Hierarchy of Conservation Laws of Diffusion--Convection Equations

We introduce notions of equivalence of conservation laws with respect to Lie symmetry groups for fixed systems of differential equations and with respect to equivalence groups or sets of admissible transformations for classes of such systems. We also revise the notion of linear dependence of conservation laws and define the notion of local dependence of potentials. To construct conservation laws, we develop and apply the most direct method which is effective to use in the case of two independent variables. Admitting possibility of dependence of conserved vectors on a number of potentials, we generalize the iteration procedure proposed by Bluman and Doran-Wu for finding nonlocal (potential) conservation laws. As an example, we completely classify potential conservation laws (including arbitrary order local ones) of diffusion--convection equations with respect to the equivalence group and construct an exhaustive list of locally inequivalent potential systems corresponding to these equations.Comment: 24 page

Active Mass Under Pressure

After a historical introduction to Poisson's equation for Newtonian gravity, its analog for static gravitational fields in Einstein's theory is reviewed. It appears that the pressure contribution to the active mass density in Einstein's theory might also be noticeable at the Newtonian level. A form of its surprising appearance, first noticed by Richard Chase Tolman, was discussed half a century ago in the Hamburg Relativity Seminar and is resolved here.Comment: 28 pages, 4 figure

Secular evolution of a satellite by tidal effect. Application to Triton

Some of the satellites in the Solar System, including the Moon, appear to have been captured from heliocentric orbits at some point in their past, and then have evolved to the present configurations. The exact process of how this trapping occurred is unknown, but the dissociation of a planetesimal binary in the gravitational field of the planet, gas drag, or a massive collision seem to be the best candidates. However, all these mechanisms leave the satellites in elliptical orbits that need to be damped to the present almost circular ones. Here we give a complete description of the secular tidal evolution of a satellite just after entering a bounding state with the planet. In particular, we take into account the spin evolution of the satellite, which has often been assumed synchronous in previous studies. We apply our model to Triton and successfully explain some geophysical properties of this satellite, as well as the main dynamical features observed for the Neptunian system.Comment: 4 pages, 1 figur

Benchmark calculations for elastic fermion-dimer scattering

We present continuum and lattice calculations for elastic scattering between a fermion and a bound dimer in the shallow binding limit. For the continuum calculation we use the Skorniakov-Ter-Martirosian (STM) integral equation to determine the scattering length and effective range parameter to high precision. For the lattice calculation we use the finite-volume method of L\"uscher. We take into account topological finite-volume corrections to the dimer binding energy which depend on the momentum of the dimer. After subtracting these effects, we find from the lattice calculation kappa a_fd = 1.174(9) and kappa r_fd = -0.029(13). These results agree well with the continuum values kappa a_fd = 1.17907(1) and kappa r_fd = -0.0383(3) obtained from the STM equation. We discuss applications to cold atomic Fermi gases, deuteron-neutron scattering in the spin-quartet channel, and lattice calculations of scattering for nuclei and hadronic molecules at finite volume.Comment: 16 pages, 5 figure

Mn local moments prevent superconductivity in iron-pnictides Ba(Fe 1-x Mn x)2As2

75As nuclear magnetic resonance (NMR) experiments were performed on Ba(Fe1-xMnx)2As2 (xMn = 2.5%, 5% and 12%) single crystals. The Fe layer magnetic susceptibility far from Mn atoms is probed by the75As NMR line shift and is found similar to that of BaFe2As2, implying that Mn does not induce charge doping. A satellite line associated with the Mn nearest neighbours (n.n.) of 75As displays a Curie-Weiss shift which demonstrates that Mn carries a local magnetic moment. This is confirmed by the main line broadening typical of a RKKY-like Mn-induced staggered spin polarization. The Mn moment is due to the localization of the additional Mn hole. These findings explain why Mn does not induce superconductivity in the pnictides contrary to other dopants such as Co, Ni, Ru or K.Comment: 6 pages, 7 figure

A Thermodynamic Approach to Predict the Metallic and Oxide Phases Precipitations in Nuclear Waste Glass Melts

AbstractAmong the large number of matrixes explored as hosts for high-level nuclear wastes, conditioning of fission products and minor actinides into a homogeneous borosilicate glass is the most promising technique already implemented at the industrial scale. The advantage of this vitrification process is the volume reduction of the high level waste coming from the spent fuel reprocessing and its stability for the long-term storage. Nevertheless, some fission products are poorly soluble in molten glasses:•Platinoids (Pd, Ru, Rh) which precipitate as (Pd-Te, Ru-Rh) metallic particles and (Rh,Ru)O2 oxide phases with acicular or polyhedral shapes during the vitrification process.•Molybdenum oxide (MoO3) which can form complex molybdates.In order to point out the chemical interactions between the glass and these precipitated phases issuing from the calcinated waste, a thermodynamic approach is developed using the Calphad method. The objective of this work is to calculate thermodynamic properties for complex fission product systems in order to predict the precipitation of platinoids or molybdate phases.This thermodynamic database is being developed on the Mo-Pd-Rh-Ru-Se-Te-O complex system. This flexible tool enables to predict phase diagrams, composition and relative stability of the metallic or oxide precipitated phases as a function of both temperature and oxygen potential in the glass melt

Helicity conservation and factorization-suppressed charmless B decays

Toward the goal of extracting the weak angle alpha, the decay B^0/B^0-bar to a_0^{+/-}pi^{-/+} was recently measured. The decay B^0 to a_0^+pi^- is not only forbidden in the factorization limit of the tree interaction, but also strongly suppressed for the penguin interaction if short-distance QCD dominates. This makes extraction of alpha very difficult from a^{+/-}\pi^{-/+}. We examine the simlar factorization-suppressed decays, in particular, B^0\to b_1^+pi^-. The prospect of obtaining alpha is even less promising with b_1^{+/-}pi^{-/+}. To probe how well the short-distance dominance works, we emphasize importance of testing helicity conservation in the charmless B decays with spins.Comment: The version to appear in Phys. Rev. D after minor alteration

Annihilation contribution and B→a0π,f0KB\to a_0 \pi, f_0 K decays

We analyze the decays $B^0 \to a^\pm_0 \pi^\mp$ and $B^{-,0} \to f_0 K^{-,0}$ and show that within the factorization approximation a phenomenological consistent picture can be obtained. We show that in this approach the $O_6$ operator provides the dominant contributions to the suppressed channel $B^0 \to a^+_0 \pi^-$. When the $a_0$ is considered a two quark state, evaluation of the annihilation form factor using Perturbative $QCD$ implies that this contribution is not negligible, and furthermore it can interfere constructively or destructively with other penguin contributions. As a consequence of this ambiguity, the positive identification of $B^0 \to \pi^+ a_0^-$ can not distinguish between the two or four quark assignment of the $a_0$. According to our calculation, a best candidate to distinguish the nature of $a_0$ scalar is $Br(B^-\to \pi^0a_0^-)$ since the predictions for a four quark model is one order of magnitude smaller than for the two quark assignment. When the scalars are seen as two quarks states, simple theoretical assumptions based on SU(2) isospin symmetry provide relations between different B decays involving one scalar and one pseudoscalar meson.Comment: 12 pages, 3 figure