Quasiparticle relaxation rate and shear viscosity of superfluid 3He-A_1 at low temperatures

Quasiparticle relaxation rate,$\tau_{p}^{-1}$, and the shear viscosity tensor of the A_1-phase of superfluid 3He are calculated at low temperatures and melting pressure, by using Boltzmann equation approach in momentum space. The collision integral is written in terms of inscattering and outscattering collision integrals. The interaction between normal and Bogoliubov quasiparticles is considered in calculating transition probabilities in the binary, decay and coalescence processes. We obtain that both $\tau_{p\uparrow}^{-1}$ and $\tau_{p\downarrow}^{-1}$ are proportional to $T^2$ >. The shear viscosities $\eta_{xy}$, $\eta_{xz}$ and $\eta_{zz}$ are proportional to $(T/T_c)^{-2}$. The constant of proportionality of the shear viscosity tensor is in nearly good agreement with the experimental results of Roobol et al., and our exact theoretical calculation.Comment: 8 pages, some typos were correcte

The rank of variants of nilpotent pseudovarieties

We investigate the rank of pseudovarieties defined by several of the variants of nilpotency conditions for semigroups in the sense of Mal'cev. For several of them, we provide finite bases of pseudoidentities. We also show that the Neumann-Taylor variant does not have finite rank.Comment: 41 page

Energy of Stable Half-Quantum Vortex in Equal-Spin-Pairing

In the triplet equal-spin-pairing states of both 3He-A phase and Sr2RuO4 superconductor, existence of Half-Quantum Vortices HQVs are possible. The vortices carry half-integer multiples of magnetic quantum flux (hc/2e). To obtain equilibrium condition for such systems, one has to take into account not only weak interaction energy but also effects of Landau Fermi liquid. Our method is based on the explanation of the HQV in terms of a BCS-like wave function with a spin-dependent boots. We have considered l=2 order effects of the Landau Fermi liquid. We have shown that the effects of Landau Fermi liquid interaction with l=2 are negligible. In stable HQV, an effective Zeeman field exists. In the thermodynamic stability state, the effective Zeeman field produces a non-zero spin polarization in addition to the polarization of external magnetic field

Micro-Mechanics Based Representative Volume Element Modeling Of Heterogeneous Cementitious Materials

The current work focuses on evaluation of the effective elastic properties of cementitious materials through a voxel based FEA approach. Voxels are generated for a heterogeneous cementitious material (Type-I cement) consisting of typical volume fractions of various constituent phases from digital microstructures. The microstructure is modeled as a micro-scale representative volume element (RVE) in ABAQUS to generate cubes several tens of microns in dimension and subjected to various prescribed deformation modes to generate the effective elastic tensor of the material. The RVE-calculated elastic properties such as moduli and Poisson\u27s ratio are validated through an asymptotic expansion homogenization (AEH) and compared with rule of mixtures. Both Periodic (PBC) and Kinematic boundary conditions (KBC) are investigated to determine if the elastic properties are invariant due to boundary conditions. In addition the method of Windowing was used to assess the randomness of the constituents and to validate how the isotropic elastic properties were determined. The average elastic properties obtained from the displacement based FEA of various locally anisotropic micro-size cubes extracted from an RVE of size 100x100x100 microns shothat the overall RVE response was fully isotropic. The effects of domain size, degree of hydration, kinematic and periodic boundary conditions, domain sampling techniques, local anisotropy, particle size distribution (PSD), and random microstructure on elastic properties are studied