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

Farmers and Social Security Reform

Agricultural Finance,

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