85 research outputs found
Finite difference approximations for a size-structured population model with distributed states in the recruitment
In this paper we consider a size-structured population model where
individuals may be recruited into the population at different sizes. First and
second order finite difference schemes are developed to approximate the
solution of the mathematical model. The convergence of the approximations to a
unique weak solution with bounded total variation is proved. We then show that
as the distribution of the new recruits become concentrated at the smallest
size, the weak solution of the distributed states-at-birth model converges to
the weak solution of the classical Gurtin-McCamy-type size-structured model in
the weak topology. Numerical simulations are provided to demonstrate the
achievement of the desired accuracy of the two methods for smooth solutions as
well as the superior performance of the second-order method in resolving
solution-discontinuities. Finally we provide an example where supercritical
Hopf-bifurcation occurs in the limiting single state-at-birth model and we
apply the second-order numerical scheme to show that such bifurcation occurs in
the distributed model as well
A Continuous-Time Mathematical Model and Discrete Approximations for the Aggregation of \u3cem\u3eβ\u3c/em\u3e-Amyloid
Alzheimer\u27s disease is a degenerative disorder characterized by the loss of synapses and neurons from the brain, as well as the accumulation of amyloid-based neuritic plaques. While it remains a matter of contention whether β-amyloid causes the neurodegeneration, β-amyloid aggregation is associated with the disease progression. Therefore, gaining a clearer understanding of this aggregation may help to better understand the disease. We develop a continuous-time model for β-amyloid aggregation using concepts from chemical kinetics and population dynamics. We show the model conserves mass and establish conditions for the existence and stability of equilibria. We also develop two discrete-time approximations to the model that are dynamically consistent. We show numerically that the continuous-time model produces sigmoidal growth, while the discrete-time approximations may exhibit oscillatory dynamics. Finally, sensitivity analysis reveals that aggregate concentration is most sensitive to parameters involved in monomer production and nucleation, suggesting the need for good estimates of such parameters
and
Recently Babar Collaboration reported a new state
and Belle Collaboration observed . We investigate the strong
decays of the excited states using the model. After
comparing the theoretical decay widths and decay patterns with the available
experimental data, we tend to conclude: (1) is probably the
state although the
assignment is not completely excluded; (2) seems unlikely to be
the and candidate; (3)
as either a or state is
consistent with the experimental data; (4) experimental search of
in the channels , , and
will be crucial to distinguish the above two possibilities.Comment: 18 pages, 7 figures, 2 tables. Some discussions added. The final
version to appear at EPJ
Unquenching the scalar glueball
Computations in the quenched approximation on the lattice predict the
lightest glueball to be a scalar in the 1.5-1.8 GeV region. Here we calculate
the dynamical effect the coupling to two pseudoscalars has on the mass, width
and decay pattern of such a scalar glueball. These hadronic interactions allow
mixing with the scalar nonet, which is largely fixed by the
well-established K_0^*(1430). This non-perturbative mixing means that, if the
pure gluestate has a width to two pseudoscalar channels of ~100 MeV as
predicted on the lattice, the resulting hadron has a width to these channels of
only ~30 MeV with a large eta-eta component. Experimental results need to be
reanalyzed in the light of these predictions to decide if either the f_0(1500)
or an f_0(1710) coincides with this dressed glueball.Comment: 12 pages, LaTex, 3 Postscript figure
Quark--antiquark states and their radiative transitions in terms of the spectral integral equation. {\Huge II.} Charmonia
In the precedent paper of the authors (hep-ph/0510410), the states
were treated in the framework of the spectral integral equation, together with
simultaneous calculations of radiative decays of the considered bottomonia. In
the present paper, such a study is carried out for the charmonium
states. We reconstruct the interaction in the -sector on the basis of
data for the charmonium levels with , , ,
, , and radiative transitions
, , ,
and , ,
. The levels and their wave functions
are calculated for the radial excitations with . Also, we determine the
component of the photon wave function using the annihilation
data: , , , , , and perform the calculations of the partial widths of
the two-photon decays for the states: , ,
, and states:
, , . We discuss the status of the recently observed states
X(3872) and Y(3941): according to our results, the X(3872) can be either
or , while Y(3941) is .Comment: 24 pages, 9 figure
Strange Decays of Nonstrange Baryons
The strong decays of excited nonstrange baryons into the final states Lambda
K, Sigma K, and for the first time into Lambda(1405) K, Lambda(1520) K,
Sigma(1385) K, Lambda K*, and Sigma K*, are examined in a relativized quark
pair creation model. The wave functions and parameters of the model are fixed
by previous calculations of N pi and N pi pi, etc., decays. Our results show
that it should be possible to discover several new negative parity excited
baryons and confirm the discovery of several others by analyzing these final
states in kaon production experiments. We also establish clear predictions for
the relative strengths of certain states to decay to Lambda(1405) K and
Lambda(1520) K, which can be tested to determine if a three-quark model of the
Lambda(1405) K is valid. Our results compare favorably with the results of
partial wave analyses of the limited existing data for the Lambda K and Sigma K
channels. We do not find large Sigma K decay amplitudes for a substantial group
of predicted and weakly established negative-parity states, in contrast to the
only previous work to consider decays of these states into the strange final
states Lambda K and Sigma K.Comment: 25 pages, 8 figures, RevTe
On the Mechanism of Open-Flavor Strong Decays
Open-flavor strong decays are mediated by pair production, which is
known to occur dominantly with \3p0 quantum numbers. The relation of the
phenomenological \3p0 model of these decays to ``microscopic" QCD decay
mechanisms has never been clearly established. In this paper we investigate
meson decay amplitudes assuming pair production from the scalar
confining interaction (sKs) and from one gluon exchange (OGE). sKs pair
production predicts decay amplitudes of approximately the correct magnitude and
D/S amplitude ratios in and which are close
to experiment. The OGE decay amplitude is found to be subdominant in most
cases, a notable exception being PSS. The full
sKs~+~OGE amplitudes differ significantly from \3p0 model predictions in some
channels and can be distinguished experimentally, for example through an
accurate comparison of the D/S amplitude ratios in and
.Comment: 44 pages, 22 eps figures, RevTex, complete postscript file available
at http://csep2.phy.ornl.gov/theory_group/people/barnes/pubs/abs.p
Coulomb Gauge QCD, Confinement, and the Constituent Representation
Quark confinement and the genesis of the constituent quark model are examined
in nonperturbative QCD in Coulomb gauge. We employ a self-consistent method to
construct a quasiparticle basis and to determine the quasiparticle interaction.
The results agree remarkably well with lattice computations. They also
illustrate the mechanism by which confinement and constituent quarks emerge,
provide support for the Gribov-Zwanziger confinement scenario, clarify several
perplexing issues in the constituent quark model, and permit the construction
of an improved model of low energy QCD.Comment: 43 pages, 14 figures, revtex, uses psfig.st
Radiative Decays of Excited Vector Mesons
Radiative decays of the radial and orbital excitations of
the , and are calculated in the quark model, using wave
functions obtained variationally from the Hamiltonian with standard quark-model
parameters. The larger radiative widths should be measurable at new
high-intensity facilities being proposed, and in some cases may be measurable
in data from existing experiments. The radiative decays are a strong
discriminator between the and excitations, and can also be
used to provide unique information about the decay products.Comment: 23 pages, 6 figure
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