Centroidal frames in dynamical systems I. Point vortices

1992 ◽  
Vol 439 (1907) ◽  
pp. 441-463 ◽  
Keyword(s):  
Point Vortices ◽  
Centre Of Mass ◽  
Permutation Symmetry ◽  
Chaotic Motions ◽  
Small Perturbations ◽  
New Class ◽  
Angular Velocities ◽  
Mass Frame ◽  
Definition Of ◽  
Asymptotic Symmetries

The dynamics of point vortices is studied in Part I of the paper. It is well known that the (translational) centre-of-mass frame decomposes the motion of a mechanical system into simpler components. It is less known, however, that special rotational frames have also been suggested for the same purpose. In contrast to the centre-of-mass frame, the angular velocities of these rotational frames are not given explicitly that limits their application to small perturbations of rigid body rotations. A new class of centroidal frames (CF) related to different groups such as translation, rotation, dilation, etc., is introduced in this paper. The CFS decompose the motion of point vortices into a group and a relative components without restriction to small perturbations of pure group motions. The definition of the CFS is based on an averaging of motion or on minimization of energy of the relative motion, where an appropriate energy function is expressed through generators of the group action. As a result, the linear and angular velocities as well as other characteristics of the CFS can be obtained explicitly. Part I of the paper presents application of the CFS to a hamiltonian system of point vortices. Examples of integrable and chaotic motions in the CFS visualize dynamical patterns that are completely hidden in the conventional fixed frame (ff). Motions which look like chaotic in the FF reveal a variety of stable and unstable structures in the CFS. Quasi-periodic and chaotic motions coexist for all energies and the CFS permit to clearly distinguish between them. A new phenomenon of asymptotic symmetries (in rotational CFS) of some chaotic motions is discovered. This is related to a permutation symmetry of the hamiltonian.

scholarly journals Some Inequalities for LR-$$\left({h}_{1}, {h}_{2}\right)$$-Convex Interval-Valued Functions by Means of Pseudo Order Relation

2021 ◽  
Vol 14 (1) ◽  
Author(s):  
Muhammad Bilal Khan ◽  
Muhammad Aslam Noor ◽  
Khalida Inayat Noor ◽  
Kottakkaran Sooppy Nisar ◽  
Khadiga Ahmed Ismail ◽  
...  
Keyword(s):  
Applied Mathematics ◽  
Critical Role ◽  
Order Relation ◽  
Strong Relationship ◽  
New Class ◽  
Starting Point ◽  
Interval Valued Function ◽  
Fejér Inequality ◽  
Definition Of ◽  
Interval Valued

AbstractIn both theoretical and applied mathematics fields, integral inequalities play a critical role. Due to the behavior of the definition of convexity, both concepts convexity and integral inequality depend on each other. Therefore, the relationship between convexity and symmetry is strong. Whichever one we work on, we introduced the new class of generalized convex function is known as LR-$$\left({h}_{1}, {h}_{2}\right)$$ h 1 , h 2 -convex interval-valued function (LR-$$\left({h}_{1}, {h}_{2}\right)$$ h 1 , h 2 -IVF) by means of pseudo order relation. Then, we established its strong relationship between Hermite–Hadamard inequality (HH-inequality)) and their variant forms. Besides, we derive the Hermite–Hadamard–Fejér inequality (HH–Fejér inequality)) for LR-$$\left({h}_{1}, {h}_{2}\right)$$ h 1 , h 2 -convex interval-valued functions. Several exceptional cases are also obtained which can be viewed as its applications of this new concept of convexity. Useful examples are given that verify the validity of the theory established in this research. This paper’s concepts and techniques may be the starting point for further research in this field.

scholarly journals Towards a Theory for Unintended Consequences in Engineering Design

2019 ◽  
Vol 1 (1) ◽  
pp. 3411-3420
Author(s):  
Hannah Walsh ◽  
Andy Dong ◽  
Irem Tumer
Keyword(s):  
Failure Analysis ◽  
Engineering Design ◽  
Bifurcation Analysis ◽  
Real World ◽  
Unintended Consequences ◽  
Novel Technologies ◽  
New Class ◽  
Failure State ◽  
Engineered Systems ◽  
Definition Of

AbstractConventional failure analysis ignores a growing challenge in the responsible implementation of novel technologies into engineered systems - unintended consequences, which impact the engineered system itself and other systems including social and environmental systems. In this paper, a theory for unintended consequences is developed. The paper proposes a new definition of unintended consequences as behaviors that are not intentionally designed-into an engineered system yet occur even when a system is operating nominally, that is, not in a failure state as conventionally understood. It is argued that the primary cause for this difference is the bounded rationality of human designers. The formation of unintended consequences is modeled with system dynamics, using a specific real-world example, and bifurcation analysis. The paper develops propositions to guide research in the development of new design methods that could mitigate or control the occurrence and impact of unintended consequences. The end goal of the research is to create a new class of failure analysis tools to manage unintended consequences responsibly to facilitate engineering design for a more sustainable future.

Super-Penrose process

2020 ◽  
Vol 35 (02n03) ◽  
pp. 2040058
Author(s):  
O. B. Zaslavskii
Keyword(s):  
Black Hole ◽  
Flat Space ◽  
Space Time ◽  
Centre Of Mass ◽  
Rotating Black Hole ◽  
Mass Frame ◽  
Penrose Process ◽  
Energy Formula ◽  
Full Classification

If two particles collide near a rotating black hole, their energy in the centre of mass frame can become unbounded under certain conditions. In doing so, the Killing energy [Formula: see text] of debris at infinity is, in general, remain restricted. If [Formula: see text] is also unbounded, this is called the super-Penrose process. We elucidate when such a process is possible and give full classification of corresponding relativistic objects for rotating space-times. We also discuss the case of a pure electric super-Penrose process that is valid even in the flat space-time. The key role in consideration is played by the Wald inequalities.

scholarly journals Inhomogeneous spatial point processes by location-dependent scaling

2003 ◽  
Vol 35 (02) ◽  
pp. 319-336 ◽  
Author(s):  
Ute Hahn ◽  
Eva B. Vedel Jensen ◽  
Marie-Colette van Lieshout ◽  
Linda Stougaard Nielsen
Keyword(s):  
Point Processes ◽  
Spatial Point Processes ◽  
New Approach ◽  
Local Scaling ◽  
New Class ◽  
Spatial Point ◽  
New Process ◽  
Markov Point Processes ◽  
Global Scaling ◽  
Definition Of

A new class of models for inhomogeneous spatial point processes is introduced. These locally scaled point processes are modifications of homogeneous template point processes, having the property that regions with different intensities differ only by a scale factor. This is achieved by replacing volume measures used in the density with locally scaled analogues defined by a location-dependent scaling function. The new approach is particularly appealing for modelling inhomogeneous Markov point processes. Distance-interaction and shot noise weighted Markov point processes are discussed in detail. It is shown that the locally scaled versions are again Markov and that locally the Papangelou conditional intensity of the new process behaves like that of a global scaling of the homogeneous process. Approximations are suggested that simplify calculation of the density, for example, in simulation. For sequential point processes, an alternative and simpler definition of local scaling is proposed.

Bifurcations and Chaos in Forced, Coupled Pendula

2001 ◽  
Author(s):  
Kazuyuki Yagasaki
Keyword(s):  
Averaging Method ◽  
Nonlinear Behavior ◽  
Melnikov Method ◽  
Original System ◽  
Chaotic Motions ◽  
Small Perturbations ◽  
Small Oscillations ◽  
Codimension One ◽  
Averaged Systems ◽  
Direct Numerical Integration

Abstract We consider forced, coupled pendula and show that they exhibit very complicated dynamics using the averaging method and Melnikov-type techniques. First, the averaged system for small oscillations of the pendula near the hanging state is analyzed. Codimension-one and -two local bifurcations at which several non-synchronized periodic orbits and quasiperiodic orbits are born in the original system are detected. The validity of the theoretical results is demonstrated by comparison with direct numerical integration results. Moreover, chaotic motions, which result from the Shilnikov type phenomena in the averaged systems, are observed in numerical simulations. Second, the second-order averaging method is applied to small perturbations of rotary orbits with no damping and external forcing. Analyzing the averaged system, we can describe nonlinear behavior in the original system. Finally, using a generalization of Melnikov method, we prove the occurrence of many other homo-clinic phenomena, which also yield chaotic dynamics.

What Are Virtual Manipulatives?

2002 ◽  
Vol 8 (6) ◽  
pp. 372-377
Author(s):  
Patricia S. Moyer ◽  
Johnna J. Bolyard ◽  
Mark A. Spikell
Keyword(s):  
Teaching And Learning ◽  
Virtual Manipulatives ◽  
The Internet ◽  
New Approach ◽  
New Class ◽  
Working Definition ◽  
Teaching And Learning Mathematics ◽  
Learning Mathematics ◽  
Definition Of ◽  
Classroom Use

As a result of innovations in technology, the prevalence of the Internet, and the increasing availability of computers in classrooms and homes, an enhanced approach for teaching and learning mathematics using manipulatives and computers is emerging. This new approach essentially creates a new class of manipulatives, called virtual manipulatives, as well as new capabilities, or toolkits, for computer programs that use visual representations. These new virtual manipulatives have all the useful properties of existing computer manipulatives while overcoming many of their disadvantages, yet very little is known or written about them. The purpose of this article is to establish a working definition of virtual manipulatives, highlight examples of virtual manipulatives on the Internet, and discuss their current and potential classroom use.

Generation of Periodic Orbits from Chaotic Attractors of Weakly Coupled Diode Resonators

1997 ◽  
Vol 07 (04) ◽  
pp. 897-902
Author(s):  
Jong Cheol Shin ◽  
Sook-Il Kwun ◽  
Youngtae Kim
Keyword(s):  
Periodic Orbits ◽  
Chaotic Dynamics ◽  
Chaotic Attractors ◽  
Unstable Periodic Orbits ◽  
Chaotic Motions ◽  
Small Perturbations ◽  
Controlling Chaos ◽  
Weakly Coupled ◽  
Dynamical Properties

We have designed coupled diode resonators to study the effect of small perturbations due to weak symmetric coupling on chaotic dynamics. Our experiment clearly demonstrated that chaos of the diode resonators was suppressed so that chaotic motions were converted into periodic ones with small modifications to the attractor when an appropriate coupling signal perturbed the diode resonators. Many unstable periodic orbits were stabilized and they were very stable depending on the dynamical properties of the coupling signals. Our results suggest that coupling of signals belonging to the same class is effective in controlling chaos.

scholarly journals Enviromics in breeding: applications and perspectives on envirotypic-assisted selection

2019 ◽  
Author(s):  
Rafael T. Resende ◽  
Hans-Peter Piepho ◽  
Orzenil B. Silva-Junior ◽  
Fabyano F. e Silva ◽  
Marcos Deon V. de Resende ◽  
...  
Keyword(s):  
Genotype By Environment Interaction ◽  
Environment Interaction ◽  
New Class ◽  
Strategic Plans ◽  
Environmental Attributes ◽  
Current Perspective ◽  
Genetic Resources Management ◽  
Definition Of ◽  
Experimental Trials

AbstractGenotype by Environment interaction (G × E) studies have focused mainly on estimating genetic parameters over a limited number of experimental trials. However, recent Geographic Information System (GIS) techniques have opened new frontiers for understanding and dealing with G × E. These advances allow increasing selection accuracy across all sites of interest, including those where experimental trials have not yet been deployed. Here, we introduce the term Enviromics under an envirotypic-assisted breeding framework and propose the GIS-GE method, i.e. a geospatial tool to maximize genetic gains by predicting the phenotypic performance of unobserved genotypes using “enviromic markers”. In summary, a particular site represents a set of envirotypes, each one representing a set of environmental factors that interact with the genetic background of genotypes, thus resulting in informative re-rankings to make decisions over different environments. Based on a simulated case study, we show that GIS-GE allows accurate (i) matching of genotypes to their most appropriate sites; (ii) definition of breeding areas that have high genetic correlation to ensure selection gains across environments; and (iii) indication of the best sites to carry out experiments for further analysis based on environments that maximize heritability. Envirotyping techniques provide a new class of markers for genetic studies, which are inexpensive, increasingly available and transferable across species. We envision a promising future for the integration of the Enviromics approach into breeding when coupled with next-generation genotyping/phenotyping and powerful statistical modeling of genetic diversity. Environmental scenarios can also be improved using information from strategic plans for biodiversity and genetic resources management, especially in the current perspective of dynamic climate change.Key messageWe propose the application of Enviromics to breeding practice, by which the similarity among sites assessed on an “omics” scale of environmental attributes drives the prediction of unobserved genotypes.

scholarly journals Lie theory for asymptotic symmetries in general relativity: The BMS Group

2022 ◽  
Author(s):  
David Nicolas Prinz ◽  
Alexander Schmeding
Keyword(s):  
General Relativity ◽  
Lie Group ◽  
Group Structure ◽  
Symmetry Groups ◽  
Asymptotic Symmetry ◽  
Infinite Dimensional ◽  
Real Analytic ◽  
Definition Of ◽  
Future Work ◽  
Asymptotic Symmetries

Abstract We study the Lie group structure of asymptotic symmetry groups in General Relativity from the viewpoint of infinite-dimensional geometry. To this end, we review the geometric definition of asymptotic simplicity and emptiness due to Penrose and the coordinate-wise definition of asymptotic flatness due to Bondi et al. Then we construct the Lie group structure of the Bondi--Metzner--Sachs (BMS) group and discuss its Lie theoretic properties. We find that the BMS group is regular in the sense of Milnor, but not real analytic. This motivates us to conjecture that it is not locally exponential. Finally, we verify the Trotter property as well as the commutator property. As an outlook, we comment on the situation of related asymptotic symmetry groups. In particular, the much more involved situation of the Newman--Unti group is highlighted, which will be studied in future work.

scholarly journals Classification of Partially Regular Microreliefs Formed on the End Surfaces of Rotary Bodies

2020 ◽  
pp. 129-135
Author(s):  
Volodymyr Dzyura ◽  
Keyword(s):  
Mutual Arrangement ◽  
Relative Area ◽  
Scientific Publications ◽  
New Class ◽  
Lack Of Information ◽  
Dimensional Parameters ◽  
Definition Of ◽  
First Time ◽  
Rotating Bodies

The aim of the article is to classify partially regular microreliefs that are formed on the end surfaces of rotating bodies. The article analyzes the known classifications of regular microreliefs in scientific publications and regulations. The parameters by which regular microreliefs are classified and their characteristics are analyzed. The lack of information on the classification of partially regular microreliefs formed on the end surfaces of rotating bodies as a new class of microreliefs has been established. The proposed classification reveals a set of options for the implementation of partially regular microreliefs formed on the end surfaces of bodies of rotation and their characteristics. For the first time the classification of partially regular microreliefs that are formed on the end surfaces of rotating bodies is offered, carried out on the basis of features of kinematics of technological process. It c can be a basis for creation of their mathematical models and definition of the relative area of vibro-rolling. Signs of classification are proposed to take: methods of forming a partially regular microrelief; the shape of the centerline of continuous regular micro-irregularities; mutual arrangement of adjacent grooves; mutual placement of axial lines of continuous regular micro-inequalities; groove shapes. Each of these features is divided into certain sub-features, which consist of the corresponding characteristics, which are expressed by the elements of the mode of vibration rolling, the dimensional parameters of the elements of the grooves, their mutual placement. For the first time, analytical dependences were obtained to determine the parameter of partially regular microreliefs classification formed on the end surfaces of rotating bodies by the nature of the change in the radii of the axial lines and their axial steps.

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