S Sundar

Microplastic in freshwater has been known to absorb, adsorb, and later desorb persistent organic pollutants as well as in its tiny size acts as an infiltrator to vital tissues; it may therefore corrupt physiological processes of organic lives. The fate of microplastic particles can be understood by revealing to what extent certain material properties (e.g., size and density) determine local behavior such as sedimentation and interaction with biofilm. This work seeks to gain an understanding of the short-range transport of microplastic particles in freshwater through devising a lid–driven cavity with a biofilm-covering obstacle as the medium. A stationary Navier–Stokes equation for an incompressible fluid at a moderate Reynolds number provides the background flow field. Microbeads are injected into the flow field, where their motion is governed by a Lagrangian system of equations. Advanced features such as dry particle–particle and particle–wall collisions as well as adhesion between particles and biofilm portraying particle entrapment are presented. Various simulations and parameterization studies are carried out to determine the impact of material properties, obstacle geometry, and adhesion force on the deposition profiles. In most cases, particles are trapped in the biofilm and in regions around the cavity with negative Okubo–Weiss numbers whereby the relative vorticity is dominating against the local strains.

In this paper, we describe the mathematical modeling of heat flow across a glass fiber medium. Using different mathematical models we try to explain the porosity dependence of the heat flow which is observed in experiments. © 2005 Elsevier Ltd. All rights reserved.

We present an investigation of extrapolation boundary conditions for lattice Boltzmann method (LBM) using asymptotic analysis. Equilibrium and non-equilibrium extrapolation methods for velocity and pressure boundary conditions proposed in the literature were tested numerically in specific cases. We analyse these boundary conditions using asymptotic expansion techniques and show an improvement in the accuracy of the lattice Boltzmann solution. We also present few numerical examples and simulate fluid flow across an unsymmetrically placed stationary cylinder in a channel with steady and unsteady flow conditions. Thus the article demonstrates application of asymptotic analysis to understand properties of extrapolation boundary conditions for LBM and show the flexibility of these boundary conditions for complex fluid flow applications. © 2009 Elsevier Ltd. All rights reserved.

In this work, we extend a microscopic rational behaviour pedestrian model and investigate it and the related macroscopic model numerically. A coupling with an eikonal equation is performed to include more complex geometries and pedestrian behaviour. We compare the microscopic and macroscopic models to classical social force type models. We observe that the more complex rational behaviour approach gives physically more reasonable results in low-density cases. However, in higher density scenarios, an additional social force type term is required to avoid nonphysical overcrowding. We present numerical experiments and a numerical comparison with social force type models for a variety of different physical scenarios, including low and high density situations and flow problems with and without obstacles. The numerical simulations are realised by solving the model equations in a Lagrangian form using a mesh-free particle method. In this numerical context, the model is easily extended, for example, to moving obstacle scenarios, as presented in a final example.

Many real time-series exhibit behavior adequate to long range dependent data. Additionally very often these time-series have constant time periods and also have characteristics similar to Gaussian processes although they are not Gaussian. Therefore there is need to consider new classes of systems to model these kinds of empirical behavior. Motivated by this fact in this paper we analyze two processes which exhibit long range dependence property and have additional interesting characteristics which may be observed in real phenomena. Both of them are constructed as the superposition of fractional Brownian motion (FBM) and other process. In the first case the internal process, which plays role of the time, is the gamma process while in the second case the internal process is its inverse. We present in detail their main properties paying main attention to the long range dependence property. Moreover, we show how to simulate these processes and estimate their parameters. We propose to use a novel method based on rescaled modified cumulative distribution function for estimation of parameters of the second considered process. This method is very useful in description of rounded data, like waiting times of subordinated processes delayed by inverse subordinators. By using the Monte Carlo method we show the effectiveness of proposed estimation procedures. Finally, we present the applications of proposed models to real time series.

This paper deals with a velocity model of production system based on hyperbolic con-servation laws. Velocity may possess nonlocal characterization as well as local feature. Due to yield loss phenomena in the production system, governing equation becomes nonhomogeneous in nature. Under certain assumptions, existence and uniqueness of weak solution have been studied. Results on regularity properties and stability analysis of the weak solution have been presented. © CSP - Cambridge, UK; I&S - Florida, USA, 2014.

This paper suggests a method for automating the process of checking for a sufficiently matching sole pattern in a given collection of sole patterns. It may take up to weeks to manually do the same, in the industry. We describe the method of finding the best match from a given set using a procedure, the basis of which is the Karhunen-Loueve transform (KLT), involving a projection onto a subspace spanned by the eigenpatterns corresponding to the largest few eigenvalues. The patterns are first scanned, stored in picture file format, and cleaned up so that they consist of a black sole and a white background, to minimize unnecessary information content. Their centers of masses are aligned and principal moment of inertia axes are arranged vertically to maximize correlation between these pictures. The eigenpatterns are found for this collection of pictures. To find the best match for the new sole pattern, its projection onto the lesser-dimensional subspace spanned by the eigenpatterns is found. The projected pattern can be decomposed into a weighted sum of the eigenpatterns. The best match is found using a minimum distance criterion in this space. This method is suitable for any highly correlated image database. © 2003 Elsevier Science Ltd. All rights reserved.

This study investigates the hemodynamics of nanofluid flow through modelled stenosis-aneurysm models. The models were created using mathematical functions to increase their realism. This study aims to explore how temperature-sensitive drugs coated on nanoparticles could be delivered to diseased areas, with the mathematical model aiding in the treatment of vascular stenosis. To effectively treat stenosis, medication-coated nanoparticles should be applied to the exterior surface of a catheter. The blood flow was modelled as a micropolar fluid flow, which led to the development of highly nonlinear coupled equations for momentum, temperature, and concentration. The dispersion of nanoparticles resulted in changing viscosity effects, making the fluid flow equations even more complex. The model considered the porous nature of the stenosis, no-slip at the catheter surface, and free slip at the blood vessel surface. The homotopy perturbation method was used to solve the formulated mathematical model. The study investigated the convergence of perturbed solutions for temperature and concentration and showed the degree of deformation. Drug delivery to a targeted region is faster in a converging tapered blood vessel than in a diverging and non-tapered artery. Concentration dispersion is more significant in the stenotic region, while temperature dispersion is more significant in the aneurysm region. The results of the study can be used to understand the improvement in mass dispersion and heat transfer in unhealthy blood arteries, which may be useful in delivering drugs to treat stenotic diseases.

Chronic obstructive pulmonary disease (COPD) is associated with the respiratory system. COPD is often treated with inhalers whose two major ingredients are the bronchodilators and the steroids. In this paper we mathematically model the deposition of the inhaled drug on the infected airway into Cauchy-Euler differential equation and use Visual Basic to simulate the evolution of the recovery of the inflamed airway. © 2012 IEEE.

We study the structure of positive solutions to steady state ecological models of the form: −∆u = λuf(u) in Ω, α(u) ∂u/∂η + [1 − α(u)]u = 0 on ∂Ω, where Ω is a bounded domain in ℝn; n > 1 with smooth boundary ∂Ω or Ω = (0, 1), ∂/∂η represents the outward normal derivative on the boundary, λ is a positive parameter, f : [0, ∞) → R is a C2 function such that f (s)/k−s > 0 for some k > 0, and α : [0, k] → [0, 1] is also a C2 function. Here f(u) represents the per capita growth rate, α(u) represents the fraction of the population that stays on the patch upon reaching the boundary, and λ relates to the patch size and the diffusion rate. In particular, we will discuss models in which the per capita growth rate is increasing for small u, and models where grazing is involved. We will focus on the cases when α′(s) ≥ 0; [0, k], which represents negative density dependent dispersal on the boundary. We employ the method of sub-super solutions, bifurcation theory, and stability analysis to obtain our results. We provide detailed bifurcation diagrams via a quadrature method for the case Ω = (0, 1).