scholarly journals Plasmid pBR322 and Nonlinear Conformational Distortions (Kinks)

2019 ◽  
Vol 14 (1) ◽  
pp. 327-339
Author(s):  
L.V. Yakushevich ◽  
L.A. Krasnobaeva
Keyword(s):  
Mathematical Modeling ◽  
Nonlinear Dynamics ◽  
Dynamic Characteristics ◽  
Structural Changes ◽  
Necessary Condition ◽  
Plasmid Pbr322 ◽  
Block Method ◽  
Coding Regions ◽  
Dna Molecule ◽  
The Matrix

Plasmid pBR322 containing two coding regions in the matrix chain is a convenient object to study the DNA nonlinear dynamics that is known to play an important role in the processes of transcription, replication, denaturation and transmission of structural changes and information along the DNA molecule. The aim of the present work is to study by the methods of mathematical modeling the dynamics of local conformational distortions – kinks, in the plasmid pBR322. To calculate the dynamic characteristics of the kinks, we applied the method of McLaughlin-Scott, complemented by the block method. This permitted us to model kinks as quasi-particles moving in the potential field of the plasmid. We calculated the time dependences of the kink energy, velocity and coordinate. Calculations were made for three different values of the initial kink velocity: 150 m/s, 1650 m/s and 1879 m/s. The results obtained presented in the form of 3D trajectories and their projections, showed that the necessary condition for kink passing the entire plasmid is the enough large value of the initial kink velocity υ not less than 1656.66 m/c which is, however, less than sound velocity (1904.60 m/c).

Application of the piecewise constant method in nonlinear dynamics of drill string

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Jialin Tian ◽  
Jie Wang ◽  
Yi Zhou ◽  
Lin Yang ◽  
Changyue Fan ◽  
...  
Keyword(s):  
Nonlinear Dynamics ◽  
Dynamic Model ◽  
Dynamic Characteristics ◽  
Drill String ◽  
Vibration Velocity ◽  
Kutta Method ◽  
Time Step ◽  
Piecewise Constant ◽  
Runge Kutta Method ◽  
Runge Kutta

Abstract Aiming at the current development of drilling technology and the deepening of oil and gas exploration, we focus on better studying the nonlinear dynamic characteristics of the drill string under complex working conditions and knowing the real movement of the drill string during drilling. This paper firstly combines the actual situation of the well to establish the dynamic model of the horizontal drill string, and analyzes the dynamic characteristics, giving the expression of the force of each part of the model. Secondly, it introduces the piecewise constant method (simply known as PT method), and gives the solution equation. Then according to the basic parameters, the axial vibration displacement and vibration velocity at the test points are solved by the PT method and the Runge–Kutta method, respectively, and the phase diagram, the Poincare map, and the spectrogram are obtained. The results obtained by the two methods are compared and analyzed. Finally, the relevant experimental tests are carried out. It shows that the results of the dynamic model of the horizontal drill string are basically consistent with the results obtained by the actual test, which verifies the validity of the dynamic model and the correctness of the calculated results. When solving the drill string nonlinear dynamics, the results of the PT method is closer to the theoretical solution than that of the Runge–Kutta method with the same order and time step. And the PT method is better than the Runge–Kutta method with the same order in smoothness and continuity in solving the drill string nonlinear dynamics.

scholarly journals On circulant codes with prescribed distances

1977 ◽  
Vol 16 (3) ◽  
pp. 361-369
Author(s):  
M. Deza ◽  
Peter Eades
Keyword(s):  
Sufficient Conditions ◽  
Difference Sets ◽  
Necessary And Sufficient Conditions ◽  
Necessary Condition ◽  
Weighing Matrices ◽  
Cyclic Difference Sets ◽  
The Matrix ◽  
Circulant Codes ◽  
Necessary And Sufficient ◽  
Square Matrix

Necessary and sufficient conditions are given for a square matrix to te the matrix of distances of a circulant code. These conditions are used to obtain some inequalities for cyclic difference sets, and a necessary condition for the existence of circulant weighing matrices.

Modified Reynolds Equation for Aerostatic Porous Radial Bearings With Quadratic Forchheimer Pressure-Flow Assumption

2007 ◽  
Author(s):  
Rodrigo Nicoletti ◽  
Zilda C. Silveira ◽  
Benedito M. Purquerio
Keyword(s):  
Mathematical Modeling ◽  
Porous Medium ◽  
Linear Model ◽  
Dynamic Characteristics ◽  
Reynolds Equation ◽  
Dimensional Parameter ◽  
Pressure Flow ◽  
Darcy Model ◽  
Linear Effects ◽  
Modified Reynolds Equation

The mathematical modeling of aerostatic porous bearings, represented by the Reynolds equation, depends on the assumptions for the flow in the porous medium. One proposes a modified Reynolds equation based on the quadratic Forchheimer assumption, which can be used for both linear and quadratic conditions. Numerical results are compared to those obtained with the linear Darcy model. It is shown that, the non-dimensional parameter Φ, related to non-linear effects, strongly affects the bearing dynamic characteristics, but for values of Φ > 10, the results tend to those obtained with the linear model.

A Review on Active Bearings and Perspectives of Using Them in Rotating Machinery

2014 ◽  
Vol 630 ◽  
pp. 181-187
Author(s):  
Denis Shutin ◽  
Leonid Savin ◽  
Alexander Babin
Keyword(s):  
Mathematical Modeling ◽  
Artificial Intelligence ◽  
Control System ◽  
Motion Control ◽  
Dynamic Characteristics ◽  
Rotating Machinery ◽  
Fluid Film ◽  
Motion Control System ◽  
Fluid Film Bearings ◽  
System Components

The paper examines the issues of improving the rotor units by means of using support units with actively changeable characteristics. An overview of the known solutions related to the use of active bearings in various types of turbomachinery is provided. A closer look is given at the design and features of active radial bearings, the main elements of which are fluid film bearings. The results of mathematical modeling of active hybrid bearings are presented. The prospects of the use of this type of supports to improve the dynamic characteristics of rotating machinery, including reducing vibrations caused by various factors, are analyzed. Promising directions of development of active bearings are considered, which primarily involves the modification of system components and rotor motion control system algorithms, including intelligent technologies and artificial intelligence methods.

scholarly journals CONSTRUCTION OF MINIMAX CONTROL FOR ALMOST CONSERVATIVE CONTROLLED DYNAMIC SYSTEMS WITH THE LIMITED PERTURBATIONS

2017 ◽  
Vol 2 ◽  
pp. 9-15
Author(s):  
Iryna Svyatovets
Keyword(s):  
Riccati Equation ◽  
Infinite System ◽  
Conservative System ◽  
Coefficient Matrix ◽  
Necessary Condition ◽  
Existence Of A Solution ◽  
Minimax Control ◽  
System Of Matrix Equations ◽  
System A ◽  
The Matrix

The problem is considered for constructing a minimax control for a linear stationary controlled dynamical almost conservative system (a conservative system with a weakly perturbed coefficient matrix) on which an unknown perturbation with bounded energy acts. To find the solution of the Riccati equation, an approach is proposed according to which the matrix-solution is represented as a series expansion in a small parameter and the unknown components of this matrix are determined from an infinite system of matrix equations. A necessary condition for the existence of a solution of the Riccati equation is formulated, as well as theorems on additive operations on definite parametric matrices. A condition is derived for estimating the parameter appearing in the Riccati equation. An example of a solution of the minimax control problem for a gyroscopic system is given. The system of differential equations, which describes the motion of a rotor rotating at a constant angular velocity, is chosen as the basis.

scholarly journals Mathematical Modeling of Open States in Double Stranded DNA Molecule Depending on 2H/1H Ratio

2019 ◽  
Vol 14 (2) ◽  
pp. 612-624 ◽  
Author(s):  
S.S. Dzhimak ◽  
M.I. Drobotenko ◽  
A.A. Basov ◽  
A.A. Svidlov ◽  
M.G. Baryshev
Keyword(s):  
Mathematical Modeling ◽  
Hydrogen Bond ◽  
Deuterium Atom ◽  
Living System ◽  
Dna Molecule ◽  
Dna Base Pair ◽  
A Chain ◽  
Time Required ◽  
Open States ◽  
Bond Disruption

The evaluation results of the possible deuterium atoms effect on the DNA base pair opening are presented in the article. The cause of these processes is the replacement of protium with deuterium atom due to the increase of energy required to break the hydrogen bond. These processes can be studied by method of mathematical modeling, with account of open states between base pairs being the key condition of the adequacy of the mathematical model of the DNA. The experiment data show that the presence of deuterium in a chain of nucleotides can cause - depending on the value of hydrogen bond disruption energy - both increase and decrease in probability of open states occurrence. For example: hydrogen bond disruption energy of 0.358·10-22 n·m, non-zero probability of open states occurrence is observed in case of the absence of deuterium in the molecule, and with hydrogen bond disruption energy of 0.359·10-22 n·m or more such probability equals zero. Also, when one deuterium atom is present in a molecule, non-zero probability is observed even with hydrogen bond disruption energy equal to 0.368·10-22 n·m (i.e. more than 0.358·10-22 n·m). Thus participation of deuterium atoms in the formation of hydrogen bonds of double helixes of a DNA molecule can cause the changes in the time required for transfer of genetic information, which can explain the effect of even minor deviations in deuterium concentration in a medium on metabolic processes in a living system.

scholarly journals Nonlinear Dynamics of the Rigid Drum for Vibratory Roller on Elastic Subgrades

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Lun Liu ◽  
Fenghui Wang ◽  
Shupeng Sun ◽  
Weiming Feng ◽  
Chao Guo
Keyword(s):  
Nonlinear Dynamics ◽  
Phase Diagram ◽  
Dynamic Characteristics ◽  
Nonlinear Dynamic ◽  
Period Doubling ◽  
Time History ◽  
Nonlinear Dynamic Model ◽  
Compaction Process ◽  
Adjustment Strategy ◽  
Vibratory Compaction

In this paper, a coupling nonlinear dynamic model of the drum and subgrade is established for the vibratory roller. The dynamic characteristics of the rigid drum of the vibratory roller in the process of vibratory compaction are comprehensively investigated by time history, phase diagram, frequency spectrum, Poincare map, and bifurcation diagram. During the compaction process, the stiffness of the subgrade increases and the motion of the rigid drum of the vibratory roller changes from a single period to multiple periods and finally enters chaos by the way of period doubling. Moreover, the roller parameters also significantly affect the dynamic characteristics of the rigid drum and the compaction effect of the subgrade. Based on detailed numerical results, a parameter adjustment strategy about the roller frequency and nominal amplitude is proposed, which can avoid the “bouncing” of the drum during compaction and improve the compaction efficiency.

scholarly journals THE GENERALIZED MATRIX VALUED HYPERGEOMETRIC EQUATION

2010 ◽  
Vol 21 (02) ◽  
pp. 145-155 ◽  
Author(s):  
P. ROMÁN ◽  
S. SIMONDI
Keyword(s):  
Differential Equation ◽  
Orthogonal Polynomials ◽  
Unit Circle ◽  
Hypergeometric Functions ◽  
Spherical Functions ◽  
Hypergeometric Equation ◽  
Necessary Condition ◽  
Hypergeometric Differential Equation ◽  
The Matrix ◽  
Generalized Matrix

The matrix valued analog of the Euler's hypergeometric differential equation was introduced by Tirao in [4]. This equation arises in the study of matrix valued spherical functions and in the theory of matrix valued orthogonal polynomials. The goal of this paper is to extend naturally the number of parameters of Tirao's equation in order to get a generalized matrix valued hypergeometric equation. We take advantage of the tools and strategies developed in [4] to identify the corresponding matrix hypergeometric functions nFm. We prove that, if n = m + 1, these functions are analytic for |z| < 1 and we give a necessary condition for the convergence on the unit circle |z| = 1.

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