101 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
Sensitivity analysis of the recovery time for a population under the impact of an environmental disturbance
Analysis of lethal and sublethal impacts of environmental disasters on sperm whales using stochastic modeling
© The Author(s), 2017. This article is distributed under the terms of the Creative Commons Attribution License. The definitive version was published in Ecotoxicology 26 (2017): 820-830, doi:10.1007/s10646-017-1813-4.Mathematical models are essential for combining data from multiple sources to quantify population endpoints. This is especially true for species, such as marine mammals, for which data on vital rates are difficult to obtain. Since the effects of an environmental disaster are not fixed, we develop time-varying (nonautonomous) matrix population models that account for the eventual recovery of the environment to the pre-disaster state. We use these models to investigate how lethal and sublethal impacts (in the form of reductions in the survival and fecundity, respectively) affect the population’s recovery process. We explore two scenarios of the environmental recovery process and include the effect of demographic stochasticity. Our results provide insights into the relationship between the magnitude of the disaster, the duration of the disaster, and the probability that the population recovers to pre-disaster levels or a biologically relevant threshold level. To illustrate this modeling methodology, we provide an application to a sperm whale population. This application was motivated by the 2010 Deepwater Horizon oil rig explosion in the Gulf of Mexico that has impacted a wide variety of species populations including oysters, fish, corals, and whales.This research is part of the Littoral Acoustic Demonstration Center-Gulf Ecological Monitoring and Modeling (LADC-GEMM) consortium project supported by Gulf of Mexico Research Initiative Year 5–7 Consortia Grants (RFP-IV). Hal Caswell also acknowledges support from ERC Advanced Grant 322989
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
Linear Size-structured Population Models with Spacial Diffusion and Optimal Harvesting Problems
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
Parameter identification problems in the modelling of cell motility
We present a novel parameter identification algorithm for the estimation of parameters in models of cell motility using imaging data of migrating cells. Two alternative formulations of the objective functional that measures the difference between the computed and observed data are proposed and the parameter identification problem is formulated as a minimisation problem of nonlinear least squares type. A Levenberg–Marquardt based optimisation method is applied to the solution of the minimisation problem and the details of the implementation are discussed. A number of numerical experiments are presented which illustrate the robustness of the algorithm to parameter identification in the presence of large deformations and noisy data and parameter identification in three dimensional models of cell motility. An application to experimental data is also presented in which we seek to identify parameters in a model for the monopolar growth of fission yeast cells using experimental imaging data. Our numerical tests allow us to compare the method with the two different formulations of the objective functional and we conclude that the results with both objective functionals seem to agree
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
- …