A Comparative Study on the Solution Techniques for Fiber Orientation in Two-Dimensional Converging and Diverging Flows

The two-dimensional steady flow of both infinite and finite aspect ratio (length to diameter ratio) fibers suspended in a Newtonian fluid is investigated numeri cally. Forty-five-degree convergent and divergent channel geometries are considered for the analysis. Due to symmetry, only half the channel geometry is considered and the ori entation field is assumed to be planar. The analysis is carried out for the creeping flows where the inertia terms are neglected. Numerical grid generation is used to generate the mesh, and the transformed governing equations in terms of the stream function are solved in the computational domain using a finite difference scheme. In this study, several solu tion strategies for solving the orientation field are investigated. The orientation of individ ual fibers are assumed to be governed by Jeffery's equation. The orientation field, which can be expressed in different forms (i.e., a unit vector, tensorial quantities, or an orienta tion distribution function), is specified by solving the orientation equations along particle paths. A tracing technique is implemented to obtain these particle paths for each grid point in the flow domain. The solution of the orientation field is obtained by using two basic techniques. First, a large number of fibers are considered, and by using analytical expres sions developed to describe the orientation state of one fiber, a statistical orientation distri bution function is generated. Second, tensorial quantities (both second- and fourth-order orientation tensors) are employed to solve for the orientation field. In order to overcome the closure problem occurring in the resulting orientation equations, quadratic approxima tions are used. Maximum orientation angles are reported from both the techniques, and their accuracies are investigated. The maximum orientation angles (i.e., preferred orienta tion) obtained from the second- and fourth-order tensorial solutions are observed to be identical. On the other hand, the degree of fiber alignments that are specified by the indi vidual tensor components differ considerably. Comparison of the solution techniques shows that the accuracy of the preferred angle obtained from statistical solution is depen dent on the number of fibers considered. In addition, the calculations for the finite fiber aspect ratio revealed some discrepancies between the statistical and tensorial results at the regions of rapid fiber tumbling.Yeshttps://us.sagepub.com/en-us/nam/manuscript-submission-guideline

Asymptotic Capture-Number and Island-Size Distributions for One-Dimensional Irreversible Submonolayer Growth

Using a set of evolution equations [J.G. Amar {\it et al}, Phys. Rev. Lett. {\bf 86}, 3092 (2001)] for the average gap-size between islands, we calculate analytically the asymptotic scaled capture-number distribution (CND) for one-dimensional irreversible submonolayer growth of point islands. The predicted asymptotic CND is in reasonably good agreement with kinetic Monte-Carlo (KMC) results and leads to a \textit{non-divergent asymptotic} scaled island-size distribution (ISD). We then show that a slight modification of our analytical form leads to an analytic expression for the asymptotic CND and a resulting asymptotic ISD which are in excellent agreement with KMC simulations. We also show that in the asymptotic limit the self-averaging property of the capture zones holds exactly while the asymptotic scaled gap distribution is equal to the scaled CND.Comment: 4 pages, 1 figure, submitted to Phys. Rev.

Homogenization of weakly coupled systems of Hamilton--Jacobi equations with fast switching rates

We consider homogenization for weakly coupled systems of Hamilton--Jacobi equations with fast switching rates. The fast switching rate terms force the solutions converge to the same limit, which is a solution of the effective equation. We discover the appearance of the initial layers, which appear naturally when we consider the systems with different initial data and analyze them rigorously. In particular, we obtain matched asymptotic solutions of the systems and rate of convergence. We also investigate properties of the effective Hamiltonian of weakly coupled systems and show some examples which do not appear in the context of single equations.Comment: final version, to appear in Arch. Ration. Mech. Ana

Determination of step--edge barriers to interlayer transport from surface morphology during the initial stages of homoepitaxial growth

We use analytic formulae obtained from a simple model of crystal growth by molecular--beam epitaxy to determine step--edge barriers to interlayer transport. The method is based on information about the surface morphology at the onset of nucleation on top of first--layer islands in the submonolayer coverage regime of homoepitaxial growth. The formulae are tested using kinetic Monte Carlo simulations of a solid--on--solid model and applied to estimate step--edge barriers from scanning--tunneling microscopy data on initial stages of Fe(001), Pt(111), and Ag(111) homoepitaxy.Comment: 4 pages, a Postscript file, uuencoded and compressed. Physical Review B, Rapid Communications, in press

Multilayer clustering: Biomarker driven segmentation of Alzheimer's disease patient population

Identification of biomarkers for the Alzheimer's disease is a challenge and a very difficult task both for medical research and data analysis. In this work we present results obtained by application of a novel clustering tool. The goal is to identify subpopulations of the Alzheimer's disease (AD) patients that are homogeneous in respect of available clinical and biological descriptors. The result presents a segmentation of the Alzheimer's disease patient population and it may be expected that within each subpopulation separately it will be easier to identify connections between clinical and biological descriptors. Through the evaluation of the obtained clusters with AD subpopulations it has been noticed that for two of them relevant biological measurements (whole brain volume and intracerebral volume) change in opposite directions. If this observation is actually true it would mean that the diagnosed severe dementia problems are results of different physiological processes. The observation may have substantial consequences for medical research and clinical trial design. The used clustering methodology may be interesting also for other medical and biological domains

A summary of the methodology for the seismic stratigraphic interpretation for the 'GlaciStore' bid to IODP

This report summarises the methodology followed for the seismic interpretation of sedimentary strata that are the overburden sequence and the Palaeogene strata that are prospective CO2 storage formations, in the UK Central North Sea. The interpretation of selected 2D and 3D seismic reflection, well and borehole data in the UK North and Central North Sea is targeted to inform the preparation of the ‘GlaciStore’ proposal for scientific drilling submitted to the International Ocean Discovery Programme (IODP). Drilling sites proposed to IODP lie within the UK and Norwegian sectors of the North Sea. The methodology is described for the interpretation of seismic data for proposed sites within UK waters. The seismic interpretation was undertaken in collaboration with Norwegian members of the GlaciStore consortium. The seismic interpretation was divided into two teams according to depth, into ‘shallower and ‘deeper’ seismic interpretation activities, appropriate to the fields of expertise and experience of the interpreters. The ‘shallower seismic’ interpreters considered strata of latest Neogene and Quaternary age which were deposited during major glacial and interglacial cycles. The ‘deeper seismic’ interpreters considered slightly older strata of Mid Eocene to Quaternary in age. Seven potential UK drill sites were selected to address the scientific objectives in the proposal. 2D and 3D seismic, well, borehole and bathymetry data were used to map buried and open tunnel valleys and to identify any evidence for the presence of shallow gas in the ‘shallower seismic’ interpretation at each drill site. Only sites without any indication of shallow gas features were considered as these pose a serious hazard for drilling. 2D and 3D seismic and well datasets and existing interpretations were collated for the ‘deeper seismic’ interpretation. The hydrocarbon exploration well log data, which were found to be of variable quality, were used to identify and map a number of stratigraphical surfaces of Cenozoic age, and included Quaternary strata, around the grid of seismic lines. Maps from some of the key stratigraphical surfaces are presented, selected to inform the drilling proposal. A plot of acoustic velocity data was prepared to inform future conversion of the seismic interpretation to true vertical depth. Future work, based on the seismic interpretation undertaken to underpin the drilling proposal, is identified. Features observed within the ‘shallower’ and ‘deeper’ seismic interpretations that warrant further investigation are: a chaotic zone within the Quaternary sequence; prograding units within the Eocene Horda Formation; basin centre sandstone bodies as prospective CO2 storage strata within the Horda Formation; systematic mapping of cross-cutting, buried tunnel valleys in the Quaternary sequence from 3D seismic data

Adsorption of Line Segments on a Square Lattice

We study the deposition of line segments on a two-dimensional square lattice. The estimates for the coverage at jamming obtained by Monte-Carlo simulations and by $7^{th}$-order time-series expansion are successfully compared. The non-trivial limit of adsorption of infinitely long segments is studied, and the lattice coverage is consistently obtained using these two approaches.Comment: 19 pages in Latex+5 postscript files sent upon request ; PTB93_

Pathogenic Potential to Humans of Bovine Escherichia coli O26, Scotland

Escherichia coli O26 and O157 have similar overall prevalences in cattle in Scotland, but in humans, Shiga toxin–producing E. coli O26 infections are fewer and clinically less severe than E. coli O157 infections. To investigate this discrepancy, we genotyped E. coli O26 isolates from cattle and humans in Scotland and continental Europe. The genetic background of some strains from Scotland was closely related to that of strains causing severe infections in Europe. Nonmetric multidimensional scaling found an association between hemolytic uremic syndrome (HUS) and multilocus sequence type 21 strains and confirmed the role of stx<sub>2</sub> in severe human disease. Although the prevalences of E. coli O26 and O157 on cattle farms in Scotland are equivalent, prevalence of more virulent strains is low, reducing human infection risk. However, new data on E. coli O26–associated HUS in humans highlight the need for surveillance of non-O157 enterohemorrhagic E. coli and for understanding stx<sub>2</sub> phage acquisition

Jamming coverage in competitive random sequential adsorption of binary mixture

We propose a generalized car parking problem where cars of two different sizes are sequentially parked on a line with a given probability $q$. The free parameter $q$ interpolates between the classical car parking problem of only one car size and the competitive random sequential adsorption (CRSA) of a binary mixture. We give an exact solution to the CRSA rate equations and find that the final coverage, the jamming limit, of the line is always larger for a binary mixture than for the uni-sized case. The analytical results are in good agreement with our direct numerical simulations of the problem.Comment: 4 pages 2-column RevTeX, Four figures, (there was an error in the previous version. We replaced it (including figures) with corrected and improved version that lead to new results and conclusions