Control of CVD diamond nucleation and effects on microcomponent processing

Different surface pretreatments of the substrates and their effect on the nucleation and early growth stages of CVD diamond were studied, and the results were used to design a procedure for growing near-net shape diamond micro machine components. The Mechanisms responsible for nucleation of diamond on various substrate material are still under study and have not been completely explained yet. Studies of different pretreatments that enhance or degrade the nucleation are important for the determination of controlling mechanisms and might lead to better applications of the CVD diamond industry.The mechanical pretreatment consisted of ultrasonic abrasion of the silicon substrate with diamond, SiC, A1203, and TiB2 powders mixed with ethanol. Scanning Electron microscopy (SEM), profilometry, and AFM were used to characterize the surfaces before and after the CVD of diamond. Measurements of the surface roughness showed no significant difference between the roughness of the various abraded samples.Nucleation density was 4 to 8 orders of magnitude higher on the samples abraded with diamond-ethanol slurry than any other material. Increasing the abrasion time appears to have slight effect on the nucleation density. Gross deformation did not seem to affect the nucleation rate either.The effect of ion implantation on the pretreated samples was investigated.Scanning electron microscopy and RBS/Channeling were used to analyze the results of this work. At an energy of 150 KeV, a dose of 2x1015 Si/cm2 was the border line for suppression of nucleation and also for amorphization of both diamond and silicon.Annealing of the substrates at various stages of the CVD process was also studied.SEM, RBS/channeling, and SEM channeling were used for the analysis in this study.Annealing the substrates did not seem to have a significant effect on the nucleation and growth of CVD diamond.The results of the studies on pretreatment were used to design a process for fabrication of diamond microcomponents. The process included ion implantation, CVD growth, and etching. Analysis on these samples was done using all the above mentioned techniques. Controlling the nucleation in the implanted regions is the major key to the control of the minimum resolution of features on the diamond near-net shape micro components

On the net reproduction rate of continuous structured populations with distributed states at birth

We consider a nonlinear structured population model with a distributed recruitment term. The question of the existence of non-trivial steady states can be treated (at least!) in three different ways. One approach is to study spectral properties of a parametrized family of unbounded operators. The alternative approach, on which we focus here, is based on the reformulation of the problem as an integral equation. In this context we introduce a density dependent net reproduction rate and discuss its relationship to a biologically meaningful quantity. Finally, we briefly discuss a third approach, which is based on the finite rank approximation of the recruitment operator.Comment: To appear in Computers and Mathematics with Application

On the spread of epidemics in a closed heterogeneous population

Heterogeneity is an important property of any population experiencing a disease. Here we apply general methods of the theory of heterogeneous populations to the simplest mathematical models in epidemiology. In particular, an SIR (susceptible-infective-removed) model is formulated and analyzed for different sources of heterogeneity. It is shown that a heterogeneous model can be reduced to a homogeneous model with a nonlinear transmission function, which is given in explicit form. The widely used power transmission function is deduced from a heterogeneous model with the initial gamma-distribution of the disease parameters. Therefore, a mechanistic derivation of the phenomenological model, which mimics reality very well, is provided. The equation for the final size of an epidemic for an arbitrary initial distribution is found. The implications of population heterogeneity are discussed, in particular, it is pointed out that usual moment-closure methods can lead to erroneous conclusions if applied for the study of the long-term behavior of the model.Comment: 23 pages, 2 figure

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

Prospects for detecting an ηc′\eta_c' in two photon processes

We argue that an experimental search for an $\eta_c'$, the first radial excitation of the $\eta_c(2980)$, may be carried out using the two photon process e^+e^- \to e^+e^- \gamma \gamma \ra e^+e^-\eta_c'. We estimate the partial width $\Gamma_{\gamma \gamma}(\eta_c')$ and the branching fraction $B(\eta_c' \to h)$, where $h$ is an exclusive hadronic channel, and find that for $h = K^o_s K^\pm \pi^\mp$ it may be possible to observe this state in two photon collisions at CLEO-II.Comment: 9 pages, LATEX forma

Sensitivity equations for measure-valued solutions to transport equations

We consider the following transport equation in the space of bounded, nonnegative Radon measures M+(Rd): θtμt + θx(v(x)μt) = 0: We study the sensitivity of the solution μt with respect to a perturbation in the vector field, v(x). In particular, we replace the vector field v with a perturbation of the form vh = v0(x) + hv1(x) and let μh t be the solution of θtμh t + θx(vh(x)μh t) = 0: We derive a partial differential equation that is satisfied by the derivative of μh t with respect to h, θh(μh t). We show that this equation has a unique very weak solution on the space Z, being the closure of M(Rd) endowed with the dual norm (C1,α(Rd))*. We also extend the result to the nonlinear case where the vector field depends on μt, i.e., v = v[μt](x).Fil: Ackleh, Azmy S.. State University of Louisiana; Estados UnidosFil: Saintier, Nicolas Bernard Claude. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Skrzeczkowski, Jakub. University of Warsaw; Poloni

Assessing critical population thresholds under periodic disturbances

Population responses to repeated environmental or anthropogenic disturbances depend on complicated interactions between the disturbance regime, population structure, and differential stage susceptibility. Using a matrix modeling approach, we develop a methodological framework to explore how the interplay of these factors impacts critical population thresholds. To illustrate the wide applicability of this approach, we present two case studies pertaining to agroecosystems and conservation science. We apply sensitivity analysis to the two case studies to examine how population and disturbance properties affect these thresholds. Contrasting outcomes between these two applications, including differences in how factors such as disturbance intensity and pre-disturbance population distributions impact population responses, highlight the importance of accounting for demographic features when performing ecological risk assessments

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