Absence of squirt singularities for the multi-phase Muskat problem

In this paper we study the evolution of multiple fluids with different constant densities in porous media. This physical scenario is known as the Muskat and the (multi-phase) Hele-Shaw problems. In this context we prove that the fluids do not develop squirt singularities.Comment: 16 page

Breakdown of smoothness for the Muskat problem

In this paper we show that there exist analytic initial data in the stable regime for the Muskat problem such that the solution turns to the unstable regime and later breaks down i.e. no longer belongs to $C^4$.Comment: 93 pages, 10 figures (6 added

Kernels and ranks of cyclic and negacyclic quaternary codes

We study the rank and kernel of Z4 cyclic codes of odd length n and give bounds on the size of the kernel and the rank. Given that a cyclic code of odd length is of the form C = , where fgh = x^n − 1, we show that ⊆ K(C) ⊆ C and C ⊆ R(C) ⊆ where K(C) is the preimage of the binary kernel and R(C) is the preimage of the space generated by the image of C. Additionally, we show that both K(C) and R(C) are cyclic codes and determine K(C) and R(C) in numerous cases. We conclude by usingthese results to determine the case for negacyclic codes as well

Nonexistence of self-similar singularities for the 3D incompressible Euler equations

We prove that there exists no self-similar finite time blowing up solution to the 3D incompressible Euler equations. By similar method we also show nonexistence of self-similar blowing up solutions to the divergence-free transport equation in $\Bbb R^n$. This result has direct applications to the density dependent Euler equations, the Boussinesq system, and the quasi-geostrophic equations, for which we also show nonexistence of self-similar blowing up solutions.Comment: This version refines the previous one by relaxing the condition of compact support for the vorticit

On Z2Z4-additive complementary dual codes and related LCD codes

Linear complementary dual codes were defined by Massey in 1992, and were used to give an optimum linear coding solution for the two user binary adder channel. In this paper, we define the analog of LCD codes over fields in the ambient space with mixed binary and quaternary alphabets. These codes are additive, in the sense that they are additive subgroups, rather than linear as they are not vector spaces over some finite field. We study the structure of these codes and we use the canonical Gray map from this space to the Hamming space to construct binary LCD codes in certain cases. We give examples of such binary LCD codes which are distance-optimal, i.e., they have the largest minimum distance among all binary LCD codes with the same length and dimension

Effects of Composite Rheology on Plate-Like Behavior in Global-Scale Mantle Convection

Earth's upper mantle rheology controls lithosphere-asthenosphere coupling and thus surface tectonics. Rock deformation experiments and seismic anisotropy measurements indicate that composite rheology (co-existing diffusion and dislocation creep) occurs in the Earth's uppermost mantle, potentially affecting convection and surface tectonics. Here, we investigate how the spatio-temporal distribution of dislocation creep in an otherwise diffusion-creep-controlled mantle impacts the planform of convection and the planetary tectonic regime as a function of the lithospheric yield strength in numerical models of mantle convection self-generating plate-like tectonics. The low upper-mantle viscosities caused by zones of substantial dislocation creep produce contrasting effects on surface dynamics. For strong lithosphere (yield strength > 35 MPa), the large lithosphere-asthenosphere viscosity contrasts promote stagnant-lid convection. In contrast, the increase of upper mantle convective vigor enhances plate mobility for lithospheric strength <35 MPa. For the here-used model assumptions, composite rheology does not facilitate the onset of plate-like behavior at large lithospheric strength

Editorial - Food Microbiology 2020

Food microbiology studies the microbiota of food products

Coherent pion production in neutrino nucleus collision in the 1 GeV region

We calculate cross sections for coherent pion production in nuclei induced by neutrinos and antineutrinos of the electron and muon type. The analogies and differences between this process and the related ones of coherent pion production induced by photons, or the (p,n) and $(^3 He, t)$ reactions are discussed. The process is one of the several ones occurring for intermediate energy neutrinos, to be considered when detecting atmospheric neutrinos. For this purpose the results shown here can be easily extrapolated to other energies and other nuclei.Comment: 13 pages, LaTex, 8 post-script figures available at [email protected]

A maximum principle for the Muskat problem for fluids with different densities

We consider the fluid interface problem given by two incompressible fluids with different densities evolving by Darcy's law. This scenario is known as the Muskat problem for fluids with the same viscosities, being in two dimensions mathematically analogous to the two-phase Hele-Shaw cell. We prove in the stable case (the denser fluid is below) a maximum principle for the $L^\infty$ norm of the free boundary.Comment: 16 page