scholarly journals The Dynamical Problem for a Non Self-adjoint Hamiltonian

2012 ◽  
pp. 109-119
Author(s):  
Fabio Bagarello ◽  
Miloslav Znojil
Keyword(s):  
Dynamical Problem

scholarly journals Approximation theorems of a solution of amperometric enzymatic reactions based on Green’s fixed point normal-S iteration

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Khanitin Muangchoo-in ◽  
Kanokwan Sitthithakerngkiet ◽  
Parinya Sa-Ngiamsunthorn ◽  
Poom Kumam
Keyword(s):  
Fixed Point ◽  
Boundary Value Problems ◽  
Iterative Methods ◽  
Dynamical Problem ◽  
Enzymatic Reactions ◽  
Nonlinear Dynamical ◽  
Numerical Examples ◽  
Approximation Theorems ◽  
Kinetics Of ◽  
Nonlinear Dynamical Problem

AbstractIn this paper, the authors present a strategy based on fixed point iterative methods to solve a nonlinear dynamical problem in a form of Green’s function with boundary value problems. First, the authors construct the sequence named Green’s normal-S iteration to show that the sequence converges strongly to a fixed point, this sequence was constructed based on the kinetics of the amperometric enzyme problem. Finally, the authors show numerical examples to analyze the solution of that problem.

scholarly journals Analysis of Implicit Type Nonlinear Dynamical Problem of Impulsive Fractional Differential Equations

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-15 ◽  
Author(s):  
Naveed Ahmad ◽  
Zeeshan Ali ◽  
Kamal Shah ◽  
Akbar Zada ◽  
Ghaus ur Rahman
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Point Theorem ◽  
Fractional Differential Equations ◽  
Nonlocal Boundary ◽  
Dynamical Problem ◽  
Krasnoselskii’S Fixed Point Theorem ◽  
Impulsive Fractional Differential Equations ◽  
Fractional Differential

We study the existence, uniqueness, and various kinds of Ulam–Hyers stability of the solutions to a nonlinear implicit type dynamical problem of impulsive fractional differential equations with nonlocal boundary conditions involving Caputo derivative. We develop conditions for uniqueness and existence by using the classical fixed point theorems such as Banach fixed point theorem and Krasnoselskii’s fixed point theorem. For stability, we utilized classical functional analysis. Also, an example is given to demonstrate our main theoretical results.

THE STABILITY OF THE CRITICAL POINTS OF THE GENERALIZED GAUSE TYPE PREDATOR-PREY FISHERY MODELS WITH PROPORTIONAL HARVESTING AND TIME DELAY

2021 ◽  
Vol 6 (2) ◽  
pp. 885
Author(s):  
Wan Natasha Wan Hussin ◽  
Rohana Embong ◽  
Che Noorlia Noor
Keyword(s):  
Time Delay ◽  
Response Function ◽  
Critical Points ◽  
Marine Ecosystem ◽  
Time Lag ◽  
Dynamical Problem ◽  
Delay Period ◽  
Prey Population ◽  
Predator Prey ◽  
Predator Response

In the marine ecosystem, the time delay or lag may occur in the predator response function, which measures the rate of capture of prey by a predator. This is because, when the growth of the prey population is null at the time delay period, the predator’s growth is affected by its population and prey population densities only after the time delay period. Therefore, the generalized Gause type predator-prey fishery models with a selective proportional harvesting rate of fish and time lag in the Holling type II predator response function are proposed to simulate and solve the population dynamical problem. From the mathematical analysis of the models, a certain dimension of time delays in the predator response or reaction function can change originally stable non-trivial critical points to unstable ones. This is due to the existence of the Hopf bifurcation that measures the critical values of the time lag, which will affect the stabilities of the non-trivial critical points of the models. Therefore, the effects of increasing and decreasing the values of selective proportional harvesting rate terms of prey and predator on the stabilities of the non-trivial critical points of the fishery models were analysed. Results have shown that, by increasing the values of the total proportion of prey and predator harvesting denoted by qx Ex and qy Ey respectively, within the range 0.3102 ≤ qx Ex ≤ 0.9984 and 0.5049 ≤ qy Ey ≤ 0.5363, the originally unstable non-trivial critical points of the fishery models can be stable.

Mixed Convolved Action Principles for Dynamics of Linear Poroelastic Continua

2015 ◽  
Author(s):  
Bradley T. Darrall ◽  
Gary F. Dargush
Keyword(s):  
Weak Form ◽  
Dynamical Problem ◽  
Inner Product ◽  
Analytical Mechanics ◽  
Convolution Operators ◽  
Dissipative Processes ◽  
Poroelastic Media ◽  
New Family ◽  
The First Variation ◽  
Mixed Approach

Although Lagrangian and Hamiltonian analytical mechanics represent perhaps the most remarkable expressions of the dynamics of a mechanical system, these approaches also come with limitations. In particular, there is inherent difficulty to represent dissipative processes and the restrictions placed on end point variations are not consistent with the definition of initial value problems. The present work on poroelastic media extends the recent formulation of a mixed convolved action to address a continuum dynamical problem with dissipation through the development of a new variational approach. The action in this proposed approach is formed by replacing the inner product in Hamilton’s principle with a time convolution. As a result, dissipative processes can be represented in a natural way and the required constraints on the variations are consistent with the actual initial and boundary conditions of the problem. The variational formulations developed here employ temporal impulses of velocity, effective stress, pore pressure and pore fluid mass flux as primary variables in this mixed approach, which also uses convolution operators and fractional calculus to achieve the desired characteristics. The resulting mixed convolved action is formulated in both the time and frequency domains to develop two new stationary principles for dynamic poroelasticity. In addition, the first variation of the action provides a temporally well-balanced weak form that leads to a new family of finite element methods in time, as well as space.

A mathematical model for the third-body concept

2017 ◽  
Vol 23 (3) ◽  
pp. 420-432 ◽  
Author(s):  
Pavel Krejčí ◽  
Adrien Petrov
Keyword(s):  
Mathematical Model ◽  
A Priori Estimates ◽  
A Priori ◽  
Dynamical Problem ◽  
Sobolev Embedding ◽  
Third Body ◽  
Embedding Theory ◽  
The Third ◽  
Galerkin Approximations ◽  
Body Concept

The third-body concept is a pragmatic tool used to understand the friction and wear of sliding materials. The wear particles play a crucial role in this approach and constitute the main part of the third-body. This paper aims to introduce a mathematical model for the motion of a third-body interface separating two surfaces in contact. This model is written in accordance with the formalism of hysteresis operators as solution operators of the underlying variational inequalities. The existence result for this dynamical problem is obtained by using a priori estimates established for Faedo–Galerkin approximations, and some more specific techniques such as anisotropic Sobolev embedding theory.

scholarly journals Effect of Deformation on Semi–infinite Viscothermoelastic Cylinder Based on Five Theories of Generalized Thermoelasticity

2017 ◽  
Vol 6 (1) ◽  
pp. 17-35 ◽  
Author(s):  
D. K. Sharma ◽  
Himani Mittal ◽  
Sita Ram Sharma ◽  
Inder Parkash
Keyword(s):  
Heat Conduction ◽  
Laplace Transformation ◽  
Numerical Technique ◽  
Equations Of Motion ◽  
Generalized Thermoelasticity ◽  
Dynamical Problem ◽  
Infinite Cylinder ◽  
Matlab Software ◽  
Voigt Model ◽  
Laplace Transformations

We considera dynamical problem for semi-infinite viscothermoelastic semi infinite cylinder loaded mechanically and thermally and investigated the behaviour of variations of displacements, temperatures and stresses. The problem has been investigated with the help of five theories of the generalized viscothermoelasticity by using the Kelvin – Voigt model. Laplace transformations and Hankel transformations are applied to equations of constituent relations, equations of motion and heat conduction to obtain exact equations in transformed domain. Hankel transformed equations are inverted analytically and for the inversion of Laplace transformation we apply numerical technique to obtain field functions. In order to obtain field functions i.e. displacements, temperature and stresses numerically we apply MATLAB software tools. Numerically analyzed results for the temperature, displacements and stresses are shown graphically.

Numerical Method for Solving the Problems of the Building Structures Dynamics with a Mobile Massive Load

2018 ◽  
Vol 931 ◽  
pp. 72-77
Author(s):  
Leonid N. Panasyuk ◽  
Galina M. Kravchenko ◽  
Vakhtang P. Matua
Keyword(s):  
Direct Methods ◽  
Dynamical Problem ◽  
Building Structures ◽  
Direct Integration ◽  
Dynamic Problems ◽  
Time Step ◽  
Explicit Schemes ◽  
Massive Structure ◽  
The Matrix ◽  
Solving Equations

The article considers the modeling of dynamic processes in buildings and structures. A general formulation of the dynamic problem of a massive load motion on a massive structure is considered. The equation of motion is obtained in the form of a finite element method. The equations solving is performed using direct methods of integrating dynamic problems. Absolutely stable schemes of direct integration are constructed, where the system of solving equations is trivial and the matrix of the system is diagonal. Due to this, the complexity at the time step is as low as in explicit schemes. Therefore, the proposed methods can be considered as explicit absolutely stable schemes of direct integration of a dynamical problem with a variable in time mass. These recommendations are for estimating the accuracy of a numerical solution.

The dynamical problem for a rigid body in special relativity

1973 ◽  
Vol 484 (4) ◽  
pp. 325-340 ◽  
Author(s):  
C. B. Kafadar
Keyword(s):  
Rigid Body ◽  
Special Relativity ◽  
Dynamical Problem
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