K. L. Kreider

Analysis of the Driving Forces for Multiple Cracks in an Infinite Nonhomogeneous Plate, Part I: Theoretical Analysis

A general methodology is constructed for the fundamental solution of an arbitrarily oriented crack embedded in an infinite nonhomogeneous plate in which the shear modulus varies exponentially with one coordinate. The stress is evaluated as a summation of two states of stresses; one is associated with a local coordinate system in an infinite plate, while the other is associated with the boundaries of finite plate defined in a structural coordinate system. The fundamental solution is used to generate stress intensity factors and strain energy release rates for fully interactive multiple crack problems. Part I of this paper focuses on the analytical development of the solution. In Part II, the numerical technique used in solving singular integral equations obtained in Part I is presented, along with a parametric study.

Analysis of the driving forces for multiple cracks in an infinite nonhomogeneous plate. Part II : Numerical solutions

In Part I of this work, an analytical model was developed for the fundamental solution for a crack embedded in an infinite nonhomogeneous plate. This fundamental solution is used here to generate the stress intensity factors and strain energy release rates for fully interactive multiple crack problems. Also, a numerical technique used in solving the singular integral equation in Part I is presented, along with a parametric study. The parametric study addresses the influence of crack distance, relative angular orientation, and the coefficient of nonhomogeneity on the crack driving forces. The strain energy release rate is recommended for use as a crack propagation criterion because it depends on the local material properties as well as all the remaining parameters contained in the stress intensity factors.

Analysis of the driving force for a generally oriented crack in a functionally graded strip sandwiched between two homogeneous half planes

The driving forces for a generally oriented crack problem embedded in a Functionally Graded strip sandwiched between two half plane are analyzed using singular integral equations with Cauchy kernels, and integrated using Lobatto-Chebyshev collocation. Mixed-mode Stress Intensity Factors (SIF) and Strain Energy Release Rates (SERR) are calculated. The Stress Intensity Factors are compared for accuracy with previously published results. Parametric studies are conducted for various non-homogeneity ratios, crack lengths, crack orientation and thickness of the strip. It is shown that the SERR is more complete and should be used for crack propagation analysis.

A wave splitting approach to time dependent inverse scattering for the stratified cylinder

This paper examines the inverse problem for the stratified inhomogeneous cylinder, in which the unknown velocity function is recovered from reflection data. The analysis is based on Weston’s theoretical wave splitting for stratified three-dimensional media [J. Math. Phys., 28 (1987), pp. 1061–1068], [J. Math.Phys., 29 (1988), pp. 36–45]. The forms of the splitting operators are presented, and the inverse problem is solved numerically by means of the r-equation, an integro-differential equation that characterizes the scattering medium independently of the wave field. Although the r-equation is singular at one round-trip time (corresponding to a caustic when a radially incoming cylindrical wave reaches the z-axis), several numerical examples indicate that the velocity function can be reconstructed quite accurately.

Nanoparticle Deposition onto Biofilms

We develop a mathematical model of nanoparticles depositing onto and penetrating into a biofilm grown in a parallel-plate flow cell. We carry out deposition experiments in a flow cell to support the modeling. The modeling and the experiments are motivated by the potential use of polymer nanoparticles as part of a treatment strategy for killing biofilms infecting the deep passages in the lungs. In the experiments and model, a fluid carrying polymer nanoparticles is injected into a parallel-plate flow cell in which a biofilm has grown over the bottom plate. The model consists of a system of transport equations describing the deposition and diffusion of nanoparticles. Standard asymptotic techniques that exploit the aspect ratio of the flow cell are applied to reduce the model to two coupled partial differential equations. We perform numerical simulations using the reduced model. We compare the experimental observations with the simulation results to estimate the nanoparticle sticking coefficient and the diffusion coefficient of the nanoparticles in the biofilm. The distributions of nanoparticles through the thickness of the biofilm are consistent with diffusive transport, and uniform distributions through the thickness are achieved in about four hours. Nanoparticle deposition does not appear to be strongly influenced by the flow rate in the cell for the low flow rates considered.

Time dependent direct and inverse electromagnetic scattering for the dispersive cylinder

Abstract Direct and inverse scattering problems for the inhomogeneous dispersive cylinder for electromagnetic wave propagation in the time domain are considered. Emphasis is placed on the inverse problem in which the reconstruction of the susceptibility kernel, a time dependent function characterizing the dispersive nature of the medium, is accomplished by using reflection data. The technique consists of splitting the electromagnetic field into cylindrical waves that would be radially incoming and outgoing in a homogeneous medium, and relating the internal field components to the applied field at the surface by means of a Greens function operator. Numerical implementation of the algorithm is described, and several examples are presented. Although the formulation becomes singular at one round trip time (corresponding to a caustic when the radially incoming wave reaches the axis of the cylinder), recovery of the susceptibility kernel can be extended beyond one round trip time by fitting the obtainable data to an assumed model by nonlinear least squares.

Development of the Pseudomonas aeruginosa mushroom morphology and cavity formation by iron-starvation: a mathematical modeling study.

We present a mathematical model of mushroom-like architecture and cavity formation in Pseudomonas aeruginosa biofilms. We demonstrate that a proposed disparity in internal friction between the stalk and cap extracellular polymeric substances (EPS) leads to spatial variation in volumetric expansion sufficient to produce the mushroom morphology. The capability of diffusible signals to induce the formation of a fluid-filled cavity within the cap is then investigated. We assume that conversion of bacteria to the planktonic state within the cap occurs in response to the accumulation or depletion of some signal molecule. We (a) show that neither simple nutrient starvation nor signal production by one or more subpopulations of bacteria is sufficient to trigger localized cavity formation. We then (b) demonstrate various hypothetical scenarios that could result in localized cavity formation. Finally, we (c) model iron availability as a detachment signal and show simulation results demonstrating cavity formation by iron starvation. We conclude that iron availability is a plausible mechanism by which fluid-filled cavities form in the cap region of mushroom-like structures.

Multiscale modeling, simulations, and experiments of coating growth on nanofibers. Part II. Deposition

This work is Part II of an integrated experimental/modeling investigation of a procedure to coat nanofibers and core-clad nanostructures with thin-film materials using plasma-enhanced physical vapor deposition. In the experimental effort, electrospun polymer nanofibers are coated with aluminum materials under different operating conditions to observe changes in the coating morphology. This procedure begins with the sputtering of the coating material from a target. Part I [J. Appl. Phys. 98, 044303 (2005)] focused on the sputtering aspect and transport of the sputtered material through the reactor. That reactor level model determines the concentration field of the coating material. This field serves as input into the present species transport and deposition model for the region surrounding an individual nanofiber. The interrelationships among processing factors for the transport and deposition are investigated here from a detailed modeling approach that includes the salient physical and chemical phenomena....

Multiscale modeling, simulations, and experiments of coating growth on nanofibers. Part I. Sputtering

This paper is Part I of an integrated experimental/modeling investigation of a procedure to coat nanofibers and core-clad nanostructures with thin-film materials using plasma-enhanced physical vapor deposition. In the experimental effort, electrospun polymer nanofibers are coated with aluminum under varying operating conditions to observe changes in the coating morphology. This procedure begins with the sputtering of the coating material from a target. This paper focuses on the sputtering process and transport of the sputtered material through the reactor. The interrelationships among the processing factors for the sputtering and transport are investigated from a detailed modeling approach that describes the salient physical and chemical phenomena. Solution strategies that couple continuum and atomistic models are used. At the continuum scale, the sheath region and the reactor dynamics near the target surface are described. At the atomic level, molecular-dynamics (MD) simulations are used to study the sputtering and deposition mechanisms. Ion kinetic energies and fluxes are passed from the continuum sheath model to the MD simulations. These simulations calculate sputtering and sticking probabilities that in turn are used to calculate parameters for the continuum reactor model. The reactor model determines the concentration field of the coating material.

Mathematical modelling of Pseudomonas aeruginosa biofilm growth and treatment in the cystic fibrosis lung.

Lung failure due to chronic bacterial infection is the leading cause of death for patients with cystic fibrosis (CF). It is thought that the chronic nature of these infections is, in part, due to the increased tolerance and recalcitrant behaviour of bacteria growing as biofilms. Inhalation of silver carbene complex (SCC) antimicrobial, either encased in polymeric biodegradable particles or in aqueous form, has been proposed as a treatment. Through a coordinated experimental and mathematical modelling effort, we examine this proposed treatment of lung biofilms. Pseudomonas aeruginosa biofilms grown in a flow-cell apparatus irrigated with an artificial CF sputum medium are analysed as an in vitro model of CF lung infection. A 2D mathematical model of biofilm growth within the flow-cell is developed. Numerical simulations demonstrate that SCC inactivation by the environment is critical in aqueous SCC, but not SCC-polymer, based treatments. Polymer particle degradation rate is shown to be an important parameter that can be chosen optimally, based on environmental conditions and bacterial susceptibility.