scholarly journals A bound on chaos from stability

2021 ◽  
Vol 2021 (11) ◽  
Author(s):  
Junggi Yoon
Keyword(s):  
Lyapunov Exponent ◽  
Quantum Chaos ◽  
Quantum Fluctuation ◽  
Soft Mode ◽  
Coadjoint Orbit ◽  
The Other ◽  
Maximal Lyapunov Exponent ◽  
Classical Analysis ◽  
Stable Orbit ◽  
The Stability

Abstract We explore the quantum chaos of the coadjoint orbit action of diffeomorphism group of S1. We study quantum fluctuation around a saddle point to evaluate the soft mode contribution to the out-of-time-ordered correlator. We show that the stability condition of the semi-classical analysis of the coadjoint orbit found in [1] leads to the upper bound on the Lyapunov exponent which is identical to the bound on chaos proven in [2]. The bound is saturated by the coadjoint orbit Diff(S1)/SL(2) while the other stable orbit Diff(S1)/U(1) where the SL(2, ℝ) is broken to U(1) has non-maximal Lyapunov exponent.

Uniformity of Magnification from Different Electron Microscopes

1967 ◽  
Vol 25 ◽  
pp. 32-33
Author(s):  
Godfrey C. Hoskins ◽  
V. Williams ◽  
V. Allison
Keyword(s):  
Diffraction Grating ◽  
The Other ◽  
Carbon Replica ◽  
Electron Microscopes ◽  
The Stability

The method demonstrated is an adaptation of a proven procedure for accurately determining the magnification of light photomicrographs. Because of the stability of modern electrical lenses, the method is shown to be directly applicable for providing precise reproducibility of magnification in various models of electron microscopes.A readily recognizable area of a carbon replica of a crossed-line diffraction grating is used as a standard. The same area of the standard was photographed in Phillips EM 200, Hitachi HU-11B2, and RCA EMU 3F electron microscopes at taps representative of the range of magnification of each. Negatives from one microscope were selected as guides and printed at convenient magnifications; then negatives from each of the other microscopes were projected to register with these prints. By deferring measurement to the print rather than comparing negatives, correspondence of magnification of the specimen in the three microscopes could be brought to within 2%.

scholarly journals Black Hole Algorithm for Sustainable Design of Counterfort Retaining Walls

2020 ◽  
Vol 12 (7) ◽  
pp. 2767 ◽  
Author(s):  
Víctor Yepes ◽  
José V. Martí ◽  
José García
Keyword(s):  
Black Hole ◽  
Sustainable Design ◽  
Retaining Walls ◽  
The Other ◽  
Trade Off ◽  
Construction Company ◽  
Geometric Variables ◽  
The Stability ◽  
The Cost ◽  
Black Hole Algorithm

The optimization of the cost and CO 2 emissions in earth-retaining walls is of relevance, since these structures are often used in civil engineering. The optimization of costs is essential for the competitiveness of the construction company, and the optimization of emissions is relevant in the environmental impact of construction. To address the optimization, black hole metaheuristics were used, along with a discretization mechanism based on min–max normalization. The stability of the algorithm was evaluated with respect to the solutions obtained; the steel and concrete values obtained in both optimizations were analyzed. Additionally, the geometric variables of the structure were compared. Finally, the results obtained were compared with another algorithm that solved the problem. The results show that there is a trade-off between the use of steel and concrete. The solutions that minimize CO 2 emissions prefer the use of concrete instead of those that optimize the cost. On the other hand, when comparing the geometric variables, it is seen that most remain similar in both optimizations except for the distance between buttresses. When comparing with another algorithm, the results show a good performance in optimization using the black hole algorithm.

scholarly journals A Fractional SAIDR Model in the Frame of Atangana–Baleanu Derivative

2021 ◽  
Vol 5 (2) ◽  
pp. 32
Author(s):  
Esmehan Uçar ◽  
Sümeyra Uçar ◽  
Fırat Evirgen ◽  
Necati Özdemir
Keyword(s):  
Existence And Uniqueness ◽  
Laplace Transformation ◽  
Cell Phones ◽  
Mobile Network ◽  
The Other ◽  
Banach Fixed Point Theorem ◽  
Propagation Models ◽  
Computer Worms ◽  
Computer Viruses ◽  
The Stability

It is possible to produce mobile phone worms, which are computer viruses with the ability to command the running of cell phones by taking advantage of their flaws, to be transmitted from one device to the other with increasing numbers. In our day, one of the services to gain currency for circulating these malignant worms is SMS. The distinctions of computers from mobile devices render the existing propagation models of computer worms unable to start operating instantaneously in the mobile network, and this is particularly valid for the SMS framework. The susceptible–affected–infectious–suspended–recovered model with a classical derivative (abbreviated as SAIDR) was coined by Xiao et al., (2017) in order to correctly estimate the spread of worms by means of SMS. This study is the first to implement an Atangana–Baleanu (AB) derivative in association with the fractional SAIDR model, depending upon the SAIDR model. The existence and uniqueness of the drinking model solutions together with the stability analysis are shown through the Banach fixed point theorem. The special solution of the model is investigated using the Laplace transformation and then we present a set of numeric graphics by varying the fractional-order θ with the intention of showing the effectiveness of the fractional derivative.

scholarly journals Competing Conventions with Costly Information Acquisition

Games ◽  
2021 ◽  
Vol 12 (3) ◽  
pp. 53
Author(s):  
Roberto Rozzi
Keyword(s):  
Information Acquisition ◽  
Evolutionary Model ◽  
Equilibrium Selection ◽  
The Other ◽  
Group Interactions ◽  
Social Coordination ◽  
Long Run ◽  
Stochastic Stability Analysis ◽  
The Stability ◽  
The Cost

We consider an evolutionary model of social coordination in a 2 × 2 game where two groups of players prefer to coordinate on different actions. Players can pay a cost to learn their opponent’s group: if they pay it, they can condition their actions concerning the groups. We assess the stability of outcomes in the long run using stochastic stability analysis. We find that three elements matter for the equilibrium selection: the group size, the strength of preferences, and the information’s cost. If the cost is too high, players never learn the group of their opponents in the long run. If one group is stronger in preferences for its favorite action than the other, or its size is sufficiently large compared to the other group, every player plays that group’s favorite action. If both groups are strong enough in preferences, or if none of the groups’ sizes is large enough, players play their favorite actions and miscoordinate in inter-group interactions. Lower levels of the cost favor coordination. Indeed, when the cost is low, in inside-group interactions, players always coordinate on their favorite action, while in inter-group interactions, they coordinate on the favorite action of the group that is stronger in preferences or large enough.

Hamiltonian Chaos in a Model Alveolus

2008 ◽  
Vol 131 (1) ◽  
Author(s):  
F. S. Henry ◽  
F. E. Laine-Pearson ◽  
A. Tsuda
Keyword(s):  
Reynolds Number ◽  
Fixed Point ◽  
Lyapunov Exponent ◽  
Fine Particles ◽  
Hamiltonian Dynamics ◽  
Maximal Lyapunov Exponent ◽  
Poincaré Sections ◽  
Pulmonary Acinus ◽  
Hamiltonian Chaos ◽  
Poincare Sections

In the pulmonary acinus, the airflow Reynolds number is usually much less than unity and hence the flow might be expected to be reversible. However, this does not appear to be the case as a significant portion of the fine particles that reach the acinus remains there after exhalation. We believe that this irreversibility is at large a result of chaotic mixing in the alveoli of the acinar airways. To test this hypothesis, we solved numerically the equations for incompressible, pulsatile, flow in a rigid alveolated duct and tracked numerous fluid particles over many breathing cycles. The resulting Poincaré sections exhibit chains of islands on which particles travel. In the region between these chains of islands, some particles move chaotically. The presence of chaos is supported by the results of an estimate of the maximal Lyapunov exponent. It is shown that the streamfunction equation for this flow may be written in the form of a Hamiltonian system and that an expansion of this equation captures all the essential features of the Poincaré sections. Elements of Kolmogorov–Arnol’d–Moser theory, the Poincaré–Birkhoff fixed-point theorem, and associated Hamiltonian dynamics theory are then employed to confirm the existence of chaos in the flow in a rigid alveolated duct.

A Biomechanical Evaluation of Three Forms of Internal Fixation Used in Ankle Arthrodesis

1994 ◽  
Vol 15 (6) ◽  
pp. 297-300 ◽  
Author(s):  
Michael P. Dohm ◽  
James B. Benjamin ◽  
Jeffrey Harrison ◽  
John A. Szivek
Keyword(s):  
Internal Fixation ◽  
Plate Fixation ◽  
Ankle Arthrodesis ◽  
Biomechanical Study ◽  
The Other ◽  
Fixation Failure ◽  
Plate Group ◽  
Biomechanical Evaluation ◽  
The Stability ◽  
Fibular Strut

A biomechanical study was undertaken to evaluate the relative stability of three types of internal fixation used for ankle arthrodesis. Crossed screw fixation, RAF fibular strut fixation, and T-plate fixation were tested in 30 cadaver ankles using an MTS machine. T-plate fixation consistantly provided the stiffest construct when compared with the other types of fixation. Failure occurred by distraction of bony surfaces, posterior to the plane of fixation, in the crossed screw and RAF groups. In contrast, failure in the T-plate group occurred through compression of bone anterior to the midcoronal plane of the tibia. Although the stability of fixation is only one factor in determining the success or failure of ankle arthrodesis, the results of this study would support T-plate fixation over the other forms tested.

scholarly journals Tetracycline Induces Stabilization of mRNA in Bacillus subtilis

2002 ◽  
Vol 184 (4) ◽  
pp. 889-894 ◽  
Author(s):  
Yi Wei ◽  
David H. Bechhofer
Keyword(s):  
Bacillus Subtilis ◽  
Mrna Stability ◽  
The Other ◽  
Leader Region ◽  
Subinhibitory Concentration ◽  
Coding Sequence ◽  
Mrna Stabilization ◽  
Threefold Increase ◽  
The Stability

ABSTRACT The tet(L) gene of Bacillus subtilis confers low-level tetracycline (Tc) resistance. Previous work examining the >20-fold-inducible expression of tet(L) by Tc demonstrated a 12-fold translational induction. Here we show that the other component of tet(L) induction is at the level of mRNA stabilization. Addition of a subinhibitory concentration of Tc results in a two- to threefold increase in tet(L) mRNA stability. Using a plasmid-borne derivative of tet(L) with a large in-frame deletion of the coding sequence, the mechanism of Tc-induced stability was explored by measuring the decay of tet(L) mRNAs carrying specific mutations in the leader region. The results of these experiments, as well as experiments with a B. subtilis strain that is resistant to Tc due to a mutation in the ribosomal S10 protein, suggest different mechanisms for the effects of Tc on translation and on mRNA stability. The key role of the 5" end in determining mRNA stability was confirmed in these experiments. Surprisingly, the stability of several other B. subtilis mRNAs was also induced by Tc, which indicates that addition of Tc may result in a general stabilization of mRNA.

Dynamic stability of running: The effects of speed and leg amputations on the maximal Lyapunov exponent

2013 ◽  
Vol 23 (4) ◽  
pp. 043131 ◽  
Author(s):  
Nicole Look ◽  
Christopher J. Arellano ◽  
Alena M. Grabowski ◽  
William J. McDermott ◽  
Rodger Kram ◽  
...  
Keyword(s):  
Lyapunov Exponent ◽  
Dynamic Stability ◽  
Maximal Lyapunov Exponent

Existence of Periodic Solution for Equation of Motion of Simple Beams With Harmonically Variable Length

1995 ◽  
Author(s):  
Ebrahim Esmailzadeh ◽  
Gholamreza Nakhaie-Jazar ◽  
Bahman Mehri
Keyword(s):  
Periodic Solution ◽  
Fixed Point ◽  
Nonlinear Function ◽  
Axial Direction ◽  
Equation Of Motion ◽  
The Other ◽  
Sufficient Condition ◽  
Vibrating String ◽  
The Stability ◽  
Special Case

Abstract The transverse vibrating motion of a simple beam with one end fixed while driven harmonically along its axial direction from the other end is investigated. For a special case of zero value for the rigidity of the beam, the system reduces to that of a vibrating string with the corresponding equation of its motion. The sufficient condition for the periodic solution of the beam is then derived by means of the Green’s function and Schauder’s fixed point theorem. The criteria for the stability of the system is well defined and the condition for which the performance of the beam behaves as a nonlinear function is stated.

The Principles Of Typological Study Of Transposition In The Uzbek And Korean Languages

2021 ◽  
Vol 03 (03) ◽  
pp. 151-162
Author(s):  
Nazarova Shakhlo ◽  
Keyword(s):  
The Other ◽  
Language Family ◽  
Word Structure ◽  
Word Stress ◽  
Word Forms ◽  
The Stability

Like Uzbek, Korean belongs to the Altaic language family, and the sources assume that: a) Korean word forms are agglutinative schemes based on the stem + affix, b) sentences are based on the syntactic scheme of “possessive + second part + cut”, c) the stability of word stress and expiratory character, etc. Additionaly in a word structure the following can be divided: 1) 뾐ꭅ덽: 뾐 + ꭅ + 덽 ; 頝ꃝꍡ겑꽽鲙: 頝 + -ꃝꍡ- + -겑- + -꽽- + -鲙such that cores and appendages can be joined one after the other and separated; 2) according to the function of affix morphemes, «뾐-, -덽-, -ꃝꍡ-» word building, «-겑-, -꽽-, -鲙» 3) the formation of transpositive and non-transpositive artificial words by means of word-forming suffixes, 4) the relative freedom of the transpositive connection between independent, auxiliary words and morphemes also point to this genetic connection.

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