Numerical and Analytical Analyses of Bi-Stable Element As Negative Stiffness

2018 ◽  
Author(s):  
Akintoye Olumide Oyelade
Keyword(s):  
Numerical Model ◽  
Nonlinear Differential Equations ◽  
Model System ◽  
Negative Stiffness ◽  
Positive Matrix ◽  
Mass Model ◽  
Static State ◽  
Small Oscillations ◽  
Stable Element ◽  
The Stability

In this paper, negative stiffness in static state is made stable by constraining it in positive matrix. The stability of the system is tested using energy function. The motion of the two mass model system is described with a system of two coupled nonlinear differential equations. The numerical results are validated by comparing the predictions with calculations from analytical method. For small oscillations about the static equilibrium position the numerical model agree with analytical model. The developed model can be served as an efficient means of eliciting negative stiffness.

DEVELOPMENT OF THE BASIC CRITERIA FOR RUSSIAN COASTS TYPIFICATION

2017 ◽  
Author(s):  
Рубен Косян ◽  
Ruben Kosyan ◽  
Viacheslav Krylenko ◽  
Viacheslav Krylenko
Keyword(s):  
Coastal Zone ◽  
Coastal Area ◽  
Economic Activity ◽  
Basic Information ◽  
Dynamic Features ◽  
Static State ◽  
Evolutionary Features ◽  
Coastal Features ◽  
The Stability

There are many types of coasts classifications that indicate main coastal features. As a rule, the "static" state of the coasts is considered regardless of their evolutionary features and ways to further transformation. Since the most part of the coastal zone studies aimed at ensuring of economic activity, it is clear that the classification of coast types should indicate total information required by the users. Accordingly, the coast classification should include the criterion, characterizing as dynamic features of the coast and the conditions and opportunities of economic activity. The coast classification, of course, should be based on geomorphological coast typification. Similar typification has been developed by leading scientists from Russia and can be used with minimal modifications. The authors propose to add to basic information (geomorphological type of coast) the evaluative part for each coast sector. It will include the estimation of the coast changes probability and the complexity of the coast stabilization for economic activity. This method will allow to assess the dynamics of specific coastal sections and the processes intensity and, as a result – the stability of the coastal area.

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 Dynamical study of infochemical influences on tropic interaction of diffusive plankton system

2021 ◽  
Vol 3 (3) ◽  
Author(s):  
Satish Kumar Tiwari ◽  
Ravikant Singh ◽  
Nilesh Kumar Thakur
Keyword(s):  
Dimethyl Sulfide ◽  
Algal Bloom ◽  
Turing Instability ◽  
Model System ◽  
Ode Model ◽  
Estuarine Ecosystem ◽  
Dynamical Study ◽  
Oscillatory Dynamics ◽  
The Stability ◽  
Microzooplankton Grazing

AbstractWe propose a model for tropic interaction among the infochemical-producing phytoplankton and non-info chemical-producing phytoplankton and microzooplankton. Volatile information-conveying chemicals (infochemicals) released by phytoplankton play an important role in the food webs of marine ecosystems. Microzooplankton is an ecologically important grazer of phytoplankton for coexistence of a large number of phytoplankton species. Here, we discuss how information transferred by dimethyl sulfide shapes the interaction of phytoplankton. Phytoplankton deterrents may lead to propagation of IPP bloom. The interaction between IPP and microzooplankton follows the Beddington–DeAngelis-type functional response. Analytically, we discuss boundedness, stability and Turing instability of the model system. We perform numerical simulation for temporal (ODE model) as well as a spatial model system. Our numerical investigation shows that microzooplankton grazing refuse of IPP leads to oscillatory dynamics. Increasing diffusion coefficient of microzooplankton shows Turing instability. Time evolution also plays an important role in the stability of system dynamics. The results obtained in this paper are useful to understand the dominance of algal bloom in coastal and estuarine ecosystem.

On the Stability of the Linearly Related Modes of Certain Nonlinear Two-Degree-of-Freedom Systems

1961 ◽  
Vol 28 (1) ◽  
pp. 71-77 ◽  
Author(s):  
C. P. Atkinson
Keyword(s):  
Nonlinear Differential Equations ◽  
Mass Ratio ◽  
Positive Mass ◽  
Fourth Degree ◽  
Real Roots ◽  
General Stability ◽  
The Stability ◽  
The Masses ◽  
Spring Constants ◽  
Two Degree Of Freedom

This paper presents a method for analyzing a pair of coupled nonlinear differential equations of the Duffing type in order to determine whether linearly related modal oscillations of the system are possible. The system has two masses, a coupling spring and two anchor springs. For the systems studied, the anchor springs are symmetric but the masses are not. The method requires the solution of a polynomial of fourth degree which reduces to a quadratic because of the symmetric springs. The roots are a function of the spring constants. When a particular set of spring constants is chosen, roots can be found which are then used to set the necessary mass ratio for linear modal oscillations. Limits on the ranges of spring-constant ratios for real roots and positive-mass ratios are given. A general stability analysis is presented with expressions for the stability in terms of the spring constants and masses. Two specific examples are given.

Bifurcation and stability analysis of stagnation points for an asymmetric peristaltic transport

2020 ◽  
Vol 98 (2) ◽  
pp. 172-182 ◽  
Author(s):  
Kaleem Ullah ◽  
Nasir Ali
Keyword(s):  
Flow Field ◽  
Amplitude Ratio ◽  
Nonlinear Differential Equations ◽  
Global Bifurcation ◽  
Flow Region ◽  
Peristaltic Transport ◽  
Trapping Region ◽  
Long Wavelength ◽  
Stagnation Points ◽  
The Stability

This paper investigates the streamline topologies and stability of stagnation points and their bifurcations for an asymmetric peristaltic flow. The asymmetry of channel is due to the propagation of peristaltic waves with different phases and amplitudes on the flexible channel walls. An exact analytic solution of the flow problem subject to the constraints of low Reynolds number and long wavelength is obtained in wave frame of reference moving with wave velocity. A system of nonlinear differential equations is established to locate and classify the stagnation points in the flow domain. Different flow situations, manifested in the flow field, are categorized as: backward flow, trapping, and augmented flow. The transition from one situation to the other corresponds to bifurcation, which is explored graphically through local and global bifurcation diagrams. This analysis discloses the stability status of stagnation points and ranges of involved parameters in which various flow conditions appear in the flow field. It is concluded that the trapping in an asymmetric peristaltic transport can be reduced by increasing the phase difference of the channel walls. It is also found that the augmented flow region shrinks and the trapping region expands by increasing the amplitude ratio of the channel walls.

Dynamics of a Continuous System With Clearance and Motion Limiting Stops

1999 ◽  
Author(s):  
P. Metallidis ◽  
S. Natsiavas
Keyword(s):  
Piecewise Linear ◽  
Research Work ◽  
Continuous System ◽  
Continuous Model ◽  
Equation Of Motion ◽  
Model System ◽  
Periodic Motions ◽  
System Parameters ◽  
Rigid Rods ◽  
The Stability

Abstract The present study generalises previous research work on the dynamics of discrete oscillators with piecewise linear characteristics and investigates the response of a continuous model system with clearance and motion-limiting constraints. More specifically, in the first part of this work, an analysis is presented for determining exact periodic response of a periodically excited deformable rod, whose motion is constrained by a flexible obstacle. This methodology is based on the exact solution form obtained within response intervals where the system parameters remain constant and its behavior is governed by a linear equation of motion. The unknowns of the problem are subsequently determined by imposing an appropriate set of periodicity and matching conditions. The analytical part is complemented by a suitable method for determining the stability properties of the located periodic motions. In the second part of the study, the analysis is applied to several cases in order to investigate the effect of the system parameters on its dynamics. Special emphasis is placed on comparing these results with results obtained for similar but rigid rods. Finally, direct integration of the equation of motion in selected areas reveals the existence of motions, which are more complicated than the periodic motions determined analytically.

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