A novel numerical approach for the stability of nanobeam exposed to hygro‐thermo‐magnetic environment embedded in elastic foundation

2022 ◽  
Author(s):  
Subrat Kumar Jena ◽  
S. Chakraverty ◽  
Vinyas Mahesh ◽  
Dineshkumar Harursampath ◽  
Hamid M. Sedighi
Keyword(s):  
Elastic Foundation ◽  
Numerical Approach ◽  
The Stability

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 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 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.

On Post-Critical Behavior of a Beam on an Elastic Foundation

2018 ◽  
Vol 18 (06) ◽  
pp. 1850082 ◽  
Author(s):  
Lidija Z. Rehlicki ◽  
Marko B. Janev ◽  
Branislava N. Novaković ◽  
Teodor M. Atanacković
Keyword(s):  
Total Energy ◽  
Elastic Foundation ◽  
Nonlinear Problem ◽  
Bifurcation Analysis ◽  
Nontrivial Solutions ◽  
Buckling Mode ◽  
Nonlinear Equilibrium ◽  
The Stability ◽  
The One ◽  
Two Parameter

In this paper, we analyze the nonlinear equilibrium equation corresponding to the two-parameter bifurcation problem arising in the stability analysis of an elastic simply supported beam on the Winkler type elastic foundation for the case when bimodal buckling occurs. We perform the bifurcation analysis of the nonlinear problem, by using Lyapunov–Schmidt reduction, thus obtaining the number of the nontrivial solutions to the nonlinear problem and qualitatively characterizing the solution patterns. We also give the formulation of the problem and bifurcation analysis from the total energy viewpoint and determine the energy of each bifurcating solution. We assert that the solution with the smallest energy is the one that will be observed in the post-critical state. For specific choice of parameters, the bifurcating solution in the form of the second buckling mode has the smallest total energy. The numerical results illustrating the theory are also provided.

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.

scholarly journals Squeal Frequency of a Railway Disc Brake Evaluation by FE Analyses

2018 ◽  
Vol 2018 ◽  
pp. 1-10 ◽  
Author(s):  
F. Cascetta ◽  
F. Caputo ◽  
A. De Luca
Keyword(s):  
Sensitivity Analysis ◽  
Finite Element ◽  
Experimental Tests ◽  
Numerical Approach ◽  
System Stability ◽  
Brake System ◽  
Physical Parameters ◽  
Disc Brake ◽  
Complex Eigenvalues ◽  
The Stability

This paper deals with the development of a numerical model, based on the Finite Element (FE) theory for the prediction of the squeal frequency of a railway disc brake. The analytical background has been discussed and presented, as well as the most efficient methods for evaluating the system stability; the attention has been paid particularly to the complex eigenvalues method, which has been adopted within this paper to investigate the railway disc brake system. Numerical results have been compared with measurements from experimental tests in order to validate the proposed numerical approach. At the end of this work, a sensitivity analysis, aimed at understanding the effects of some physical parameters influencing the stability of the brake system and the squeal propensity, has been carried out.

On the Influence of the Elastic Medium Stiffness in the Buckling Behavior of Compressed Beams on Elastic Foundation

2012 ◽  
Vol 166-169 ◽  
pp. 776-783 ◽  
Author(s):  
Fabio de Angelis ◽  
Donato Cancellara
Keyword(s):  
Elastic Medium ◽  
Elastic Foundation ◽  
Elastic Stiffness ◽  
Structural System ◽  
Buckling Loads ◽  
Buckling Behavior ◽  
Half Wave ◽  
Overall Stability ◽  
Beams On Elastic Foundation ◽  
The Stability

In the present work the stability and buckling behavior of compressed beams on elastic foundation are analyzed. The influence of the elastic stiffness of the medium on the overall stability of the structural system is investigated. The analysis is performed via energetic methods. The buckling loads are evaluated as a function of the stiffness of the beam and the stiffness of the elastic medium. Considerations are illustrated on the influence of the elastic medium stiffness and on the effects of the ratio of the length of the beam and the characteristic half-wave on the stability of the structural system.

A numerical approach for the stability analysis of open thin-walled beams

2013 ◽  
Vol 48 ◽  
pp. 76-86 ◽  
Author(s):  
Egidio Lofrano ◽  
Achille Paolone ◽  
Giuseppe Ruta
Keyword(s):  
Stability Analysis ◽  
Numerical Approach ◽  
Thin Walled ◽  
The Stability

scholarly journals Stability of a micro-tidal inlet using semi-numerical approach

2017 ◽  
Vol 8 (3) ◽  
pp. 113-125
Author(s):  
R Senthilkumar ◽  
K Murali ◽  
V Sundar
Keyword(s):  
East Coast ◽  
Wave Model ◽  
Numerical Approach ◽  
Wave Climate ◽  
Tidal Range ◽  
Tidal Inlets ◽  
Littoral Drift ◽  
East Coast Of India ◽  
Longshore Sediment Transport ◽  
The Stability

Tidal inlets get disconnected depending on the seasons due to the formation of sand bars near its mouth are termed as “seasonally open tidal inlets.” These inlets are usually small of width of about 100 m and occur in micro-tide (tidal range not exceeding 1 m). Since the east coast of India experiences a net littoral drift of up to about 0.8 Mm3/annum, which is one of the largest in magnitudes that needs to be considered in the analysis of modeling of the sand bar formation and the associated phenomena. Kondurpalem inlet situated along the South east coast of India is considered as a case study. A frequency domain wave model (STeady-state spectral WAVE) has been used to compute the nearshore wave climate. The wave-induced currents have been obtained, and the longshore sediment transport rate is obtained through empirical relations. The tidal prism is found from measured depth and tidal velocity by solving shallow water equations. The stability of the inlet is investigated by applying the criteria developed by Bruun (1986). The effect of a pair of training walls on maintaining the stability of the mouth is reassessed over the periods.

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