Semi-Discretization of Delayed Dynamical Systems

2001 ◽  
Author(s):  
Tamás Insperger ◽  
Gábor Stépán
Keyword(s):  
Dynamical Systems ◽  
Mathieu Equation ◽  
Special Kind ◽  
Delayed Systems ◽  
The Past ◽  
Linear Discrete System ◽  
Approximate System ◽  
Discretization Technique ◽  
The Stability ◽  
Time Periodic

Abstract An efficient numerical method is presented for the stability analysis of linear retarded dynamical systems. The method is based on a special kind of discretization technique with respect to the past effect only. The resulting approximate system is delayed and time-periodic in the same time, but still, it can be transformed analytically into a high dimensional linear discrete system. The method is especially efficient for time varying delayed systems, including the case when the time delay itself varies in time. The method is applied to determine the stability charts of the delayed Mathieu equation with damping.

Galerkin Approximations for Stability of Delay Differential Equations With Time Periodic Coefficients

2015 ◽  
Vol 10 (2) ◽  
Author(s):  
Anwar Sadath ◽  
C. P. Vyasarayani
Keyword(s):  
Differential Equations ◽  
Delay Differential Equations ◽  
Approximate Model ◽  
Periodic Coefficients ◽  
Galerkin Approximations ◽  
Approximate System ◽  
The Stability ◽  
Delay Differential ◽  
Time Periodic ◽  
Least Squares Approach

A numerical method to determine the stability of delay differential equations (DDEs) with time periodic coefficients is proposed. The DDE is converted into an equivalent partial differential equation (PDE) with a time periodic boundary condition (BC). The PDE, along with its BC, is then converted into a system of ordinary differential equations (ODEs) with time periodic coefficients using the Galerkin least squares approach. In the Galerkin approach, shifted Legendre polynomials are used as basis functions, allowing us to obtain explicit expressions for the approximate system of ODEs. We analyze the stability of the discretized ODEs, which represent an approximate model of the DDEs, using Floquet theory. We use numerical examples to show that the stability charts obtained with our method are in excellent agreement with those existing in the literature and those obtained from direct numerical simulation.

Faraday waves on a cylindrical fluid filament – generalised equation and simulations

2018 ◽  
Vol 857 ◽  
pp. 80-110 ◽  
Author(s):  
Sagar Patankar ◽  
Palas Kumar Farsoiya ◽  
Ratul Dasgupta
Keyword(s):  
Linear Theory ◽  
Body Force ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Mathieu Equation ◽  
Faraday Waves ◽  
Stability Chart ◽  
Fluid Filament ◽  
The Stability ◽  
Time Periodic

We perform linear stability analysis of an interface separating two immiscible, inviscid, quiescent fluids subject to a time-periodic body force. In a generalised, orthogonal coordinate system, the time-dependent amplitude of interfacial perturbations, in the form of standing waves, is shown to be governed by a generalised Mathieu equation. For zero forcing, the Mathieu equation reduces to a (generalised) simple harmonic oscillator equation. The generalised Mathieu equation is shown to govern Faraday waves on four time-periodic base states. We use this equation to demonstrate that Faraday waves and instabilities can arise on an axially unbounded, cylindrical capillary fluid filament subject to radial, time-periodic body force. The stability chart for solutions to the Mathieu equation is obtained through numerical Floquet analysis. For small values of perturbation and forcing amplitude, results obtained from direct numerical simulations (DNS) of the incompressible Euler equation (with surface tension) show very good agreement with theoretical predictions. Linear theory predicts that unstable Rayleigh–Plateau modes can be stabilised through forcing. This prediction is borne out by DNS results at early times. Nonlinearity produces higher wavenumbers, some of which can be linearly unstable due to forcing and thus eventually destabilise the filament. We study axisymmetric as well as three-dimensional perturbations through DNS. For large forcing amplitude, localised sheet-like structures emanate from the filament, suffering subsequent fragmentation and breakup. Systematic parametric studies are conducted in a non-dimensional space of five parameters and comparison with linear theory is provided in each case. Our generalised analysis provides a framework for understanding free and (parametrically) forced capillary oscillations on quiescent base states of varying geometrical configurations.

Stability of a Time-Delayed System With Parametric Excitation

2006 ◽  
Vol 129 (2) ◽  
pp. 125-135 ◽  
Author(s):  
Nitin K. Garg ◽  
Brian P. Mann ◽  
Nam H. Kim ◽  
Mohammad H. Kurdi
Keyword(s):  
Time Delay ◽  
Parametric Excitation ◽  
Mathieu Equation ◽  
Periodic Coefficient ◽  
Single Element ◽  
New Approach ◽  
Delayed System ◽  
Representative Problem ◽  
The Stability ◽  
Time Periodic

This paper investigates two different temporal finite element techniques, a multiple element (h-version) and single element (p-version) method, to analyze the stability of a system with a time-periodic coefficient and a time delay. The representative problem, known as the delayed damped Mathieu equation, is chosen to illustrate the combined effect of a time delay and parametric excitation on stability. A discrete linear map is obtained by approximating the exact solution with a series expansion of orthogonal polynomials constrained at intermittent nodes. Characteristic multipliers of the map are used to determine the unstable parameter domains. Additionally, the described analysis provides a new approach to extract the Floquet transition matrix of time periodic systems without a delay.

Parametric Oscillations and Stability of a Periodically Charged Liquid Droplet

1973 ◽  
Vol 51 (13) ◽  
pp. 1443-1445 ◽  
Author(s):  
G. N. Ionides
Keyword(s):  
Incompressible Fluid ◽  
Electric Charge ◽  
Liquid Droplet ◽  
Mathieu Equation ◽  
Parametric Oscillations ◽  
The Stability ◽  
Time Periodic ◽  
Constant Charge

The stability of an incompressible fluid droplet, carrying a time periodic electric charge, is considered. It is shown that this electrohydrodynamic problem is described by a Mathieu equation. As a result, the amplitude of the charge required to induce instability may be much smaller than in the corresponding case of a constant charge. The calculations are applicable to the dynamics of raindrops in electrified clouds.

A Generalization of Poincaré’s Theorem to Periodic Hybrid and Impulsive Dynamical Systems

2001 ◽  
Author(s):  
V. Chellaboina ◽  
S. G. Nersesov ◽  
W. M. Haddad
Keyword(s):  
Dynamical Systems ◽  
Periodic Orbits ◽  
Discrete Time ◽  
Discrete Time System ◽  
Time System ◽  
Stability Of Periodic Orbits ◽  
Poincaré Return Map ◽  
The Stability ◽  
Time Periodic ◽  
Special Case

Abstract Poincaré’s method is well known for analyzing the stability of continuous-time periodic dynamical systems by studying the stability properties of a fixed point as an equilibrium point of a discrete-time system. In this paper we generalize Poincaré’s method to dynamical systems possessing left-continuous flows to address the stability of limit cycles and periodic orbits of left-continuous, hybrid, and impulsive dynamical systems. It is shown that resetting manifold (which gives rise to the state discontinuities) provides a natural hyperplane for defining a Poincaré return map. In the special case of impulsive dynamical systems, we show the Poincaré map replaces an nth-order impulsive dynamical system by an (n − 1)th-order discrete-time system for analyzing the stability of periodic orbits.

Feedback Control of Periodic Delayed Systems

2013 ◽  
Author(s):  
Morad Nazari ◽  
Oleg A. Bobrenkov ◽  
Eric A. Butcher
Keyword(s):  
Closed Loop ◽  
Control Strategies ◽  
Control Design ◽  
Mathieu Equation ◽  
Periodic Systems ◽  
Control Effort ◽  
Delayed Systems ◽  
Combined Use ◽  
Chebyshev Spectral Collocation ◽  
Time Periodic

In this study, three control strategies based on Chebyshev spectral collocation and the Lyapunov-Floquet transformation (LFT) are explored for regulation control of linear periodic time delayed systems. In previous studies, control design based on Chebyhev spectral continuous time approximation (CSCTA) has been demonstrated for the delayed systems and the LFT has been utilized for the control of time-periodic non-delayed systems. However, the combined use of CSCTA and reduced LFT (RLFT) has thus far not been investigated for their application in control design for delayed periodic systems. The delayed Mathieu equation is used as an illustrative example, and the closed-loop response of the system and the control effort are investigated for all three control strategies.

Stability and Folding of the Unusually Stable Hemoglobin from Synechocystis is Subtly Optimized and Dependent on the Key Heme Pocket Residues.

2020 ◽  
Vol 27 ◽  
Author(s):  
Sheetal Uppal ◽  
Mohd. Asim Khan ◽  
Suman Kundu
Keyword(s):  
Molten Globule ◽  
Life Forms ◽  
Model System ◽  
Heme Pocket ◽  
The Past ◽  
Specific Manner ◽  
Delivery Vehicles ◽  
The Stability ◽  
Key Residues ◽  
Synechocystis Sp

Aims: The aim of our study is to understand the biophysical traits that govern the stability and folding of Synechocystis hemoglobin, a unique cyanobacterial globin that displays unusual traits not observed in any of the other globins discovered so far. Background: For the past few decades, classical hemoglobins such as vertebrate hemoglobin and myoglobin have been extensively studied to unravel the stability and folding mechanisms of hemoglobins. However, the expanding wealth of hemoglobins identified in all life forms with novel properties, like heme coordination chemistry and globin fold, have added complexity and challenges to the understanding of hemoglobin stability, which has not been adequately addressed. Here, we explored the unique truncated and hexacoordinate hemoglobin from the freshwater cyanobacterium Synechocystis sp. PCC 6803 known as “Synechocystis hemoglobin (SynHb)”. The “three histidines” linkages to heme are novel to this cyanobacterial hemoglobin. Objective: Mutational studies were employed to decipher the residues within the heme pocket that dictate the stability and folding of SynHb. Methods: Site-directed mutants of SynHb were generated and analyzed using a repertoire of spectroscopic and calorimetric tools. Result: The results revealed that the heme was stably associated to the protein under all denaturing conditions with His117 playing the anchoring role. The studies also highlighted the possibility of existence of a “molten globule” like intermediate at acidic pH in this exceptionally thermostable globin. His117 and other key residues in the heme pocket play an indispensable role in imparting significant polypeptide stability. Conclusion: Synechocystis hemoglobin presents an important model system for investigations of protein folding and stability in general. The heme pocket residues influenced the folding and stability of SynHb in a very subtle and specific manner and may have been optimized to make this Hb the most stable known as of date. Other: The knowledge gained hereby about the influence of heme pocket amino acid side chains on stability and expression is currently being utilized to improve the stability of recombinant human Hbs for efficient use as oxygen delivery vehicles.

scholarly journals Copper Phyllosilicates-Derived Catalysts in the Production of Alcohols from Hydrogenation of Carboxylates, Carboxylic Acids, Carbonates, Formyls, and CO2: A Review

Catalysts ◽  
2021 ◽  
Vol 11 (2) ◽  
pp. 255
Author(s):  
Dien-Thien To ◽  
Yu-Chuan Lin
Keyword(s):  
Carboxylic Acids ◽  
Catalytic Performance ◽  
Spatial Effect ◽  
Synthesis Methods ◽  
The Past ◽  
Surface Areas ◽  
Preparation Conditions ◽  
Remedial Actions ◽  
The Stability ◽  
Size Interaction

Copper phyllosilicates-derived catalysts (CuPS-cats) have been intensively explored in the past two decades due to their promising activity in carbonyls hydrogenation. However, CuPS-cats have not been completely reviewed. This paper focuses on the aspects concerning CuPS-cats from synthesis methods, effects of preparation conditions, and dopant to catalytic applications of CuPS-cats. The applications of CuPS-cats include the hydrogenation of carboxylates, carboxylic acids, carbonates, formyls, and CO2 to their respective alcohols. Besides, important factors such as the Cu dispersion, Cu+ and Cu0 surface areas, particles size, interaction between Cu and supports and dopants, morphologies, and spatial effect on catalytic performance of CuPS-cats are discussed. The deactivation and remedial actions to improve the stability of CuPS-cats are summarized. It ends up with the challenges and prospective by using this type of catalyst.

scholarly journals Thermodynamic and Energy Efficiency Analysis of a Domestic Refrigerator Using Al2O3 Nano-Refrigerant

2021 ◽  
Vol 13 (10) ◽  
pp. 5659
Author(s):  
Farhood Sarrafzadeh Javadi ◽  
Rahman Saidur
Keyword(s):  
Temperature Gradient ◽  
Technological Changes ◽  
Nanoparticle Concentration ◽  
Evaporator Temperature ◽  
Domestic Refrigerator ◽  
The Past ◽  
Nano Lubricant ◽  
The Stability ◽  
Energy Efficiency Analysis ◽  
Al2o3 Nanofluid

Refrigeration systems have experienced massive technological changes in the past 50 years. Nanotechnology can lead to a promising technological leap in the refrigeration industry. Nano-refrigerant still remains unknown because of the complexity of the phase change process of the mixture including refrigerant, lubricant, and nanoparticle. In this study, the stability of Al2O3 nanofluid and the performance of a nano-refrigerant-based domestic refrigerator have been experimentally investigated, with the focus on the thermodynamic and energy approaches. It was found that by increasing the nanoparticle concentration, the stability of nano-lubricant was decreased and evaporator temperature gradient was increased. The average of the temperature gradient increment in the evaporator was 20.2% in case of using 0.1%-Al2O3. The results showed that the energy consumption of the refrigerator reduced around 2.69% when 0.1%-Al2O3 nanoparticle was added to the system.

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