7,447 research outputs found
Decay Process for Three - Species Reaction - Diffusion System
We propose the deterministic rate equation of three-species in the reaction -
diffusion system. For this case, our purpose is to carry out the decay process
in our three-species reaction-diffusion model of the form . The
particle density and the global reaction rate are also shown analytically and
numerically on a two-dimensional square lattice with the periodic boundary
conditions. Especially, the crossover of the global reaction rate is discussed
in both early-time and long-time regimes.Comment: 6 pages, 3 figures, Late
Analysis of the decay
In this paper we study the angular distribution of the rare B decay , which is expected to be observed soon. We use the
standard effective Hamiltonian approach, and use the form factors that have
already been estimated for the corresponding radiative decay . The additional form factors that come into play for the dileptonic
channel are estimated using the large energy effective theory (LEET), which
enables one to relate the additional form factors to the form factors for the
radiative mode. Our results provide, just like in the case of the
resonance, an opportunity for a straightforward comparison of the basic theory
with experimental results which may be expected in the near future for this
channel.Comment: 14 pages, 5 figures; as accepted for Phys. Rev.
Lepton flavour violation in The Little Higgs model
Little Higgs models with T-parity have a new source of lepton flavour
violation. In this paper we consider the anomalous magnetic moment of the muon
\gmtwo and the lepton flavour violating decays \mutoeg and \tautomug in Little
Higgs model with T-parity \cite{Goyal:2006vq}. Our results shows that present
experimental constraints of \mutoeg is much more useful to constrain the new
sources of flavour violation which are present in T-parity models.Comment: LaTeX file with 13 eps figures (included
Influence of a Realistic Multiorbital Band Structure on Conducting Domain Walls in Perovskite Ferroelectrics
Domain wall morphologies in ferroelectrics are believed to be largely shaped
by electrostatic forces. Here, we show that for conducting domain walls, the
morphology also depends on the details of the charge-carrier band structure.
For concreteness, we focus on transition-metal perovskites like BaTiO and
SrTiO. These have a triplet of orbitals attached to the Ti atoms
that form the conduction bands when electron doped. We solve a set of coupled
equations -- Landau-Ginzburg-Devonshire (LGD) equations for the polarization,
tight-binding Schr\"odinger equations for the electron bands, and Gauss' law
for the electric potential -- to obtain polarization and electron density
profiles as a function of electron density. We find that at low electron
densities, the electron gas is pinned to the surfaces of the ferroelectric by a
Kittel-like domain structure. As the electron density increases, the domain
wall evolves smoothly through a zigzag head-to-head structure, eventually
becoming a flat head-to-head domain wall at high density. We find that the
Kittel-like morphology is protected by orbital asymmetry at low electron
densities, while at large electron densities the high density of states of the
multiorbital band structure provides effective screening of depolarizing fields
and flattens the domain wall relative to single-orbital models. Finally, we
show that in the zigzag phase, the electron gas develops tails that extend away
from the domain wall, in contrast to na\"{i}ve expectations.Comment: 17 pages, 13 figure
Nontrivial Exponent for Simple Diffusion
The diffusion equation \partial_t\phi = \nabla^2\phi is considered, with
initial condition \phi( _x_ ,0) a gaussian random variable with zero mean.
Using a simple approximate theory we show that the probability p_n(t_1,t_2)
that \phi( _x_ ,t) [for a given space point _x_ ] changes sign n times between
t_1 and t_2 has the asymptotic form p_n(t_1,t_2) \sim
[\ln(t_2/t_1)]^n(t_1/t_2)^{-\theta}. The exponent \theta has predicted values
0.1203, 0.1862, 0.2358 in dimensions d=1,2,3, in remarkably good agreement with
simulation results.Comment: Minor typos corrected, affecting table of exponents. 4 pages, REVTEX,
1 eps figure. Uses epsf.sty and multicol.st
Persistence in systems with conserved order parameter
We consider the low-temperature coarsening dynamics of a one-dimensional
Ising ferromagnet with conserved Kawasaki-like dynamics in the domain
representation. Domains diffuse with size-dependent diffusion constant, with . We generalize this model to arbitrary
, and derive an expression for the domain density, with , using a scaling argument. We also
investigate numerically the persistence exponent characterizing the
power-law decay of the number, , of persistent (unflipped) spins at
time , and find where depends on
. We show how the results for and are related to
similar calculations in diffusion-limited cluster-cluster aggregation (DLCA)
where clusters with size-dependent diffusion constant diffuse through an
immobile `empty' phase and aggregate irreversibly on impact. Simulations show
that, while is the same in both models, is different except for
. We also investigate models that interpolate between symmetric
domain diffusion and DLCA.Comment: 9 pages, minor revision
Bogoliubov-Cerenkov radiation in a Bose-Einstein condensate flowing against an obstacle
We study the density modulation that appears in a Bose-Einstein condensate
flowing with supersonic velocity against an obstacle. The experimental density
profiles observed at JILA are reproduced by a numerical integration of the
Gross-Pitaevskii equation and then interpreted in terms of Cerenkov emission of
Bogoliubov excitations by the defect. The phonon and the single-particle
regions of the Bogoliubov spectrum are respectively responsible for a conical
wavefront and a fan-shaped series of precursors
Renormalization Group Study of the A+B->0 Diffusion-Limited Reaction
The diffusion-limited reaction, with equal initial densities
, is studied by means of a field-theoretic renormalization
group formulation of the problem. For dimension an effective theory is
derived, from which the density and correlation functions can be calculated. We
find the density decays in time as a,b \sim C\sqrt{\D}(Dt)^{-d/4} for , with \D = n_0-C^\prime n_0^{d/2} + \dots, where is a universal
constant, and is non-universal. The calculation is extended to the
case of unequal diffusion constants , resulting in a new
amplitude but the same exponent. For a controlled calculation is not
possible, but a heuristic argument is presented that the results above give at
least the leading term in an expansion. Finally, we address
reaction zones formed in the steady-state by opposing currents of and
particles, and derive scaling properties.Comment: 17 pages, REVTeX, 13 compressed figures, included with epsf. Eq.
(6.12) corrected, and a moderate rewriting of the introduction. Accepted for
publication in J. Stat. Phy
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