21,393 research outputs found
Primordial fluctuations without scalar fields
We revisit the question of whether fluctuations in hydrodynamical,
adiabatical matter could explain the observed structures in our Universe. We
consider matter with variable equation of state w=p_0/\ep_0 and a concomitant
(under the adiabatic assumption) density dependent speed of sound, . We
find a limited range of possibilities for a set up when modes start inside the
Hubble radius, then leaving it and freezing out. For expanding Universes,
power-law w(\ep_0) models are ruled out (except when ,
requiring post-stretching the seeded fluctuations); but sharper profiles in
do solve the horizon problem. Among these, a phase transition in is
notable for leading to scale-invariant fluctuations if the initial conditions
are thermal. For contracting Universes all power-law w(\ep_0) solve the
horizon problem, but only one leads to scale-invariance: w\propto \ep_0^2 and
c_s\propto \ep_0. This model bypasses a number of problems with single scalar
field cyclic models (for which is large but constant)
Space-time decay of Navier-Stokes flows invariant under rotations
We show that the solutions to the non-stationary Navier-Stokes equations in
, which are left invariant under the action of discrete subgroups
of the orthogonal group decay much faster as or than in the generic case and we compute, for each subgroup, the
precise decay rates in space-time of the velocity field
Subspace subcodes of Reed-Solomon codes
We introduce a class of nonlinear cyclic error-correcting codes, which we call subspace subcodes of Reed-Solomon (SSRS) codes. An SSRS code is a subset of a parent Reed-Solomon (RS) code consisting of the RS codewords whose components all lie in a fixed ν-dimensional vector subspace S of GF (2m). SSRS codes are constructed using properties of the Galois field GF(2m). They are not linear over the field GF(2ν), which does not come into play, but rather are Abelian group codes over S. However, they are linear over GF(2), and the symbol-wise cyclic shift of any codeword is also a codeword. Our main result is an explicit but complicated formula for the dimension of an SSRS code. It implies a simple lower bound, which gives the true value of the dimension for most, though not all, subspaces. We also prove several important duality properties. We present some numerical examples, which show, among other things, that (1) SSRS codes can have a higher dimension than comparable subfield subcodes of RS codes, so that even if GF(2ν) is a subfield of GF(2m), it may not be the best ν-dimensional subspace for constructing SSRS codes; and (2) many high-rate SSRS codes have a larger dimension than any previously known code with the same values of n, d, and q, including algebraic-geometry codes. These examples suggest that high-rate SSRS codes are promising candidates to replace Reed-Solomon codes in high-performance transmission and storage systems
Factors Dictating Carbene Formation at (PNP)Ir
The mechanistic subtleties involved with the interaction of an amido/bis(phosphine)-supported (PNP)Ir fragment with a series of linear and cyclic ethers have been investigated using density functional theory. Our analysis has revealed the factors dictating reaction direction toward either an iridium-supported carbene or a vinyl ether adduct. The (PNP)Ir structure will allow carbene formation only from accessible carbons α to the ethereal oxygen, such that d electron back-donation from the metal to the carbene ligand is possible. Should these conditions be unavailable, the main competing pathway to form vinyl ether can occur, but only if the (PNP)Ir framework does not sterically interfere with the reacting ether. In situations where steric hindrance prevents unimpeded access to both pathways, the reaction may progress to the initial C−H activation but no further. Our mechanistic analysis is density functional independent and whenever possible confirmed experimentally by trapping intermediate species experimentally. We have also highlighted an interesting systematic error present in the DFT analysis of reactions where steric environment alters considerably within a reaction
Constraints on the Detectability of Cosmic Topology from Observational Uncertainties
Recent observational results suggest that our universe is nearly flat and
well modelled within a CDM framework. The observed values of
and inevitably involve uncertainties. Motivated
by this, we make a systematic study of the necessary and sufficient conditions
for undetectability as well as detectability (in principle) of cosmic topology
(using pattern repetition) in presence of such uncertainties. We do this by
developing two complementary methods to determine detectability for nearly flat
universes. Using the first method we derive analytical conditions for
undetectability for infinite redshift, the accuracy of which is then confirmed
by the second method. Estimates based on WMAP data together with other
measurements of the density parameters are used to illustrate both methods,
which are shown to provide very similar results for high redshifts.Comment: 16 pages, 1 figure, LaTeX2
Vortex solutions in the noncommutative torus
Vortex configurations in the two-dimensional torus are considered in
noncommutative space. We analyze the BPS equations of the Abelian Higgs model.
Numerical solutions are constructed for the self-dual and anti-self dual cases
by extending an algorithm originally developed for ordinary commutative space.
We work within the Fock space approach to noncommutative theories and the
Moyal-Weyl connection is used in the final stage to express the solutions in
configuration space.Comment: 18 pages, 5 figure
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