Plasma equilibrium in axisymmetric poloidal magnetic field configurations in flux coordinates

A simple derivation is given of equilibrium equations in flux coordinates in the general case of an anisotropic-pressure plasma. The issue of how to formulate the boundary conditions for these equations is discussed for two types of configurations—a straight system and a system with an internal conductor. Examples of numerical solutions to the equilibrium problem for these configurations are presented.     

Plasmastatic models of galathea traps with magnetically transparent boundaries

Mathematical models and results of calculation of plasma equilibrium in a circular cylinder with three helical or straight imbedded current-carrying conductors (i.e., in a straightened analog of a toroidal Galathea trap) are presented. The equilibrium is described in the framework of two-dimensional boundary value problems with plane and helical analogs of the Grad-Shafranov equation for the scalar magnetic flux function. Problems with first-kind boundary conditions corresponding to a magnetically transparent boundary of the cylinder and problems with second-kind boundary conditions and a given value of the electric current flowing in plasma (in addition to those flowing in the conductors) are considered. Deformations of magnetoplasma configurations in the cylinder for different formulations of the above-specified problems are investigated numerically.     

A modeling study of anaerobic biofilm systems: I. Detailed biofilm modeling

A detailed model acetate-utilizing methanogenic biofilms accounting for the diffusion of neutral and ionic species, chemical equilibrium, electroneutrality, gas production within the biofilm, pH-dependent Monod kinetics, and the presence of a concentration boundary layer is presented. The model qualitatively fits the pH profiles that are reported for acetate-utilizing methanogenic aggregates. A sensitivity analysis on the biological parameters showed that the flux of acetate is sensitive to the maximum utilization rate, half-saturation constant, and biofilm density for the bulk conditions investigated. Criteria when traditional biofilm models can be used to predict the flux of acetate into the biofilm are established. If the maximum pH change predicted using a hypothetical system is within +/-0.05, the traditional model predicts the flux to within +/-5% of the value calculated with the model developed in this study. (c) 1995 John Wiley & Sons, Inc.     

Sedimentation of generalized systems of interacting particles. I. Solution of systems of complete Lamm equations.

A very general approach to the chemical equilibria between many interacting molecules during sedimentation (boundary, band, or active enzyme) taking into account boundary conditions, cell geometry, equilibrium constants, diffusion, enzyme kinetics, etc., is presented. Through a Fortran program, the method has been applied to two very simple but typical cases. With only minor adjustments, the method presented here for sedimentation studies can be extended to all sorts of problems in which “pools” of various species are interacting with each other.     

Hamiltonian formalism in the equilibrium problem for a plasma with islands

Hamiltonian formalism is applied to the equilibrium problem for a plasma with islands by using an analogy between the equilibrium problem for a plasma with one island and the nonlinear mechanics of a physical pendulum. A relationship is established between magnetic flux coordinates with straightened magnetic field lines and the action-angle variables. The flux and current representations of a magnetic field with islands are obtained, and the solution to the equilibrium problem for a narrow island is presented.     

Properties of solution of the diffusion-reaction equation. II

Two theorems relating to properties of the solutions of the equations of continuity for the concentrations of the chemical species in a diffusion-reaction system are proved. The theorems concern boundary conditions under which the flux of a specified species can be guaranteed to be directed into the reaction region and the circumstances under which any two of the conditions (i) stationarity, (ii) flux equilibrium, and (iii) chemical equilibrium, imply the third. Application of these theorems to apparent active transport and to the properties of the differential equations for specific activities in a distributed tracer system are noted.     

Two-dimensional Fourier representation used in the bioelectric forward problem.

The objective of this paper is the application of two-dimensional discrete Fourier transformation for solving the integral equation of the bioelectric forward problem. Therefore, the potential, the source term, and the integral equation kernel are assumed to be sampled at evenly spaced intervals. Thus the continuous functions of the problem domain can be expressed by their two-dimensional discrete Fourier transform in the spatial frequency domain. The method is applied to compute the surface potential generated by an eccentric dipole in a homogeneous spherical conducting medium. The integral equation for the potential is solved in the spatial frequency domain and the value of the potential at the sampling points is obtained from inverse Fourier transformation. The solution of the presented method is compared to both, an analytic solution and a solution gained from applying the boundary element method. Isoparametric quadrilateral boundary elements are used for modeling the spherical volume conductor in the boundary element solution, while in the two-dimensional Fourier transformation method the volume conductor is represented by a parametric boundary surface approximation.     

Pseudosymmetry near a magnetic surface in a plasma confinement system

The possibility is demonstrated of finding vacuum equilibrium magnetic configurations with an exactly pseudosymmetric nonparaxial boundary magnetic surface in the vicinity of which the pseudosymmetry condition is satisfied approximately. Equations are derived for calculating the boundary surface from a prescribed particular dependence of the magnetic field strength in special magnetic flux coordinates. In calculations, magnetic coordinates serve as ordinary angular coordinates, while their “magnetic” character is specified by additional integral conditions. As an example, a “tubular” orthogonal magnetic surface is calculated analytically.     

Dinoflagellate cysts from sediment traps deployed in the Bellingshausen,Weddell and Scotia seas,Antarctica

Dinoflagellate cysts have been recovered from six long-term (1–2 yr) sediment trap moorings deployed in the Bellingshausen, Weddell and Scotia seas, Antarctica. These traps, mostly moored near the sea bed to sample the nepheloid layer, were located both within and to the north of the maximum sea-ice limit. The numbers of cysts, together with the composition of the assemblages, reinforce the importance of the maximum sea-ice limit as a modern biogeographic boundary for the distribution of dinoflagellate cysts. Cysts derived from heterotrophic dinoflagellates make up the highest proportions within the assemblages recovered from the traps. One trap sampled the export production, revealing little difference in cyst flux over those sampling the nepheloid layer. Cyst flux appears to be highest in areas closest to the Antarctic Convergence, north of the maximum sea-ice limit, and to high nutrient availability. There are, however, differences between the sediment trap assemblages and those recovered from core-top samples at the same or nearby sites. These differences, in the greater number of cysts, and in the higher numbers of round, brown Protoperidinium cysts in the traps, may reflect annual differences in the primary productivity and/or cyst production in the area. In some areas the sediment record may preserve little information about local surface water productivity because of the activity of bottom water currents, for example those arising from the Antarctic Circumpolar Current.     

Asymptotic behaviour of solutions of the diffusive Lotka-Volterra equations

A spatially discrete version of the diffusive Lotka-Volterra equations is considered. Asymptotical spatial homogeneity of solutions of the equations with equilibrium, periodic or zero flux boundary conditions is proved without regard to crowding effects. The proof does not require the assumption of equal diffusion coefficients and the restrictions on the dimension of space and on the initial data, which are necessary in the spatially continuous model.     

Effects of dispersion on stability of multispecies prey-predator systems

The general multispecies prey-predator system with Gompertz's antisymmetric interactions is nonlinearly stable in the absence of dispersion and continues to remain stable with dispersion under both homogeneous reservoir and zero flux boundary conditions in a region containing the equilibrium state. It is proved that a general multispecies food-web model without antisymmetric interactions is stable in the absence of dispersion and remains stable with dispersion in the above-mentioned region.     

The origin of the human auditory brain-stem response wave II

Auditory brain-stem responses (ABRs) were recorded from human subjects undergoing neurosurgical procedures which exposed the auditory nerve. Scalp recordings indicated that the latency of the negativity between waves (I_n) and II (I_n) and the latency of positive peak II (II_p) were shorter when the nerve was suspended in air than when the nerve was submerged in cerebrospinal fluid or saline, while earlier and later waves remained unaffected. These results could not be attributed to changes in stimulus or recording parameters or conduction velocity. Computational and somatosensory experimental evidence of stationary potentials generated by physical properties of the volume conductor, including changes in conductivity or geometry, are presented to develop a model of wave II_p generation. The results of this study suggest that wave II_p (and probably I_n) are manifestations of current flux asymmetries across conductivity boundaries created by the temporal bone-cerebrospinal fluid intradural space-brain-stem interfaces. The current flux asymmetries are generated as the propagating auditory nerve action potential crosses the conductivity boundaries. These results also indicate that the physical characteristics of the volume conductor and neural pathways must be considered when interpreting surface recorded evoked potentials.     

Equilibrium electropotentials in electrolyte systems

The determinationof electric potentials in finite regions of symmetrical electrolyte in one-dimensional equilibrium situations requires the solution of the one-dimensional Poisson-Boltzmann equation in which the dependent variable is linearly related to the electric potential and contains unknown parameters. These require evaluation as part of the solution to a given boundary value problem. The general solution of the equation is presented. This involves elliptic functions and integrals and is sectionally isomorphic with respect to an integration parameter. The application to problems posed in terms of both initial values and two-point boundary values is discussed. The solution is used to determine the potential and concentration distributions between two flat-faced charged particles immersed in an electrolyte liquid and having interacting double layers.     

Topological analysis of metabolic networks based on Petri net theory

Petri net concepts provide additional tools for the modelling of metabolic networks. Here, the similarities between the counterparts in traditional biochemical modelling and Petri net theory are discussed. For example the stoichiometry matrix of a metabolic network corresponds to the incidence matrix of the Petri net. The flux modes and conservation relations have the T-invariants, respectively, P-invariants as counterparts. We reveal the biological meaning of some notions specific to the Petri net framework (traps, siphons, deadlocks, liveness). We focus on the topological analysis rather than on the analysis of the dynamic behaviour. The treatment of external metabolites is discussed. Some simple theoretical examples are presented for illustration. Also the Petri nets corresponding to some biochemical networks are built to support our results. For example, the role of triose phosphate isomerase (TPI) in Trypanosoma brucei metabolism is evaluated by detecting siphons and traps. All Petri net properties treated in this contribution are exemplified on a system extracted from nucleotide metabolism.     

Theoretical analysis of mixed Plasmodium malariae and Plasmodium falciparum infections with partial cross-immunity

A deterministic model for assessing the dynamics of mixed species malaria infections in a human population is presented to investigate the effects of dual infection with Plasmodium malariae and Plasmodium falciparum. Qualitative analysis of the model including positivity and boundedness is performed. In addition to the disease free equilibrium, we show that there exists a boundary equilibrium corresponding to each species. The isolation reproductive number of each species is computed as well as the reproductive number of the full model. Conditions for global stability of the disease free equilibrium as well as local stability of the boundary equilibria are derived. The model has an interior equilibrium which exists if at least one of the isolation reproductive numbers is greater than unity. Among the interesting dynamical behaviours of the model, the phenomenon of backward bifurcation where a stable boundary equilibrium coexists with a stable interior equilibrium, for a certain range of the associated invasion reproductive number less than unity is observed. Results from analysis of the model show that, when cross-immunity between the two species is weak, there is a high probability of coexistence of the two species and when cross-immunity is strong, competitive exclusion is high. Further, an increase in the reproductive number of species i increases the stability of its boundary equilibrium and its ability to invade an equilibrium of species j. Numerical simulations support our analytical conclusions and illustrate possible behaviour scenarios of the model.     

A reliable simulator for dynamic flux balance analysis

Dynamic flux balance analysis (DFBA) provides a platform for detailed design, control and optimization of biochemical process technologies. It is a promising modeling framework that combines genome‐scale metabolic network analysis with dynamic simulation of the extracellular environment. Dynamic flux balance analysis assumes that the intracellular species concentrations are in equilibrium with the extracellular environment. The resulting underdetermined stoichiometric model is solved under the assumption of a biochemical objective such as growth rate maximization. The model of the metabolism is coupled with the dynamic mass balance equations of the extracellular environment via expressions for the rates of substrate uptake and product excretion, which imposes additional constraints on the linear program (LP) defined by growth rate maximization of the metabolism. The linear program is embedded into the dynamic model of the bioreactor, and together with the additional constraints this provides an accurate model of the substrate consumption, product secretion, and biomass production during operation. A DFBA model consists of a system of ordinary differential equations for which the evaluation of the right‐hand side requires not only function evaluations, but also the solution of one or more linear programs. The numerical tool presented here accurately and efficiently simulates large‐scale dynamic flux balance models. The main advantages that this approach has over existing implementation are that the integration scheme has a variable step size, that the linear program only has to be solved when qualitative changes in the optimal flux distribution of the metabolic network occur, and that it can reliably simulate behavior near the boundary of the domain where the model is defined. This is illustrated through large‐scale examples taken from the literature. Biotechnol. Bioeng. 2013; 110: 792–802. © 2012 Wiley Periodicals, Inc.     

Effect of vesicle traps on traffic jam formation in fast axonal transport

The purpose of this paper is to develop a model for simulation of the formation of organelle traps in fast axonal transport. Such traps may form in the regions of microtubule polar mismatching. Depending on the orientation of microtubules pointing toward the trap region, these traps can accumulate either plus-end or minus-end oriented vesicles. The model predicts that the maximum concentrations of organelles occur at the boundaries of the trap regions; the overall concentration of organelles in the axon with traps is greatly increased compared to that in a healthy axon, which is expected to contribute to mechanical damages of the axon. The organelle traps induce hindrance to organelle transport down the axon; the total organelle flux down the axon with traps is found to be significantly reduced compared to that in a healthy axon.     

Gravitational Effects in a Passive Transmembrane Transport: The Flux Graviosmotic and Gravidiffusive Effects in Non-Electrolytes

In this paper the classification ofthe gravitational effects in a passive transmembranetransport is presented. Among these effects there arethe flux and force gravitational effects (fluxgraviosmotic effect, osmotic pressure graviosmoticeffect, flux gravidiffusive effect, osmotic pressuregravidiffusive effect, voltage gravielectric effectand current gravielectric effect). The volume fluxgraviosmotic and solute flux gravidiffusive effectsmodel equations for a single-membrane system areelaborated. These models for binary and ternarynon-electrolyte solutions have been verified using anexperimental data volume and solute fluxes forosmotic-diffusion cell with horizontally mountedmembrane. In the experimental set-up, water was placedon one side of the membrane. The opposite side of themembrane was exposed to binary or ternary solutions ofdensities greater than that of water (aqueous glucoseor glucose-0.2 mole/l aqueous ethanol) and binary andternary solutions of densities larger than that ofwater (aqueous ethanol or ethanol-0.05 mole/l aqueousglucose). These experimental results are interpretedin terms of the convective instability that increasesthe diffusive permeability coefficient of junction:boundary layer/membrane/boundary layer.