3,158 research outputs found
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
On the Geometry of Surface Stress
We present a fully general derivation of the Laplace--Young formula and
discuss the interplay between the intrinsic surface geometry and the extrinsic
one ensuing from the immersion of the surface in the ordinary euclidean
three-dimensional space. We prove that the (reversible) work done in a general
surface deformation can be expressed in terms of the surface stress tensor and
the variation of the intrinsic surface metric
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
Wetting and Minimal Surfaces
We study minimal surfaces which arise in wetting and capillarity phenomena.
Using conformal coordinates, we reduce the problem to a set of coupled boundary
equations for the contact line of the fluid surface, and then derive simple
diagrammatic rules to calculate the non-linear corrections to the Joanny-de
Gennes energy. We argue that perturbation theory is quasi-local, i.e. that all
geometric length scales of the fluid container decouple from the
short-wavelength deformations of the contact line. This is illustrated by a
calculation of the linearized interaction between contact lines on two opposite
parallel walls. We present a simple algorithm to compute the minimal surface
and its energy based on these ideas. We also point out the intriguing
singularities that arise in the Legendre transformation from the pure Dirichlet
to the mixed Dirichlet-Neumann problem.Comment: 22 page
Pressure as a Source of Gravity
The active mass density in Einstein's theory of gravitation in the analog of
Poisson's equation in a local inertial system is proportional to .
Here is the density of energy and its pressure for a perfect fluid.
By using exact solutions of Einstein's field equations in the static case we
study whether the pressure term contributes towards the mass
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