scholarly journals Decay of Hamiltonian Breathers Under Dissipation

2020 ◽  
Vol 380 (1) ◽  
pp. 71-102
Author(s):  
Jean-Pierre Eckmann ◽  
C. Eugene Wayne
Keyword(s):  
Phase Space ◽  
Systems Theory ◽  
Hamiltonian Systems ◽  
Initial Conditions ◽  
Asymptotic Estimates ◽  
Discrete Nonlinear Schrödinger Equation ◽  
Rate Of Evolution ◽  
Energy Flows ◽  
The Family ◽  
Almost All

Abstract We study metastable behavior in a discrete nonlinear Schrödinger equation from the viewpoint of Hamiltonian systems theory. When there are $$n<\infty $$ n < ∞ sites in this equation, we consider initial conditions in which almost all the energy is concentrated in one end of the system. We are interested in understanding how energy flows through the system, so we add a dissipation of size $$\gamma $$ γ at the opposite end of the chain, and we show that the energy decreases extremely slowly. Furthermore, the motion is localized in the phase space near a family of breather solutions for the undamped system. We give rigorous, asymptotic estimates for the rate of evolution along the family of breathers and the width of the neighborhood within which the trajectory is confined.

scholarly journals ON PERIODIC SOLUTIONS OF 2-PERIODIC LYNESS' EQUATIONS

2013 ◽  
Vol 23 (04) ◽  
pp. 1350071 ◽  
Author(s):  
GUY BASTIEN ◽  
VÍCTOR MAÑOSA ◽  
MARC ROGALSKI
Keyword(s):  
Periodic Solutions ◽  
Initial Conditions ◽  
Periodic Sequences ◽  
The Family ◽  
Existence Of Periodic Solutions ◽  
Almost All

We study the existence of periodic solutions of the nonautonomous periodic Lyness' recurrenceun+2 = (an + un+1)/un, where {an}n is a cycle with positive values a, b and with positive initial conditions. It is known that for a = b = 1 all the sequences generated by this recurrence are 5-periodic. We prove that for each pair (a, b) ≠ (1, 1) there are infinitely many initial conditions giving rise to periodic sequences, and that the family of recurrences have almost all the even periods. If a ≠ b, then any odd period, except 1, appears.

scholarly journals Orbit Classification and Sensitivity Analysis in Dynamical Systems Using Surrogate Models

2021 ◽  
Vol 2 (1) ◽  
pp. 5
Author(s):  
Katharina Rath ◽  
Christopher G. Albert ◽  
Bernd Bischl ◽  
Udo von Toussaint
Keyword(s):  
Sensitivity Analysis ◽  
Phase Space ◽  
Dynamical Systems ◽  
Hamiltonian Systems ◽  
Initial Conditions ◽  
Plasma Boundary ◽  
Surrogate Models ◽  
Alpha Particles ◽  
Hamiltonian Flow ◽  
Chaotic Orbits

Dynamics of many classical physics systems are described in terms of Hamilton’s equations. Commonly, initial conditions are only imperfectly known. The associated volume in phase space is preserved over time due to the symplecticity of the Hamiltonian flow. Here we study the propagation of uncertain initial conditions through dynamical systems using symplectic surrogate models of Hamiltonian flow maps. This allows fast sensitivity analysis with respect to the distribution of initial conditions and an estimation of local Lyapunov exponents (LLE) that give insight into local predictability of a dynamical system. In Hamiltonian systems, LLEs permit a distinction between regular and chaotic orbits. Combined with Bayesian methods we provide a statistical analysis of local stability and sensitivity in phase space for Hamiltonian systems. The intended application is the early classification of regular and chaotic orbits of fusion alpha particles in stellarator reactors. The degree of stochastization during a given time period is used as an estimate for the probability that orbits of a specific region in phase space are lost at the plasma boundary. Thus, the approach offers a promising way to accelerate the computation of fusion alpha particle losses.

Analisis Perbandingan Manajemen Keuangan Ojek Online Dan Ojek Reguler Studi Kasus Kecamatan Duren Sawit Jakarta Timur

Liquidity ◽  
2018 ◽  
Vol 7 (1) ◽  
pp. 41-52
Author(s):  
M. Koesmawan ◽  
Darwin Erhandy ◽  
Dede Dahlan
Keyword(s):  
Financial Management ◽  
Average Income ◽  
Savings And Loans ◽  
Financial Difficulties ◽  
The Family ◽  
Family Finances ◽  
The Subject ◽  
Almost All

In order to meet the needs of living which consists of primary as well as secondary needs, human can work in either a formal or an informal job. One of the informal jobs that is became the subject of this research was to become an ojek driver. Ojek is a ranting motorcycle.  Revenue of ojek drivers, accordingly, should be well managed following the concept of financial management. This research was conducted for the driver of the online motorcycle drivers as well as the regular motorcycle drivers they are called “The Ojek”. Ojek’s location is in Kecamatan (subdistrict) Duren Sawit, East Jakarta with 70 drivers of ojeks. The online ojeks earn an average of Rp 100,000 per day, can save Rp 11,000 to 21,000 per day, while, the regular ojek has an average income per day slightly lower amounted to Rp 78,500, this kind of ojeks generally have other businesses and always record the outflow of theirs money. Both the online and regular ojeks feel a tight competition in getting passengers, but their income can help the family finances and both ojeks want a cooperative especially savings and loans, especially to overcome the urgent financial difficulties. Almost all rivers, do not dare to borrow money. They are afraid of can not refund the money as scheduled.

Two new species of the genus Syngastes (Copepoda, Harpacticoida, Tegastidae) from South Korea

Crustaceana ◽  
2016 ◽  
Vol 89 (4) ◽  
pp. 431-458 ◽  
Author(s):  
Jong Guk Kim ◽  
Jong Guk Kim ◽  
Tae Won Jung ◽  
Jong Guk Kim ◽  
Tae Won Jung ◽  
...  
Keyword(s):  
New Species ◽  
South Korea ◽  
First Record ◽  
Exopodal Segment ◽  
Key To Species ◽  
Korean Waters ◽  
The Family ◽  
Two New Species ◽  
Almost All

Herein two new species of the genusSyngastesMonard, 1924 are described from South Korea, with detailed descriptions and illustrations. Both new copepods,Syngastesmulticavussp. nov. andS. pseudofoveatussp. nov., have two inner setae on the first exopodal segment of P2 and P3.Syngastesmulticavussp. nov. most closely resemblesS. gibbosusBartsch, 1999 reported from Australia, as they both have a five-segmented antennule in the female. However,Syngastesmulticavussp. nov. has a rounded body outline instead of the gibbose outline observed inS. gibbosus.Syngastespseudofoveatussp. nov. resemblesS. foveatusBartsch, 1994 in almost all aspects. However, they differ clearly in the number of setae on the first exopodal segment of P2 and P3. We also provide a key to species of the genusSyngastesworldwide. The present study is the first record of the family Tegastidae in Korean waters.

3D Printing — The Basins of Tristability in the Lorenz System

2017 ◽  
Vol 27 (08) ◽  
pp. 1750128 ◽  
Author(s):  
Anda Xiong ◽  
Julien C. Sprott ◽  
Jingxuan Lyu ◽  
Xilu Wang
Keyword(s):  
Lorenz System ◽  
Initial Conditions ◽  
Equilibrium Points ◽  
Basins Of Attraction ◽  
Symmetric Pair ◽  
State Space Approach ◽  
3D Printers ◽  
The Lorenz System ◽  
Almost All ◽  
Space Approach

The famous Lorenz system is studied and analyzed for a particular set of parameters originally proposed by Lorenz. With those parameters, the system has a single globally attracting strange attractor, meaning that almost all initial conditions in its 3D state space approach the attractor as time advances. However, with a slight change in one of the parameters, the chaotic attractor coexists with a symmetric pair of stable equilibrium points, and the resulting tri-stable system has three intertwined basins of attraction. The advent of 3D printers now makes it possible to visualize the topology of such basins of attraction as the results presented here illustrate.

scholarly journals The Lusternik–Fet theorem for autonomous Tonelli Hamiltonian systems on twisted cotangent bundles

2016 ◽  
Vol 08 (03) ◽  
pp. 545-570 ◽  
Author(s):  
Luca Asselle ◽  
Gabriele Benedetti
Keyword(s):  
Periodic Orbits ◽  
Hamiltonian Systems ◽  
Symplectic Form ◽  
Critical Value ◽  
Closed Manifold ◽  
Hamiltonian Flow ◽  
Cotangent Bundles ◽  
Almost All

Let [Formula: see text] be a closed manifold and consider the Hamiltonian flow associated to an autonomous Tonelli Hamiltonian [Formula: see text] and a twisted symplectic form. In this paper we study the existence of contractible periodic orbits for such a flow. Our main result asserts that if [Formula: see text] is not aspherical, then contractible periodic orbits exist for almost all energies above the maximum critical value of [Formula: see text].

Resolving the Lourinia armata (Claus, 1866) complex with remarks on the monophyletic status of Louriniidae, Monard 1927 (Copepoda: Harpacticoida)

Zootaxa ◽  
2021 ◽  
Vol 5051 (1) ◽  
pp. 346-386
Author(s):  
SÜPHAN KARAYTUĞ ◽  
SERDAR SAK ◽  
ALP ALPER ◽  
SERDAR SÖNMEZ
Keyword(s):  
Comparative Evaluation ◽  
Species Complex ◽  
Detailed Examination ◽  
The Other ◽  
Phylogenetic Position ◽  
Nicobar Island ◽  
Other Hand ◽  
The Family ◽  
Close Relationship ◽  
Almost All

An attempt was made to test if Lourinia armata (Claus, 1866)—as it is currently diagnosed—represents a species complex. Detailed examination and comparisons of several specimens collected from different localities suggest that L. armata indeed represents a complex of four closely related morphospecies that can be differentiated from one another by only detailed observations. One of the four species is identified as Lourinia aff. armata and the other three species are described as new to science and named as Lourinia wellsi sp. nov., L. gocmeni sp. nov., and L. aldabraensis sp. nov. Detailed review of previous species records indicates that the genus Lourinia Wilson, 1924 is distributed worldwide. Ceyloniella nicobarica Sewell, 1940, originally described from Nicobar Island and previously considered a junior subjective synonym of L. armata is reinstated as Lourinia nicobarica (Sewell, 1940) comb. nov. on the basis of the unique paddle-shaped caudal ramus seta V. It is postulated that almost all of these records are unreliable in terms of representing true Lourinia aff. armata described herein. On the other hand, the comparative evaluation of the illustrations and descriptions in the published literature indicates the presence of several new species waiting to be discovered in the genus Lourinia.                 It has been determined that, according to updated modern keys, the recent inclusion of the monotypic genus Archeolourinia Corgosinho & Schizas, 2013 in the Louriniidae is not justified since Archeolourinia shermani Corgosinho & Schizas, 2013 does not belong to this family but should be assigned to the Canthocamptidae. On the other hand, it has been argued that the exact phylogenetic position of the Louriniidae still remains problematic since none of the diagnostic characters supports the monophyly of the family within the Oligoarthra. It has also been argued that the close relationship between Louriniidae and Canthocamptidae is supported since both families share the homologous sexual dimorphism (apophysis) on P3 endopod. The most important characteristic that can possibly be used to define Louriniidae is the reduction of maxilliped.  

THE PATIENT BOY—A POPULAR LESSON, READ TO CHILDREN IN THE 1820'S

PEDIATRICS ◽  
1969 ◽  
Vol 43 (4) ◽  
pp. 526-526
Author(s):  
T. E. C.
Keyword(s):  
The Family ◽  
Almost All

The story below depicts a favorite subject of those who wrote for children in the early days of our country. The inebriated father leading his family inexorably into destitution by his intemperance is counterbalanced by a son who holds the family together. During the last century many children cried over this and similar stories. The Patient Boy There was a journeyman bricklayer in this town, a good workman, but a very drunken idle fellow; he spent at the dram shop almost all he earned, and left his wife and children to take care of themselves; to get food and clothes as they could. They might all have starved, but for the eldest son, whom his father had brought up to help him at his work; and who was so industrious and attentive, that being now at the age of thirteen or fourteen, he was able to earn pretty good wages, every penny of which that he could keep out of his father's hands, he brought to his mother. When the brute of a father came home drunk, cursing and swearing, and in such an ill humour that his mother, and the rest of the children, durst not come near him for fear of a beating, this good lad (Tom was his name) kept close to him, to pacify him, and get him quietly to bed. His mother looked upon Tom as the support of the family, and loved him dearly. It happened one day, Tom in climbing up a high ladder, with a load of mortar on his head, missed his hold, and fell down to the bottom, on a heap of bricks and rubbish.

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