Models for damped water waves

In this paper we derive some new weakly nonlinear asymptotic models describing viscous waves in deep water with or without surface tension effects. These asymptotic models take into account several different dissipative effects and are obtained from the free bound- ary problems formulated in the works of Dias, Dyachenko and Zakharov (Physics Letters A, 2008 ), Jiang, Ting, Perlin and Schultz (Journal of Fluid Mechanics,1996 ) and Wu, Liu and Yue (Journal of Fluid Mechanics, 2006 )

Bianchi type-II cosmological model: some remarks

Within the framework of Bianchi type-II (BII) cosmological model the behavior of matter distribution has been considered. It is shown that the non-zero off-diagonal component of Einstein tensor implies some severe restriction on the choice of matter distribution. In particular for a locally rotationally symmetric Bianchi type-II (LRS BII) space-time it is proved that the matter distribution should be strictly isotropic if the corresponding matter field possesses only non-zero diagonal components of the energy-momentum tensor.Comment: 3 page

Local solvability and turning for the inhomogeneous Muskat problem

In this work we study the evolution of the free boundary between two different fluids in a porous medium where the permeability is a two dimensional step function. The medium can fill the whole plane R^2 or a bounded strip S=RX(-pi/2,pi/2). The system is in the stable regime if the denser fluid is below the lighter one. First, we show local existence in Sobolev spaces by means of energy method when the system is in the stable regime. Then we prove the existence of curves such that they start in the stable regime and in finite time they reach the unstable one. This change of regime (turning) was first proven in [5] for the homogenous Muskat problem with infinite depth

Bulk viscous cosmology with causal transport theory

We consider cosmological scenarios originating from a single imperfect fluid with bulk viscosity and apply Eckart's and both the full and the truncated M\"uller-Israel-Stewart's theories as descriptions of the non-equilibrium processes. Our principal objective is to investigate if the dynamical properties of Dark Matter and Dark Energy can be described by a single viscous fluid and how such description changes when a causal theory (M\"uller-Israel-Stewart's, both in its full and truncated forms) is taken into account instead of Eckart's non-causal theory. To this purpose, we find numerical solutions for the gravitational potential and compare its behaviour with the corresponding LambdaCDM case. Eckart's and the full causal theory seem to be disfavoured, whereas the truncated theory leads to results similar to those of the LambdaCDM model for a bulk viscous speed in the interval 10^{-11} << c_b^2 < 10^{-8}. Tentatively relating such value to a square propagation velocity of the order of T/m of perturbations in a non-relativistic gas of particles with mass m at the epoch of matter-radiation equality, this may be compatible with a mass range 0.1 GeV < m << 100 GeV.Comment: 23 pages, 7 figure

Adiabatic decaying vacuum model for the universe

We study a model that the entropy per particle in the universe is constant. The sources for the entropy are the particle creation and a lambda decaying term. We find exact solutions for the Einstein field equations and show the compatibilty of the model with respect to the age and the acceleration of the universe.Comment: 10 pages, 2 figure

Some remarks on Bianchi type-II, VIII and IX models

Within the scope of anisotropic non-diagonal Bianchi type-II, VIII and IX spacetime it is shown that the off-diagonal components of the corresponding metric impose severe restrictions on the components of the energy momentum tensor in general. If the energy momentum tensor is considered to be diagonal one, the spacetime, expect a partial case of BII, becomes locally rotationally symmetric.Comment: 8 page

Disruption of Yarrowia lipolytica TPS1 Gene Encoding Trehalose-6-P Synthase Does Not Affect Growth in Glucose but Impairs Growth at High Temperature

We have cloned the Yarrowia lipolytica TPS1 gene encoding trehalose-6-P synthase by complementation of the lack of growth in glucose of a Saccharomyces cerevisiae tps1 mutant. Disruption of YlTPS1 could only be achieved with a cassette placed in the 3′half of its coding region due to the overlap of its sequence with the promoter of the essential gene YlTFC1. The Yltps1 mutant grew in glucose although the Y. lipolytica hexokinase is extremely sensitive to inhibition by trehalose-6-P. The presence of a glucokinase, insensitive to trehalose-6-P, that constitutes about 80% of the glucose phosphorylating capacity during growth in glucose may account for the growth phenotype. Trehalose content was below 1 nmol/mg dry weight in Y. lipolytica, but it increased in strains expressing YlTPS1 under the control of the YlTEF1promoter or with a disruption of YALI0D15598 encoding a putative trehalase. mRNA levels of YlTPS1 were low and did not respond to thermal stresses, but that of YlTPS2 (YALI0D14476) and YlTPS3 (YALI0E31086) increased 4 and 6 times, repectively, by heat treatment. Disruption of YlTPS1 drastically slowed growth at 35°C. Homozygous Yltps1 diploids showed a decreased sporulation frequency that was ascribed to the low level of YALI0D20966 mRNA an homolog of the S. cerevisiae MCK1 which encodes a protein kinase that activates early meiotic gene expression

Global Existence in the Lipschitz Class for the N-Peskin Problem

In this paper we study a toy model of the Peskin problem that captures the motion of the full Peskin problem in the normal direction and discards the tangential elastic stretching contributions. This model takes the form of a fully nonlinear scalar contour equation. The Peskin problem is a fluid-structure interaction problem that describes the motion of an elastic rod immersed in an incompressible Stokes fluid. We prove global in time existence of the solution for initial data in the critical Lipschitz space. By using a new decomposition together with cancellation properties, pointwise methods allow us to obtain the desired estimates in the Lipschitz class. Moreover, we perform energy estimates in order to obtain that the solution lies in the space L2([0, T];H3/2) to satisfy the contour equation pointwis