Analysis of the transient behavior of kidney models

Non-steady-state equations for kidney models are stated. General conservation relations for these equations are derived. Transient equations for the central core model of the renal medulla are developed. Solution of the equations by Laplace transform methods for time invariant volume flows is discussed. The general theory of solving models with time dependent flows by finite difference methods is developed.     

Digestion of fatty acids in ruminants: a meta-analysis of flows and variation factors: 2. C18 fatty acids

In ruminants, dietary lipids are extensively hydrogenated by rumen micro-organisms, and the extent of this biohydrogenation is a major determinant of long-chain fatty acid profiles of animal products (milk, meat). This paper reports on the duodenal flows of C18 fatty acids and their absorption in the small intestine, using a meta-analysis of a database of 77 experiments (294 treatments). We established equations for the prediction of duodenal flows of various 18-carbon (C18) fatty acids as a function of the intakes of their precursors and other dietary factors (source and/or technological treatment of dietary lipids). We also quantified the influence of several factors modifying rumen metabolism (pH, forage : concentrate ratio, level of intake, fish oil supplementation). We established equations for the apparent absorption of these fatty acids in the small intestine as a function of their duodenal flows. For all C18 unsaturated fatty acids, apparent absorption was a linear function of duodenal flow. For 18:0, apparent absorption levelled off for high duodenal flows. From this database, with fatty acid flows expressed in g/kg dry matter intake, we could not find any significant differences between animal categories (lactating cows, other cattle or sheep) in terms of rumen metabolism or intestinal absorption of C18 fatty acids.     

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.     

On the discrimination between band-limited coherent and random apparent stresses in transitional pulsatile flow

A frequency domain approach that incorporates a matched filter was examined for discriminating between ordered velocity fluctuations with band-limited frequency content and random velocity variations in pulsatile disturbed flows. Fluctuations at pseudo-discrete frequencies may yield a significant contribution to the apparent stress tensor computed from the unsteady Navier Stokes equations, and an estimate of the stresses arising from these ordered structures can be obtained once the velocity variations have been decomposed. This type of decomposition permits the estimation of the apparent stresses in turbulent flows, consisting of coherent and random parts, in blood flow applications such as diseased constricted arteries or downstream of artificial heart valves.     

Pulp Nonfiction: Regionalized Dynamic Model of the U.S. Pulp and Paper Industry

This article presents a modeling framework that enhances our ability to analyze the implications of policy for future sustainability of industrial systems. The framework quantifies the relationship between physical input and waste flows, capital vintage, and investment behavior in the U.S. pulp and paper industry. A regional vintage model is developed that simultaneously incorporates investment decisions, vintage structure of the capital stock, and physical material and energy flows, in addition to paper demand. Each capital vintage is specified by size, output structure, and age-specific retirement rates, as well as fiber use and energy intensities. Both embodied and disembodied technological change are incorporated, as well as greenhouse gas emissions from fuel use, and decomposition and incineration of waste. Estimated equations are used to simulate industrial futures until 2020, from a system of nonlinear differential equations.
Our results demonstrate the economic and physical inter-dependence between material and energy flows and the central role energy prices have in decision-making. For instance, an increase in average energy prices, ceteris paribus , will on average discourage paper recycling, which has implications for greenhouse gas emissions as well as for changes in energy intensity. The analysis of the data reveals diminishing rates of energy self-generation, and the immense longevity of capital, which hampers rapid change in input and carbon intensity. This stresses the importance of investment-led strategies in facilitating faster capital turnover to enhance future sustainability of the system.     

Bacteriorhodopsin in liposomes. II. Experimental evidence in support of a theoretical model

In the preceding article equations describing relevant ion flows in illuminated suspensions of bacteriorhodopsin liposomes have been derived. Here these equations are subjected to experimental tests. Changes in permeability characteristics of the liposomal membrane are brought about by addition of specific ionophores and change of medium composition. Using light-driven proton uptake and electrochemical potential differences for protons across the membrane as observation parameters, ridig attempts to falsify the derived equations are unsuccessful.Agreement between equations and experimental results is established on the point of: (i) the antagonistic effect of valinomycin and nigericin on the two components of the proton-motive force, (ii) the time dependence of the changes in transmembrane electrical and chemical potential differences after the onset of illumination.In three independent experimental systems evidence was obtained for the correctness of the postulated dependence of the turnover rate of the photochemical cycle on back pressure by the transmembrane electrochemical potential difference for protons.     

Geometric and potential driving formation and evolution of biomolecular surfaces

This paper presents new geometrical flow equations for the theoretical modeling of biomolecular surfaces in the context of multiscale implicit solvent models. To account for the local variations near the biomolecular surfaces due to interactions between solvent molecules, and between solvent and solute molecules, we propose potential driven geometric flows, which balance the intrinsic geometric forces that would occur for a surface separating two homogeneous materials with the potential forces induced by the atomic interactions. Stochastic geometric flows are introduced to account for the random fluctuation and dissipation in density and pressure near the solvent–solute interface. Physical properties, such as free energy minimization (area decreasing) and incompressibility (volume preserving), are realized by some of our geometric flow equations. The proposed approach for geometric and potential forces driving the formation and evolution of biological surfaces is illustrated by extensive numerical experiments and compared with established minimal molecular surfaces and molecular surfaces. Local modification of biomolecular surfaces is demonstrated with potential driven geometric flows. High order geometric flows are also considered and tested in the present work for surface generation. Biomolecular surfaces generated by these approaches are typically free of geometric singularities. As the speed of surface generation is crucial to implicit solvent model based molecular dynamics, four numerical algorithms, a semi-implicit scheme, a Crank–Nicolson scheme, and two alternating direction implicit (ADI) schemes, are constructed and tested. Being either stable or conditionally stable but admitting a large critical time step size, these schemes overcome the stability constraint of the earlier forward Euler scheme. Aided with the Thomas algorithm, one of the ADI schemes is found to be very efficient as it balances the speed and accuracy.      

Effect of the magnetic field curvature on the generation of zonal flows by drift-Alfvén waves

The generation of zonal flows by drift-Alfvén waves is studied with allowance for magnetic curvature effects. The basic plasmadynamic equations relating the electrostatic potential, vector potential, and perturbed plasma density are the vorticity equation, longitudinal Ohm’s law, and continuity equation. The basic equations are analyzed by applying a parametric formalism similar to that used in the theory of the generation of convective cells. In contrast to most previous investigations on the subject, consideration is given to primary modes having an arbitrary spectrum rather than to an individual monochromatic wave packet. The parametric approach so modified makes it possible to reveal a new class of instabilities of zonal flows that are analogous to two-stream instabilities in linear theory. It is shown that, in the standard theory of zonal flows, the zonal components of the vector potential and perturbed density are not excited. It is pointed out that zonal flows can be generated both in the case of a magnetic hill and in the case of a magnetic well. In the first case, the instabilities of zonal flows are analogous to negative-mass instabilities in linear theory, and, in the second case, they are analogous to two-stream instabilities.     

Bacteriorhodopsin in liposomes. II. Experimental evidence in support of a theoretical model.

In the preceding article equations describing relevant ion flows in illuminated suspensions of bacteriorhodopsin liposomes have been derived. Here these equations are subjected to experimental tests. Changes in permeability characteristics of the liposomal membrane are brought about by addition of specific ionophores and change of medium composition. Using light-driven proton uptake and electrochemical potential differences for protons across the membrane as observation parameters, ridig attempts to falsify the derived equations are unsuccessful. Agreement between equations and experimental results is established on the point of: (i) the antagonistic effect of valinomycin and nigericin on the two components of the proton-motive force, (ii) the time dependence of the changes in transmembrane electrical and chemical potential differences after the onset of illumination. In three independent experimental systems evidence was obtained for the correctness of the postulated dependence of the turnover rate of the photochemical cycle on back pressure by the transmembrane electrochemical potential difference for protons.     

A variational calculus approach to the suspension flow problem using the minimal force hypothesis

Analytic expressions for the velocity profile and distribution of neutrally buoyant particles in laminar flow were obtained as functions of the radial distance. A modified Einstein viscosity model and the hypothesis that the total force on all the particles flowing in the tube is a minimum were used. The methods of the variational calculus were used in the mathematical development. A velocity profile differing only slightly from the parabolic form of that for Hagan-Poiseuille flow was obtained. For particle distribution the equations developed predict a maximum concentration along the center-line for some flows and a maximum concentration in a ring some distance from the center line in other flows. Both of these concentration profiles have been observed experimentally. Quantitative predictions from the equations derived must await further experimental work to permit calculation of the parameters included in the equations.     

Nonequilibrium linear behavior of biological systems. Existence of enzyme-mediated multidimensional inflection points.

The linear phenomenological equations of nonequilibrium thermodynamics are limited theoretically to near equilibrium although a number of biological systems have been shown to exhibit a "linear" relationship between steady-state flows and conjugate thermodynamic forces outside the range of equilibrium. We have found a multidimensional inflection point which can exist well outside the range of equilibrium around with enzyme-catalyzed reactions exhibit "linear" behavior between the logarithm of reactant concentrations and enzyme catalyzed flows. A set of sufficient conditions has been derived which can be applied to any enzyme mechanism to determine whether a multidimensional inflection point exists. The conditions do not appear overly restrictive and may be satisfied by a large variety of coupled enzyme reactions. It is thus possible that the linearity observed in some biological systems may be explained in terms of enzyme operating near this multidimensional point.     

Numerical simulation of local blood flow in the carotid and cerebral arteries under altered gravity

A computational fluid dynamics (CFD) approach was presented to model the blood flows in the carotid bifurcation and the brain arteries under altered gravity. Physical models required for CFD simulation were introduced including a model for arterial wall motion due to fluid-wall interactions, a shear thinning fluid model of blood, a vascular bed model for outflow boundary conditions, and a model for autoregulation mechanism. The three-dimensional unsteady incompressible Navier-Stokes equations coupled with these models were solved iteratively using the pseudocompressibility method and dual time stepping. Gravity source terms were added to the Navier-Stokes equations to take the effect of gravity into account. For the treatment of complex geometry, a chimera overset grid technique was adopted to obtain connectivity between arterial branches. For code validation, computed results were compared with experimental data for both steady-state and time-dependent flows. This computational approach was then applied to blood flows through a realistic carotid bifurcation and two Circle of Willis models, one using an idealized geometry and the other using an anatomical data set. A three-dimensional Circle of Willis configuration was reconstructed from subject-specific magnetic resonance images using an image segmentation method. Through the numerical simulation of blood flow in two model problems, namely, the carotid bifurcation and the brain arteries, it was observed that the altered gravity has considerable effects on arterial contraction/dilatation and consequent changes in flow conditions.     

Finite element simulation of pulsatile flow through arterial stenosis.

The problem of blood flow through a stenosis is solved using the incompressible Navier-Stokes equations in a rigid circular tube presenting a partial occlusion. Calculations are based on a Galerkin finite element method. The time marching scheme employs a predictor-corrector technique using a variable time step. Results are obtained for steady and physiological pulsatile flows. Computational experiments analyse the effect of varying the degree of stenosis, the stricture length, the Reynolds number and Womersley number. The method gives results which agree well with previous computations for steady flows and experimental findings for steady and pulsatile flows.     

A Continuum Mechanical Approach to the Flow Equations for Membrane Transport: I. Water Flow

A concept is presented for modeling flows through membranes using continuum mechanics. Viscous interactions (due to velocity gradients) are explicitly incorporated and position-dependent local water-membrane interactions are taken into account before obtaining slab averages. This is in distinction to other treatments where strictly one-dimensional force balance equations are written using slab average friction coefficients which are really composite functions of local interactions. It is shown that the viscous and other frictional interactions do not simply form linear combinations in the solutions to the equations of motion. Flow profiles for pressure-driven flows ranging from Poiseuille's flow to “diffusion” flow are obtained depending on the strength and extent of the water-membrane interaction. The model is also applied to self-diffusion flows and the measurement of “equivalent pore size.” It is shown that for a fixed pore size the ratio of filtration flow to self-diffusion flow for equal driving forces is able to vary over a wide range depending on the water-membrane interaction.     

Reduced MHD equations with allowance for slow magnetosonic waves

The so-called reduced magnetohydrodynamics, which deals with the motion of incompressible fluids and is usually applied to describe plasma flows in a strong toroidal magnetic field, has a number of drawbacks and, in some cases, fails to produce correct results. The equations proposed here are simpler than the original MHD equations and are free of these drawbacks. These equations, like reduced MHD equations, make it possible to remove from consideration fast magnetosonic waves and to introduce the vector potential for the poloidal magnetic field. However, our equations differ from the reduced MHD equations in that they completely incorporate slow magnetosonic waves, the specific features of the toroidal geometry, and the effects of the toroidal velocity.     

Comment on 'The nature of the fluid boundary layer and the selection of parameters for benthic ecology' (Carling, 1992)

• 1 Near-bed flow equations and definitions have been reviewed by Carling (1992). The main errors and ambiguities in this contribution are identified.
• 2 The hypotheses required to derive the governing equations are usually violated in complex flows of natural streams.

     

Dissipative Irreversibility from Nosé's Reversible Mechanics

Abstract

Nose's Hamiltonian mechanics makes possible the efficient simulation of irreversible flows of mass, momentum and energy. Such flows illustrate the paradox that reversible microscopic equations of motion underlie the irreversible behavior described by the second law of thermodynamics. This generic behavior of molecular many-body systems is illustrated here for the simplest possible system, with only one degree of freedom: a one-body Frenkel-Kontorova model for isothermal electronic conduction. This model system, described by Nosé-Hoover Hamiltonian dynamics, exhibits several interesting features: (1) deterministic and reversible equations of motion; (2) Lyapunov instability, with phase-space offsets increasing exponentially with time; (3) limit cycles; (4) dissipative conversion of work (potential energy) into heat (kinetic energy): and (5) phase-space contraction, a characteristic feature of steady irreversible flows. The model is particularly instructive in illustrating and explaining a paradox associated with steady-state statistical mechanics: the Gibbs entropy of a nonequilibrium steady state decreases continuously to minus infinity.     

Time-accurate,parallel, multi-zone,multi-block solver to study the human cardio-vascular system

A parallel, time-accurate flow solver is devised to study the human cardio-vascular system. The solver is capable of dealing with moving boundaries and moving grids. It is designed to handle complex, three-dimensional vascular systems. The computational domain is divided into multiple block subdomains. At each cross section the plane is divided into twelve sub-zones to allow flexibility for handling complex geometries and, if needed, appropriate parallel data partitioning. The unsteady, three-dimensional, incompressible Navier-Stokes equations are solved numerically. A second-order in time and third-order upwind finite volume method for solving time-accurate incompressible flows based on pseudo-compressibility and dual time-stepping technique is used. For parallel execution, the flow domain is partitioned. Communication between the subdomains of the flow on Riken's VPP/700E supercomputer is implemented using MPI message-passing library. A series of numerical simulations of biologically relevant flows is used to validate this code.     

A numerical simulation of the flow in a T-type bifurcation and its application to an "end to side" fistula

Some recent surgical procedures such as arteriovenous fistula, or coronary and cerebral by-passes were observed to yield counterdirectional branching blood flows. There is a lack of knowledge about the role of the counterdirectional flow ratio, the angle of anastomosis and the shear stresses in the process of thrombogenesis that leads to shunt occlusion. The program developed to simulate these hemodynamic conditions uses an efficient numerical scheme for the solution of the 2-D Navier-Stokes equations and can be easily adapted to flows in other geometrical configurations.     

Oscillatory flow in a cone-and-plate bioreactor

Motivated by biometric applications, we analyze oscillatory flow in a cone-and-plate geometry. The cone is rotated in a simple harmonic way on a stationary plate. Based on assuming that the angle between the cone and plate is small, we describe the flow analytically by a perturbation method in terms of two small parameters, the Womersley number and the Reynolds number, which account for the influences of the local acceleration and centripetal force, respectively. Working equations for the shear stresses induced both by laminar primary and secondary flows on the plate surface are presented.