Mathematical Modeling of a Carrier-Mediated Transport Process in a Liquid Membrane

An analysis of the reaction diffusion in a carrier-mediated transport process through a membrane is presented. A simple approximate analytical expression of concentration profiles is derived in terms of all dimensionless parameters. Furthermore, in this work we employ the homotopy perturbation method to solve the nonlinear reaction–diffusion equations. Moreover, the analytical results have been compared to the numerical simulation using the Matlab program. The simulated results are comparable with the appropriate theories. The results obtained in this work are valid for the entire solution domain.     

Optimal and Numerical Solutions for an MHD Micropolar Nanofluid between Rotating Horizontal Parallel Plates

The present analysis deals with flow and heat transfer aspects of a micropolar nanofluid between two horizontal parallel plates in a rotating system. The governing partial differential equations for momentum, energy, micro rotation and nano-particles concentration are presented. Similarity transformations are utilized to convert the system of partial differential equations into system of ordinary differential equations. The reduced equations are solved analytically with the help of optimal homotopy analysis method (OHAM). Analytical solutions for velocity, temperature, micro-rotation and concentration profiles are expressed graphically against various emerging physical parameters. Physical quantities of interest such as skin friction co-efficient, local heat and local mass fluxes are also computed both analytically and numerically through mid-point integration scheme. It is found that both the solutions are in excellent agreement. Local skin friction coefficient is found to be higher for the case of strong concentration i.e. n=0, as compared to the case of weak concentration n=0.50. Influence of strong and weak concentration on Nusselt and Sherwood number appear to be similar in a quantitative sense.     

Thermal and Concentration Stratifications Effects in Radiative Flow of Jeffrey Fluid over a Stretching Sheet

In this article we investigate the heat and mass transfer analysis in mixed convective radiative flow of Jeffrey fluid over a moving surface. The effects of thermal and concentration stratifications are also taken into consideration. Rosseland''s approximations are utilized for thermal radiation. The nonlinear boundary layer partial differential equations are converted into nonlinear ordinary differential equations via suitable dimensionless variables. The solutions of nonlinear ordinary differential equations are developed by homotopic procedure. Convergence of homotopic solutions is examined graphically and numerically. Graphical results of dimensionless velocity, temperature and concentration are presented and discussed in detail. Values of the skin-friction coefficient, the local Nusselt and the local Sherwood numbers are analyzed numerically. Temperature and concentration profiles are decreased when the values of thermal and concentration stratifications parameters increase. Larger values of radiation parameter lead to the higher temperature and thicker thermal boundary layer thickness.     

A new asymptotic analysis of the nth order reaction-diffusion problem: analytical and numerical studies

We present a new formulation of the steady state, isothermal, nonlinear reaction-diffusion problem involving nth order reaction kinetics for slab geometry. This results in tractable expressions for the effectiveness factor as a function of the Thiele modulus, the Thiele modulus as a function of the centerline concentration, and the concentration profiles in the slab. The expressions are valid asymptotically in the limit of large orders n. We compare these results with the exact numerical solutions obtained by transforming the nonlinear differential equation into an integral form, using Green's function methods, and solving by successive approximations. The formulation for a membrane is also given, and the nature of the asymmetrical solution discussed. The analysis is facilitated through the introduction of pseudo-reaction orders. A comparison of the asymptotic Thiele modulus obtained herein with a previously given expression shows the present theory to be an improvement.     

Diffusion through a membrane: Approach to equilibrium

The transfer of solute through a membrane separating two aqueous solutions is studied with the time-dependent diffusion equation for composite media. By introducing new independent and dependent variables it is shown that the differential equations and boundary conditions can be transformed into a dimensionless form which does not explicitly depend on the diffusivities of the media. Laplace transforms are used to derive explicit solutions for the solute concentration as a function of position and time. It is shown that at large time the concentration approaches the equilibrium distribution exponentially. Explicit results are given for the decay time as a function of the parameters of the system. In addition, an accurate and simplified expression is derived for the decay time for the case of small membrane permeability. The accuracy of the analytic solutions for the concentration profiles is tested by comparing them with numerical results obtained by solving the diffusion equations by the method of finite differences. Excellent agreement is found. Research supported in part by a grant from the National Science Foundation.     

Phyllotaxis: cooperation and competition between mechanical and biochemical processes

Current theories and models of the formation of phyllotactic patterns at plant apical meristems center on either transport of the growth hormone auxin or the mechanical buckling of the plant tunica. By deriving a continuum approximation of an existing discrete biochemical model and comparing it with a mechanical model, we show that the model partial differential equations are similar in form. The implications of this universality in the form of the equations on interpreting the results of simulations are discussed. We develop a combined model that incorporates the coupling of biochemistry and mechanics. The combined model is accessible to analysis by reduction to a set of ordinary differential equations for the amplitudes of shapes associated with both the auxin concentration field and plant surface deformation. Analysis of these amplitude equations reveals the parameter choices under which the two mechanisms may cooperate in determining the pattern, or under which one or the other mechanism may dominate.     

Comparison of substance supply in static and perfusion cultures based on mass transport phenomena

Mass transport phenomena in cell culture can be formulated by using classical reaction-diffusion equations; however, in practice, it is difficult to solve these equations analytically. Here, we used computer simulation to solve these equations, and compared the time-dependent concentration profile of substances in conventional static culture with that in perfusion culture. The simulated glucose consumption in static culture agreed with that of actual culture conditions used in a general cell culture experiment. The simulation of perfusion culture revealed that the geometry of the chamber and its operating parameters are critical to obtaining a sufficient supply of substances. We also found that the previously reported perfusion chambers are well designed and operate under adequate conditions. Our kinetic model of time-dependent concentration profiles for general substances based on mass transport phenomena could, therefore, be used for the optimal design of a microfluidic perfusion culture chip.     

Modeling Tick-Borne Disease: A Metapopulation Model

Recent increases in reported outbreaks of tick-borne diseases have led to increased interest in understanding and controlling epidemics involving these transmission vectors. Mathematical disease models typically assume constant population size and spatial homogeneity. For tick-borne diseases, these assumptions are not always valid. The disease model presented here incorporates non-constant population sizes and spatial heterogeneity utilizing a system of differential equations that may be applied to a variety of spatial patches. We present analytical results for the one patch version and find parameter restrictions under which the populations and infected densities reach equilibrium. We then numerically explore disease dynamics when parameters are allowed to vary spatially and temporally and consider the effectiveness of various tick-control strategies.     

反向Northern Blotting对绵羊卵巢组织差异表达 ESTs的鉴定

利用地高辛DNA标记与检测技术反向Northern斑点杂交,对小尾寒羊和滩羊卵巢组织差异显示ESTs进行鉴定,避免同位素放射性污染,安全性很高且操作简单,提高了实验的准确性,一种鉴定差异显示ESTs简单而有效的方法。在研究基因表达、比较不同环境条件下动物组织的mRNA差异表达等方面具有广阔的应用前景。     

Double Diffusive Magnetohydrodynamic (MHD) Mixed Convective Slip Flow along a Radiating Moving Vertical Flat Plate with Convective Boundary Condition

In this study combined heat and mass transfer by mixed convective flow along a moving vertical flat plate with hydrodynamic slip and thermal convective boundary condition is investigated. Using similarity variables, the governing nonlinear partial differential equations are converted into a system of coupled nonlinear ordinary differential equations. The transformed equations are then solved using a semi-numerical/analytical method called the differential transform method and results are compared with numerical results. Close agreement is found between the present method and the numerical method. Effects of the controlling parameters, including convective heat transfer, magnetic field, buoyancy ratio, hydrodynamic slip, mixed convective, Prandtl number and Schmidt number are investigated on the dimensionless velocity, temperature and concentration profiles. In addition effects of different parameters on the skin friction factor, , local Nusselt number, , and local Sherwood number are shown and explained through tables.     

Boundary Layer Flow Past a Stretching Surface in a Porous Medium Saturated by a Nanofluid: Brinkman-Forchheimer Model

In this study, the steady forced convection flow and heat transfer due to an impermeable stretching surface in a porous medium saturated with a nanofluid are investigated numerically. The Brinkman-Forchheimer model is used for the momentum equations (porous medium), whereas, Bongiorno’s model is used for the nanofluid. Uniform temperature and nanofluid volume fraction are assumed at the surface. The boundary layer equations are transformed to ordinary differential equations in terms of the governing parameters including Prandtl and Lewis numbers, viscosity ratio, porous medium, Brownian motion and thermophoresis parameters. Numerical results for the velocity, temperature and concentration profiles, as well as for the reduced Nusselt and Sherwood numbers are obtained and presented graphically.     

Isoelectric focusing using non-amphoteric buffers in free solution: I. Determination of stable concentration profiles

For large-scale separations of proteins, the use of simple non-amphoteric buffers in free solution and in multicompartment electrolyzers seems promising for industrial applications. The stabilization of a pH profile with this type of buffer requires the strict observation of two conditions: choice of an adequate buffer; stationary profiles of concentrations. During electrolysis in free solution, the ions of the buffer are displaced across the compartments by migration and by diffusion. To keep a stationary composition, the inflow and outflow of all individual ionic species through each compartment must be identical. At high current, diffusion may be neglected against migration and the ionic flows will be identical if the transport number of each ion is constant at each location within the cell. In these conditions, stationary compositions will be independent of the electric current. This condition of constant transport numbers implies the use of profiles of buffer concentrations different from those published up to now. The new equations for these profiles of concentrations are given in the present paper. The constant migration of the ions must be compensated in the end compartments of the isoelectric focusing cell to provide a stable steady state. Two methods are proposed in the literature: the buffer renewal method and the external recycling method (rheoelectrolysis). Here modified buffer renewal method is proposed. Using stationary mass balances, analytical equations are given to calculate the flows and the composition of the solutions to be recycled or added. Using these equations and the profiles of concentrations to keep constant transport numbers, it is demonstrated that only a renewal of the buffers in the end compartments may lead to stable pH profiles and thus to valid conditions of separation.     

Analysis of the equations of renal network flows

Solution of the nonlinear differential equations for renal network flows are investigated, and conditions are given under which a unique solution to these equations exists.     

The effect of diffusion, electric transport and convection on heterogeneous enzyme catalysis]

The consideration of electric and volume transport additionally to diffusion leads to the dependence of concentration profiles in heterogeneous enzyme catalysis on additional parameters (e. g. electrical field strength, convection velocity) which are valuable for influencing and optimizing these systems. For autocatalysis the local periodic concentration profiles are influenced essentially by these phenomena (change of onset and wavelength). When diffusion is negligible equations are given to determine the kinetic parameters vmax and KM from transport measurements.     

Expressions for the interpretation of circular intensity differential scattering of chiral aggregates

The derivation of compact expressions of the circular intensity differential scattering (CIDS) of chiral molecules is presented in the first Born approximation of the fields. The expressions derived are valid for a suspension of scattering chiral particles free to adopt any orientation in solution. The connection is established between the preferential scattering cross section for right- vs left-circularly polarized light for a given scattering angle and the geometrical parameters of the molecule. As observed experimentally, the equations predict that the circular differential scattering patterns must show as a function of the scattering angle a series of lobes of alternating sign. In between these lobes, zeros in the differential scattering cross section occur. For the case of two dipole moments arranged in chiral fashion, an expression is derived that shows how the relative arrangement of the dipoles and their separation relative to the wavelength of light control the number and the position of the zeros. A compact expression predicting the CIDS of a sample for very small angles of scattering is derived for a system of helices whose dimensions are small compared with the wavelength of light. Finally, the presence of CIDS in a sample is related to the appearance of anomalous signals in the CD spectrum of chiral systems. Expressions and computations of the magnitudes and sign of the anomalies are presented. The expressions obtained confirm the main features of the experimental CIDS patterns of chiral molecules previously published.     

Genomic expression patterns distinguish long-term from short-term glioblastoma survivors: a preliminary feasibility study

We used microarray analysis to investigate associations between genotypic expression profiles and survival phenotypes in patients with primary glioblastoma (GBM). Tumor samples from 7 long-term glioblastoma survivors (>24 months) and 13 short-term survivors (<9 months) were analyzed to detect differential patterns of gene expression between these groups and to identify genotypic subclasses of glioblastomas that correlate with survival phenotypes. Five unsupervised and three supervised clustering algorithms consistently and accurately grouped the tumors into genotypic subgroups corresponding to the two clinical survival phenotypes. Three unique prospective mathematical classification algorithms were subsequently trained to use expression data to stratify unknown glioblastomas between survival groups and performed this task with 100% accuracy in validation studies. A set of 1478 genes with significant differential expression (p<0.01) between long-term and short-term survivors was identified, and additional mathematical filtering was used to isolate a 43-gene "fingerprint" that distinguished survival phenotypes. Differential regulation of a subset of these genes was confirmed using RT-PCR. Gene ontology analysis of the fingerprint demonstrated pathophysiologic functions for the gene products that are consistent with current models of tumor biology, suggesting that differential expression of these genes may contribute etiologically to the observed differences in survival. These results demonstrate that unique expression profiles characterize genotypic subsets of primary GBMs associated with differential survival phenotypes, and these profiles can be used in a prospective fashion to assign unknown tumors to survival groups. Future efforts will focus on building more robust classifiers and identifying additional subclasses of gliomas with phenotypic significance.     

A program to simulate drug elimination interactions: warfarin and BSP - an illustrative example

The kinetics of drug elimination of interactive drug systems is stimulated by a set of differential equations based on mass balances, the mass of organs and blood flow rates. Experimentally determined concentration profiles of the drugs in the plasma and bile are used to evaluate clearance rate parameters. An example is shown in which the clearance of the anticoagulant warfarin is reduced to less than 50% of its normal rate due to the interference by BSP.