scholarly journals Mathematical Modeling of the Phytoplankton Populations Geographic Dynamics for Possible Scenarios of Changes in the Azov Sea Hydrological Regime

Mathematics ◽  
2021 ◽  
Vol 9 (23) ◽  
pp. 3025
Author(s):  
Alexander Sukhinov ◽  
Yulia Belova ◽  
Alexander Chistyakov ◽  
Alexey Beskopylny ◽  
Besarion Meskhi
Keyword(s):  
Hydrological Regime ◽  
Marine Species ◽  
Anthropogenic Factors ◽  
Freshwater Species ◽  
Algebraic Equations ◽  
Central Difference ◽  
Coastal Systems ◽  
Azov Sea ◽  
Linear Algebraic Equations ◽  
Biological Kinetics

Increased influence of abiotic and anthropogenic factors on the ecological state of coastal systems leads to uncontrollable changes in the overall ecosystem. This paper considers the crucial problem of studying the effect of an increase in the water’s salinity in the Azov Sea and the Taganrog Bay on hydrobiological processes. The main aim of the research is the diagnostic and predictive modeling of the geographic dynamics of the general phytoplankton populations. A mathematical model that describes the dynamics of three types of phytoplankton is proposed, considering the influence of salinity and nutrients on algae development. Discretization is carried out based on a linear combination of Upwind Leapfrog difference schemes and a central difference scheme, which makes it possible to increase the accuracy of solving the biological kinetics problem at large values of the grid Péclet number (Peh > 2). A software package has been developed that implements interrelated models of hydrodynamics and biogeochemical cycles. A modified alternating-triangular method was used to solve large-dimensional systems of linear algebraic equations (SLAE). Based on the scenario approach, several numerical experiments were carried out to simulate the dynamics of the main species of phytoplankton populations at different levels of water salinity in coastal systems. It is shown that with an increase in the salinity of waters, the habitats of phytoplankton populations shift, and marine species invasively replace freshwater species of algae.

Numerical Solution of Transonic Stream Function Equation on S1 Stream Surface in Cascade

1986 ◽  
Author(s):  
Hua Yaonan ◽  
Wu Wenquan
Keyword(s):  
Stream Function ◽  
Transonic Flow ◽  
Momentum Equation ◽  
Curvilinear Coordinates ◽  
Algebraic Equations ◽  
Central Difference ◽  
Linear Algebraic Equations ◽  
Difference Formula ◽  
Grid Nodes ◽  
Transonic Cascade

A method is presented in this paper for calculating transonic flow field in turbomachinery cascades. With respect to non-orthogoanl curvilinear coordinates, the stream function equation governing fluid flow was established. Using the Artificial Compressibility Method, the discretization of the partial differential equation was carried out by use of the standard central difference formula. The set of linear algebraic equations obtained is solved by means of the Direct Matrix Method. In order to overcome the non-uniqueness of density in transonic flow in the stream function method, the velocities at grid nodes are first obtained by integrating the momentum equation and then the densities are determined from the energy equation. Application of this method to some transonic cascade-flow with supersonic or subsonic inlet velocity shows that the solution obtained is in fair agreement with experimental data.

On Improved Approximate Solution of the Fredholm Integral Equation

2006 ◽  
Vol 6 (3) ◽  
pp. 264-268
Author(s):  
G. Berikelashvili ◽  
G. Karkarashvili
Keyword(s):  
Integral Equation ◽  
Approximate Solution ◽  
Fredholm Integral Equation ◽  
Algebraic Equations ◽  
Order Convergence ◽  
One Dimensional ◽  
Averaging Operator ◽  
Linear Algebraic Equations ◽  
Convergence Solution

AbstractA method of approximate solution of the linear one-dimensional Fredholm integral equation of the second kind is constructed. With the help of the Steklov averaging operator the integral equation is approximated by a system of linear algebraic equations. On the basis of the approximation used an increased order convergence solution has been obtained.

scholarly journals Exact statistical solution for the hopping transport of trapped charge via finite Markov jump processes

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Andrey A. Pil’nik ◽  
Andrey A. Chernov ◽  
Damir R. Islamov
Keyword(s):  
Charge Transport ◽  
Thin Layers ◽  
Jump Processes ◽  
Dielectric Films ◽  
Algebraic Equations ◽  
Markov Jump ◽  
Statistical Solution ◽  
Linear Algebraic Equations ◽  
Special Cases ◽  
Thin Dielectric Films

AbstractIn this study, we developed a discrete theory of the charge transport in thin dielectric films by trapped electrons or holes, that is applicable both for the case of countable and a large number of traps. It was shown that Shockley–Read–Hall-like transport equations, which describe the 1D transport through dielectric layers, might incorrectly describe the charge flow through ultra-thin layers with a countable number of traps, taking into account the injection from and extraction to electrodes (contacts). A comparison with other theoretical models shows a good agreement. The developed model can be applied to one-, two- and three-dimensional systems. The model, formulated in a system of linear algebraic equations, can be implemented in the computational code using different optimized libraries. We demonstrated that analytical solutions can be found for stationary cases for any trap distribution and for the dynamics of system evolution for special cases. These solutions can be used to test the code and for studying the charge transport properties of thin dielectric films.

scholarly journals Two matrix methods for solution of nonlinear and linear Lane-Emden type equations with mixed condition by operational matrix

2015 ◽  
Vol 4 (3) ◽  
pp. 420 ◽  
Author(s):  
Behrooz Basirat ◽  
Mohammad Amin Shahdadi
Keyword(s):  
Bernstein Polynomials ◽  
Operational Matrix ◽  
Numerical Procedure ◽  
Operational Matrices ◽  
Algebraic Equations ◽  
Mixed Condition ◽  
Matrix Methods ◽  
Numerical Examples ◽  
Linear Algebraic Equations ◽  
The Given

<p>The aim of this article is to present an efficient numerical procedure for solving Lane-Emden type equations. We present two practical matrix method for solving Lane-Emden type equations with mixed conditions by Bernstein polynomials operational matrices (BPOMs) on interval [<em>a; b</em>]. This methods transforms Lane-Emden type equations and the given conditions into matrix equation which corresponds to a system of linear algebraic equations. We also give some numerical examples to demonstrate the efficiency and validity of the operational matrices for solving Lane-Emden type equations (LEEs).</p>

scholarly journals Optimal Random Packing of Spheres and Extremal Effective Conductivity

Symmetry ◽  
2021 ◽  
Vol 13 (6) ◽  
pp. 1063
Author(s):  
Vladimir Mityushev ◽  
Zhanat Zhunussova
Keyword(s):  
Effective Conductivity ◽  
Dimensional Space ◽  
Elementary Function ◽  
Voronoi Tessellation ◽  
Random Packing ◽  
Periodicity Cell ◽  
Algebraic Equations ◽  
Optimal Packing ◽  
Linear Algebraic Equations ◽  
Initial Location

A close relation between the optimal packing of spheres in Rd and minimal energy E (effective conductivity) of composites with ideally conducting spherical inclusions is established. The location of inclusions of the optimal-design problem yields the optimal packing of inclusions. The geometrical-packing and physical-conductivity problems are stated in a periodic toroidal d-dimensional space with an arbitrarily fixed number n of nonoverlapping spheres per periodicity cell. Energy E depends on Voronoi tessellation (Delaunay graph) associated with the centers of spheres ak (k=1,2,…,n). All Delaunay graphs are divided into classes of isomorphic periodic graphs. For any fixed n, the number of such classes is finite. Energy E is estimated in the framework of structural approximations and reduced to the study of an elementary function of n variables. The minimum of E over locations of spheres is attained at the optimal packing within a fixed class of graphs. The optimal-packing location is unique within a fixed class up to translations and can be found from linear algebraic equations. Such an approach is useful for random optimal packing where an initial location of balls is randomly chosen; hence, a class of graphs is fixed and can dynamically change following prescribed packing rules. A finite algorithm for any fixed n is constructed to determine the optimal random packing of spheres in Rd.

The laminar boundary-layer equation: a method of solution by means of an automatic computer

1955 ◽  
Vol 51 (2) ◽  
pp. 320-332 ◽  
Author(s):  
D. C. F. Leigh
Keyword(s):  
Boundary Layer ◽  
Asymptotic Solution ◽  
Laminar Boundary Layer ◽  
Iterative Process ◽  
Boundary Layer Equation ◽  
Algebraic Equations ◽  
Automatic Computer ◽  
Linear Algebraic Equations ◽  
Method Of Solution ◽  
Incompressible Boundary

ABSTRACTA method, very suitable for use with an automatic computer, of solving the Hartree-Womersley approximation to the incompressible boundary-layer equation is developed. It is based on an iterative process and the Choleski method of solving a simultaneous set of linear algebraic equations. The programming of this method for an automatic computer is discussed. Tables of a solution of the boundary-layer equation in a region upstream of the separation point are given. In the upstream neighbourhood of separation this solution is compared with Goldstein's asymptotic solution and the agreement is good.

Solution of Levi Civita’s Problem by Infinite Matrix Inversion

1973 ◽  
Vol 40 (1) ◽  
pp. 31-36 ◽  
Author(s):  
M. Bentwich
Keyword(s):  
Flow Pattern ◽  
Flow Direction ◽  
Leading Edge ◽  
Arbitrary Cross Section ◽  
Matrix Inversion ◽  
Infinite Matrix ◽  
Algebraic Equations ◽  
Flow Past ◽  
Linear Algebraic Equations ◽  
Wet Surface

The author proposes a new method by which one can solve for the two-dimensional irrotational fully cavitating flow past a cylinder of arbitrary cross section. Unlike the available solutions, it is in the form of two expansions each valid in part of the complex potential plane w = Φ + iΨ. The a priori unknown coefficients in the two expansions are linked by infinitely many linear algebraic equations. By inverting the associated matrix and utilizing the boundary condition, that represent the geometry of the wet surface, the coefficients in the expansions are evaluated and the solution is completed. Cases in which the wet surface is circular, the pressure along the free streamlines is constant, and the entire flow pattern is symmetric with respect to flow direction at infinity are considered in detail. Also, the well-known solution for the flow past a flat plate is compared to that obtained by the method of matrix inversion. Judging from these results, the convergence of the series appears to be very rapid. The author finally discusses the applicability of the method to cases in which the obstacle has a sharp leading edge, the pressure in the cavity is not uniform, or the flow pattern is not symmetric.

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