10,870 research outputs found
The effect of magnetic dipolar interactions on the interchain spin wave dispersion in CsNiF_3
Inelastic neutron scattering measurements were performed on the ferromagnetic
chain system CsNiF_3 in the collinear antiferromagnetic ordered state below T_N
= 2.67K. The measured spin wave dispersion was found to be in good agreement
with linear spin wave theory including dipolar interactions. The additional
dipole tensor in the Hamiltonian was essential to explain some striking
phenomena in the measured spin wave spectrum: a peculiar feature of the
dispersion relation is a jump at the zone center, caused by strong dipolar
interactions in this system. The interchain exchange coupling constant and the
planar anisotropy energy were determined within the present model to be J'/k_B
= -0.0247(12)K and A/k_B = 3.3(1)K. This gives a ratio J/J' \approx 500, using
the previously determined intrachain coupling constant J/k_B = 11.8$. The small
exchange energy J' is of the same order as the dipolar energy, which implies a
strong competition between the both interactions.Comment: 18 pages, TeX type, 7 Postscript figures included. To be published in
Phys. Rev.
Categorification of persistent homology
We redevelop persistent homology (topological persistence) from a categorical
point of view. The main objects of study are diagrams, indexed by the poset of
real numbers, in some target category. The set of such diagrams has an
interleaving distance, which we show generalizes the previously-studied
bottleneck distance. To illustrate the utility of this approach, we greatly
generalize previous stability results for persistence, extended persistence,
and kernel, image and cokernel persistence. We give a natural construction of a
category of interleavings of these diagrams, and show that if the target
category is abelian, so is this category of interleavings.Comment: 27 pages, v3: minor changes, to appear in Discrete & Computational
Geometr
A Logic of Blockchain Updates
Blockchains are distributed data structures that are used to achieve
consensus in systems for cryptocurrencies (like Bitcoin) or smart contracts
(like Ethereum). Although blockchains gained a lot of popularity recently,
there is no logic-based model for blockchains available. We introduce BCL, a
dynamic logic to reason about blockchain updates, and show that BCL is sound
and complete with respect to a simple blockchain model
On The Evolution of Magnetic White Dwarfs
We present the first radiation magnetohydrodynamics simulations of the
atmosphere of white dwarf stars. We demonstrate that convective energy transfer
is seriously impeded by magnetic fields when the plasma-beta parameter, the
thermal to magnetic pressure ratio, becomes smaller than unity. The critical
field strength that inhibits convection in the photosphere of white dwarfs is
in the range B = 1-50 kG, which is much smaller than the typical 1-1000 MG
field strengths observed in magnetic white dwarfs, implying that these objects
have radiative atmospheres. We have then employed evolutionary models to study
the cooling process of high-field magnetic white dwarfs, where convection is
entirely suppressed during the full evolution (B > 10 MG). We find that the
inhibition of convection has no effect on cooling rates until the effective
temperature (Teff) reaches a value of around 5500 K. In this regime, the
standard convective sequences start to deviate from the ones without convection
owing to the convective coupling between the outer layers and the degenerate
reservoir of thermal energy. Since no magnetic white dwarfs are currently known
at the low temperatures where this coupling significantly changes the
evolution, effects of magnetism on cooling rates are not expected to be
observed. This result contrasts with a recent suggestion that magnetic white
dwarfs with Teff < 10,000 K cool significantly slower than non-magnetic
degenerates.Comment: 11 pages, 12 figures, accepted for publication in the Astrophysical
Journa
Preserving entanglement under decoherence and sandwiching all separable states
Every entangled state can be perturbed, for instance by decoherence, and stay
entangled. For a large class of pure entangled states, we show how large the
perturbation can be. Our class includes all pure bipartite and all maximally
entangled states. For an entangled state, E, the constucted neighborhood of
entangled states is the region outside two parallel hyperplanes, which sandwich
the set of all separable states. The states for which these neighborhoods are
largest are the maximally entangled ones. As the number of particles, or the
dimensions of the Hilbert spaces for two of the particles increases, the
distance between two of the hyperplanes which sandwich the separable states
goes to zero. It is easy to decide if a state Q is in the neighborhood of
entangled states we construct for an entangled state E. One merely has to check
if the trace of EQ is greater than a constant which depends upon E and which we
determine.Comment: Corrected first author's e-mail address. All the rest remains
unchange
Transition Density and Pressure at the Inner Edge of Neutron Star Crusts
Using the nuclear symmetry energy that has been recently constrained by the
isospin diffusion data in intermediate-energy heavy ion collisions, we have
studied the transition density and pressure at the inner edge of neutron star
crusts, and they are found to be 0.040 fm
fm and 0.01 MeV/fm MeV/fm,
respectively, in both the dynamical and thermodynamical approaches. We have
also found that the widely used parabolic approximation to the equation of
state of asymmetric nuclear matter gives significantly higher values of
core-crust transition density and pressure, especially for stiff symmetry
energies. With these newly determined transition density and pressure, we have
obtained an improved relation between the mass and radius of neutron stars.Comment: 7 pages, 3 figures, proceeding of "The International Workshop on
Nuclear Dynamics in Heavy-Ion Reactions and the Symmetry Energy (IWND2009)
Global equality of resources and the problem of valuation
The principle that every individual on the planet has a claim to an equal share of Earth’s natural resources has an intuitive attraction. Yet the Principle of Natural Resource Equality is not without its problems. This article focuses on the problem of valuation. Unless and until its adherents are able to develop an adequate theoretical mechanism for determining the comparative value of two or more bundles of natural resources the principle lacks applicability and persuasive force. Three adequacy constraints on such a mechanism are presented and then applied to a theorisation of the Principle of Natural Resource Equality that I have already expounded elsewhere: Global Equality of Resources. In each case I try to argue that Global Equality of Resources could satisfy the adequacy constraint, provided that both this theory and the relevant constraint are properly understood
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