12,229 research outputs found
Galaxy size trends as a consequence of cosmology
We show that recently documented trends in galaxy sizes with mass and
redshift can be understood in terms of the influence of underlying cosmic
evolution; a holistic view which is complimentary to interpretations involving
the accumulation of discreet evolutionary processes acting on individual
objects. Using standard cosmology theory, supported with results from the
Millennium simulations, we derive expected size trends for collapsed cosmic
structures, emphasising the important distinction between these trends and the
assembly paths of individual regions. We then argue that the observed variation
in the stellar mass content of these structures can be understood to first
order in terms of natural limitations of cooling and feedback. But whilst these
relative masses vary by orders of magnitude, galaxy and host radii have been
found to correlate linearly. We explain how these two aspects will lead to
galaxy sizes that closely follow observed trends and their evolution, comparing
directly with the COSMOS and SDSS surveys. Thus we conclude that the observed
minimum radius for galaxies, the evolving trend in size as a function of mass
for intermediate systems, and the observed increase in the sizes of massive
galaxies, may all be considered an emergent consequence of the cosmic
expansion.Comment: 14 pages, 13 figures. Accepted by MNRA
Time relaxation of interacting single--molecule magnets
We study the relaxation of interacting single--molecule magnets (SMMs) in
both spatially ordered and disordered systems. The tunneling window is assumed
to be, as in Fe8, much narrower than the dipolar field spread. We show that
relaxation in disordered systems differs qualitatively from relaxation in fully
occupied cubic and Fe_8 lattices. We also study how line shapes that develop in
''hole--digging'' experiments evolve with time t in these fully occupied
lattices. We show (1) that the dipolar field h scales as t^p in these hole line
shapes and show (2) how p varies with lattice structure. Line shapes are not,
in general, Lorentzian. More specifically, in the lower portion of the hole,
they behave as (h/t^p)^{(1/p)-1} if h is outside the tunnel window. This is in
agreement with experiment and with our own Monte Carlo results.Comment: 21 LaTeX pages, 6 eps figures. Submitted to PRB on 15 June 2005.
Accepted on 13 August 200
Y-compatible and strict Y-compatible functions
AbstractLet Y ∈ Rn. A function f : Rn → Rk is Y-compatible, if for any Z ∈ Rn, Z ≤ Y if and only if f(Z) ≤ f(Y) and is strict Y-compatible, if for any Z ∈ Rn, Z < Y if and only if f(Z) < f(Y). It is proved that for any Y ∈ Rn, n ≥ 2, there is no Y-compatible polynomial function f : Rn → Rk, 1 ≤ k < n. It is also proved that for a differentiable strict Y-compatible map f, Jf(Y) = 0, where Jf(Y) denote the Jacobian matrix of the mapping f in Y. These problems arose in studying data compression of analog signatures
Influence of antisymmetric exchange interaction on quantum tunneling of magnetization in a dimeric molecular magnet Mn6
We present magnetization measurements on the single molecule magnet Mn6,
revealing various tunnel transitions inconsistent with a giant-spin
description. We propose a dimeric model of the molecule with two coupled spins
S=6, which involves crystal-field anisotropy, symmetric Heisenberg exchange
interaction, and antisymmetric Dzyaloshinskii-Moriya exchange interaction. We
show that this simplified model of the molecule explains the experimentally
observed tunnel transitions and that the antisymmetric exchange interaction
between the spins gives rise to tunneling processes between spin states
belonging to different spin multiplets.Comment: 5 pages, 4 figure
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