scholarly journals Ecology through the eyes of a non-ecologist

2020 ◽  
Vol 18 (5) ◽  
pp. 259-270
Author(s):  
Janusz Uchmański
Keyword(s):  
Differential Equations ◽  
Mathematical Models ◽  
Density Dependence ◽  
Evolutionary Biology ◽  
Ecological Systems ◽  
Living Environment ◽  
Mathematical Methods ◽  
Nature Protection ◽  
Practical Applications ◽  
The Stability

Ecology is a branch of biology that deals with the life of plants and animals in their environment. Nature protection are practical actions where ecology is applied. Ecology is the most biological branch of biology because it deals with individuals in their living environment, and individuals "exist" only in biology. The most important issue being considered in ecology is biodiversity: its changes and its persistence. In their research, ecologists focus on the functioning of ecological systems. In classical terms, they assume that the most important mechanism is density dependence. Mathematical models traditionally applied in ecology include ordinary difference and differential equations, which fits well with the assumption of density dependence, but this results in ecology being dominated by considerations of the stability of ecological systems. Evolutionary biology and ecology have separate areas of interest. Evolutionary biology explains the formation of optimal characteristics of individuals. Ecology also takes into account those individuals who have lost in the process of natural selection. The mathematical methods used in classical ecology were developed for the use of physics. The question arises whether they give a precise picture of the dynamics of ecological systems. Recently, a view has emerged stating that in order to see the importance of full-scale biodiversity, we should refer to individuals (rather than population density) as basic "atoms" that make up ecological systems. In ecology, we call this an individual-based approach. However, it gives a very complex picture of how ecological systems work. In ecology, however, there is an alternative way to describe the dynamics of ecological systems, i.e. through the circulation of matter in them and the flow of energy through them. It allows the use of traditional difference and differential equations in the formulation of mathematical models, which has proven itself in practical applications many times.

scholarly journals The development of scientific outlook of students when teaching inverse problems for differential equations

2019 ◽  
Vol 16 (1) ◽  
pp. 46-55
Author(s):  
Viktor Semenovich Kornilov
Keyword(s):  
Inverse Problems ◽  
Differential Equations ◽  
Mathematical Models ◽  
Research Work ◽  
Teaching Experience ◽  
Physical Processes ◽  
Mathematical Methods ◽  
Important Place ◽  
The World ◽  
Scientific Worldview

Problem and goal. Modern achievements of the world Science of nature and the world, physical laws and laws should be disclosed at an accessible level to University students. Among the scientific methods of research of physical processes and phenomena, an important place is the method of mathematical modeling, because mathematical models have scientific and cognitive potential and versatility (see, for example, [2-4]). The use of mathematical models of inverse problems for differential equations (IPDE) allows to effectively investigate many processes and phenomena occurring in the air, earth and water environment. It is not surprising that in some Russian universities in the physical and mathematical areas of training are taught IPDE in the form of a choice of courses. The goals and objectives of such teaching are set, as a result of which students would develop creative mathematical abilities, formed fundamental knowledge in the field of physical education, developed a scientific worldview. Methodology. The development of scientific outlook of students of physical and mathematical directions of preparation, as a result of teaching IPDE, ensured the successful will be implemented in practice, such conditions as: 1. the involvement of experts in the field IPDE with teaching experience at the university; 2. development of the content of lectures and practical classes on the basis of modern achievements of the theory of inverse and incorrect problems, taking into account the professional orientation of training students; 3. the implementation of the principles, methods and means of education IPDE; 4. involvement of students in research work in scientific seminars and participation in scientific conferences devoted to IPDE; 5. implementation of methodological approaches that allow students to develop the skills and abilities of independent analysis of applied and humanitarian nature of the results of research of IPDE. Results. In practical classes on the IPDE students acquire the ability and skills to apply effective approaches and mathematical methods of finding solutions to inverse problems, followed by a logical analysis of their solutions. As a result, students gain useful experience in the analysis of new information about the studied physical processes and phenomena, form new scientific knowledge about the world on the basis of which develop a scientific worldview. Conclusion. Developed, in the process of teaching IPDE, the scientific outlook helps students to understand that mathematical models IPDE are relevant to theory, experiment and philosophy - the basic methods of knowledge researchers; to understand the humanitarian value of mathematical models IPDE.

Stability of High Speed Rotors With Internal Friction

1974 ◽  
Vol 96 (3) ◽  
pp. 960-968 ◽  
Author(s):  
J. M. Vance ◽  
J. Lee
Keyword(s):  
Internal Friction ◽  
Differential Equations ◽  
Numerical Solution ◽  
High Speed ◽  
Critical Speed ◽  
Rotating Machinery ◽  
Rigid Foundation ◽  
Flexible Rotor ◽  
Mathematical Methods ◽  
The Stability

The problem of nonsynchronous whirl induced by internal friction is shown to be important when rotating machinery is designed for operation at supercritical speeds. Mathematical methods are used to determine the stability speed threshold of nonsyncronous whirl instability for an unbalanced flexible rotor on a rigid foundation. This threshold of instability is shown to be the same as the threshold for balanced rotors established by previous investigations. The location of the external damping (foundation or rotor) is shown to be important in determining stability when the foundation is made very rigid. The effect of shaft stiffness orthotropy on nonsynchronous whirl induced by internal friction is also investigated. Results from the stability analyses are verified by numerical solution of the differential equations. It is concluded that rotors can be safely operated up to speeds about eighty percent above the significant critical speed if the external damping is larger than the internal friction, and that shaft stiffness orthotropy has an insignificant effect on friction-induced whirl.

scholarly journals Study of mathematical methods and models usage in the pesticide degradation and residue prediction

2019 ◽  
pp. 67-71
Author(s):  
Fang Li ◽  
V.I. Dubovyk ◽  
Runqiang Liu
Keyword(s):  
Mathematical Models ◽  
Future Perspectives ◽  
Mathematical Methods ◽  
Pesticide Degradation ◽  
Practical Applications ◽  
Advantages And Disadvantages ◽  
Pesticide Pollution ◽  
Yield And Quality ◽  
Agriculture Industry ◽  
Crops Yield

Pesticide was widely used in agriculture industry to ensure the crops’ yield and quality, followed that pesticide pollution had become one of the most serious issues for public health in the world. Therefore, it’s necessary to develop mathematical models for the prediction of pesticide degradation and residue. In this paper, we introduced four kinds of mathematical models in pesticide prediction, and offered the basis theories and practical applications for each model. Then we compared their advantages and disadvantages systematically by analyzing the roles of each one. Finally, present challenges and future perspectives in pesticide residue prediction fields were discussed.

MHD stagnation-point flow and heat transfer of a nanofluid over a stretching/shrinking sheet with melting, convective heat transfer and second-order slip

2018 ◽  
Vol 28 (9) ◽  
pp. 2089-2110 ◽  
Author(s):  
Ioan Pop ◽  
Natalia C. Roşca ◽  
Alin V. Roşca
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Stagnation Point ◽  
Second Order ◽  
Shrinking Sheet ◽  
Lower Branch ◽  
Content Type ◽  
Practical Applications ◽  
Branch Solution ◽  
The Stability

PurposeThe purpose of this paper is to study the effects of MHD, suction, second-order slip and melting on the stagnation-point and heat transfer of a nanofluid past a stretching/shrinking sheet.Design/methodology/approachUsing appropriate variables, the governing partial differential equations were transformed into ordinary (similarity) differential equations, which are then solved numerically using the function bvp4c from Matlab.FindingsIt is found that dual (upper and lower branch) solutions exist for some values of the governing parameters. From the stability analysis, it is found that the upper branch solution is stable, while the lower branch solution is unstable. The sample velocity, temperature and concentration profiles along both solution branches are graphically presented.Originality/valueThe results of the paper are new and original with many practical applications of nanofluids in the modern industry.

scholarly journals Deterministic and Stochastic Holling-Tanner Prey-Predator Models

2021 ◽  
Vol 1 (1) ◽  
pp. 1-8
Author(s):  
Bharat Bahadur Thapa ◽  
Samir Shrestha ◽  
Dil Bahadur Gurung
Keyword(s):  
Differential Equations ◽  
Functional Response ◽  
Ecological Systems ◽  
Volterra Model ◽  
Stable Node ◽  
Euler Scheme ◽  
Numerical Schemes ◽  
Stochastic Environments ◽  
Predator Model ◽  
The Stability

A modified version of the so called Holling-Tanner prey-predator models with prey dependent functional response is introduced. We improved some new results on Holling-Tanner model from Lotka-Volterra model on real ecological systems and studied the stability of this model in the deterministic and stochastic environments. The study was focused on three types of stability, namely, stable node, spiral node, and center. The numerical schemes are employed to get the approximated solutions of the differential equations. We have used Euler scheme to solve the deterministic prey-predator model and we used Euler-Maruyama scheme to solve stochastic prey-predator model.

Evolution and Selection of Quantitative Traits

2018 ◽  
Author(s):  
Bruce Walsh ◽  
Michael Lynch
Keyword(s):  
Mathematical Models ◽  
Quantitative Genetics ◽  
Complex Traits ◽  
Evolutionary Biology ◽  
Quantitative Traits ◽  
Specific Gene ◽  
Real World Data ◽  
Holistic Treatment ◽  
Genetics And Genomics ◽  
Selection Of

Quantitative traits—be they morphological or physiological characters, aspects of behavior, or genome-level features such as the amount of RNA or protein expression for a specific gene—usually show considerable variation within and among populations. Quantitative genetics, also referred to as the genetics of complex traits, is the study of such characters and is based on mathematical models of evolution in which many genes influence the trait and in which non-genetic factors may also be important. Evolution and Selection of Quantitative Traits presents a holistic treatment of the subject, showing the interplay between theory and data with extensive discussions on statistical issues relating to the estimation of the biologically relevant parameters for these models. Quantitative genetics is viewed as the bridge between complex mathematical models of trait evolution and real-world data, and the authors have clearly framed their treatment as such. This is the second volume in a planned trilogy that summarizes the modern field of quantitative genetics, informed by empirical observations from wide-ranging fields (agriculture, evolution, ecology, and human biology) as well as population genetics, statistical theory, mathematical modeling, genetics, and genomics. Whilst volume 1 (1998) dealt with the genetics of such traits, the main focus of volume 2 is on their evolution, with a special emphasis on detecting selection (ranging from the use of genomic and historical data through to ecological field data) and examining its consequences. This extensive work of reference is suitable for graduate level students as well as professional researchers (both empiricists and theoreticians) in the fields of evolutionary biology, genetics, and genomics. It will also be of particular relevance and use to plant and animal breeders, human geneticists, and statisticians.

scholarly journals Implicit nonlinear fractional differential equations of variable order

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Amar Benkerrouche ◽  
Mohammed Said Souid ◽  
Kanokwan Sitthithakerngkiet ◽  
Ali Hakem
Keyword(s):  
Differential Equations ◽  
Boundary Value Problem ◽  
Fractional Differential Equations ◽  
Boundary Value ◽  
Variable Order ◽  
Stability Of Solutions ◽  
Nonlinear Fractional Differential Equations ◽  
Caputo Fractional Differential Equations ◽  
Fractional Differential ◽  
The Stability

AbstractIn this manuscript, we examine both the existence and the stability of solutions to the implicit boundary value problem of Caputo fractional differential equations of variable order. We construct an example to illustrate the validity of the observed results.

Non-adhesive lotus and other hydrophobic materials

2008 ◽  
Vol 366 (1870) ◽  
pp. 1539-1556 ◽  
Author(s):  
David Quéré ◽  
Mathilde Reyssat
Keyword(s):  
Solid Surface ◽  
Room Temperature ◽  
Water Repellency ◽  
Short Review ◽  
Water Repellent ◽  
Practical Applications ◽  
Hydrophobic Materials ◽  
Volatile Liquid ◽  
Air Cushion ◽  
The Stability

Superhydrophobic materials recently attracted a lot of attention, owing to the potential practical applications of such surfaces—they literally repel water, which hardly sticks to them, bounces off after an impact and slips on them. In this short review, we describe how water repellency arises from the presence of hydrophobic microstructures at the solid surface. A drop deposited on such a substrate can float above the textures, mimicking at room temperature what happens on very hot plates; then, a vapour layer comes between the solid and the volatile liquid, as described long ago by Leidenfrost. We present several examples of superhydrophobic materials (either natural or synthetic), and stress more particularly the stability of the air cushion—the liquid could also penetrate the textures, inducing a very different wetting state, much more sticky, due to the possibility of pinning on the numerous defects. This description allows us to discuss (in quite a preliminary way) the optimal design to be given to a solid surface to make it robustly water repellent.

scholarly journals Stability Analysis of Distributed Order Fractional Differential Equations

2011 ◽  
Vol 2011 ◽  
pp. 1-12 ◽  
Author(s):  
H. Saberi Najafi ◽  
A. Refahi Sheikhani ◽  
A. Ansari
Keyword(s):  
Stability Analysis ◽  
Characteristic Function ◽  
Differential Equations ◽  
Density Function ◽  
Robust Stability ◽  
Fractional Differential Equations ◽  
Stability Condition ◽  
Fractional Differential ◽  
The Stability ◽  
Distributed Order

We analyze the stability of three classes of distributed order fractional differential equations (DOFDEs) with respect to the nonnegative density function. In this sense, we discover a robust stability condition for these systems based on characteristic function and new inertia concept of a matrix with respect to the density function. Moreover, we check the stability of a distributed order fractional WINDMI system to illustrate the validity of proposed procedure.

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