Theory of cell age distribution in suspension culture with feed and/or drain

A mixed problem for the M'Kendrick-von Foerster equation satisfied by the number density function in terms of the age of the viable cells in a suspension culture with feed and/or drain is solved, and a method of calculating the number density function and time-dependent generation time from observed data of cell number and cell mass is presented. This theory is adequate to analyze the growth of cells that undergo binary fission. The equation of mass balance follows as a natural consequence of this treatment. The equation of substrate balance in consideration of the effect of cell volume is derived rigorously.     

The effect of biota on global climate

A model consisting of two blocks (equations) was proposed for the analytical study of the biosphere-climate system over great periods of time. The first equation describes the balance of carbon dioxide in the atmosphere and represents the biological block of the model. The second equation is the equation of the energy balance or the physical block of the system. The model is based on the most general conceptions of living matter and the evolution process. A possible interpretation of some events and phenomena in the earth history in terms of the model is given.     

自然植被净第一性生产力模型初探

本文根据植物的生理生态学特点及联系能量平衡方程和水量平衡方程的区域蒸散模式建立了联系植物生理生态学特点和水热平衡关系的植物的净第一性生产力模型：该模型的建立为宏观地确定地带性景观的生产潜力、植物净第一性生产力的区域分布和全球分布,以及全球变化的影响提供了理论基础,对于合理地利用气候资源,扬长避短,充分发挥气候生产潜力,最大限度地提高植物的产量具有重要的意义。     

Estimation of Infiltration Parameters and the Irrigation Coefficients with the Surface Irrigation Advance Distance

A theory based on Manning roughness equation, Philip equation and water balance equation was developed which only employed the advance distance in the calculation of the infiltration parameters and irrigation coefficients in both the border irrigation and the surge irrigation. The improved procedure was validated with both the border irrigation and surge irrigation experiments. The main results are shown as follows. Infiltration parameters of the Philip equation could be calculated accurately only using water advance distance in the irrigation process comparing to the experimental data. With the calculated parameters and the water balance equation, the irrigation coefficients were also estimated. The water advance velocity should be measured at about 0.5 m to 1.0 m far from the water advance in the experimental corn fields.     

全球气候变化的中国自然植被的净第一性生产力研究

本文根据已建立的植物生理生态学特点与水热平衡关系的植物净第一性生产力模型对中国自然植被的净第一性生产力现状及全球变化后的自然植被的净第一性生产力进行了分析,给出了中国陆地生态系统自然植被的净第一性生产力在全球气候变化条件下的变化图景,为合理开发、利用自然资源,以及监测和预测中国陆地生态系统自然植被净第一性生产力的变化及应采取的策略提供了科学依据。     

Relation between pH and the strong ion difference (SID) in body fluids

Acid-base balance evaluation according to the Henderson-Hasselbalch equation enable us to assess the contribution of respiratory (pCO2) and/or non-respiratory (metabolic, HCO3(-)) components to the acid-base balance status. A new approach to acid-base balance evaluation according to Stewart-Fencl, which is based on a detailed physical-chemical analysis of body fluids shows that metabolic acid-base balance disorders are characterized not only by [HCO3(-)]. According to this concept independent variables must be taken into an account. The abnormality of concentration of one or more of the independent variable(s) determines the pH of a solution. The independent variables are: 1. strong ion difference (SID); 2. total concentration of nonvolatile weak acids [A(tot)]; 3. in agreement with the Henderson-Hasselbalch concept also pCO2. Traditional evaluation of acid-base balance disorders is based on the pH of body fluids (though pH may be within normal range if several acid-base balance disturbances are present). In order to maintain this view and simultaneously to respect the Stewart-Fencl principle, we invented a new equation, which uses only the independent variables to define the pH of body fluids. This analysis shows that for a given value of pCO2, the pH of body fluids is determined by a difference between SID and [A(tot)-]. pH = 6.1 + log((SID - [A(tot)-])/(0.03pCO2)) or in itemized form: pH = 6.1 + log((([Na+] + [K+] + [Ca2+] + [Mg2+] - [Cl-] - [UA-]) - (k1[Alb] + k2[P(i)]))/(0.03 x pCO2)). Evaluation of the individual components of this equation enables us to detect, which of the independent variable (or a combination of independent variables) deviates from the normal range and therefore which one or ones is a cause of the acid-base balance disorder. At the end of this paper we give examples of a practical application of this equation.     

Equation of state and life span of poikilothermic animals

An equation of state of a living organism that corresponds to the Kleiber's empirical dependence has been found using the conditions of entropy and energy balance. Life span of animals has been calculated using the equation obtained and it was found to depend inversely on metabolism intensity.     

How NOT to Approach the Obesity Problem

FLATT, JP. How NOT to approach the obesity problem. The emphasis given to the energy balance equation has fostered the widespread belief that obesity is a problem of energy balance. This mistaken view has led to many unjustified and unfortunate interpretations, because obesity is, rather, a problem of the interaction between body composition and food intake regulation.     

Improvement of a β-glucanase activity test by taking into account the batch reactor balance of the test system

Activity tests of enzymes are often applied for determining their concentration. In the easiest case, just one product concentration is measured after a given time. This often leads to nonlinear dependences of the apparent activity with enzyme protein concentration. A general solution of this problem consists in using the balance equation of the assay system, which commonly represents a batch reactor. Here, the balance equation of the batch for a general Michaelis Menten-type reaction kinetics is used as the calibration function. The correlation of the apparent activity and enzyme concentration was established by capturing the enzyme by means of metal chelate interaction owing to a hexahistidine tag attached to the β-glucanase.     

A novel approach to the van der pol oscillator: Natural frequency and entrainment

Abstract

The physics of the van der Pol oscillator as realized by the Meissner circuit is discussed by analogy to the beat phenomenon and by a consequent analysis of current balance. The current balance method leads to a new, very accurate equation for the dependence of the oscillator frequency on the feedback parameter. Several aspects of entrainment (existence, limited frequency range, dependence on parameters, phase shift) can be explained, too. Numerical results are presented which have been obtained by solving the homogeneous and inhomogeneous van der Pol equation with a Runge‐Kutta method.     

黄土地区防护林生态系统水量平衡研究

根据黄土地区的防护林生态系统水分循环的特征,提出了防护林生态系统水量平衡方程,通过对１９８８￣１９９２年刺槐、油松、沙棘、虎榛子林地、草地和裸地６种生态系统水量平衡的分析,结果表明降雨是防护林生态系统主要的水分输入量,刺槐和油松林根际层以下土壤水分的上升补给,也是重要的水分输入项,特别是春季的４￣６月份,更是防护林生态系统极为重要的水分来源,刺槐林和油松林平均根际区下层土壤水分上升补给量占降雨量的     

Analytical Model of a Surface Barrier Discharge Development

Plasma Physics Reports - The propagation of the front of a single surface dielectric barrier microdischarge is studied using an analytical model based on the charge balance equation. The model...     

拟自然水景的水均衡分析及水量设计研究

低影响设计和开发（LID）雨水资源,有助于水资源的保护和水景减量设计,形成具有自我调节能力的水景海绵体。将水均衡法运用于水景参数化设计中,构建拟自然水景水量平衡方程式,探寻汇水区雨水汇水量最佳值,进而为水景水量设计提供参考。由水均衡法核心思想质量守恒原理,即区域总输入水量等于总输出水量,提出拟自然水景水均衡分析方法,并以习水箐山森林公园主入口景观区为例,探讨水均衡分析在水景参数化设计中的应用。     

A Model of Respiratory Heat Transfer in a Small Mammal

A steady-state model of the heat and water transfer occurring in the upper respiratory tract of the kangaroo rat, Dipodomys spectabilis, is developed and tested. The model is described by a steady-state energy balance equation in which the rate of energy transfer from a liquid stream (representing the flow of heat and blood from the body core to the nasal region) is equated with the rate of energy transfer by thermal conduction from the nose tip to the environment. All of the variables in the equation except the flow rate of the liquid stream can be either measured directly or estimated from physiological measurements, permitting the solution of the equation for the liquid stream flow rate. After solving for the liquid stream flow rate by using data from three animals, the energy balance equation is used to compute values of energy transfer, expired air temperature, rates of water loss, and efficiency of vapor recovery for a variety of ambient conditions. These computed values are compared with values measured or estimated from physiological measurements on the same three animals, and the equation is thus shown to be internally consistent. To evaluate the model's predictive value, calculated expired air temperatures are compared with measured expired air temperatures of eight additional animals. Finally, the model is used to examine the general dependence of expired air temperature, of rates of water loss, and of efficiency of vapor recovery on ambient conditions.     

Metabolic network simulation using logical loop algorithm and Jacobian matrix

A novel method to accomplish efficient numerical simulation of metabolic networks for flux analysis was developed. The only inputs required are the set of stoichiometric balances and the atom mapping matrices of all components of the reaction network. The latter are used to automatically calculate isotopomer mapping matrices. Using the symbolic toolbox of MATLAB the analytical solution of the stoichiometric balance equation system, isotopomer balances and the analytical Jacobian matrix of the total set of stoichiometric and isotopomer balances are created automatically. The number of variables in the isotopomer distribution equation system is significantly reduced applying modified isotopomer mapping matrices. These allow lumping of several consecutive isotopomer reactions into a single one. The solution of the complete system of equations is improved by implementing an iterative logical loop algorithm and using the analytical Jacobian matrix. This new method provided quick and robust convergence to the root of such equation systems in all cases tested. The method was applied to a network of lysine producing Corynebacterium glutamicum. The resulting equation system with the dimension of 546 x 546 was directly derived from 12 isotopomer balance equations. The results obtained yielded identical labeling patterns for metabolites as compared to the relaxation method.     

High-voltage stage of a vacuum arc

An elementary theory of the cathode region at the high-voltage stage of an arc discharge is proposed. The theory is based on the balance equations for the particles in an active plasma layer, the power balance at the cathode, and the equation for the Richardson-Dushman electron emission with allowance for the Schottky effect. The most characteristic features of this type of discharge are considered. A non-Langmuir cathode sheath model is proposed for a low-voltage arc on a tungsten electrode.     

两种作物套种生态系统动态模型的建立及分析

本文主要建立小麦、大豆两种作物套种共生生态系统的Volterra方程模型．分析该模型得知,此生态系统是相互竞争的,其自身增长率因环境因素而受抑制,且是全局稳定的．其次计算出该生态系统在平衡状态处受到标准扰动之后,向平衡状态恢复的时间,有利套种作物生长的调控。     

Metabolic cost of walking: equation and model

Twenty years of published experience with the Workman-Armstrong equation for predicting walking VO2 is reviewed. The equation is reexpressed in currently accepted terminology, and it is shown that the equation serves well as a basic model of normal walking. Employing this model to analyze VO2/step leads to the elaboration of a three-compartment model of the metabolic cost of walking. This three-compartment model provides a rational estimate of the fraction of walking's metabolic cost that powers the actual walking movement. Doubt is expressed that "comfortable speed of walking" is definable in energy terms. It is suggested that the requirements of maintaining balance while walking may determine both the comfortable speed of walking and the curvilinearity of the relationship between ground-speed and freely chosen step frequency of walking.     

State-dependent neutral delay equations from population dynamics

A novel class of state-dependent delay equations is derived from the balance laws of age-structured population dynamics, assuming that birth rates and death rates, as functions of age, are piece-wise constant and that the length of the juvenile phase depends on the total adult population size. The resulting class of equations includes also neutral delay equations. All these equations are very different from the standard delay equations with state-dependent delay since the balance laws require non-linear correction factors. These equations can be written as systems for two variables consisting of an ordinary differential equation (ODE) and a generalized shift, a form suitable for numerical calculations. It is shown that the neutral equation (and the corresponding ODE—shift system) is a limiting case of a system of two standard delay equations.     

Self-consistent modeling of radio-frequency plasma generation in stellarators

A self-consistent model of radio-frequency (RF) plasma generation in stellarators in the ion cyclotron frequency range is described. The model includes equations for the particle and energy balance and boundary conditions for Maxwell’s equations. The equation of charged particle balance takes into account the influx of particles due to ionization and their loss via diffusion and convection. The equation of electron energy balance takes into account the RF heating power source, as well as energy losses due to the excitation and electron-impact ionization of gas atoms, energy exchange via Coulomb collisions, and plasma heat conduction. The deposited RF power is calculated by solving the boundary problem for Maxwell’s equations. When describing the dissipation of the energy of the RF field, collisional absorption and Landau damping are taken into account. At each time step, Maxwell’s equations are solved for the current profiles of the plasma density and plasma temperature. The calculations are performed for a cylindrical plasma. The plasma is assumed to be axisymmetric and homogeneous along the plasma column. The system of balance equations is solved using the Crank-Nicholson scheme. Maxwell’s equations are solved in a one-dimensional approximation by using the Fourier transformation along the azimuthal and longitudinal coordinates. Results of simulations of RF plasma generation in the Uragan-2M stellarator by using a frame antenna operating at frequencies lower than the ion cyclotron frequency are presented. The calculations show that the slow wave generated by the antenna is efficiently absorbed at the periphery of the plasma column, due to which only a small fraction of the input power reaches the confinement region. As a result, the temperature on the axis of the plasma column remains low, whereas at the periphery it is substantially higher. This leads to strong absorption of the RF field at the periphery via the Landau mechanism.