scholarly journals Insights into the dynamic trajectories of protein filament division revealed by numerical investigation into the mathematical model of pure fragmentation

2021 ◽  
Vol 17 (9) ◽  
pp. e1008964
Author(s):  
Magali Tournus ◽  
Miguel Escobedo ◽  
Wei-Feng Xue ◽  
Marie Doumic
Keyword(s):  
Mathematical Theory ◽  
Length Distribution ◽  
Numerical Approach ◽  
Distribution Profile ◽  
Fragmentation Dynamics ◽  
Mathematical Equations ◽  
Fragmentation Reactions ◽  
The Stability ◽  
Fragmentation Equation ◽  
The Mathematical Model

The dynamics by which polymeric protein filaments divide in the presence of negligible growth, for example due to the depletion of free monomeric precursors, can be described by the universal mathematical equations of ‘pure fragmentation’. The rates of fragmentation reactions reflect the stability of the protein filaments towards breakage, which is of importance in biology and biomedicine for instance in governing the creation of amyloid seeds and the propagation of prions. Here, we devised from mathematical theory inversion formulae to recover the division rates and division kernel information from time dependent experimental measurements of filament size distribution. The numerical approach to systematically analyze the behaviour of pure fragmentation trajectories was also developed. We illustrate how these formulae can be used, provide some insights on their robustness, and show how they inform the design of experiments to measure fibril fragmentation dynamics. These advances are made possible by our central theoretical result on how the length distribution profile of the solution to the pure fragmentation equation aligns with a steady distribution profile for large times.

scholarly journals On the optimal control of coronavirus (2019-nCov) mathematical model; a numerical approach

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
N. H. Sweilam ◽  
S. M. Al-Mekhlafi ◽  
A. O. Albalawi ◽  
D. Baleanu
Keyword(s):  
Mathematical Model ◽  
Optimal Control ◽  
Weighted Average ◽  
Necessary Optimality Conditions ◽  
Numerical Approach ◽  
Population Number ◽  
Infected People ◽  
The Stability ◽  
Novel Coronavirus ◽  
Theoretical Results

Abstract In this paper, a novel coronavirus (2019-nCov) mathematical model with modified parameters is presented. This model consists of six nonlinear fractional order differential equations. Optimal control of the suggested model is the main objective of this work. Two control variables are presented in this model to minimize the population number of infected and asymptotically infected people. Necessary optimality conditions are derived. The Grünwald–Letnikov nonstandard weighted average finite difference method is constructed for simulating the proposed optimal control system. The stability of the proposed method is proved. In order to validate the theoretical results, numerical simulations and comparative studies are given.

scholarly journals NECESSITY TO IMPROVE THE MATHEMATICAL MODEL OF FREIGHT CARS TO STUDY CASES OF ITS DERAILMENTS

2020 ◽  
pp. 442-451
Author(s):  
А.V. Batig ◽  
A. Ya. Kuzyshyn
Keyword(s):  
Mathematical Model ◽  
Mathematical Models ◽  
Computer Experiment ◽  
Rolling Stock ◽  
Software Systems ◽  
Freight Car ◽  
The Stability ◽  
The Many ◽  
The Impact ◽  
The Mathematical Model

One of the most important problems that pose a serious threat to the functioning of railways is the problem of freight cars derailment. However, according to statistics, the number of cases of the derailments of freight cars in trains annually grows. Тo prevent such cases, the necessary preventive measures are developed, and to study the causes of their occurrence, a significant number of mathematical models, programs and software systems created by leading domestic and foreign scientists. Studies of such mathematical models by the authors of this work have led to the conclusion that they are not sufficiently detailed to the extent that it is necessary for analyze the reasons of its derailment. At the same time, an analysis of the causes of the rolling stock derailments on the railways of Ukraine over the past five years showed that in about 20 % of cases they are obvious, and in 7 % of cases they are not obvious and implicitly expressed. The study of such cases of rolling stock derailment during an official investigation by the railway and during forensic railway transport expertises requires the use of an improved mathematical model of a freight car, which would allow a quantitative assessment of the impact of its parameters and rail track on the conditions of railway accidents. Therefore, taking into account the main reasons that caused the occurrence of such railroad accidents over the last five years on the railways of Ukraine, the article selected the main directions for improving the mathematical model of a freight car, allowing to cover all the many factors (explicit and hidden) and identify the most significant ones regarding the circumstances of the derailment rolling stock off the track, established on the basis of a computer experiment. It is proposed in the mathematical model of a freight car to take into account the guiding force, the value of which is one of the main indicators of the stability of the rolling stock. The authors of the article noted that not taking into account the influence of the guiding forces on the dynamics of the freight car can lead to an erroneous determination of the reasons for the rolling stock derailment or even to the impossibility of establishing them.

scholarly journals Vision-Based Target Detection and Tracking for a Miniature Pan-Tilt Inertially Stabilized Platform

Electronics ◽  
2021 ◽  
Vol 10 (18) ◽  
pp. 2243
Author(s):  
Jianchuan Guo ◽  
Chenhu Yuan ◽  
Xu Zhang ◽  
Fan Chen
Keyword(s):  
Target Detection ◽  
Feedback Linearization ◽  
Visual Servoing ◽  
Control Method ◽  
Sliding Mode ◽  
Optical Axis ◽  
Detection And Tracking ◽  
The Stability ◽  
Stabilized Platform ◽  
The Mathematical Model

This paper presents a novel visual servoing sheme for a miniature pan-tilt intertially stabilized platform (ISP). A fully customized ISP can be mounted on a miniature quadcopter to achieve stationary or moving target detection and tracking. The airborne pan-tilt ISP can effectively isolate a disturbing rotational motion of the carrier, ensuring the stabilization of the optical axis of the camera in order to obtain a clear video image. Meanwhile, the ISP guarantees that the target is always on the optical axis of the camera, so as to achieve the target detection and tracking. The vision-based tracking control design adopts a cascaded control structure based on the mathematical model, which can accurately reflect the dynamic characteristics of the ISP. The inner loop of the proposed controller employs a proportional lag compensator to improve the stability of the optical axis, and the outer loop adopts the feedback linearization-based sliding mode control method to achieve the target tracking. Numerical simulations and laboratory experiments demonstrate that the proposed controller can achieve satisfactory tracking performance.

Walking Stability Analysis of Multi-Legged Crablike Robot over Slope

2013 ◽  
Vol 572 ◽  
pp. 636-639
Author(s):  
Xi Chen ◽  
Gang Wang
Keyword(s):  
Mathematical Model ◽  
Stability Analysis ◽  
Stability Criterion ◽  
Stability Margin ◽  
Static Stability ◽  
Matlab Simulation ◽  
And Performance ◽  
The Stability ◽  
The Mathematical Model ◽  
The Relationship

This paper deals with the walking stability analysis of a multi-legged crablike robot over slope using normalized energy stability margin (NESM) method in order to develop a common stabilization description method and achieve robust locomotion for the robot over rough terrains. The robot is simplified with its static stability being described by NESM. The mathematical model of static stability margin is built so as to carry out the simulation of walking stability over slope for the crablike robot that walks in double tetrapod gait. As a consequence, the relationship between stability margin and the height of the robots centroid, as well as its inclination relative to the ground is calculated by the stability criterion. The success and performance of the stability criterion proposed is verified through MATLAB simulation and real-world experiments using multi-legged crablike robot.

scholarly journals An overview of various kinds of wind effects on unmanned aerial vehicle

2019 ◽  
Vol 52 (7-8) ◽  
pp. 731-739 ◽  
Author(s):  
Bo Hang Wang ◽  
Dao Bo Wang ◽  
Zain Anwar Ali ◽  
Bai Ting Ting ◽  
Hao Wang
Keyword(s):  
Unmanned Aerial Vehicle ◽  
Great Influence ◽  
Wind Disturbance ◽  
Wind Fields ◽  
Wind Model ◽  
Aerial Vehicle ◽  
Low Altitude ◽  
The Stability ◽  
The Mathematical Model ◽  
Vehicle Movement

Attitude, speed, and position of unmanned aerial vehicles are susceptible to wind disturbance. The types, characteristics, and mathematical models of the wind, which have great influence on unmanned aerial vehicle in the low-altitude environment, are summarized, including the constant wind, turbulent flow, many kinds of wind shear, and the propeller vortex. Combined with the mathematical model of the unmanned aerial vehicle, the mechanism of unmanned aerial vehicle movement in the wind field is illustrated from three different kinds of viewpoints including velocity viewpoint, force viewpoint, and energy viewpoint. Some simulation tests have been implemented to show the effects of different kinds of wind on unmanned aerial vehicle’s path and flight states. Finally, some proposals are presented to tell reader in which condition, which wind model should be added to simulation, and how to enhance the stability of unmanned aerial vehicle for different kinds of wind fields.

On A Formulation of the Elastic Stability Equations of Circular Cylindrical Shells Under Variable Internal Pressure

1985 ◽  
Vol 9 (2) ◽  
pp. 64-69
Author(s):  
J.L. Urrutia-Galicia ◽  
A.N. Sherbourne
Keyword(s):  
Mathematical Model ◽  
Internal Pressure ◽  
Cylindrical Shells ◽  
Direct Analysis ◽  
Elastic Stability ◽  
Equilibrium Path ◽  
Circular Cylindrical Shells ◽  
The Stability ◽  
Variable Internal Pressure ◽  
The Mathematical Model

The mathematical model of the stability analysis of circular cylindrical shells under arbitrary internal pressure is presented. The paper consists of a direct analysis of the equilibrium modes in the neighbourhood of the unperturbed principal equilibrium path. The final stability condition results in a completely symmetric differential operator which is then compared with current theories found in the literature.

scholarly journals On the Effect of Finite Buffer Truncation in a Two-Node Jackson Network

2005 ◽  
Vol 42 (01) ◽  
pp. 199-222 ◽  
Author(s):  
Yutaka Sakuma ◽  
Masakiyo Miyazawa
Keyword(s):  
Stability Condition ◽  
Queue Length ◽  
Length Distribution ◽  
Buffer Size ◽  
Finite Buffer ◽  
Jackson Network ◽  
Numerical Examples ◽  
Queue Length Distribution ◽  
Special Cases ◽  
The Stability

We consider a two-node Jackson network in which the buffer of node 1 is truncated. Our interest is in the limit of the tail decay rate of the queue-length distribution of node 2 when the buffer size of node 1 goes to infinity, provided that the stability condition of the unlimited network is satisfied. We show that there can be three different cases for the limit. This generalizes some recent results obtained for the tandem Jackson network. Special cases and some numerical examples are also presented.

scholarly journals Numerical Exploration of Kaldorian Interregional Macrodynamics: Enhanced Stability and Predominance of Period Doubling under Flexible Exchange Rates

2010 ◽  
Vol 2010 ◽  
pp. 1-29 ◽  
Author(s):  
Toichiro Asada ◽  
Christos Douskos ◽  
Vassilis Kalantonis ◽  
Panagiotis Markellos
Keyword(s):  
Exchange Rates ◽  
Government Expenditure ◽  
Period Doubling ◽  
Numerical Approach ◽  
Capital Movement ◽  
Dimensional Parameter ◽  
Stability Of Equilibrium ◽  
The Stability ◽  
Flexible Exchange Rates ◽  
Enhanced Stability

We present a discrete two-regional Kaldorian macrodynamic model with flexible exchange rates and explore numerically the stability of equilibrium and the possibility of generation of business cycles. We use a grid search method in two-dimensional parameter subspaces, and coefficient criteria for the flip and Hopf bifurcation curves, to determine the stability region and its boundary curves in several parameter ranges. The model is characterized by enhanced stability of equilibrium, while its predominant asymptotic behavior when equilibrium is unstable is period doubling. Cycles are scarce and short-lived in parameter space, occurring at large values of the degree of capital movementβ. By contrast to the corresponding fixed exchange rates system, for cycles to occur sufficient amount of trade is requiredtogetherwith high levels of capital movement. Rapid changes in exchange rate expectations and decreased government expenditure are factors contributing to the creation of interregional cycles. Examples of bifurcation and Lyapunov exponent diagrams illustrating period doubling or cycles, and their development into chaotic attractors, are given. The paper illustrates the feasibility and effectiveness of the numerical approach for dynamical systems of moderately high dimensionality and several parameters.

Analysis of the Dynamics of Piecewise Linear Memristors

2016 ◽  
Vol 26 (13) ◽  
pp. 1650217 ◽  
Author(s):  
Fangfang Jiang ◽  
Zhicheng Ji ◽  
Qing-Guo Wang ◽  
Jitao Sun
Keyword(s):  
Piecewise Linear ◽  
Equilibrium Points ◽  
Characteristic Curve ◽  
Piecewise Linear Function ◽  
Excited Oscillation ◽  
Exciting Source ◽  
Memristive Circuits ◽  
The Stability ◽  
Straight Lines ◽  
The Mathematical Model

In this paper, we consider a class of flux controlled memristive circuits with a piecewise linear memristor (i.e. the characteristic curve of the memristor is given by a piecewise linear function). The mathematical model is described by a discontinuous planar piecewise smooth differential system, which is defined on three zones separated by two parallel straight lines [Formula: see text] (called as discontinuity lines in discontinuous differential systems). We first investigate the stability of equilibrium points and the existence and uniqueness of a crossing limit cycle for the memristor-based circuit under self-excited oscillation. We then analyze the existence of periodic orbits of forced nonlinear oscillation for the memristive circuit with an external exciting source. Finally, we give numerical simulations to show good matches between our theoretical and simulation results.

A Numerical Study on Water Flooding in a Damaged Oil Carrier

2011 ◽  
Author(s):  
Liang-Yee Cheng ◽  
Diogo Vieira Gomes ◽  
Adriano Mitsuo Yoshino ◽  
Kazuo Nishimoto
Keyword(s):  
Numerical Study ◽  
Numerical Approach ◽  
Water Flooding ◽  
Oil Leakage ◽  
Complex Fluid ◽  
Oil Water ◽  
Moving Particle ◽  
The Stability ◽  
Fluid Solid Interaction ◽  
Interaction Problem

The objective of the present paper is to carry out numerical simulations on the coupled transient processes of oil leakage, water flooding and study of the stability in a damaged crude oil carrier. For this purpose, numerical approach based on Moving Particle Semi-Implicit (MPS) method is applied to model the complex fluid-solid interaction problem with free surface and oil-water multiphase flow. Changes on the modeling of the towing tank utilized in a previous study on oil leakage carried by the author are done to reduce the undesirable effects of the wave reflection. As a consequence, the improved results of the transient behaviors of hull motions are obtained for the cases with oil leak, as well as the final list angle and volume inside the tank in cases of water flooding. The results of the simulations show that the volume of flooded water is inversely proportional to the filling ratio. Also, the height of the opening has not significant effect on the final list and flooded volume.

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