1,073 research outputs found
Validity of the Brunet-Derrida formula for the speed of pulled fronts with a cutoff
We establish rigorous upper and lower bounds for the speed of pulled fronts
with a cutoff. We show that the Brunet-Derrida formula corresponds to the
leading order expansion in the cut-off parameter of both the upper and lower
bounds. For sufficiently large cut-off parameter the Brunet-Derrida formula
lies outside the allowed band determined from the bounds. If nonlinearities are
neglected the upper and lower bounds coincide and are the exact linear speed
for all values of the cut-off parameter.Comment: 8 pages, 3 figure
On a Conjecture of Goriely for the Speed of Fronts of the Reaction--Diffusion Equation
In a recent paper Goriely considers the one--dimensional scalar
reaction--diffusion equation with a polynomial reaction
term and conjectures the existence of a relation between a global
resonance of the hamiltonian system and the asymptotic
speed of propagation of fronts of the reaction diffusion equation. Based on
this conjecture an explicit expression for the speed of the front is given. We
give a counterexample to this conjecture and conclude that additional
restrictions should be placed on the reaction terms for which it may hold.Comment: 9 pages Revtex plus 4 postcript figure
On the Integrability, B\"Acklund Transformation and Symmetry Aspects of a Generalized Fisher Type Nonlinear Reaction-Diffusion Equation
The dynamics of nonlinear reaction-diffusion systems is dominated by the
onset of patterns and Fisher equation is considered to be a prototype of such
diffusive equations. Here we investigate the integrability properties of a
generalized Fisher equation in both (1+1) and (2+1) dimensions. A Painlev\'e
singularity structure analysis singles out a special case () as
integrable. More interestingly, a B\"acklund transformation is shown to give
rise to a linearizing transformation for the integrable case. A Lie symmetry
analysis again separates out the same case as the integrable one and
hence we report several physically interesting solutions via similarity
reductions. Thus we give a group theoretical interpretation for the system
under study. Explicit and numerical solutions for specific cases of
nonintegrable systems are also given. In particular, the system is found to
exhibit different types of travelling wave solutions and patterns, static
structures and localized structures. Besides the Lie symmetry analysis,
nonclassical and generalized conditional symmetry analysis are also carried
out.Comment: 30 pages, 10 figures, to appear in Int. J. Bifur. Chaos (2004
Design, Synthesis, and Biological Activity of 5\u27-Phenyl-1,2,5,6-tetrahydro-3,3\u27-bipyridine Analogues as Potential Antagonists of Nicotinic Acetylcholine Receptors
Starting from a known non-specific agonist (1) of nicotinic acetylcholine receptors (nAChRs), rationally guided structural-based design resulted in the discovery of a small series of 5′-phenyl-1,2,5,6-tetrahydro-3,3′-bipyridines (3a – 3e) incorporating a phenyl ring off the pyridine core of 1. The compounds were synthesized via successive Suzuki couplings on a suitably functionalized pyridine starting monomer 4 to append phenyl and pyridyl substituents off the 3- and 5-positions, respectively, and then make subsequent modifications on the flanking pyridyl ring to provide target compounds. Compound 3a is a novel antagonist which is highly selective for α3β4 nAChR (Ki = 123 nM) over the α4β2, and α7 receptors
Elastic breakup cross sections of well-bound nucleons
The 9Be(28Mg,27Na) one-proton removal reaction with a large proton separation
energy of Sp(28Mg)=16.79 MeV is studied at intermediate beam energy.
Coincidences of the bound 27Na residues with protons and other light charged
particles are measured. These data are analyzed to determine the percentage
contributions to the proton removal cross section from the elastic and
inelastic nucleon removal mechanisms. These deduced contributions are compared
with the eikonal reaction model predictions and with the previously measured
data for reactions involving the re- moval of more weakly-bound protons from
lighter nuclei. The role of transitions of the proton between different bound
single-particle configurations upon the elastic breakup cross section is also
quantified in this well-bound case. The measured and calculated elastic breakup
fractions are found to be in good agreement.Comment: Phys. Rev. C 2014 (accepted
The observation of long-range three-body Coloumb effects in the decay of 16Ne
The interaction of an =57.6-MeV Ne beam with a Be target was used
to populate levels in Ne following neutron knockout reactions. The decay
of Ne states into the three-body O++ continuum was observed
in the High Resolution Array (HiRA). For the first time for a 2p emitter,
correlations between the momenta of the three decay products were measured with
sufficient resolution and statistics to allow for an unambiguous demonstration
of their dependence on the long-range nature of the Coulomb interaction.
Contrary to previous experiments, the intrinsic decay width of the Ne
ground state was found to be narrow (~keV), consistent with
theoretical estimates.Comment: 6 pages, 5 figure
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