autonomous one-dimensional wave equation u(tt) A(t)u with general Wentzell boundary conditions A(t)u(j, t) + (-1)(j-1) beta(j) (t) partial derivative u/partial derivative x (j, t) + gamma(j) (t)u(j, t) = 0, for j = 0, 1. Here A(t)u := (a(x,t)u(x))(x), a(x,t) >= epsilon > 0 in [0, 1] x (0, + infinity) and, beta(j)(t) > 0, gamma(j) (t) >= 0, (gamma 0 (t), gamma 1 (t)) not equal (0, 0). Under suitable regularity conditions on a, beta(j), gamma(j) we prove the well-posedness in a suitable (energy) Hilbert space