Numerical Investigations of the Dynamics of Development of Two-Dimensional Perturbations in Magnetic Galathea Traps

Differential Equations - Studying the stability of traps for magnetic plasma confinement is one of the main tasks in solving the problem of controlled thermonuclear fusion. The main trends and...     

大小结构种群模型的平衡解的稳定性

考虑了一个大小结构的非线性种群模型,其各变化率不但依赖于个体的大小,而且依赖于总群口.利用扰动方法,得到了特征方程并分析了平衡解的稳定性,对于特殊的变化率,给出了平衡解稳定的充分条件.     

Mathematical Models in Landscape Ecology: Stability Analysis and Numerical Tests

In the present paper a review of some mathematical models for the ecological evaluation of environmental systems is considered. Moreover a new model, capable to furnish more detailed information at the level of landscape units, is proposed. Numerical tests are then performed for a case study in the province of Viterbo (central Italy).     

On the Stability of Plasma Equilibrium in the Neighborhood of a Straight Current Conductor

Computational Mathematics and Mathematical Physics - The article presents a mathematical model of an equilibrium magnetoplasma configuration in a plasma cylinder containing on its axis a conductor...     

Mathematical Models in Medicine

Several mathematical models are discussed to illustrate their applications in medicine. Examples chosen are from different areas of medicine and they utilize various degrees of mathematical sophistication. Problem areas in distribution of drugs in the body, diets for hospital patients, differential diagnosis, body burden in environmental health and patient care in the operating room are developed. The major aim of this survey is to bring to the attention of biomedical scientists and educators the power of mathematical concepts and techniques.     

State-Space Stability of Two-Dimensional Systems

State-space stability of two-dimensional systems is considered.The stability criterion is simple: it consists of two one-dimensionalstability tests and the requirement that a single polynomialis devoid of roots on [—1, 1]. Along the same lines, wepropose a general relative-stability test and stability-margincomputation.     

二维离散数学模型模拟肿瘤内外血管生成

建立九点差分格式的二维离散数学模型,模拟肿瘤内外的血管生成,模型扩展了内皮细胞沿9个方向运动,考虑存在两根母血管的情况下,耦合内皮细胞在肿瘤内外不同力学环境下的随机、趋化和趋触性运动,数值生成了肿瘤内外异构的血管网.结果表明,该模型可以产生相对真实的具有接近肿瘤病理生理特性的血管网,可为临床研究提供有益的信息.     

Equilibrium State of Inhomogeneous Plasma

We consider the problem of a self-consistent determination of an essentially inhomogeneous equilibrium state of classical plasma. The solutions of the stationary Vlasov–Poisson equations are constructed in the form of a localized transition layer that separates the domains of homogeneous plasmas with different equilibrium parameters. The layer can also transform into a local perturbation inside a homogeneous plasma. In both cases, the solution contains neither mass currents nor electric currents, and all electrodynamic and hydrodynamic quantities and their derivatives are continuous. The parameters of the adjacent domains uniquely determine the transition layer structure.     

电法勘探中的数学模型

文章介绍了地球物理勘探中大地电磁法 ( MT)在二维构造上的数学模型和正反演方法 ,也给出了可控源音频大地电磁测深 ( CSA MT)的二维正演数学模型 .     

Structural Stability for Two Convection Models in a Reacting Fluid with Magnetic Field Effect

This paper deals with two fundamental models for convection in a reacting fluid and porous medium with magnetic field effect. We demonstrate that the solution depends continuously on changes in the chemical reaction and the electrical conductivity coefficients. The continuous dependence is unconditional in two dimensions but conditional in three dimensions.     

Computation of Magnetic Fields in Open Traps with Oppositely Directed Fields

The article presents the results of numerical calculation of the magnetic field in open traps. The magnetic field in traps is generated by a system of circular conductors carrying currents in opposite directions. Each pair of conductors creates a magnetic field configuration of so-called cusped geometry (an antiprobkotron). Such configurations may be called traps with oppositely directed fields. Their main shortcoming is the high loss of particles along the magnetic forcelines through the annular slit and the axial opening. These particle losses are reduced by introducing a system of conductors with different configurations of circular loops that carry currents in opposite directions. The magnetic fields of the complex system of current carrying loops are calculated by summing over all pairs of conductors. Computation results are reported for open traps with a cusped magnetic field (antiprobkotrons) for various configurations of conductor pairs.     

Estimates for Errors in Two-Dimensional Models of Elasticity Theory

Explicit (computable) estimates for errors in some simplified two-dimensional models of the theory of elastic body are obtained. Such models are usually used if one of the characteristic sizes of a domain is significantly less than two others. In particular, the model of plane stresses is considered. To obtain estimates for the deviation of reduced solutions from exact solutions, the direct and dual variational problems are considered and the duality methods are used. Bibliography: 9 titles.     

Mathematical Programming with System of Equilibrium Constraints

In this paper, we study the mathematical program with system of equilibrium constraints. This problem contains bilevel program with system of equilibrium constraints, semi-infinite program with system of equilibrium constraints, mathematical program with Nash equilibrium constraints, mathematical program with system of mixed variational like inequalities constraints. We establish the existence theorems of mathematical program with system of equilibrium constraints under various assumptions.     

Mathematical Problems in Elastic Equilibrium with Finite Deformations

We consider functions such that their curves of steepest descent are straight lines. We prove that, along these curves, all principal curvatures of level surfaces of such functions satisfy a simple nonlinear ordinary differential equation. This result is used to get quantitative geometrical information on the level surfaces     

Mathematical Models of Oscillator Antennas

Numerical methods for the solution of oscillator antennas are reviewed. Mathematical models are considered for the computation of the current distribution in a system of thin conducting oscillator radiators arranged in an arbitrary configuration above a conducting ground.     

Mathematical Models of Discrete Self-Similarity

Natural phenomena which exhibit discrete self-similarity are under consideration. Earlier, self-similarity of some non-smooth phenomena was studied using the concept of log-periodicity, however there was a gap in this field. Recently it was attempted to fill this gap by concentrating on the study of a new concept of parametric-homogeneity (PH) based on the use of discrete group of coordinate dilations. It is argued that parametric-homogeneity can be helpful in the modelling of self-similar non-smooth phenomena. Some models of natural phenomena which have PH-features are presented and some properties of PH-functions are discussed. As an example of practical usage of these functions, the phenomenon of seismic activation prior to a major earthquake is considered.