The Different Periodic Tables of Dmitrii Mendeleev
Laing, Michael
2008-01-01
Between 1869 and 1905 the Russian chemist Dmitrii Mendeleev published several tables with different arrangements of the chemical elements. Four of these are compared with periodic tables by Russian scientists from 1934 and 1969. The difficulties caused by the lanthanoid elements are clearly seen in the table of 1905, which satisfactorily includes…
Novelty, coherence, and Mendeleev's periodic table.
Schindler, Samuel
2014-03-01
Predictivism is the view that successful predictions of "novel" evidence carry more confirmational weight than accommodations of already known evidence. Novelty, in this context, has traditionally been conceived of as temporal novelty. However temporal predictivism has been criticized for lacking a rationale: why should the time order of theory and evidence matter? Instead, it has been proposed, novelty should be construed in terms of use-novelty, according to which evidence is novel if it was not used in the construction of a theory. Only if evidence is use-novel can it fully support the theory entailing it. As I point out in this paper, the writings of the most influential proponent of use-novelty contain a weaker and a stronger version of use-novelty. However both versions, I argue, are problematic. With regard to the appraisal of Mendeleev' periodic table, the most contentious historical case in the predictivism debate, I argue that temporal predictivism is indeed supported, although in ways not previously appreciated. On the basis of this case, I argue for a form of so-called symptomatic predictivism according to which temporally novel predictions carry more confirmational weight only insofar as they reveal the theory's presumed coherence of facts as real. PMID:24984451
Interaction properties of ytterbium with elements of Mendeleev periodic table
This article presents the new data on ytterbium interaction with elements of Mendeleev periodic table. The state diagrams of ytterbium with magnesium, calcium, strontium, and barium are constructed. The state diagrams of ytterbium with Cu, Ag, Au, Zn, Cd, Hg, B,Al, Ga, In, Tl are considered.
Modification and expansion of Mendeleev's periodic table
The periodic table of the chemical elements has provided guidance for the discovery of many elements since its formulation as a guiding principle 125 years ago. It has misled investigators on occasion into temporary excursions along erroneous routes to new elements. Even these tortuous paths, however, have eventually led to the correct destination. It is described, the part that the periodic table has played in the discovery of the man-made elements, especially the transuranium elements, and its possible future role. (author). 7 refs., 6 figs
Energy capacity of elements in periodic table of D.I.Mendeleev
A great difference in the intensity of heat constent variation from one element to another is detected. The notion of energy capacity of elements is introduced. It is an energy characteristic, determining arrangement of elements in the D.I.Mendeleev Periodic system. The value of energy capacity depends on external conditions (temperature, pressure, etc.). Lanthanides and actinides are systematized on the basis of their energy capacity, atomic mass and melting points. It is shown, that energy capcity, determining element location in thePeriodic system, characterizes the intensity of their energy state variation. Energy state of monocomponent systems with any mass number determines their physicomechanical properties
From the Mendeleev periodic table to particle physics and back to the periodic table
Kibler, Maurice R. [Universite de Lyon, Institut de Physique Nucleaire, Universite Lyon 1 and CNRS/IN2P3, 43 Bd du 11 Novembre 1918, F-69622 Villeurbanne Cedex (France)
2006-11-15
We briefly describe in this paper the passage from Mendeleev's chemistry (1869) to atomic physics (in the 1900's), nuclear physics (in the 1932's) and particle physics (from 1953 to 2006). We show how the consideration of symmetries, largely used in physics since the end of the 1920's, gave rise to a new format of the periodic table in the 1970's. More specifically, this paper is concerned with the application of the group SO(4,2)xSU(2) to the periodic table of chemical elements. It is shown how the Madelung rule of the atomic shell model can be used for setting up a periodic table that can be further rationalized via the group SO(4,2)xSU(2) and some of its subgroups. Qualitative results are obtained from this nonstandard table. (author)
From the Mendeleev periodic table to particle physics and back to the periodic table
We briefly describe in this paper the passage from Mendeleev's chemistry (1869) to atomic physics (in the 1900's), nuclear physics (in the 1932's) and particle physics (from 1953 to 2006). We show how the consideration of symmetries, largely used in physics since the end of the 1920's, gave rise to a new format of the periodic table in the 1970's. More specifically, this paper is concerned with the application of the group SO(4,2)xSU(2) to the periodic table of chemical elements. It is shown how the Madelung rule of the atomic shell model can be used for setting up a periodic table that can be further rationalized via the group SO(4,2)xSU(2) and some of its subgroups. Qualitative results are obtained from this nonstandard table. (author)
From the Mendeleev periodic table to particle physics and back to the periodic table
Kibler, M R
2006-01-01
We briefly describe in this paper the passage from Mendeleev's chemistry (1869) to atomic physics (in the 1900's), nuclear physics (in the 1932's) and particle physics (from 1953 to 2006). We show how the consideration of symmetries, largely used in physics since the end of the 1920's, gave rise to a new format of the periodic table in the 1970's. More specifically, this paper is concerned with the application of the group SO(4,2)xSU(2) to the periodic table of chemical elements. It is shown how the Madelung rule of the atomic shell model can be used for setting up a periodic table that can be further rationalized via the group SO(4,2)xSU(2) and some of its subgroups. Qualitative results are obtained from this nonstandard table.
From the Mendeleev periodic table to particle physics and back to the periodic table
Kibler, M. R.
2007-01-01
15 pages; accepted for publication in Foundations of Chemistry (special issue to commemorate the one hundredth anniversary of the death of Mendeleev who died in 1907); version 2: 16 pages; some sentences added; acknowledgment and references added; misprints corrected We briefly describe in this paper the passage from Mendeleev's chemistry (1869) to atomic physics (in the 1900's), nuclear physics (in the 1932's) and particle physics (from 1953 to 2006). We show how the consideration of symm...
Evidence for Energy Regularity in the Mendeleev Periodic Table
Amador, Cassio H. S.; Zambrano, Liliana S.
2008-01-01
We show that the dependence of the total energy of the atoms on their atomic number follows a q-exponential (function proposed by C. Tsallis), for almost all elements of the periodic table. The result is qualitatively explained in terms of the way the atomic configurations are arranged to minimize energy.
Kaji, Masanori
2003-05-01
The favorable and relatively rapid reception of Mendeleev's periodic table of the elements can be attributed, in part at least, to his social connections. These connections were evident in the recently organized Russian Chemical Society. In addition, Mendeleev enjoyed the support of the editorial board of the journal of the German Chemical Society. PMID:12796115
Superconductivity, antiferromagnetism and ferromagnetism in periodic table of D.I. Mendeleev
Basic tendencies in the distribution of ferromagnetic (FM), antiferromagnetic (AFM) and superconductive (SC) elements in the periodic table D.I. Mendeleev are traced. FM is observed at the elements in which 3d-shell is more than half-filled (the number of 3d-electrons 6≤n≤8), and at the elements with 4f-shell, contained k electrons in 4f-shell, at which the sum k+n≥8. Estimation of the radii of the d-, f- and p-orbitals on Slater method shown that 3d- and 4f-shells of FM are more pressing, than the ones with smaller n and k+n, and are well separated in crystal. AFM is observed at the elements, at which 3d- or 4f-shells are precisely half-filled. SC is observed in the 3d-, 4d- and 5d-elements at 1≤n≤x, x grows from 3 in 3d-elements to 7 in 4d- and 5d-elements, and in 7th period only at n=2 and k+n=3. Further, SC is observed at the elements, at which 3p-, 4p-, 5p- and 6p-shells contain no more than 4 electrons. In SC crystals the wave functions of external d- and p-electrons of each atom penetrate inside neighbor atoms and overlap with corresponding wave functions with smaller main quantum number than of central atom. In this case the separation of spin and charge in electron is quite possible and the charges without spin become bosons. Spins obtained magnetic moments are ordered antiparallel by two. At transfer that pair in the parallel state by magnetic field its magnetic flux from magnetic field component along of magnetic field is equal to 1 fluxon (quant of magnetic flux)
The share of free neutral atoms, N0, for all elements in Protoplanet nebula has been determined with the account of their abundance and physico-chemical properties. The linear dependence for the ratio of nonvolatile and volatile elements in chondrites and igneous rocks of the Earth on N0 was obtained. The Mendeleev Periodic Law was used to obtain the proof of the existence of the hypothetical process of element magnetic separation in Protoplanet nebula. To this end the concentration ratios of element-analogous with different N0 in the matters of Venus, Earth, Mars, and chondrites were compared. The data obtained are sufficient demonstration of the existence of the hypothetical process of element magnetic separation in Protoplanet nebula. With the account of the above said, it was shown that Shergotty and Tunguska meteorites by their relative elemental composition are close to Mars and asteroids, respectively. (author)
Superconductivity, antiferromagnetism and ferromagnetism in periodic table of D.I. Mendeleev
Definite regularity in the distribution of ferromagnetic, antiferromagnetic and superconducting elements is observed in the periodic table starting with the 4th period. Elements with superconductivity, by which d-shells start to fill up, are at the beginning of each period; then follow antiferromagnetics and ferromagnetics (in 4th period and lanthanides), or elements without any of the three listed order types (5th period and 6th period), in which the d (f)-shells continue to fill up almost exceedingly; then again appear superconductors by filling the p-shell up to the number is equal to 4. We calculated the radii of the external d (f)- and p-orbitals and the nearest to them orbitals with the Slater method. These trends were explained by distinction of degree of division of the external d (f)- or p-orbitals of the neighboring atoms in the crystal. Largest division occurs in ferromagnetics. In antiferromagnetics it is smaller than in ferromagnetics. It is demonstrated that in the superconducting crystals the external dor p-shells approach the nucleus of neighboring atoms are much closely those for ferromagnetic or antiferromagnetic crystals. Furthermore the external d- or p-shells of some elements in the 5th and 6th periods approach the deeper shells of neighboring atoms. Hence the electron in this shell is situated in neighboring atoms in a different electric field from its own. This fact is open to speculation that the separation of spin and charge in electron, disposed on the external d- or p-orbitals, is quite possible. The charges without spin become bosons. Spins that have the magnetic moments are ordered antiparallel in pairs. Magnetic field transfers this pair in a parallel state and a magnetic flux component along of magnetic field from the pair is equal to one fluxon (the quant of the magnetic flux).
Lanthanides and actinides among other groups of elements of the D.I. Mendeleev's Periodic Table
The extent to which actinides are similar to other elements of the periodic table is discussed. Actinides show certain similarity with transition metals in trends in variation of stability of the highest and lowest oxidation states with increasing atomic number. Similarity between elements of the first half of the lanthanide family and those of the second half of the actinides family is demonstrated. In the lowest oxidation states, actinides and lanthanide are analogs of alkali and alkaline-earth elements, and in the tetravalent state they start to exhibit noticeable similarity with d elements. The formation of Pu(VIII) is suggested on the basis of essentially similar volatility of oxides of Os and Ru with that of Pu. Bivalent actinides and lanthanide ions with one d electron are of particular interest. Being analogs of bivalent elements, they form various types of clusters
The slow penetration of the Mendeleev Table in the French school curricula
The great influence of the Berthelot's ideas about the non existence of atoms froze the teaching of chemistry in France for quite a long time. It is only after the Second World War that the study of the atom structure appeared in school curricula. The Mendeleev periodic system that sets the relationship between chemical properties and atom structure entered the curriculum even later in 1978. The article shows that the authors of most school manuals had anticipated the change, for in 1966 all the chemistry manuals of the 6. form had a chapter dedicated to the Mendeleev table while the issue was not yet on the syllabus. (A.C.)
Geometrochemistry vs Soft Computing of Mendeleev's Brain
Gottvald, Aleš
Brno: Brno University of Technology, 2010, s. 558-564. ISBN 978-80-214-4120-0. [Mendel 2010 - International Conference on Soft Computing /16./. Brno (CZ), 23.06.2010-25.06.2010] Institutional research plan: CEZ:AV0Z20650511 Keywords : projective geometry * Law of Mass Action * Mendeleev periodic table * brain information processing * artificial neural networks * cross-ratio * incidence structures Subject RIV: BD - Theory of Information
Štrbáňová, Soňa
Oxford : Oxford University Press, 2015 - (Kaji, M.; Kragh, H.; Pallo, G.), s. 121-149 ISBN 978-0-19-020007-7 R&D Projects: GA AV ČR IAAX00630801 Institutional support: RVO:68378114 Keywords : D. I. Mendeleev * B. Brauner * history of the periodic system of elements Subject RIV: AB - History
Reports of the XVII Mendeleev congress on general and applied chemistry, volume 3 (Kazan', 21 - 26 September, 2003) are presented. Current status and prospects of chemical science in the field of materials testing and nanoengineering are the subject of considerable discussion. Energetic and ecological problems of modern structural materials production, prospects for the development of ceramic structural materials, polymer nanocomposites are treated. Chemical aspects, outlook for the study and application of different substances and elements of the Periodic system in various areas of chemical science and practice are noted
The role of the Czech chemists in reception and dissemination of the periodic system in Europe
Štrbáňová, Soňa
Budapest : MKE, 2009. s. 40. ISBN 978-963-9319-96-7. [International conference on the history of chemistry. Consumers and experts. The uses of chemistry ( and alchemy) /7./. 02.08.2009-05.08.2009, Sopron] Institutional research plan: CEZ:AV0Z80630520 Keywords : D.I. Mendeleev * B. Brauner * periodic system of elements * history of chemistry * history of Czech chemistry Subject RIV: AB - History
The 5 volume of the XVIII Mendeleev congress on general and applied chemistry includes summaries of reports on the subjects of sypramolecular systems in chemistry and biology, organic chemistry, modern radiochemistry, green chemistry - development and social responsibility of chemists, nucleophilic hydrogen substitution in aromatic systems and related chemical reactions
Tomalia, Donald A; Khanna, Shiv N
2016-02-24
Development of a central paradigm is undoubtedly the single most influential force responsible for advancing Dalton's 19th century atomic/molecular chemistry concepts to the current maturity enjoyed by traditional chemistry. A similar central dogma for guiding and unifying nanoscience has been missing. This review traces the origins, evolution, and current status of such a critical nanoperiodic concept/framework for defining and unifying nanoscience. Based on parallel efforts and a mutual consensus now shared by both chemists and physicists, a nanoperiodic/systematic framework concept has emerged. This concept is based on the well-documented existence of discrete, nanoscale collections of traditional inorganic/organic atoms referred to as hard and soft superatoms (i.e., nanoelement categories). These nanometric entities are widely recognized to exhibit nanoscale atom mimicry features reminiscent of traditional picoscale atoms. All unique superatom/nanoelement physicochemical features are derived from quantized structural control defined by six critical nanoscale design parameters (CNDPs), namely, size, shape, surface chemistry, flexibility/rigidity, architecture, and elemental composition. These CNDPs determine all intrinsic superatom properties, their combining behavior to form stoichiometric nanocompounds/assemblies as well as to exhibit nanoperiodic properties leading to new nanoperiodic rules and predictive Mendeleev-like nanoperiodic tables, and they portend possible extension of these principles to larger quantized building blocks including meta-atoms. PMID:26821999
Raos, N.
2011-12-01
Full Text Available The Croatian (Yugoslav Academy of Sciences and Arts was the first academy to elect D. I. Mendeleev as its honorary member (1882, whereas the periodic table of the elements has been taught regularly at the Zagreb University since 1888. The early interest of Croatian chemists in the periodic table should be attributed primarily to their pan-Slavic attitude, particularly as proof that Slavic people were able to produce "their own Newtons" (M. V. Lomonosov and D. I. Mendeleev. Such enthusiastic views, however, did not help in analyzing the contribution of Mendeleev and other scientists to the discovery and development of the periodic table of the elements.
Superheavy elements in D I Mendeleev's Periodic Table
The results on the synthesis of new superheavy elements, synthesized in complete fusion reactions of 48Ca ions with actinide targets, are summarized and analyzed. The perspectives for the synthesis of element 117, as well as of elements with Z≥118 are also considered.
Raos, N.
2011-01-01
The Croatian (Yugoslav) Academy of Sciences and Arts was the first academy to elect D. I. Mendeleev as its honorary member (1882), whereas the periodic table of the elements has been taught regularly at the Zagreb University since 1888. The early interest of Croatian chemists in the periodic table should be attributed primarily to their pan-Slavic attitude, particularly as proof that Slavic people were able to produce "their own Newtons" (M. V. Lomonosov and D. I. Mendeleev). Such enthusiasti...
The final elements of the Mendeleev table
Over two centuries ago, chemical elements classification has witnessed several surprising variations, which we live approximately their last stages. Workers in this field are similar to runners who progressed actively at the beginning for few seconds. Then they should struggle thereafter to gain very few percentage of a second. Physicists have shown, over the past three years, unlimited patience and ingenuity towards the filling of the final empty spaces of Mendeleiev table, especially that created elements usually disappear after its formation in about a millisecond time period. Identification of new elements is similar to police investigation, and we find here that the family of strange behavior and accurately tracked one is the trans actinides family. This article illustrates the great moments of this investigation which recently has been achieved. 16 refs., 8 figs
Holonomic systems for period mappings
Chen, Jingyue, E-mail: jychen@brandeis.edu [Department of Mathematics, Brandeis University, Waltham, MA 02454 (United States); Huang, An, E-mail: anhuang@math.harvard.edu [Department of Mathematics, Harvard University, Cambridge, MA 02138 (United States); Lian, Bong H., E-mail: lian@brandeis.edu [Department of Mathematics, Brandeis University, Waltham, MA 02454 (United States)
2015-09-15
Period mappings were introduced in the sixties [4] to study variation of complex structures of families of algebraic varieties. The theory of tautological systems was introduced recently [7,8] to understand period integrals of algebraic manifolds. In this paper, we give an explicit construction of a tautological system for each component of a period mapping. We also show that the D-module associated with the tautological system gives rise to many interesting vanishing conditions for period integrals at certain special points of the parameter space.
Periodic solutions of periodically harvested lotka-volterra systems
Hausrath, Alan R.; Manasevich, Raul F.
2012-01-01
We study a Lotka-Volterra system with periodic harvesting, find sufficient conditions for the existence of periodic solutions with the same period, and, under certain conditions, count the number of such periodic solutions.
Availability of periodically tested systems
There is at the present time a need in accurate models to asess the availability of periodically tested stand-by systems. This paper shows how to improve the well known 'saw-tooth curve' model in order to take into account various reliability parameters. A model is developed to assess the pointwise and the mean availabilities of periodically tested stand-by systems. Exact and approxination formulae are given. In addition, the model developed herein leads to optimize the test interval in order to minimize the mean unavailability. A safety diesel in a nuclear power plant is given as an example
Elkina, D.
2014-12-01
Nowadays the Arctic Ocean is an area of higher scientific interest. Investigation of composition, genesis, sources and source areas of marine sediments is necessary for a gain of geological knowledge and geo-engineering development of the region. One should note that the dating issue in the Arctic Ocean is a challenge by itself. However, magnetostratigraphy can offer a powerful stratigraphic tool applying to marine sediments here. The 6-meters length core was retrieved from the Mendeleev Ridge in 2012 and subjected to paleomagnetic studies. The examined core was revealed to dominate by normal polarity up to 123 cm below seafloor (cmbsf) and assigned there to the Brunhes polarity chron of the geomagnetic field (0.78 Ma). Then prevalence of reverse polarity persists up to 394-397 cmbsf, assigned to Matuyama age, and short positive intervals are believed to be subchrons of normal polarity. Change from reverse to normal polarity at 394-397 cmbsf is considered as the Matuyama - Gauss (2.58 Ma) boundary and is traced up to 530-531 cmbsf including one short reversal. After this depth a drop back to reverse polarity is ascribed to the beginning of the Gilbert polarity chron (3.58 Ma). The resultant magnetostratigraphy is presented on Figure 1. The stepwise alternating field demagnetization and demagnetization by heating were performed to remove viscous overprints and then to define component magnetization directions. Spikes of natural remanent magnetization intensity and magnetic susceptibility are discovered near almost all assigned chron boundaries, and it may act as an independent factor for determination of polarity boundaries. Anisotropy of magnetic susceptibility is also considered in order to find out additional peculiarities of the sedimentation. The relative abundance of shallow inclinations at least implies the existence of secondary processes, which may have altered the paleomagnetic record. The mean sedimentation rates on the Mendeleev Ridge do not exceed 1
A Periodic Lotka-Volterra System
Tsvetkov, D.
1996-01-01
In this paper periodic time-dependent Lotka-Volterra systems are considered. It is shown that such a system has positive periodic solutions. It is done without constructive conditions over the period and the parameters.
Fractional-period excitations in continuum periodic systems
We investigate the generation of fractional-period states in continuum periodic systems. As an example, we consider a Bose-Einstein condensate confined in an optical-lattice potential. We show that when the potential is turned on nonadiabatically, the system explores a number of transient states whose periodicity is a fraction of that of the lattice. We illustrate the origin of fractional-period states analytically by treating them as resonant states of a parametrically forced Duffing oscillator and discuss their transient nature and potential observability
无
2002-01-01
The relationship between the types of binary alloy phase diagrams of Vlll and IB group elements and the Men deleev numbers was discussed for the first time using the Vlll and IB group elements as solvent metals (A) and the other elements as solute metals (B), basesd on their alloy phase diagram types. The Mendeleev numbers of the solvent metals and the solute metals were expressed as Ma and MB, respectively. A two-dimension map of MdMB was drawn. It is indicated that there is an oblique line in the map, which divides the binary alloy phase diagram types of solvent metals into two symmetry parts, the phase diagram types of the other elements with solvent metals located at the above or down of the line respectively, while on the line, AM= 0. The phase diagrams between the solvent metals basically are simple systems, mainly belong to the types of continues solid solution and the peritectic (about 40% for each type). The solvent metals can be divided into three groups: Co, Ir, Rh, Ni, Pt, and Pd as the first group; Ag, Au, and Cu as the second group;and Fe, Os, and Ru as the third group. The characteristics of the phase diagrams formed between the elements in each group were discussed. About 80% phase diagrams belong to complex systems and less than 20% belong to the simple systems. The regular variation of the chemical scale, the metallic radii of the atoms, the number of valence electrons, and the first ionization energy with the Mendeleev numbers and the crystal structure were introduced as well.
Positive periodic solutions of delayed periodic Lotka-Volterra systems
Lin Wei [Laboratory of Nonlinear Mathematics Science, Institute of Mathematics, Fudan University, Shanghai 200433 (China)]. E-mail: weilin@fudan.edu.cn; Chen Tianping [Laboratory of Nonlinear Mathematics Science, Institute of Mathematics, Fudan University, Shanghai 200433 (China)]. E-mail: tchen@fudan.edu.cn
2005-01-17
In this Letter, for a general class of delayed periodic Lotka-Volterra systems, we prove some new results on the existence of positive periodic solutions by Schauder's fixed point theorem. The global asymptotical stability of positive periodic solutions is discussed further, and conditions for exponential convergence are given. The conditions we obtained are weaker than the previously known ones and can be easily reduced to several special cases.
Positive periodic solutions of delayed periodic Lotka-Volterra systems
Lin, Wei; Chen, Tianping
2005-01-01
In this Letter, for a general class of delayed periodic Lotka-Volterra systems, we prove some new results on the existence of positive periodic solutions by Schauder's fixed point theorem. The global asymptotical stability of positive periodic solutions is discussed further, and conditions for exponential convergence are given. The conditions we obtained are weaker than the previously known ones and can be easily reduced to several special cases.
Gabor systems on discrete periodic sets
2009-01-01
Due to its good potential for digital signal processing, discrete Gabor analysis has interested some mathematicians. This paper addresses Gabor systems on discrete periodic sets, which can model signals to appear periodically but intermittently. Complete Gabor systems and Gabor frames on discrete periodic sets are characterized; a sufficient and necessary condition on what periodic sets admit complete Gabor systems is obtained; this condition is also proved to be sufficient and necessary for the existence of sets E such that the Gabor systems generated by χE are tight frames on these periodic sets; our proof is constructive, and all tight frames of the above form with a special frame bound can be obtained by our method; periodic sets admitting Gabor Riesz bases are characterized; some examples are also provided to illustrate the general theory.
Khazan A.
2009-07-01
Full Text Available This paper gives a survey for the methods how a possible upper limit in Mendeleev's Periodic Table can be found. It is show, only the method of hyperbolas leads to exact answering this question.
The nature of the acoustic basement on Mendeleev and northwestern Alpha ridges, Arctic Ocean
Bruvoll, Vibeke; Kristoffersen, Yngve; Coakley, Bernard J.; Hopper, John R.; Planke, Sverre; Kandilarov, Aleksandre
2012-01-01
The Alpha-Mendeleev ridge complex, over 1500 km long and 250-400 km wide, is the largest submarine structure in the Arctic Ocean basin. Its origin is unknown, but often inferred to represent a large igneous province where domains of continental crust may also be a possibility. We investigate the basement geology of part of this large scale feature using 1100 km of multichannel seismic reflection data, sonobuoy recordings and marine gravity data acquired in 2005 from USCG icebreaker Healy. The sonobuoy results show top and intra-acoustic basement velocities in the range of 2.3-4.0 km/s and the seismic reflection attributes define three main acoustic facies: 1) continuous high amplitude reflections often with abrupt breaks, 3) weak wedge geometry and 3) segmented, disrupted to chaotic reflections. The acoustic characteristics and seismic velocities compare more closely with basement on Ontong Java Plateau than normal ocean crust or wedges of seaward dipping reflections at volcanic margins. The acoustic facies are interpreted to represent basalt flows and sills capping voluminous tuff deposits and possible sediments. At least two volcanic centres are identified. The upper volcanic carapace on the surveyed part of Mendeleev and northwestern Alpha ridges was emplaced during a brief igneous episode no later than Campanian (80 Ma) and most likely part of wider Late Cretaceous circum Arctic volcanism. The horst and graben morphology on Mendeleev Ridge is largely a result of post-emplacement faulting where a number of the major extensional faults remained active until a late Miocene intrusive event.
Mistake of Having Students Be Mendeleev Just for a Day
Criswell, Brett
2007-01-01
The study describes a new methodology and learning cycle, which will give a better understanding of the periodic table to the students. The students following the cycle have now started focusing more on the chemical instead of physical properties when developing their schemes.
Attractors of the periodically forced Rayleigh system
Petre Bazavan
2011-07-01
Full Text Available The autonomous second order nonlinear ordinary differential equation(ODE introduced in 1883 by Lord Rayleigh, is the equation whichappears to be the closest to the ODE of the harmonic oscillator withdumping.In this paper we present a numerical study of the periodic andchaotic attractors in the dynamical system associated with the generalized Rayleigh equation. Transition between periodic and quasiperiodic motion is also studied. Numerical results describe the system dynamics changes (in particular bifurcations, when the forcing frequency is varied and thus, periodic, quasiperiodic or chaotic behaviour regions are predicted.
Dynamics of Coulombic and gravitational periodic systems
Kumar, Pankaj; Miller, Bruce N.
2016-04-01
We study the dynamics and the phase-space structures of Coulombic and self-gravitating versions of the classical one-dimensional three-body system with periodic boundary conditions. We demonstrate that such a three-body system may be reduced isomorphically to a spatially periodic system of a single particle experiencing a two-dimensional potential on a rhombic plane. For the case of both Coulombic and gravitational versions, exact expressions of the Hamiltonian have been derived in rhombic coordinates. We simulate the phase-space evolution through an event-driven algorithm that utilizes analytic solutions to the equations of motion. The simulation results show that the motion exhibits chaotic, quasiperiodic, and periodic behaviors in segmented regions of the phase space. While there is no evidence of global chaos in either the Coulombic or the gravitational system, the former exhibits a transition from a completely nonchaotic phase space at low energies to a mixed behavior. Gradual yet striking transitions from mild to intense chaos are indicated with changing energy, a behavior that differentiates the spatially periodic systems studied in this Rapid Communication from the well-understood free-boundary versions of the three-body problem. Our treatment of the three-body systems opens avenues for analysis of the dynamical properties exhibited by spatially periodic versions of various classes of systems studied in plasma and gravitational physics as well as in cosmology.
Periodic orbits in hyperchaotic Chen systems
Susanna Maza
2015-08-01
Full Text Available In this work, we show a zero-Hopf bifurcation in a Hyperchaotic Chen system. Using averaging theory, we prove the existence of two periodic orbits bifurcating from the zero-Hopf equilibria located at the origin of the Hyperchaotic Chen system.
Subcortical cytoskeleton periodicity throughout the nervous system.
D'Este, Elisa; Kamin, Dirk; Velte, Caroline; Göttfert, Fabian; Simons, Mikael; Hell, Stefan W
2016-01-01
Superresolution fluorescence microscopy recently revealed a ~190 nm periodic cytoskeleton lattice consisting of actin, spectrin, and other proteins underneath the membrane of cultured hippocampal neurons. Whether the periodic cytoskeleton lattice is a structural feature of all neurons and how it is modified when axons are ensheathed by myelin forming glial cells is not known. Here, STED nanoscopy is used to demonstrate that this structure is a commonplace of virtually all neuron types in vitro. To check how the subcortical meshwork is modified during myelination, we studied sciatic nerve fibers from adult mice. Periodicity of both actin and spectrin was uncovered at the internodes, indicating no substantial differences between unmyelinated and myelinated axons. Remarkably, the actin/spectrin pattern was also detected in glial cells such as cultured oligodendrocyte precursor cells. Altogether our work shows that the periodic subcortical cytoskeletal meshwork is a fundamental characteristic of cells in the nervous system and is not a distinctive feature of neurons, as previously thought. PMID:26947559
Periodicity and map for discovery of new ionic liquids
无
2006-01-01
There is virtually no limit in the number of ionic liquids. How to select proper ones or discover new ones with desirable properties in such a large pool of ionic liquids? It has become a bottleneck in the researches and applications of ionic liquids. Mendeleev's periodic law states that the properties of the elements vary periodically. Whether the similar regularity exists among ionic or molecular fragments of compounds is an interesting topic. In this work, we attempted to establish a periodicity and draw a "map" of ionic liquids for providing definite guidance to discover, design, and select the proper ionic liquids rather than trial-and-error. If a complete regularity of the system of ionic liquids can be finally established in the future, we are near an epoch in understanding the existing differences and the reasons for the similarity of the ions or molecular fragments.
Periodic testing of instrumentation and control systems
During normal operation, protection systems are on stand-by; therefore possible failure of system components may go undetected. The ability of these systems to function as intended, should they be initiated after a long period of time on stand-by, is thus questionable. For this reason, French as well as international rules require that protection systems be subjected to periodic tests. Given the equipment available when the units in the French 900 MW(e) series were designed, the instrumentation and control systems were equipped with manual periodic test systems. In the case of the reactor protection system, the manual test equipment has been replaced successfully on the 28 units in the French 900 MW(e) series by the automatic tester discussed in the paper. The manual test system is still used with the process instrumentation system which receives analogue signals from sensors or transmitters connected to the process equipment. These input signals are subjected to varying degrees of signal conditioning, including, in some cases, the combining of some of the signals. The electronic conditioning circuits generate a signal that is the direct input to a threshold detector. In practice, each element in the instrumentation channel, including the signal conditioning unit, has an uncertainty associated with it. It is important to check periodically that the actual trip values for the input variables are lower than the physical limits established by the safety studies. Framatome has carried out a study for Electricite de France with the objective both of modernizing this operation and of considering, as a possibility, the complete automation of the testing. This second subject is also discussed in the paper. (author). 2 figs
The long period seismic system of Gauribidanur
This report describes the seismic long-period data acquisition system at Gauribidanur. The field electronics was designed to achieve a configuration of improved stability and dynamic range in the pass band of 0.025-0.1 hz. Some typical records obtained by the system are shown. Surface wave magnitudes estimated at the Gauribidanur Seismic Array are found to be in general agreement with those of international estimates. (author)
Clustering of periodic orbits in chaotic systems
In the framework of the semiclassical approach, the universal spectral correlations in Hamiltonian systems with classical chaotic dynamics can be attributed to the systematic correlations between the actions of periodic orbits which (up to the switch in the momentum direction) pass through approximately the same points of the phase space. By considering symbolic dynamics of the system one can introduce a natural ultrametric distance between periodic orbits and organize them into clusters of orbits approaching each other in the phase space. We study the distribution of cluster sizes for the baker's map in the asymptotic limit of long trajectories. This problem is equivalent to the one of counting degeneracies in the length spectrum of the de Bruijn graphs. Based on this fact, we derive the probability Pk that k randomly chosen periodic orbits belong to the same cluster. Furthermore, we find asymptotic behaviour of the largest cluster size |Cmax| and derive the probability P(t) that a random periodic orbit belongs to a cluster smaller than t|Cmax|, t ∈ [0, 1]. (paper)
Competing periodicities in a convecting system
In this study, a variety of novel phases was discovered in a nonequilibrium system that has undergone an instability. These phases are closely related to commensurate and incommensurate states found in many solid state materials. It is widely recognized that this behavior is a general phenomenon resulting from the presence of two competing lengths. To study the effects of competing periodicities in a nonequilibrium system, a convective flow was subjected to spatially periodic forcing with a period different from the naturally chosen one. For reasons of experimental convenience, an electrohydrodynamic instability in a thin layer of nematic liquid crystal was utilized. Samples containing several hundred rolls are easily obtained and visualized; thus, phenomena occurring in an effectively infinite layer could be studied. The periodic forcing is imposed by using a specially designed interdigitated electrode. The author found, both commensurate and incommensurate states of several distinct types, and used digital image analysis to study their structure. In a separate investigation, the first direct observation was made of the Eckhaus instability, a phenomenon characterized by long wavelength modulations of a primary roll structure
Periodic inspections of the primary system
An impression is given of the inspection techniques, preparations and background for periodic examinations of the primary system of the Dodewaard Nuclear Reactor over the past 10 years. Unfortunately reliable integral inspection techniques to enable 'listening-in' to developing faults, are not yet available. Until they are, inspections will continue to be executed from a distance using different continuous methods, often under water and with a shortage of space and in the presence of ionising radiations. (C.F.)
Scaling concepts in periodically modulated noisy systems
We show that scaling arguments are very useful to analyze the dynamics of periodically modulated noisy systems. Information about the behavior of the relevant quantities, such as the signal-to-noise ratio, upon variations of the noise level, can be obtained by analyzing the symmetries and invariances of the system. In this way, it is possible to predict diverse physical manifestations of the cooperative behavior between noise and input signal, as for instance stochastic resonance, spatiotemporal stochastic resonance, and stochastic multiresonance. (Copyright (c) 1999 Elsevier Science B.V., Amsterdam. All rights reserved.)
Homogenization of Periodic Systems with Large Potentials
Allaire, Grégoire; Capdeboscq, Yves; Piatnitski, Andrey; Siess, Vincent; Vanninathan, M.
2004-11-01
We consider the homogenization of a system of second-order equations with a large potential in a periodic medium. Denoting by ɛ the period, the potential is scaled as ɛ-2. Under a generic assumption on the spectral properties of the associated cell problem, we prove that the solution can be approximately factorized as the product of a fast oscillating cell eigenfunction and of a slowly varying solution of a scalar second-order equation. This result applies to various types of equations such as parabolic, hyperbolic or eigenvalue problems, as well as fourth-order plate equation. We also prove that, for well-prepared initial data concentrating at the bottom of a Bloch band, the resulting homogenized tensor depends on the chosen Bloch band. Our method is based on a combination of classical homogenization techniques (two-scale convergence and suitable oscillating test functions) and of Bloch waves decomposition.
Central configurations, periodic orbits, and Hamiltonian systems
Llibre, Jaume; Simó, Carles
2015-01-01
The notes of this book originate from three series of lectures given at the Centre de Recerca Matemàtica (CRM) in Barcelona. The first one is dedicated to the study of periodic solutions of autonomous differential systems in Rn via the Averaging Theory and was delivered by Jaume Llibre. The second one, given by Richard Moeckel, focusses on methods for studying Central Configurations. The last one, by Carles Simó, describes the main mechanisms leading to a fairly global description of the dynamics in conservative systems. The book is directed towards graduate students and researchers interested in dynamical systems, in particular in the conservative case, and aims at facilitating the understanding of dynamics of specific models. The results presented and the tools introduced in this book include a large range of applications.
An Application-Oriented Periodic Table of the Elements.
Bouma, J.
1989-01-01
A brief history of several of the early forms of the periodic table of the elements are discussed including those of Mendeleev, Meyer, Hubbard, Gmelin, Von Antropoff, and Strong. A more every-day-life form of the table is presented. (CW)
Periodic thermodynamics of open quantum systems
Brandner, Kay; Seifert, Udo
2016-06-01
The thermodynamics of quantum systems coupled to periodically modulated heat baths and work reservoirs is developed. By identifying affinities and fluxes, the first and the second law are formulated consistently. In the linear response regime, entropy production becomes a quadratic form in the affinities. Specializing to Lindblad dynamics, we identify the corresponding kinetic coefficients in terms of correlation functions of the unperturbed dynamics. Reciprocity relations follow from symmetries with respect to time reversal. The kinetic coefficients can be split into a classical and a quantum contribution subject to an additional constraint, which follows from a natural detailed balance condition. This constraint implies universal bounds on efficiency and power of quantum heat engines. In particular, we show that Carnot efficiency cannot be reached whenever quantum coherence effects are present, i.e., when the Hamiltonian used for work extraction does not commute with the bare system Hamiltonian. For illustration, we specialize our universal results to a driven two-level system in contact with a heat bath of sinusoidally modulated temperature.
On periodic orbits in discrete-time cascade systems
Huimin Li
2006-01-01
Full Text Available We present some results on existence, minimum period, number of periodic orbits, and stability of periodic orbits in discrete-time cascade systems. Some examples are presented to illustrate these results.
Estimates on the minimal period for periodic solutions of nonlinear second order Hamiltonian systems
In this paper, we prove a sharper estimate on the minimal period for periodic solutions of autonomous second order Hamiltonian systems under precisely Rabinowitz' superquadratic condition. (author). 20 refs, 1 fig
Periodicity of Rauzy scheme and substitutional systems
Kanel-Belov, Alexei
2011-01-01
In the paper the notion of {\\em Rauzy scheme} is introduced. From Rauzy graph Rauzy Scheme can be obtaining by uniting sequence of vertices of ingoing and outgoing degree 1 by arches. This notion is a tool to describe Rauzy graph behavior. For morphic superword we prove periodicity of Rauzy schemes. This is generalization of fact that quadratic irrationals have periodic chain fractions.
Monitoring system of ECCS injection system upon periodical inspection
An ECCS reactor injection system is automatically monitored upon periodical inspection. That is, a memory device stores information of the stand-by state of the ECCS reactor injection system upon periodical inspection. A data input means inputs monitoring item data in the present state. A required monitoring target is designated by the input means. A judging means compares the data of the monitoring target with the stand-by state information successively, to judge whether or not the monitoring target is in a predetermined stand-by state. A display means displays the result of the judgment. In the present system thus constituted, since it can be automatically judged whether or not the ECCS reactor injection system, as a monitoring target, is in the predetermined stand-by state, it is possible to reduce the operator's burden and improve the safety. (I.S.)
The electrostatic surface term: (I) periodic systems.
Herce, Henry David; Garcia, Angel Enrique; Darden, Thomas
2007-03-28
The authors propose a new approach to understand the electrostatic surface contributions to the interactions of large but finite periodic distributions of charges. They present a simple method to derive and interpret the surface contribution to any electrostatic field produced by a periodic distribution of charges. They discuss the physical and mathematical interpretations of this term. They present several examples and physical details associated with the calculation of the surface term. Finally, they provide a simple derivation of the surface contribution to the virial. This term does not disappear even if tinfoil boundary conditions are applied. PMID:17411107
Almost periodic solutions for Lotka-Volterra systems with delays
Liang, Yanlai; Li, Lijie; Chen, Lansun
2009-09-01
This paper studies a general class of delayed almost periodic Lotka-Volterra system with time-varying delays and distributed delays. By using the definition of almost periodic function, the sufficient conditions for the existence and uniqueness of globally exponentially stable almost periodic solution are obtained. The conditions can be easily reduced to special cases of cooperative systems and competitive systems.
Positive periodic solutions of periodic neutral Lotka-Volterra system with state dependent delays
Li, Yongkun
2007-06-01
By using a fixed point theorem of strict-set-contraction, some new criteria are established for the existence of positive periodic solutions of the following periodic neutral Lotka-Volterra system with state dependent delays where (i,j=1,2,...,n) are [omega]-periodic functions and (i=1,2,...,n) are [omega]-periodic functions with respect to their first arguments, respectively.
Sun Wen [School of Mathematics and Statistics, Wuhan University, Wuhan 430072 (China); Chen Shihua [School of Mathematics and Statistics, Wuhan University, Wuhan 430072 (China)]. E-mail: shcheng@whu.edu.cn; Hong Zhiming [School of Mathematics and Statistics, Wuhan University, Wuhan 430072 (China); Wang Changping [Department of Mathematics and Statistics, Dalhousie University, Halifax, NS, B3H 3J5 (Canada)
2007-08-15
A two-species periodic competition Lotka-Volterra system with time delay and diffusion is investigated. Some sufficient conditions of the existence of positive periodic solution are established for the system by using the continuation theorem of coincidence degree theory.
Periodicity and quasi-periodicity for super-integrable hamiltonian systems
Classical trajectories are calculated for two Hamiltonian systems with ring shaped potentials. Both systems are super-integrable, but not maximally super-integrable, having four globally defined single-valued integrals of motion each. All finite trajectories are quasi-periodical; they become truly periodical if a commensurability condition is imposed on an angular momentum component
A spectral method different from previously known methods has been proposed for the study of nonautonomous systems of ordinary differential equations with periodic and polynomially periodic matrices. The asymptotic expression has been constructed for solutions of linear systems of this class
Holistic Approach to the Periodic System of Elements
Trunov, N. N.
2009-01-01
For studying the objectivity and the quality of a given form of the Periodic system as a single whole we compare plots of functions presenting properties of elements in pairs of periods. Using mathematical statistics we introduce a dimensionless parameter which indicates high quality of the long form of the Periodic system.
Periodic Table of the Elements in the Perspective of Artificial Neural Networks
Lemes, Mauricio R.; Dal Pino, Arnaldo
2011-01-01
Although several chemical elements were not known by end of the 19th century, Mendeleev came up with an astonishing achievement, the periodic table of elements. He was not only able to predict the existence of (then) new elements, but also to provide accurate estimates of their chemical and physical properties. This is a profound example of the…
Periodically sheared 2D Yukawa systems
We present non-equilibrium molecular dynamics simulation studies on the dynamic (complex) shear viscosity of a 2D Yukawa system. We have identified a non-monotonic frequency dependence of the viscosity at high frequencies and shear rates, an energy absorption maximum (local resonance) at the Einstein frequency of the system at medium shear rates, an enhanced collective wave activity, when the excitation is near the plateau frequency of the longitudinal wave dispersion, and the emergence of significant configurational anisotropy at small frequencies and high shear rates
Existence of periodic solutions of impulsive differential systems
L. H. Erbe
1991-01-01
Full Text Available In this paper, the existence of periodic solutions of impulsive differential systems is considered. Since the solutions of such a system are peicewise continuous, it is necessary to introduce piecewise continuous Lyapunov functions. By means of such functions, together with the comparison principle, some sufficient conditions for the existence of periodic solutions of impulsive differential systems are established.
Almost Periodic Solution of a Discrete Commensalism System
Yalong Xue
2015-01-01
Full Text Available A nonautonomous discrete two-species Lotka-Volterra commensalism system with delays is considered in this paper. Based on the discrete comparison theorem, the permanence of the system is obtained. Then, by constructing a new discrete Lyapunov functional, a set of sufficient conditions which guarantee the system global attractivity are obtained. If the coefficients are almost periodic, there exists an almost periodic solution and the almost periodic solution is globally attractive.
Almost Periodic Solution of a Discrete Commensalism System
Yalong Xue; Xiangdong Xie; Fengde Chen; Rongyu Han
2015-01-01
A nonautonomous discrete two-species Lotka-Volterra commensalism system with delays is considered in this paper. Based on the discrete comparison theorem, the permanence of the system is obtained. Then, by constructing a new discrete Lyapunov functional, a set of sufficient conditions which guarantee the system global attractivity are obtained. If the coefficients are almost periodic, there exists an almost periodic solution and the almost periodic solution is globally attractive.
Periodic solution of neutral Lotka-Volterra system with periodic delays
Liu, Zhijun; Chen, Lansun
2006-12-01
A nonautonomous n-species Lotka-Volterra system with neutral delays is investigated. A set of verifiable sufficient conditions is derived for the existence of at least one strictly positive periodic solution of this Lotka-Volterra system by applying an existence theorem and some analysis techniques, where the assumptions of the existence theorem are different from that of Gaines and Mawhin's continuation theorem [R.E. Gaines, J.L. Mawhin, Coincidence Degree and Nonlinear Differential Equations, Springer-Verlag, Berlin, 1977] and that of abstract continuation theory for k-set contraction [W. Petryshyn, Z. Yu, Existence theorem for periodic solutions of higher order nonlinear periodic boundary value problems, Nonlinear Anal. 6 (1982) 943-969]. Moreover, a problem proposed by Freedman and Wu [H.I. Freedman, J. Wu, Periodic solution of single species models with periodic delay, SIAM J. Math. Anal. 23 (1992) 689-701] is answered.
Scientific Realism and the Periodic Table of Chemical Elements
Sides, Jonathan David
2006-01-01
The periodic table poses a difficulty for both scientific realists and anti-realists. The antirealist has difficulty accounting for the success of the table during a period in chemistry when many theories and concepts changed; the spatial relations of current tables in use do not show fundamental changes from the original tables proposed by Mendeleev. Yet, most versions of scientific realism are based upon the understanding that theories are some collection of written propositi...
Implicit numerical integration for periodic solutions of autonomous nonlinear systems
Thurston, G. A.
1982-01-01
A change of variables that stabilizes numerical computations for periodic solutions of autonomous systems is derived. Computation of the period is decoupled from the rest of the problem for conservative systems of any order and for any second-order system. Numerical results are included for a second-order conservative system under a suddenly applied constant load. Near the critical load for the system, a small increment in load amplitude results in a large increase in amplitude of the response.
Lorenz, Daniel S.; Reiman, Michael P.; Walker, John C.
2010-01-01
Background: Clinicians are constantly faced with the challenge of designing training programs for injured and noninjured athletes that maximize healing and optimize performance. Periodization is a concept of systematic progression—that is, resistance training programs that follow predictable patterns of change in training variables. The strength training literature is abundant with studies comparing periodization schemes on uninjured, trained, and untrained athletes. The rehabilitation litera...
The linking number in systems with Periodic Boundary Conditions
Panagiotou, E.
2015-11-01
Periodic Boundary Conditions (PBC) are often used for the simulation of complex physical systems. Using the Gauss linking number, we define the periodic linking number as a measure of entanglement for two oriented curves in a system employing PBC. In the case of closed chains in PBC, the periodic linking number is an integer topological invariant that depends on a finite number of components in the periodic system. For open chains, the periodic linking number is an infinite series that accounts for all the topological interactions in the periodic system. In this paper we give a rigorous proof that the periodic linking number is defined for the infinite system, i.e., that it converges for one, two, and three PBC models. It gives a real number that varies continuously with the configuration and gives a global measure of the geometric complexity of the system of chains. Similarly, for a single oriented chain, we define the periodic self-linking number and prove that it also is defined for open chains. In addition, we define the cell periodic linking and self-linking numbers giving localizations of the periodic linking numbers. These can be used to give good estimates of the periodic linking numbers in infinite systems. We also define the local periodic linking number associated to chains in the immediate cell neighborhood of a chain in order to study local linking measures in contrast to the global linking measured by the periodic linking numbers. Finally, we study and compare these measures when applied to a PBC model of polyethylene melts.
An index defined by focal points for periodic hamiltonians systems
Associated to an n-dimensional linear Hamiltonian system a real number μ is defined as the mean number of focal points per unit of time. For general one parameter families of Hamiltonian systems with periodic coefficients the existence and the continuity of μ can be proved. Moreover, if the periodic system is hyperbolic, μ is associated to an integer. These results are extentions of Poincare's Study of Manpertuis' focal points. (Author)
Early warning signals of tipping points in periodically forced systems
Williamson, Mark S.; Bathiany, Sebastian; Lenton, Timothy M.
2016-04-01
The prospect of finding generic early warning signals of an approaching tipping point in a complex system has generated much interest recently. Existing methods are predicated on a separation of timescales between the system studied and its forcing. However, many systems, including several candidate tipping elements in the climate system, are forced periodically at a timescale comparable to their internal dynamics. Here we use alternative early warning signals of tipping points due to local bifurcations in systems subjected to periodic forcing whose timescale is similar to the period of the forcing. These systems are not in, or close to, a fixed point. Instead their steady state is described by a periodic attractor. For these systems, phase lag and amplification of the system response can provide early warning signals, based on a linear dynamics approximation. Furthermore, the Fourier spectrum of the system's time series reveals harmonics of the forcing period in the system response whose amplitude is related to how nonlinear the system's response is becoming with nonlinear effects becoming more prominent closer to a bifurcation. We apply these indicators as well as a return map analysis to a simple conceptual system and satellite observations of Arctic sea ice area, the latter conjectured to have a bifurcation type tipping point. We find no detectable signal of the Arctic sea ice approaching a local bifurcation.
Tang, Xianhua; Cao, Daomin; Zou, Xingfu
We consider a periodic Lotka-Volterra competition system without instantaneous negative feedbacks (i.e., pure-delay systems) x(t)=x(t)[r(t)-∑j=1na(t)x(t-τ(t))], i=1,2,…,n. We establish some 3/2-type criteria for global attractivity of a positive periodic solution of the system, which generalize the well-known Wright's 3/2 criteria for the autonomous delay logistic equation, and thereby, address the open problem proposed by both Kuang [Y. Kuang, Global stability in delayed nonautonomous Lotka-Volterra type systems without saturated equilibria, Differential Integral Equations 9 (1996) 557-567] and Teng [Z. Teng, Nonautonomous Lotka-Volterra systems with delays, J. Differential Equations 179 (2002) 538-561].
Optimization of maintenance periodicity of complex of NPP safety systems
The analysis of the positive and negative aspects connected to maintenance of the safety systems equipment which basically is in a standby state is executed. Tests of systems provide elimination of the latent failures and raise their reliability. Poor quality of carrying out the tests can be a source of the subsequent failures. Therefore excess frequency of tests can result in reducing reliability of safety systems. The method of optimization of maintenance periodicity of the equipment taking into account factors of its reliability and restoration procedures quality is submitted. The unavailability factor is used as a criterion of optimization of maintenance periodicity. It is offered to use parameters of reliability of the equipment and each of safety systems of NPPs received at developing PSA. And it is offered to carry out the concordance of maintenance periodicity of systems within the NPP maintenance program taking into account a significance factor of the system received on the basis of the contribution of system in CDF. Basing on the submitted method the small computer code is developed. This code allows to calculate reliability factors of a separate safety system and to determine optimum maintenance periodicity of its equipment. Optimization of maintenance periodicity of a complex of safety systems is stipulated also. As an example results of optimization of maintenance periodicity at Zaporizhzhya NPP are presented. (author)
Periodic solutions of nonautonomous differential systems modeling obesity population
Arenas, Abraham J. [Departamento de Matematicas y Estadistica, Universidad de Cordoba Monteria (Colombia)], E-mail: aarenas@sinu.unicordoba.edu.co; Gonzalez-Parra, Gilberto [Departamento de Calculo, Universidad de los Andes, Merida (Venezuela, Bolivarian Republic of)], E-mail: gcarlos@ula.ve; Jodar, Lucas [Instituto de Matematica Multidisciplinar, Universidad Politecnica de Valencia Edificio 8G, 2o, 46022 Valencia (Spain)], E-mail: ljodar@imm.upv.es
2009-10-30
In this paper we study the periodic behaviour of the solutions of a nonautonomous model for obesity population. The mathematical model represented by a nonautonomous system of nonlinear ordinary differential equations is used to model the dynamics of obese populations. Numerical simulations suggest periodic behaviour of subpopulations solutions. Sufficient conditions which guarantee the existence of a periodic positive solution are obtained using a continuation theorem based on coincidence degree theory.
Three positive doubly periodic solutions of a nonlinear telegraph system
Fang-lei WANG; Yu-kun AN
2009-01-01
This paper studies existence of at least three positive doubly periodic solutions of a coupled nonlinear telegraph system with doubly periodic boundary conditions. First, by using the Green function and maximum principle, existence of solutions of a nonlinear telegraph system is equivalent to existence of fixed points of an operator. By imposing growth conditions on the nonlinearities, existence of at least three fixed points in cone is obtained by using the Leggett-Williams fixed point theorem to cones in ordered Banach spaces. In other words, there exist at least three positive doubly periodic solutions of nonlinear telegraph system.
Four positive periodic solutions for the first order differential system
Zhang, Zhengqiu; Tang, Hengsheng
2007-08-01
In this paper, we establish the existence of four positive periodic solutions for the first order differential system by using the continuation theorem of coincidence degree theory. When our result is applied to a competition Lotka-Volterra population model, we obtain the existence of four positive periodic solutions for this model.
The periodic system of chemical elements: old and new developments
Some historical facts about the construction of a periodic system of chemical elements are reviewed. The Madelung rule is used to generate an unusual format for the periodic table. Following the work of Byakov, Kulakov, Rumer and Fet, such a format is further refined on the basis of a chain of groups starting with SU(2)xS0(4.2)
Nonlinear Stability of Periodic Traveling Waves of the BBM System
Hakkaev, S.
2013-01-01
This paper is concerned with the nonlinear stability of periodic traveling wave solutions for the coupled Benjamin-Bona-Mahony system. We show the existence of a family of dnoidal type traveling waves. We find conditions on parameters of the waves which imply the nonlinear stability of periodic traveling waves.
Periodicity of a class of nonlinear fuzzy systems with delays
The well known Takagi-Sugeno (T-S) model gives an effective method to combine some simple local systems with their linguistic description to represent complex nonlinear dynamic systems. By using the T-S method, a class of local nonlinear systems having nice dynamic properties can be employed to represent some global complex nonlinear systems. This paper proposes to study the periodicity of a class of global nonlinear fuzzy systems with delays by using T-S method. Conditions for guaranteeing periodicity are derived. Examples are employed to illustrate the theory.
Distribution of periodic trajectories of Anosov C-system
Görlich, Andrzej; Savvidy, Konstantin; Savvidy, George
2016-01-01
The hyperbolic Anosov C-systems have a countable set of everywhere dense periodic trajectories which have been recently used to generate pseudorandom numbers. The asymptotic distribution of periodic trajectories of C-systems with periods less than a given number is well known, but a deviation of this distribution from its asymptotic behaviour is less known. Using fast algorithms, we are studying the exact distribution of periodic trajectories and their deviation from asymptotic behaviour for hyperbolic C-systems which are defined on high dimensional tori and are used for Monte-Carlo simulations. A particular C-system which we consider in this article is the one which was implemented in the MIXMAX generator of pseudorandom numbers. The generator has the best combination of speed, reasonable size of the state, and availability for implementing the parallelization and is currently available generator in the ROOT and CLHEP software packages at CERN.
Real numbers having ultimately periodic representations in abstract numeration systems
Lecomte, P.; Rigo, M
2002-01-01
Using a genealogically ordered infinite regular language, we know how to represent an interval of R. Numbers having an ultimately periodic representation play a special role in classical numeration systems. The aim of this paper is to characterize the numbers having an ultimately periodic representation in generalized systems built on a regular language. The syntactical properties of these words are also investigated. Finally, we show the equivalence of the classical "theta"-expansions with o...
Inverse crystallization if Abrikosov vortex system at periodic pinning
Zyubin, M V; Kashurnikov, V A
2002-01-01
The vortex system in the quasi-two-dimensional HTSC plate is considered in the case of the periodic pinning. The M(H) magnetization curves by various values of the external magnetic field and different temperatures are calculated through the Monte Carlo method. It is shown that in the case of the periodic pinning the crystallization of the vortex system is possible by the temperature increase. A number of peculiarities conditioned by the impact of the pinning centers periodic lattice are identified on the magnetization curves. The pictures of the vortex distribution corresponding to various points on the M(H) curve are obtained
Lyapunov spectra of Coulombic and gravitational periodic systems
Kumar, Pankaj
2016-01-01
We compute Lyapunov spectra for Coulombic and gravitational versions of the one-dimensional systems of parallel sheets with periodic boundary conditions. Exact time evolution of tangent-space vectors are derived and are utilized toward computing Lypaunov characteristic exponents using an event-driven algorithm. The results indicate that the energy dependence of the largest Lyapunov exponent emulates that of Kolmogorov-entropy density for each system at different degrees of freedom. Our approach forms an effective and approximation-free tool toward studying the dynamical properties exhibited by the Coulombic and gravitational systems and finds applications in investigating indications of thermodynamic transitions in large versions of the spatially periodic systems.
Stroboscopic prethermalization in weakly interacting periodically driven systems
Canovi, Elena; Kollar, Marcus; Eckstein, Martin
2016-01-01
Time-periodic driving provides a promising route toward engineering nontrivial states in quantum many-body systems. However, while it has been shown that the dynamics of integrable, noninteracting systems can synchronize with the driving into a nontrivial periodic motion, generic nonintegrable systems are expected to heat up until they display a trivial infinite-temperature behavior. In this paper we show that a quasiperiodic time evolution over many periods can also emerge in weakly interacting systems, with a clear separation of the timescales for synchronization and the eventual approach of the infinite-temperature state. This behavior is the analog of prethermalization in quenched systems. The synchronized state can be described using a macroscopic number of approximate constants of motion. We corroborate these findings with numerical simulations for the driven Hubbard model.
Perturbative solution of Vlasov equation for periodically driven systems
Shah, Kushal
2015-01-01
Statistical systems with time-periodic spatially non-uniform forces are of immense importance in several areas of physics. In this paper, we provide an analytical expression of the time-periodic probability distribution function of particles in such a system by perturbatively solving the 1D Vlasov equation in the limit of high frequency and slow spatial variation of the time-periodic force. We find that the time-averaged distribution function and density cannot be written simply in terms of an effective potential, also known as the fictitious ponderomotive potential. We also find that the temperature of such systems is spatially non-uniform leading to a non-equilibrium steady state which can further lead to a complex statistical time evolution of the system. Finally, we outline a method by which one can use these analytical solutions of the Vlasov equation to obtain numerical solutions of the self-consistent Vlasov-Poisson equations for such systems.
Lei, Ling
2009-01-01
This work studies the stabilization for a periodic parabolic system under perturbations in the system conductivity. A perturbed system does not have any periodic solution in general. However, we will prove that the perturbed system can always be pulled back to a periodic system after imposing a control from a fixed finite dimensional subspace.
Bifurcations, Period doubling and chaos in clarinet-like systems
Maganza, Christian; Caussé, René; Laloë, Franck
1986-01-01
Wind instruments provide interesting hydrodynamical systems where non-linearities are important but well localized. A simple analysis shows that these systems should undergo Feignebaum-type route to chaos, with a cascade of period doublings. Experiments have been performed fo confirm these predictions
Electrostatics of solvated systems in periodic boundary conditions
Andreussi, Oliviero; Marzari, Nicola
2014-01-01
Continuum solvation methods can provide an accurate and inexpensive embedding of quantum simulations in liquid or complex dielectric environments. Notwithstanding a long history and manifold applications to isolated systems in open boundary conditions, their extension to materials simulations --- typically entailing periodic-boundary conditions --- is very recent, and special care is needed to address correctly the electrostatic terms. We discuss here how periodic-boundary corrections develop...
Periodic solutions and flip bifurcation in a linear impulsive system
Jiang Gui-Rong; Yang Qi-Gui
2008-01-01
In this paper,the dynamical behaviour of a linear impulsive system is discussed both theoretically and numerically.The existence and the stability of period-one solution are discussed by using a discrete map.The conditions of existence for flip bifurcation are derived by using the centre manifold theorem and bifurcation theorem.The bifurcation analysis shows that chaotic solutions appear via a cascade of period-doubling in some interval of parameters.Moreover,the periodic solutions,the bifurcation diagram,and the chaotic attractor,which show their consistence with the theoretical analyses,are given in an example.中图分类:O547
Mario Tolentino
1997-02-01
Full Text Available A history of the periodic table of the elements is presented, from the first tentative classifications, passing through Meyer and Mendeleev, up to recent speculations on super-heavy elements still to be synthesized. Many of the discussions and discoveries related to chemical elements and their proper periodic classification are also presented.
Mario Tolentino; Rocha-Filho, Romeu C.; Aécio Pereira Chagas
1997-01-01
A history of the periodic table of the elements is presented, from the first tentative classifications, passing through Meyer and Mendeleev, up to recent speculations on super-heavy elements still to be synthesized. Many of the discussions and discoveries related to chemical elements and their proper periodic classification are also presented.
Development of Seismic Isolation Systems Using Periodic Materials
Yan, Yiqun [Univ. of Houston, Houston, TX (United States); Mo, Yi-Lung [Univ. of Houston, Houston, TX (United States); Menq, Farn-Yuh [Univ. of Texas, Austin, TX (United States); Stokoe, II, Kenneth H. [Univ. of Texas, Austin, TX (United States); Perkins, Judy [Prairie View A & M University, Prairie View, TX (United States); Tang, Yu [Argonne National Lab. (ANL), Argonne, IL (United States)
2014-12-10
Advanced fast nuclear power plants and small modular fast reactors are composed of thin-walled structures such as pipes; as a result, they do not have sufficient inherent strength to resist seismic loads. Seismic isolation, therefore, is an effective solution for mitigating earthquake hazards for these types of structures. Base isolation, on which numerous studies have been conducted, is a well-defined structure protection system against earthquakes. In conventional isolators, such as high-damping rubber bearings, lead-rubber bearings, and friction pendulum bearings, large relative displacements occur between upper structures and foundations. Only isolation in a horizontal direction is provided; these features are not desirable for the piping systems. The concept of periodic materials, based on the theory of solid-state physics, can be applied to earthquake engineering. The periodic material is a material that possesses distinct characteristics that prevent waves with certain frequencies from being transmitted through it; therefore, this material can be used in structural foundations to block unwanted seismic waves with certain frequencies. The frequency band of periodic material that can filter out waves is called the band gap, and the structural foundation made of periodic material is referred to as the periodic foundation. The design of a nuclear power plant, therefore, can be unified around the desirable feature of a periodic foundation, while the continuous maintenance of the structure is not needed. In this research project, three different types of periodic foundations were studied: one-dimensional, two-dimensional, and three-dimensional. The basic theories of periodic foundations are introduced first to find the band gaps; then the finite element methods are used, to perform parametric analysis, and obtain attenuation zones; finally, experimental programs are conducted, and the test data are analyzed to verify the theory. This procedure shows that the
General approach for dealing with dynamical systems with spatiotemporal periodicities.
Casado-Pascual, Jesús; Cuesta, José A; Quintero, Niurka R; Alvarez-Nodarse, Renato
2015-02-01
Dynamical systems often contain oscillatory forces or depend on periodic potentials. Time or space periodicity is reflected in the properties of these systems through a dependence on the parameters of their periodic terms. In this paper we provide a general theoretical framework for dealing with these kinds of systems, regardless of whether they are classical or quantum, stochastic or deterministic, dissipative or nondissipative, linear or nonlinear, etc. In particular, we are able to show that simple symmetry considerations determine, to a large extent, how their properties depend functionally on some of the parameters of the periodic terms. For the sake of illustration, we apply this formalism to find the functional dependence of the expectation value of the momentum of a Bose-Einstein condensate, described by the Gross-Pitaewskii equation, when it is exposed to a sawtooth potential whose amplitude is periodically modulated in time. We show that, by using this formalism, a small set of measurements is enough to obtain the functional form for a wide range of parameters. This can be very helpful when characterizing experimentally the response of systems for which performing measurements is costly or difficult. PMID:25768567
Characterization of a periodically driven chaotic dynamical system
Crisanti, A; Lacorata, G; Purini, R; Crisanti, A
1996-01-01
We discuss how to characterize the behavior of a chaotic dynamical system depending on a parameter that varies periodically in time. In particular, we study the predictability time, the correlations and the mean responses, by defining a local--in--time version of these quantities. In systems where the time scale related to the time periodic variation of the parameter is much larger than the ``internal'' time scale, one has that the local quantities strongly depend on the phase of the cycle. In this case, the standard global quantities can give misleading information.
Long period seismic ground motions for isolation systems
In this paper numerical simulations of long period strong ground motions are calculated based on theoretical seismological models of the seismic source and wave propagation. The method includes both near-field and far-field terms and surface waves as well as body waves which allows valid simulations at both short and large distances. Long period ground motions for magnitude 6.75 and magnitude 8.0 events are computed at distances of 3 to 30 km. The resulting response spectral displacements are compared to the SEAOC 1990 spectrum for base-isolated system. At a period of 2 seconds, the SEAOC spectrum is close to the spectrum for a magnitude 8.0 earthquake. However, at a period of 5 seconds, the SEAOC spectrum is much larger than the simulated notions even for a magnitude 8 event
Periodic orbits near heteroclinic cycles in a cyclic replicator system.
Wang, Yuanshi; Wu, Hong; Ruan, Shigui
2012-04-01
A species is semelparous if every individual reproduces only once in its life and dies immediately after the reproduction. While the reproduction opportunity is unique per year and the individual's period from birth to reproduction is just n years, the individuals that reproduce in the ith year (modulo n) are called the ith year class, i = 1, 2, . . . , n. The dynamics of the n year-class system can be described by a differential equation system of Lotka-Volterra type. For the case n = 4, there is a heteroclinic cycle on the boundary as shown in previous works. In this paper, we focus on the case n = 4 and show the existence, growth and disappearance of periodic orbits near the heteroclinic cycle, which is a part of the conjecture by Diekmann and van Gils (SIAM J Appl Dyn Syst 8:1160-1189, 2009). By analyzing the Poincaré map near the heteroclinic cycle and introducing a metric to measure the size of the periodic orbit, we show that (i) when the average competitive degree among subpopulations (year classes) in the system is weak, there exists an asymptotically stable periodic orbit near the heteroclinic cycle which is repelling; (ii) the periodic orbit grows in size when some competitive degree increases, and converges to the heteroclinic cycle when the average competitive degree tends to be strong; (iii) when the average competitive degree is strong, there is no periodic orbit near the heteroclinic cycle which becomes asymptotically stable. Our results provide explanations why periodic solutions expand and disappear and why all but one subpopulation go extinct. PMID:21656008
Directed transport of coupled systems in symmetric periodic potentials
郑志刚; 刘凤芝; 高建
2003-01-01
In this paper, we discuss the damped unidirectional motions of a coupled lattice in a periodic potential. Each particle in the lattice is subject to a time-periodic ac force. Our studies reveal that a directed transport process can be observed when the ac forces acting on the coupled lattice have a phase shift (mismatch). This directed motion is a collaboration of the coupling, the substrate potential, and the periodic force, which are all.symmetric. The absence of any one of these three factors will not give rise to a directed current. We discuss the complex relations between the directed current and parameters in the system. Results in this paper can be accomplished in experiments. Moreover,our results can be generalized to the studies of directed transport processes in more complicated spatially extended systems.
Kubo formulas for dispersion in heterogeneous periodic nonequilibrium systems.
Guérin, T; Dean, D S
2015-12-01
We consider the dispersion properties of tracer particles moving in nonequilibrium heterogeneous periodic media. The tracer motion is described by a Fokker-Planck equation with arbitrary spatially periodic (but constant in time) local diffusion tensors and drifts, eventually with the presence of obstacles. We derive a Kubo-like formula for the time-dependent effective diffusion tensor valid in any dimension. From this general formula, we derive expressions for the late time effective diffusion tensor and drift in these systems. In addition, we find an explicit formula for the late finite-time corrections to these transport coefficients. In one dimension, we give a closed analytical formula for the transport coefficients. The formulas derived here are very general and provide a straightforward method to compute the dispersion properties in arbitrary nonequilibrium periodic advection-diffusion systems. PMID:26764628
Positive periodic solutions of periodic neutral Lotka-Volterra system with distributed delays
Li Yongkun [Department of Mathematics, Yunnan University Kunming, Yunnan 650091 (China)], E-mail: yklie@ynu.edu.cn
2008-07-15
By using a fixed point theorem of strict-set-contraction, some criteria are established for the existence of positive periodic solutions of the following periodic neutral Lotka-Volterra system with distributed delays (dx{sub i}(t))/(dt) =x{sub i}(t)[a{sub i}(t)-{sigma}{sub j=1}{sup n}b{sub ij}(t){integral}{sub -T{sub ij}}{sup 0}K{sub ij}({theta})x{sub j}( t+{theta})d{theta}-{sigma}{sub j=1}{sup n}c{sub ij}(t){integral}{sub -T{sub ij}}{sup 0}K{sub ij}({theta}) x{sub j}{sup '}(t+{theta})d{theta}],i=1,2,...,n, where a{sub i},b{sub ij},c{sub ij} element of C(R,R{sup +}) (i, j = 1, 2, ..., n) are {omega}-periodic functions, T{sub ij},T{sub ij} element of (0,{infinity}) (i, j = 1, 2, ..., n) and K{sub ij},K{sub ij} element of (R,R{sup +}) satisfying {integral}{sub -T{sub ij}}{sup 0}K{sub ij}({theta})d{theta}=1,{integral}{sub -T{sub ij}}{sup 0}K{sub ij}({theta})d{theta}=1, i, j = 1, 2, ..., n.
Almost periodic solutions to systems of parabolic equations
Janpou Nee
1994-01-01
Full Text Available In this paper we show that the second-order differential solution is 𝕃2-almost periodic, provided it is 𝕃2-bounded, and the growth of the components of a non-linear function of a system of parabolic equation is bounded by any pair of con-secutive eigenvalues of the associated Dirichlet boundary value problems.
Performance evaluation using periodic system-state measurements
Ellens, W.; Mandjes, M.; Berg, J.L. van den; Worm, D.T.H.; Błaszczuk, S.
2015-01-01
This paper deals with the problem of inferring short time-scale fluctuations of a system's behavior from periodic state measurements. In particular, we devise a novel, efficient procedure to compute four interesting performance metrics for a transient birth-death process on an interval of fixed leng
Transport of quantum states of periodically driven systems
Breuer, H. P.; Dietz, K.; Holthaus, M.
1990-01-01
We discuss the transport of quantum states on quasi-energy surfaces of periodically driven systems and establish their non-trivial structure. The latter is shown to be caused by diabatic transitions at lines of narrow avoided crossings. Some experimental consequences pertaining to adiabatic transport and Landau-Zener transitions among Floquet states are briefly sketched.
PERIODIC-ORBITS IN K-SYMMETRICAL DYNAMICAL-SYSTEMS
BRANDS, H; LAMB, JSW; HOVEIJN, [No Value
1995-01-01
A map L is called k-symmetric if its kth iterate L(k) possesses more symmetry than L, for some value of k. In k-symmetric systems, there exists a notion of k-symmetric orbits. This paper deals with k-symmetric periodic orbits. We derive a relation between orbits that are k-symmetric with respect to
Periodic Orbits for a Three-Dimensional Biological Differential Systems
Renato Colucci
2013-01-01
Full Text Available We study the existence of periodic orbit for a differential system describing the effects of indirect predation over two preys. Besides discussing a generalized version of the model, we present some remarks and numerical experiments for the nonautonomous version of the two models.
Population Growth and Periodic Instability of the International System
Piepers, Ingo
2006-01-01
From the perspective developed in this paper, it can be argued that exponential population growth resulted in the exponential decrease of the life-span of consecutive stable periods during the life-span of the European international system (1480-1945). However, it becomes evident as well that population growth as such is not a sufficient condition to generate a punctuated equilibrium dynamic in the war dynamics of the international system: other conditions and factors - and their interplay - ...
Bifurcation, Period Doublings and Chaos in Clarinetlike Systems
Maganza, Christian; Causse, René; Laloë, Franck
1986-01-01
cote interne IRCAM: Maganza86a / National audience Wind instrument provide interesting hydrodynamical systems where non-linearities are importantbut well localized. A simple analysis shows that these systems should undergo Feigenbaum-typeroute to chaos, with a cascade of period doublings. Experiments have been performed with anacoustical resonator and an "artificial" excitation (nonlinearities controlled by either analogic ordigital devices); they have confirmed these predictions.
Meng, Xinzhu; Chen, Lansun
2008-03-01
This paper studies a nonautonomous Lotka-Volterra dispersal systems with infinite time delay which models the diffusion of a single species into n patches by discrete dispersal. Our results show that the system is uniformly persistent under an appropriate condition. The sufficient condition for the global asymptotical stability of the system is also given. By using Mawhin continuation theorem of coincidence degree, we prove that the periodic system has at least one positive periodic solution, further, obtain the uniqueness and globally asymptotical stability for periodic system. By using functional hull theory and directly analyzing the right functional of almost periodic system, we show that the almost periodic system has a unique globally asymptotical stable positive almost periodic solution. We also show that the delays have very important effects on the dynamic behaviors of the system.
Second-order Green's function perturbation theory for periodic systems
Rusakov, Alexander A
2015-01-01
Despite recent advances, systematic quantitative treatment of the electron correlation problem in extended systems remains a formidable task. Systematically improvable Green's function methods capable of quantitatively describing weak and at least qualitatively strong correlations appear promising candidates for computational treatment of periodic systems. We present a periodic implementation of temperature-dependent self-consistent 2nd-order Green's function method (GF2), where the self-energy is evaluated in the basis of atomic orbitals. Evaluating the real-space self-energy in atomic orbitals and solving the Dyson equation in $\\mathbf{k}$-space are the key components of a computationally feasible algorithm. We apply this technique to the 1D hydrogen lattice - a prototypical crystalline system with a realistic Hamiltonian. By analyzing the behavior of the spectral functions, natural occupations, and self-energies, we claim that GF2 is able to recover metallic, band insulating, and at least qualitatively Mot...
Zhao, Guangyu; Ruan, Shigui
2011-01-01
We study the existence, uniqueness, and asymptotic stability of time periodic traveling wave solutions to a periodic diffusive Lotka-Volterra competition system. Under certain conditions, we prove that there exists a maximal wave speed c* such that for each wave speed c ≤ c*, there is a time periodic traveling wave connecting two semi-trivial periodic solutions of the corresponding kinetic system. It is shown that such a traveling wave is unique modulo translation and is monotone with respect...
Period Changes of the Algol System SZ Herculis
Lee, J. W.; Lee, C.-U.; Kim, S.-L.; Kim, H.-I.; Park, J.-H.; Hinse, T. C.
2012-04-01
New CCD photometric observations of SZ Her were obtained between February and May 2008. More than 1,100 times of minimum light spanning more than one century were used for the period analysis. We find that the orbital period of SZ Her has varied due to a combination of two periodic variations, with cycle lengths of P3 = 85.8 yr and P4 = 42.5 yr and semi-amplitudes of K3 = 0.013 days and K4 = 0.007 days, respectively. The most reasonable explanation for them is a pair of light-time-travel (LTT) effects driven by the existence of two M-type companions with minimum masses of M3 = 0.22 M⊙ and M4 = 0.19 M⊙, located at nearly 2:1 mean motion resonance. Then, SZ Her is a quadruple system and the 3rd and 4th components would stay in the stable orbital resonance.
Projective synchronization of a hyperchaotic system via periodically intermittent control
Huang Jun-Jian; Li Chuan-Dong; Zhang Wei; Wei Peng-Cheng
2012-01-01
We further study the projective synchronization of a new hyperchaotic system.Different from the most existing methods,intermittent control is applied to chaotic synchronization in the present paper.We formulate the intermittent control system that governs the dynamics of the projective synchronization error,then derive the sufficient conditions for the exponential stability of intermittent control system by using the Lyapunov stability theory,and finally establish the periodically intermittent controller according to the stability criterion by which the projective synchronization is expected to be achieved.The analytical results are also demonstrated by several numerical simulations.
Electrostatics of solvated systems in periodic boundary conditions
Andreussi, Oliviero; Marzari, Nicola
2014-12-01
Continuum solvation methods can provide an accurate and inexpensive embedding of quantum simulations in liquid or complex dielectric environments. Notwithstanding a long history and manifold applications to isolated systems in open boundary conditions, their extension to materials simulations, typically entailing periodic boundary conditions, is very recent, and special care is needed to address correctly the electrostatic terms. We discuss here how periodic boundary corrections developed for systems in vacuum should be modified to take into account solvent effects, using as a general framework the self-consistent continuum solvation model developed within plane-wave density-functional theory [O. Andreussi et al., J. Chem. Phys. 136, 064102 (2012), 10.1063/1.3676407]. A comprehensive discussion of real- and reciprocal-space corrective approaches is presented, together with an assessment of their ability to remove electrostatic interactions between periodic replicas. Numerical results for zero- and two-dimensional charged systems highlight the effectiveness of the different suggestions, and underline the importance of a proper treatment of electrostatic interactions in first-principles studies of charged systems in solution.
Floquet analysis of a quantum system with modulated periodic driving
Novičenko, Viktor; Juzeliūnas, Gediminas
2016-01-01
We consider a generic quantum system periodically driven with a strength which varies slowly on the scale of the driving period. The analysis is based on a general formulation of the Floquet theory relying on the extended Hilbert space. In addition to a fast periodic modulation we allow the Hamiltonian to have an extra (slow) time-dependence. The dynamics of the system can then be described in terms of a slowly varying effective Floquet Hamiltonian that captures the long-term evolution, as well as rapidly oscillating micromotion operators. We obtain a systematic high-frequency expansion of all these operators. In contrast to the previous studies, the expanded effective Hamiltonian is now time-dependent and contains extra terms reflecting the modulation of the periodic Hamiltonian. The same applies to the micromotion operators which exhibit a slow temporal dependence in addition to the rapid oscillations. As an illustration, we consider a quantum-mechanical spin in an oscillating magnetic field with a slowly c...
Dynamic steady-state of periodically-driven quantum systems
Yudin, V I; Basalaev, M Yu; Kovalenko, D
2015-01-01
Using the density matrix formalism, we prove an existence theorem of the periodic steady-state for an arbitrary periodically-driven system. This state has the same period as the modulated external influence, and it is realized as an asymptotic solution ($t$$\\to$$+\\infty$) due to relaxation processes. The presented derivation simultaneously contains a simple computational algorithm non-using both Floquet and Fourier theories, i.e. our method automatically guarantees a full account of all frequency components. The description is accompanied by the examples demonstrating a simplicity and high efficiency of our method. In particular, for three-level $\\Lambda$-system we calculate the lineshape and field-induced shift of the dark resonance formed by the field with periodically modulated phase. For two-level atom we obtain the analytical expressions for signal of the direct frequency comb spectroscopy with rectangular light pulses. In this case it was shown the radical dependence of the spectroscopy lineshape on pul...
Periodic orbits of hybrid systems and parameter estimation via AD
Rhythmic, periodic processes are ubiquitous in biological systems; for example, the heart beat, walking, circadian rhythms and the menstrual cycle. Modeling these processes with high fidelity as periodic orbits of dynamical systems is challenging because: (1) (most) nonlinear differential equations can only be solved numerically; (2) accurate computation requires solving boundary value problems; (3) many problems and solutions are only piecewise smooth; (4) many problems require solving differential-algebraic equations; (5) sensitivity information for parameter dependence of solutions requires solving variational equations; and (6) truncation errors in numerical integration degrade performance of optimization methods for parameter estimation. In addition, mathematical models of biological processes frequently contain many poorly-known parameters, and the problems associated with this impedes the construction of detailed, high-fidelity models. Modelers are often faced with the difficult problem of using simulations of a nonlinear model, with complex dynamics and many parameters, to match experimental data. Improved computational tools for exploring parameter space and fitting models to data are clearly needed. This paper describes techniques for computing periodic orbits in systems of hybrid differential-algebraic equations and parameter estimation methods for fitting these orbits to data. These techniques make extensive use of automatic differentiation to accurately and efficiently evaluate derivatives for time integration, parameter sensitivities, root finding and optimization. The boundary value problem representing a periodic orbit in a hybrid system of differential algebraic equations is discretized via multiple-shooting using a high-degree Taylor series integration method (GM00, Phi03). Numerical solutions to the shooting equations are then estimated by a Newton process yielding an approximate periodic orbit. A metric is defined for computing the distance
Periodic orbits of hybrid systems and parameter estimation via AD.
Guckenheimer, John. (Cornell University); Phipps, Eric Todd; Casey, Richard (INRIA Sophia-Antipolis)
2004-07-01
Rhythmic, periodic processes are ubiquitous in biological systems; for example, the heart beat, walking, circadian rhythms and the menstrual cycle. Modeling these processes with high fidelity as periodic orbits of dynamical systems is challenging because: (1) (most) nonlinear differential equations can only be solved numerically; (2) accurate computation requires solving boundary value problems; (3) many problems and solutions are only piecewise smooth; (4) many problems require solving differential-algebraic equations; (5) sensitivity information for parameter dependence of solutions requires solving variational equations; and (6) truncation errors in numerical integration degrade performance of optimization methods for parameter estimation. In addition, mathematical models of biological processes frequently contain many poorly-known parameters, and the problems associated with this impedes the construction of detailed, high-fidelity models. Modelers are often faced with the difficult problem of using simulations of a nonlinear model, with complex dynamics and many parameters, to match experimental data. Improved computational tools for exploring parameter space and fitting models to data are clearly needed. This paper describes techniques for computing periodic orbits in systems of hybrid differential-algebraic equations and parameter estimation methods for fitting these orbits to data. These techniques make extensive use of automatic differentiation to accurately and efficiently evaluate derivatives for time integration, parameter sensitivities, root finding and optimization. The boundary value problem representing a periodic orbit in a hybrid system of differential algebraic equations is discretized via multiple-shooting using a high-degree Taylor series integration method [GM00, Phi03]. Numerical solutions to the shooting equations are then estimated by a Newton process yielding an approximate periodic orbit. A metric is defined for computing the distance
Fractal spectrum of a quasi-periodically driven spin system
Guarneri, I; Guarneri, I; DiMeo, M
1995-01-01
We numerically perform a spectral analysis of a quasi-periodically driven spin 1/2 system, the spectrum of which is Singular Continuous. We compute fractal dimensions of spectral measures and discuss their connections with the time behaviour of various dynamical quantities, such as the moments of the distribution of the wave packet. Our data suggest a close similarity between the information dimension of the spectrum and the exponent ruling the algebraic growth of the 'entropic width' of wavepackets.
Vibration isolation of automotive vehicle engine using periodic mounting systems
Asiri, S.
2005-05-01
Customer awareness and sensitivity to noise and vibration levels have been raised through increasing television advertisement, in which the vehicle noise and vibration performance is used as the main market differentiation. This awareness has caused the transportation industry to regard noise and vibration as important criteria for improving market shares. One industry that tends to be in the forefront of the technology to reduce the levels of noise and vibration is the automobile industry. Hence, it is of practical interest to reduce the vibrations induced structural responses. The automotive vehicle engine is the main source of mechanical vibrations of automobiles. The engine is vulnerable to the dynamic action caused by engine disturbance force in various speed ranges. The vibrations of the automotive vehicle engines may cause structural failure, malfunction of other parts, or discomfort to passengers because of high level noise and vibrations. The mounts of the engines act as the transmission paths of the vibrations transmitted from the excitation sources to the body of the vehicle and passengers. Therefore, proper design and control of these mounts are essential to the attenuation of the vibration of platform structures. To improve vibration resistant capacities of engine mounting systems, vibration control techniques may be used. For instance, some passive and semi-active dissipation devices may be installed at mounts to enhance vibration energy absorbing capacity. In the proposed study, a radically different concept is presented whereby periodic mounts are considered because these mounts exhibit unique dynamic characteristics that make them act as mechanical filters for wave propagation. As a result, waves can propagate along the periodic mounts only within specific frequency bands called the "Pass Bands" and wave propagation is completely blocked within other frequency bands called the "Stop Bands". The experimental arrangements, including the design of
Driven nonequilibrium lattice systems with shifted periodic boundary conditions
Valles, J.L. (New York Univ., NY (USA)); Leung, K.; Zia, R.K.P. (Virginia Polytechnic Institute and State Univ., Blacksburg (USA))
1989-07-01
The authors present the first study of a driven nonequilibrium lattice system in the two-phase region, with shifted periodic boundary conditions, forcing steps into the interface. When the shift corresponds to small angles with respect to the driving field, they find nonanalytic behavior in the (internal) energy of the system, supporting numerical evidence that interface roughness is suppressed by the field. For larger shifts, the competition between the driving field and the boundary induces the breakup of a single strip with tilted interfaces into many narrower strips with aligned interfaces. The size and temperature dependences of the critical angles of such breakup transitions are studied.
Stability Analysis for Multi-Parameter Linear Periodic Systems
Seyranian, A.P.; Solem, Frederik; Pedersen, Pauli
1999-01-01
This paper is devoted to stability analysis of general linear periodic systems depending on real parameters. The Floquet method and perturbation technique are the basis of the development. We start out with the first and higher-order derivatives of the Floquet matrix with respect to problem...... parameters. Then the behaviour of simple and multiple multipliers of the system with a change of parameters is studied. Weak and strong interactions of multipliers in the complex plane are treated separately. The presented theory is exemplified and discussed....
Signatures of resonant terrestrial planets in long-period systems
Kennedy, Gareth F
2009-01-01
The majority of extrasolar planets discovered to date have significantly eccentric orbits, some if not all of which may have been produced through planetary migration. During this process, any planets interior to such an orbit would therefore have been susceptible to resonance capture, and hence may exhibit measurable orbital period variations. Here we summarize the results of our investigation into the possibility of detecting low-mass planets which have been captured into the strong 2:1 resonance. Using analytical expressions together with simulated data we showed that it is possible to identify the existence of a low-mass companion in the internal 2:1 resonance by estimating the time-dependant orbital period for piecewise sections of radial velocity data. This works as long as the amplitude of modulation of the orbital period is greater than its uncertainty, which in practice means that the system should not be too close to exact resonance. Here we provide simple expressions for the libration period and th...
Geometric method for forming periodic orbits in the Lorenz system
Nicholson, S. B.; Kim, Eun-jin
2016-04-01
Many systems in nature are out of equilibrium and irreversible. The non-detailed balance observable representation (NOR) provides a useful methodology for understanding the evolution of such non-equilibrium complex systems, by mapping out the correlation between two states to a metric space where a small distance represents a strong correlation [1]. In this paper, we present the first application of the NOR to a continuous system and demonstrate its utility in controlling chaos. Specifically, we consider the evolution of a continuous system governed by the Lorenz equation and calculate the NOR by following a sufficient number of trajectories. We then show how to control chaos by converting chaotic orbits to periodic orbits by utilizing the NOR. We further discuss the implications of our method for potential applications given the key advantage that this method makes no assumptions of the underlying equations of motion and is thus extremely general.
Periodically driven ergodic and many-body localized quantum systems
We study dynamics of isolated quantum many-body systems whose Hamiltonian is switched between two different operators periodically in time. The eigenvalue problem of the associated Floquet operator maps onto an effective hopping problem. Using the effective model, we establish conditions on the spectral properties of the two Hamiltonians for the system to localize in energy space. We find that ergodic systems always delocalize in energy space and heat up to infinite temperature, for both local and global driving. In contrast, many-body localized systems with quenched disorder remain localized at finite energy. We support our conclusions by numerical simulations of disordered spin chains. We argue that our results hold for general driving protocols, and discuss their experimental implications
Zijian Liu
2015-01-01
Full Text Available We study a two-patch impulsive migration periodic N-species Lotka-Volterra competitive system. Based on analysis method, inequality estimation, and Lyapunov function method, sufficient conditions for the permanence and existence of a unique globally stable positive periodic solution of the system are established. Some numerical examples are shown to verify our results and discuss the model further.
Discrete changes of current statistics in periodically driven stochastic systems
We demonstrate that the counting statistics of currents in periodically driven ergodic stochastic systems can show sharp changes of some of its properties in response to continuous changes of the driving protocol. To describe this effect, we introduce a new topological phase factor in the evolution of the moment generating function which is akin to the topological geometric phase in the evolution of a periodically driven quantum mechanical system with time-reversal symmetry. This phase leads to the prediction of a sign change for the difference of the probabilities to find even and odd numbers of particles transferred in a stochastic system in response to cyclic evolution of control parameters. The driving protocols that lead to this sign change should enclose specific degeneracy points in the space of control parameters. The relation between the topology of the paths in the control parameter space and the sign changes can be described in terms of the first Stiefel–Whitney class of topological invariants. (letter)
Semiclassical quantization of nonadiabatic systems with hopping periodic orbits
Fujii, Mikiya, E-mail: mikiya.fujii@gmail.com; Yamashita, Koichi [Department of Chemical System Engineering, School of Engineering, The University of Tokyo, Tokyo 113-8656 (Japan); JST, CREST, Tokyo 113-8656 (Japan)
2015-02-21
We present a semiclassical quantization condition, i.e., quantum–classical correspondence, for steady states of nonadiabatic systems consisting of fast and slow degrees of freedom (DOFs) by extending Gutzwiller’s trace formula to a nonadiabatic form. The quantum–classical correspondence indicates that a set of primitive hopping periodic orbits, which are invariant under time evolution in the phase space of the slow DOF, should be quantized. The semiclassical quantization is then applied to a simple nonadiabatic model and accurately reproduces exact quantum energy levels. In addition to the semiclassical quantization condition, we also discuss chaotic dynamics involved in the classical limit of nonadiabatic dynamics.
Khazan A.
2011-01-01
Full Text Available In the earlier study (Khazan A. Upper Limit in Mendeleev's Periodic Table - Element No.155. 2nd ed., Svenska fysikarkivet, Stockholm, 2010 the author showed how Rhodium can be applied to the hyperbolic law of the Periodic Table of Elements in order to calculate, with high precision, all other elements conceivable in the Table. Here we obtain the same result, with use of fraction linear functions (adjacent hyperbolas.
Non-dispersive wave packets in periodically driven quantum systems
Buchleitner, A; Zakrzewski, J; Buchleitner, Andreas; Delande, Dominique; Zakrzewski, Jakub
2002-01-01
With the exception of the harmonic oscillator, quantum wave-packets usually spread as time evolves. We show here that, using the nonlinear resonance between an internal frequency of a system and an external periodic driving, it is possible to overcome this spreading and build non-dispersive (or non-spreading) wave-packets which are well localized and follow a classical periodic orbit without spreading. From the quantum mechanical point of view, the non-dispersive wave-packets are time periodic eigenstates of the Floquet Hamiltonian, localized in the nonlinear resonance island. We discuss the general mechanism which produces the non-dispersive wave-packets, with emphasis on simple realization in the electronic motion of a Rydberg electron driven by a microwave field. We show the robustness of such wavepackets for a model one-dimensional as well as for realistic three dimensional atoms. We consider their essential properties such as the stability versus ionization, the characteristic energy spectrum and long li...
Characterizing the Period Ratio Distribution of Kepler Exoplanetary Systems
Conaway, James L.; Ragozzine, Darin
2016-01-01
Many of the exoplanetary systems discovered by the Kepler space telescope demonstrate unusual properties which need to be explored in order to better understand planetary system formation and evolution. Among these interesting properties is an excess in the number of planets orbiting in resonance or near-resonance with their neighbors. The prevailing assumption in the planetary sciences community is that these are real features of the exoplanet population, but many theories developed on this assumption produce a resonance structure quite different from what we see. In our work we explore the possibility that the actual resonances may not be as we observe them, and may instead be explained by a combination of real resonance features and/or observational bias resulting from geometric effects. In particular, if the near-resonant systems have a different inclination distribution than other systems, then it is possible for them to be over or under-represented.We analyze the existing Kepler data and generate models which approximately represent the empirical period ratio distribution. The 2:1 and 3:2 just-wide-of-resonance excesses are included in the model, along with the deficit of period ratios just short of the 2:1 resonance. We test the Kepler data set against these models using the Python emcee package in order to determine the best-fit parameters for each model. We then address the inclination distribution question by generating two-planet systems with different inclination distributions for the near-resonant systems. We use the CORBITS package (https://github.com/jbrakensiek/CORBITS, Brakensiek & Ragozzine, submitted) to determine the probability of detecting both planets in transit. These tests adjust the relative sizes of the resonance excesses as well as orbital parameters (primarily inclination and nodal alignments) in order to determine which combinations of parameters would create in an observational bias resulting in the resonance excesses seen in the
Statistics of work distribution in periodically driven closed quantum systems.
Dutta, Anirban; Das, Arnab; Sengupta, K
2015-07-01
We study the statistics of the work distribution P(w) in a d-dimensional closed quantum system with linear dimension L subjected to a periodic drive with frequency ω(0). We show that the corresponding rate function I(w)=-ln[P(w)/Λ(0)]/L^{d} after a drive period satisfies a universal lower bound I(0)≥n(d) and has a zero at w=QL(d)/N, where n(d) and Q are the excitation and the residual energy densities generated during the drive, Λ(0) is a constant fixed by the normalization of P(w), and N is the total number of constituent particles or spins in the system. We supplement our results by calculating I(w) for a class of d-dimensional integrable models and show that I(w) has an oscillatory dependence on ω(0) originating from Stuckelberg interference generated due to double passage through the critical point or region during the drive. We suggest experiments to test our theory. PMID:26274122
Wide aperture periodic lens system for multiple Compton backscattering
Miyahara, Y
2002-01-01
Polarized gamma-ray generation by Compton backscattering in a periodic focusing system of electron and laser beams is discussed for the production of polarized positron beam in a linear collider. Circularly polarized CO sub 2 laser beams are focused by an optical lens series and collided with a 5.8 GeV electron beam to generate circularly polarized gamma-rays with 60 MeV at a maximum. In the present work, the basic concept of periodic lens system discussed previously is reconsidered to reduce the laser power required for a gamma-ray yield of 7x10 sup 1 sup 5 gamma/s and the peak laser power density at lenses as much as possible for technical practice. The electron beam is focused by a series of permanent quadrupole magnets with a FODO structure. The power is reduced to six sources with 5.6 kW each, and the peak power density is reduced to 1.4 GW/cm sup 2. These values can be reduced further by using a longer laser pulse length and a damping ring for the electron beam.
Periodic inspection optimization model for a complex repairable system
Taghipour, Sharareh, E-mail: sharareh@mie.utoronto.c [Department of Mechanical and Industrial Engineering, University of Toronto, Toronto, Ont., M5S 3G8 (Canada); Banjevic, Dragan; Jardine, Andrew K.S. [Department of Mechanical and Industrial Engineering, University of Toronto, Toronto, Ont., M5S 3G8 (Canada)
2010-09-15
This paper proposes a model to find the optimal periodic inspection interval on a finite time horizon for a complex repairable system. In general, it may be assumed that components of the system are subject to soft or hard failures, with minimal repairs. Hard failures are either self-announcing or the system stops when they take place and they are fixed instantaneously. Soft failures are unrevealed and can be detected only at scheduled inspections but they do not stop the system from functioning. In this paper we consider a simple policy where soft failures are detected and fixed only at planned inspections, but not at moments of hard failures. One version of the model takes into account the elapsed times from soft failures to their detection. The other version of the model considers a threshold for the total number of soft failures. A combined model is also proposed to incorporate both threshold and elapsed times. A recursive procedure is developed to calculate probabilities of failures in every interval, and expected downtimes. Numerical examples of calculation of optimal inspection frequencies are given. The data used in the examples are adapted from a hospital's maintenance data for a general infusion pump.
Eigenvalues, eigenfunctions, and surface states in finite periodic systems
Using a simple approach that requires neither the Bloch functions nor the reciprocal lattice, new, compact, and rigorous analytical formulas are derived for an accurate evaluation of resonant energies, resonant states, energy eigenvalues and eigenfunctions of open and bounded n-cell periodic systems with arbitrary 1D potential shapes, provided the single cell transfer matrix is given. These formulas are applied to obtain the energy spectra and wave functions of a number of simple but representative open and bounded superlattices. We solve the fine structure in bands and exhibit unambiguously that the true eigenfunctions do no not fulfill the periodicity property vertical bar Ψμ,ν (z + l c)vertical bar 2 = vertical bar Ψ μ,ν (z)vertical bar 2, with l c the single cell length. We show that the well known surface states and surface energy levels come out naturally. We analyze the surface repulsion effect and calculate exactly the surface energy levels for different potential discontinuities an the ends
Period of K system generator of pseudorandom numbers
Akopov, N Z; Floratos, Emmanuel G; Savvidy, G K
1996-01-01
We analyze the structure of the periodic trajectories of the matrix generator of pseudorandom numbers which has been proposed earlier. The structure of the periodic trajectories becomes more transparent when the rational sublattice coincides with the Galois field GF[p]. We are able to compute the period of the trajectories as a function of p and the dimension of the matrix d.
Z Cha in superoutburst - Periodic variation in the systemic velocity
Honey, W. B.; Charles, P. A.; Whitehurst, R.; Barrett, P. E.; Smale, A. P.
1988-03-01
The authors present photometric and spectroscopic data from the May 1984 and December 1985 superoutbursts of the SU UMa system Z Cha. By fitting composite absorption and emission profiles to the spectroscopic data, radial velocity curves were produced for each night using Hβ, Hγ, Hδ, He I λ4471, and Ca II K. The mean (γ) of each of these velocity curves is found to be non-zero (i.e. they do not represent the quiescent value of the systemic velocity) and it is found that γ is modulated on the superhump beat period of 2.1 days with a zero-velocity phase of ≡0.75, and amplitude of ≡80 km s-1. The mean of the modulation is compatible with the quiescent value of γ = 0±9 km s-1. This observational result is interpreted with new non-axisymmetric disc simulations as arising in an eccentric, precessing disc which is tidally distorted by the secondary.
Z Cha in superoutburst: periodic variation in the systemic velocity
Honey, W.B.; Charles, P.A.; Whitehurst, R.; Barrett, P.E.; Smale, A.P.
1988-03-01
Photometric and spectroscopic data from the May 1984 and December 1985 superoutbursts of the SU UMa system Z Cha are presented. By fitting composite absorption and emission profiles to the spectroscopic data, radial velocity curves were produced for each night using H..beta.., H..gamma.., Hdelta, He Ilambda4471, and Ca II K. The mean (..gamma..) of each of these velocity curves is found to be non-zero (i.e. they do not represent the quiescent value of the systemic velocity) and it is found that ..gamma.. is modulated on the superhump beat period of 2.1 days with a zero-velocity phase of approx. 0.75, and amplitude of approx. 80 km s/sup -1/. The mean of the modulation is compatible with the quiescent value of ..gamma.. = 0 +- 9 km s/sup -1/. This observational result is interpreted with new non-axisymmetric disc simulations as arising in an eccentric, precessing disc which is tidally distorted by the secondary.
Interior crises in quasiperiodically forced period-doubling systems
As a representative model for quasiperiodically forced period-doubling systems, we consider the quasiperiodically forced logistic map, and investigate the dynamical mechanism for the interior crises. For small quasiperiodic forcing ε, a chaotic attractor abruptly widens via a 'standard' interior crisis when it collides with a smooth unstable torus. However, as ε passes a threshold value, the smooth unstable torus loses its accessibility from the interior of the basin of the attractor. For this case, we use the rational approximation to the quasiperiodic forcing, and find that a nonstandard interior crisis occurs for a nonchaotic attractor (smooth torus or strange nonchaotic attractor) as well as a chaotic attractor when it collides with an invariant 'ring-shaped' unstable set. Particularly, we note that a three-band smooth torus transforms into a single-band intermittent strange nonchaotic attractor through the nonstandard interior crisis. The intermittent strange nonchaotic attractor is also characterized in terms of the average interburst time and the local Lyapunov exponent
Analysis of the Mode of the Periodically Time-varying Vibration Systems
WANG Sheng-ze; REN Ji-ge
2007-01-01
By Liapunov reducibility theorem, the periodically time-varying vibration system can be transformed to a linear time-invariant system. Based on the dynamic characteristics of the linear time-invariant system, the mode of the periodically time-varying vibration system has been discussed. The paper defines the mode and analyzes its characteristics. It can be found that the mode of the periodically time-varying system is periodically time-varing but has such characteristics as orthogonality. Finally, a method is given to solve the mode. By solving the eigenvalues and the eigenvectors of the state transition matrix in one period, the periodically time-varying mode can be obtained.
A reliability model of a system which includes a protected object and a safety system has been proposed. The model allows taking into consideration the sequence of the system elements failures resulting in the system failure, as well as periodic serviceability testing of the elements. The described procedure of asymptotic estimations obtaining the mean time to failure and the failure probability depending on time is based in the renewal theory and considerably more simple than traditionally used Markov and semi-Markov models. The model application for rector control system sub-system reliability analysis was demonstrated
Gravitational waves from periodic three-body systems.
Dmitrašinović, V; Suvakov, Milovan; Hudomal, Ana
2014-09-01
Three bodies moving in a periodic orbit under the influence of Newtonian gravity ought to emit gravitational waves. We have calculated the gravitational radiation quadrupolar waveforms and the corresponding luminosities for the 13+11 recently discovered three-body periodic orbits in Newtonian gravity. These waves clearly allow one to distinguish between their sources: all 13+11 orbits have different waveforms and their luminosities (evaluated at the same orbit energy and body mass) vary by up to 13 orders of magnitude in the mean, and up to 20 orders of magnitude for the peak values. PMID:25238346
Molecular Dynamics ofa Coulomb System with Deformable Periodic Boundary Conditions
Totsuji, Hiroo; Shirokoshi, Hideki; Nara, Shigetoshi
1991-01-01
Variable shape molecular dynamics is formulated for the one-component plasma and the structural transition from the fcc lattice to the bcc lattice has been observed. It is emphasized that the condition of constant volume should be imposed when deformations of periodic boundary conditions are taken into account.
Dynamical System Approach to a Coupled Dispersionless System: Localized and Periodic Traveling Waves
Gambo Betchewe; Kuetche Kamgang Victor; Bouetou Bouetou Thomas; Timoleon Crepin Kofane
2009-01-01
We investigate the dynamical behavior of a coupled dispersionlees system describing a current-conducting string with infinite length within a magnetic field.Thus,following a dynamical system approach,we unwrap typical miscellaneous traveling waves including localized and periodic ones.Studying the relative stabilities of such structures through their energy densities,we find that under some boundary conditions,localized waves moving in positive directions are more stable than periodic waves which in contrast stand for the most stable traveling waves in another boundary condition situation.
The periodic table: icon and inspiration.
Poliakoff, Martyn; Tang, Samantha
2015-03-13
To start this discussion meeting on the new chemistry of the elements held on 12 May 2014, Martyn Poliakoff, Foreign Secretary of the Royal Society, was invited to give the opening remarks. As a chemist and a presenter of the popular online video channel 'The periodic table of videos', Martyn communicates his personal and professional interest in the elements to the public, who in turn use these videos both as an educational resource and for entertainment purposes. Ever since Mendeleev's first ideas for the periodic table were published in 1869, the table has continued to grow as new elements have been discovered, and it serves as both icon and inspiration; its form is now so well established that it is recognized the world over as a symbol for science. This paper highlights but a few of the varied forms that the table can take, such as an infographic, which can convey the shortage of certain elements with great impact. PMID:25666072
Wiediger, Susan D.
2009-01-01
The periodic table and the periodic system are central to chemistry and thus to many introductory chemistry courses. A number of existing activities use various data sets to model the development process for the periodic table. This paper describes an image arrangement computer program developed to mimic a paper-based card sorting periodic table…
Chaos in periodically forced Holling type IV predator-prey system with impulsive perturbations
The effect of periodic forcing and impulsive perturbations on predator-prey model with Holling type IV functional response is investigated. The periodic forcing is affected by assuming a periodic variation in the intrinsic growth rate of the prey. The impulsive perturbations are affected by introducing periodic constant impulsive immigration of predator. The dynamical behavior of the system is simulated and bifurcation diagrams are obtained for different parameters. The results show that periodic forcing and impulsive perturbation can easily give rise to complex dynamics, including (1) quasi-periodic oscillating, (2) period doubling cascade, (3) chaos, (4) period halfing cascade
Chaos in periodically forced Holling type II predator-prey system with impulsive perturbations
The effect of periodic forcing and impulsive perturbations on predator-prey model with Holling type II functional response is investigated. The periodic forcing is affected by assuming a periodic variation in the intrinsic growth rate of prey. The impulsive perturbation is affected by introducing periodic constant impulsive immigration of predator. The dynamical behavior of the system is simulated and bifurcation diagrams are obtained for different parameters. The results show that periodic forcing and impulsive perturbation can very easily give rise to complex dynamics, including (1) quasi-periodic oscillating, (2) period doubling cascade, (3) chaos, (4) period halfing cascade, (5) non-unique dynamics
State of the glutathione system at different periods after irradiation
The effect of the 3-fold irradiation on the glutatione system was studied. Activation of these system was shown to take place at early terms (1 hour) after irradiation, then it was exhausted that resulted in accumulation of lipid peroxidation products in blood. This phase changes in glutathione system could be correspond to certain stages of stress-syndrome. (author)
Diffusion in stochastically and periodically modulated Hamiltonian systems
We consider an area preserving map whose linear frequency is stochastically perturbed. When no low order resonances are present a Fokker-Planck equation for the action diffusion is written and its solution agrees with the simulation of the process. The key point is the description of the map with an interpolating hamiltonian for which the action diffusion coefficient can be analytically computed. When the frequency has a slow periodic modulation, then for low amplitudes the diffusion is limited to the action interval swept by a chain of islands, whereas for large amplitudes the diffusion reaches the dynamic aperture as in the stochastic case
Periodic solutions of systems with asymptotically even nonlinearities
Peter E. Kloeden
2000-01-01
Full Text Available New conditions of solvability based on a general theorem on the calculation of the index at infinity for vector fields that have degenerate principal linear part as well as degenerate next order terms are obtained for the 2π-periodic problem for the scalar equation x″+n2x=g(|x|+f(t,x+b(t with bounded g(u and f(t,x→0 as |x|→0. The result is also applied to the solvability of a two-point boundary value problem and to resonant problems for equations arising in control theory.
On-Iine Management System for the Periodicals in JAERl
Itabashi, Keizo; Mineo, Yukinobu
The article describes the outlines of the on-line serials control system utilizing a mini-computer. The system is dealt with subscription, check-in, claiming, inquiry of serials information and binding of journals. In this system journal acquisition with serial arrival prediction in an on-line mode is carried on a priority principle to record the actual receipt of incoming issues.
Positive periodic solutions for a neutral Lotka-Volterra system with state dependent delays
Li, Yongkun; Zhao, Lili
2009-04-01
By using a fixed point theorem of strict-set-contraction, some new criteria are established for the existence of positive periodic solutions of the following periodic neutral Lotka-Volterra system with state dependent delays
Feedback Control in a General Almost Periodic Discrete System of Plankton Allelopathy
Wenshuang Yin
2014-01-01
We study the properties of almost periodic solutions for a general discrete system of plankton allelopathy with feedback controls and establish a theorem on the uniformly asymptotic stability of almost periodic solutions.
Enhancing Quantum Effects via Periodic Modulations in Optomechanical Systems
Farace, Alessandro; Giovannetti, Vittorio
2012-01-01
Parametrically modulated optomechanical systems have been recently proposed as a simple and efficient setting for the quantum control of a micromechanical oscillator: relevant possibilities include the generation of squeezing in the oscillator position (or momentum) and the enhancement of entanglement between mechanical and radiation modes. In this paper we further investigate this new modulation regime, considering an optomechanical system with one or more parameters being modulated over tim...
Shimeld, John; Li, Qingmou; Chian, Deping; Lebedeva-Ivanova, Nina; Jackson, Ruth; Mosher, David; Hutchinson, Deborah
2016-01-01
The Canada Basin and the southern Alpha-Mendeleev ridge complex underlie a significant proportion of the Arctic Ocean, but the geology of this undrilled and mostly ice-covered frontier is poorly known. New information is encoded in seismic wide-angle reflections and refractions recorded with expendable sonobuoys between 2007 and 2011. Velocity-depth samples within the sedimentary succession are extracted from published analyses for 142 of these records obtained at irregularly spaced stations across an area of 1.9E + 06 km2. The samples are modelled at regional, subregional and station-specific scales using an exponential function of inverse velocity versus depth with regionally representative parameters determined through numerical regression. With this approach, smooth, non-oscillatory velocity-depth profiles can be generated for any desired location in the study area, even where the measurement density is low. Practical application is demonstrated with a map of sedimentary thickness, derived from seismic reflection horizons interpreted in the time domain and depth converted using the velocity-depth profiles for each seismic trace. A thickness of 12-13 km is present beneath both the upper Mackenzie fan and the middle slope off of Alaska, but the sedimentary prism thins more gradually outboard of the latter region. Mapping of the observed-to-predicted velocities reveals coherent geospatial trends associated with five subregions: the Mackenzie fan; the continental slopes beyond the Mackenzie fan; the abyssal plain; the southwestern Canada Basin; and, the Alpha-Mendeleev magnetic domain. Comparison of the subregional velocity-depth models with published borehole data, and interpretation of the station-specific best-fitting model parameters, suggests that sandstone is not a predominant lithology in any of the five subregions. However, the bulk sand-to-shale ratio likely increases towards the Mackenzie fan, and the model for this subregion compares favourably with
Evaluation of electric power distribution systems: period 1984/89
The historical evolution of electric power distribution systems in Brazil, during 1984 to 1989 is described, showing the consumer market with the physical expansion of Distribution Networks and the results of quality from the services made by the companies to their clients. (C.G.C.)
Portable system for periodical verification of area monitors for neutrons
The Neutrons Laboratory develops a project viewing the construction of a portable test system for verification of functioning conditions of neutron area monitors. This device will allow to the users the verification of the calibration maintenance of his instruments at the use installations, avoiding the use of an inadequate equipment related to his answer to the neutron beam response
Enhancing Quantum Effects via Periodic Modulations in Optomechanical Systems
Farace, Alessandro
2012-01-01
Parametrically modulated optomechanical systems have been recently proposed as a simple and efficient setting for the quantum control of a micromechanical oscillator: relevant possibilities include the generation of squeezing in the oscillator position (or momentum) and the enhancement of entanglement between mechanical and radiation modes. In this paper we further investigate this new modulation regime, considering an optomechanical system with one or more parameters being modulated over time. We first apply a sinusoidal modulation of the mechanical frequency and characterize the optimal regime in which the visibility of purely quantum effects is maximal. We then introduce a second modulation on the input laser intensity and analyze the interplay between the two. We find that an interference pattern shows up, so that different choices of the relative phase between the two modulations can either enhance or cancel the desired quantum effects.
Enhancing quantum effects via periodic modulations in optomechanical systems
Farace, Alessandro; Giovannetti, Vittorio
2012-07-01
Parametrically modulated optomechanical systems have been recently proposed as a simple and efficient setting for the quantum control of a micromechanical oscillator: relevant possibilities include the generation of squeezing in the oscillator position (or momentum) and the enhancement of entanglement between mechanical and radiation modes. In this paper we further investigate this modulation regime, considering an optomechanical system with one or more parameters being modulated over time. We first apply a sinusoidal modulation of the mechanical frequency and characterize the optimal regime in which the visibility of purely quantum effects is maximal. We then introduce a second modulation on the input laser intensity and analyze the interplay between the two. We find that an interference pattern shows up, so that different choices of the relative phase between the two modulations can either enhance or cancel the desired quantum effects, opening new possibilities for optimal quantum control strategies.
Periodic inspection for safety of CANDU heat transport piping systems
An approach has been developed for the prediction of the risk of failure or the survival of heat transport piping systems in a nuclear power plant. The effects of various inspection schemes on the risk of failure have been investigated and an inspection method proposed. A list of input data required to apply this method to real situations is specified. Using an example of a pressurized pipe containing a defect, it is shown that the required data can be obtained easily
P Systems Computing the Period of Irreducible Markov Chains
Cardona Roca, Mónica; Colomer Cugat, M. Angeles; Riscos Núñez, Agustín; Rius Font, Miquel
2009-01-01
It is well known that any irreducible and aperiodic Markov chain has exactly one stationary distribution, and for any arbitrary initial distribution, the sequence of distributions at time n converges to the stationary distribution, that is, the Markov chain is approaching equilibrium as n→∞. In this paper, a characterization of the aperiodicity in existential terms of some state is given. At the same time, a P system with external output is associated with any irreducible Ma...
Quantum mechanics of rapidly and periodically driven systems
Malay Bandyopadhyay; Sushanta Dattagupta
2008-03-01
This review deals with the dynamics of quantum systems that are subject to high frequency external perturbations. Though the problem may look hopelessly time-dependent, and poised on the extreme opposite side of adiabaticity, there exists a `Kapitza Window' over which the dynamics can be treated in terms of effective time-independent Hamiltonians. The consequent results are important in the context of atomic traps as well as quantum optic properties of atoms in intense and high-frequency electromagnetic fields.
Optoelectronic timing system. Period covered: April--June 1976
Hanes, L.D.
1976-01-01
An optoelectronic timing system is being developed for the measurement of detonation front arrival times in an initiation sensitivity test currently in use at Pantex. The primary goal this quarter was the design, construction, and testing of a photodiode circuit which would have a two-nanosecond rise time response proportional to light intensity and which would have an adequate voltage output for the level of light intensity encountered in the sensitivity test. The results were satisfactory.
Feng Cao; Yelai Fu
2014-01-01
In this article, we study the asymptotic dynamics in nonmonotone comparable almost periodic reaction-diffusion systems with Dirichlet boundary condition, which are comparable with uniformly stable strongly order-preserving system. By appealing to the theory of skew-product semiflows, we obtain the asymptotic almost periodicity of uniformly stable solutions to the comparable reaction-diffusion system.
Feng Cao
2014-04-01
Full Text Available In this article, we study the asymptotic dynamics in nonmonotone comparable almost periodic reaction-diffusion systems with Dirichlet boundary condition, which are comparable with uniformly stable strongly order-preserving system. By appealing to the theory of skew-product semiflows, we obtain the asymptotic almost periodicity of uniformly stable solutions to the comparable reaction-diffusion system.
Global Analysis of Almost Periodic Solution of a Discrete Multispecies Mutualism System
Hui Zhang
2014-01-01
of the system. Assuming that the coefficients in the system are almost periodic sequences, we obtain the sufficient conditions for the existence of a unique almost periodic solution which is globally attractive. In particular, for the discrete two-species Lotka-Volterra mutualism system, the sufficient conditions for the existence of a unique uniformly asymptotically stable almost periodic solution are obtained. An example together with numerical simulation indicates the feasibility of the main result.
Periodic Flows to Chaos Based on Discrete Implicit Mappings of Continuous Nonlinear Systems
Luo, Albert C. J.
This paper presents a semi-analytical method for periodic flows in continuous nonlinear dynamical systems. For the semi-analytical approach, differential equations of nonlinear dynamical systems are discretized to obtain implicit maps, and a mapping structure based on the implicit maps is employed for a periodic flow. From mapping structures, periodic flows in nonlinear dynamical systems are predicted analytically and the corresponding stability and bifurcations of the periodic flows are determined through the eigenvalue analysis. The periodic flows predicted by the single-step implicit maps are discussed first, and the periodic flows predicted by the multistep implicit maps are also presented. Periodic flows in time-delay nonlinear dynamical systems are discussed by the single-step and multistep implicit maps. The time-delay nodes in discretization of time-delay nonlinear systems were treated by both an interpolation and a direct integration. Based on the discrete nodes of periodic flows in nonlinear dynamical systems with/without time-delay, the discrete Fourier series responses of periodic flows are presented. To demonstrate the methodology, the bifurcation tree of period-1 motion to chaos in a Duffing oscillator is presented as a sampled problem. The method presented in this paper can be applied to nonlinear dynamical systems, which cannot be solved directly by analytical methods.
Stability and periodicity of solutions for delay dynamic systems on time scales
Zhi-Qiang Zhu
2014-04-01
Full Text Available This article concerns the stability and periodicity of solutions to the delay dynamic system $$ x^{\\triangle}(t=A(t x(t + F(t, x(t, x(g(t+C(t $$ on a time scale. By the inequality technique for vectors, we obtain some stability criteria for the above system. Then, by using the Horn fixed point theorem, we present some conditions under which our system is asymptotically periodic and its periodic solution is unique. In particular, the periodic solution is positive under proper assumptions.
On angular momentum balance for particle systems with periodic boundary conditions
Kuzkin, Vitaly A.
2013-01-01
The well-known issue with the absence of conservation of angular momentum in classical particle systems with periodic boundary conditions is addressed. It is shown that conventional theory based on Noether's theorem fails to explain the simplest possible example, notably jumps of angular momentum in the case of single particle moving in a periodic cell. It is suggested to consider the periodic cell as an open system, exchanging mass, momentum, angular momentum, and energy with surrounding cel...
WU Bo; CHEN Gang; JIANG Zhengfeng; ZHENG Junyi
2006-01-01
Approximate calculation methods of prevention maintenance period under the random distribution are given, and three kinds of approximate calculation models of prevention maintenance period based on different security demands are come up with according to maintenance problems of machinery systems in modern enterprise and starting with different demands of systems. And then, how to make certain the best maintenance period by using the approximate calculation methods is illustrated by an example.
Controlling chaos in a high dimensional system with periodic parametric perturbations
Mirus, K.A.; Sprott, J.C.
1998-10-01
The effect of applying a periodic perturbation to an accessible parameter of a high-dimensional (coupled-Lorenz) chaotic system is examined. Numerical results indicate that perturbation frequencies near the natural frequencies of the unstable periodic orbits of the chaotic system can result in limit cycles or significantly reduced dimension for relatively small perturbations.
PERMANENCE AND PERIODIC SOLUTION IN AN INTEGRODIFFERENTIAL SYSTEM WITH DISCRETE DIFFUSION
XIAO Yanni; CHEN Lansun; TANG Sanyi
2003-01-01
Dynamical characteristics of an integrodifferential modelling competitive sys-tem with diffusion are investigated. In particular, we derive sufficient conditions for thepermanence of species, existence of an attracting periodic solution to the periodic system.The results of Wang Ke in 1994 and 1998 are improved and extended.
Spiral organization of periodic structures in the Lorenz–Stenflo system
Rech, Paulo C.
2016-07-01
This paper reports the existence of organized periodic structures embedded in chaotic regions of a parameter plane of the Lorenz–Stenflo system. More specifically, this work reports on spiral organization of periodic structures observed in the (σ, s) parameter plane of the Lorenz–Stenflo system.
The virial theorem and exact properties of density functionals for periodic systems
Mirhosseini, H.; Cangi, A.; Baldsiefen, T.; Sanna, A.; Proetto, C. R.; Gross, E. K. U.
2014-01-01
In the framework of density functional theory, scaling and the virial theorem are essential tools for deriving exact properties of density functionals. Preexisting mathematical difficulties in deriving the virial theorem via scaling for periodic systems are resolved via a particular scaling technique. This methodology is employed to derive universal properties of the exchange-correlation energy functional for periodic systems.
Tropical Krichever construction for the non-periodic box and ball system
Iwao, Shinsuke; Isojima, Shin
2012-01-01
A solution for an initial value problem of the box and ball system is constructed from a solution of the periodic box and ball system. The construction is done through a specific limiting process based on the theory of tropical geometry. This method gives a tropical analogue of the Krichever construction, which is an algebro-geometric method to construct exact solutions to integrable systems, for the non-periodic system.
Responses of a Noisy Excitable System to External Signals with Different Periods
JIA Xun; ZHOU Lu-Qun; OUYANG Qi
2004-01-01
@@ The behaviour of an excitable system under Gaussian white noise and external periodic forcing is systematically studied. In a large range of noise intensity, the n:1 phase locking patterns are obtained for certain ranges of the input periods, where n input periods give one spike. In the phase locking regimes, the system presents low noise-to-signal ratios and shows better regularities. Out of the regimes the system behavesless regularly and the relations between the noise-to-signal ratio and the noise intensity exhibit typical stochastic resonance phenomena.At a higher noise level, the system shows the characteristic behaviour of the noise.
Periodic Solutions for n-Species Lotka-Volterra Competitive Systems with Pure Delays
Ahmadjan Muhammadhaji
2015-01-01
Full Text Available We study a class of periodic general n-species competitive Lotka-Volterra systems with pure delays. Based on the continuation theorem of the coincidence degree theory and Lyapunov functional, some new sufficient conditions on the existence and global attractivity of positive periodic solutions for the n-species competitive Lotka-Volterra systems are established. As an application, we also examine some special cases of the system, which have been studied extensively in the literature.
Controlling chaos in low and high dimensional systems with periodic parametric perturbations
The effect of applying a periodic perturbation to an accessible parameter of various chaotic systems is examined. Numerical results indicate that perturbation frequencies near the natural frequencies of the unstable periodic orbits of the chaotic systems can result in limit cycles for relatively small perturbations. Such perturbations can also control or significantly reduce the dimension of high-dimensional systems. Initial application to the control of fluctuations in a prototypical magnetic fusion plasma device will be reviewed
Chaotic Dynamics of One-Dimensional Systems with Periodic Boundary Conditions
Kumar, Pankaj; Miller, Bruce N.
2014-01-01
We provide appropriate tools for the analysis of dynamics and chaos for one-dimensional systems with periodic boundary conditions. Our approach allows for the investigation of the dependence of the largest Lyapunov exponent on various initial conditions of the system. The method employs an effective approach for defining the phase-space distance appropriate for systems with periodic boundary and allows for an unambiguous test-orbit rescaling in the phase space required to calculate the Lyapun...
Controlling chaos in low and high dimensional systems with periodic parametric perturbations
Mirus, K.A.; Sprott, J.C.
1998-06-01
The effect of applying a periodic perturbation to an accessible parameter of various chaotic systems is examined. Numerical results indicate that perturbation frequencies near the natural frequencies of the unstable periodic orbits of the chaotic systems can result in limit cycles for relatively small perturbations. Such perturbations can also control or significantly reduce the dimension of high-dimensional systems. Initial application to the control of fluctuations in a prototypical magnetic fusion plasma device will be reviewed.
Existence of Almost-Periodic Solutions for Lotka-Volterra Cooperative Systems with Time Delay
Kaihong Zhao
2012-01-01
Full Text Available This paper considers the existence of positive almost-periodic solutions for almost-periodic Lotka-Volterra cooperative system with time delay. By using Mawhin’s continuation theorem of coincidence degree theory, sufficient conditions for the existence of positive almost-periodic solutions are obtained. An example and its simulation figure are given to illustrate the effectiveness of our results.
Periodic Solutions of the 1D Vlasov-Maxwell System with Boundary Conditions
Bostan, Mihai
1998-01-01
We study the 1D Vlasov-Maxwell system with time periodic boundary conditions in its classical and relativistic form. For small data we prove existence of weak periodic solutions. It is necessary to impose non vanishing conditions for the incoming velocities in order to control the life-time of particles in the domain. In order to preserve the periodicity, another condition of vanishing the time average of the incoming current is imposed.
Immune system adaptations during competition period in female cross-country skiers
Stenholm, Johanna
2011-01-01
Stenholm, Johanna. Immune system adaptations during competition period in female cross-country skiers. Master’s Thesis in Exercise Physiology, Department of Biology of Physical Activity. University of Jyväskylä. 95pp. Purpose. This study was undertaken to characterize the extent of immune and endocrine changes in competition period and related to two competition weekends in well trained athletes in different parts of the competition period. An additional purpose was to evaluate if the cha...
Periodically Controlled Hybrid Systems: Verifying A Controller for An Autonomous Vehicle
Wongpiromsarn, Tichakorn; Mitra, Sayan; Murray, Richard M.; Lamperski, Andrew
2008-01-01
This paper introduces Periodically Controlled Hybrid Automata (PCHA) for describing a class of hybrid control systems. In a PCHA, control actions occur roughly periodically while internal and input actions, may occur in the interim changing the discrete-state or the setpoint. Based on periodicity and subtangential conditions, a new sufficient condition for verifying invariance of PCHAs is presented. This technique is used in verifying safety of the planner-controller subsystem of an autonomou...
Dynamic behaviors of the periodic Lotka-Volterra competing system with impulsive perturbations
Liu Bing [Department of Mathematics, Anshan Normal University, Anshan 114005, Liaoning (China) and Department of Mathematics, Xinjiang University, Urumqi 830046, Xinjiang (China)]. E-mail: liubing529@126.com; Teng Zhidong [Department of Mathematics, Xinjiang University, Urumqi 830046, Xinjiang (China); Liu Wanbo [Senior Middle School of Anshan Steel-Iron Company, Anshan 114034, Liaoning (China)
2007-01-15
In this paper, we investigate a classical periodic Lotka-Volterra competing system with impulsive perturbations. The conditions for the linear stability of trivial periodic solution and semi-trivial periodic solutions are given by applying Floquet theory of linear periodic impulsive equation, and we also give the conditions for the global stability of these solutions as a consequence of some abstract monotone iterative schemes introduced in this paper, which will be also used to get some sufficient conditions for persistence. By using the method of coincidence degree, the conditions for the existence of at least one strictly positive (componentwise) periodic solution are derived. The theoretical results are confirmed by a specific example and numerical simulations. It shows that the dynamic behaviors of the system we consider are quite different from the corresponding system without pulses.
Stochastic Long Term Modelling of a Drainage System with Estimation of Return Period Uncertainty
Thorndahl, Søren
2008-01-01
Long term prediction of maximum water levels and combined sewer overflow (CSO) in drainage systems are associated with large uncertainties. Especially on rainfall inputs, parameters, and assessment of return periods. This paper proposes a Monte Carlo based methodology for stochastic prediction of...... both maximum water levels as well as CSO volumes based on operations of the urban drainage model MOUSE (Lindberg and Joergensen 1986) in a single catchment case study. Results show quite a wide confidence interval of the model predictions especially on the large return periods. Traditionally, return...... periods of drainage system predictions are based on ranking, but this paper proposes a new methodology for the assessment of return periods. Based on statistics of characteristic rainfall parameters and correlation with drainage system predictions, it is possible to predict return periods more reliably...
Stochastic long term modelling of a drainage system with estimation of return period uncertainty
Thorndahl, Søren
2009-01-01
Long term prediction of maximum water levels and combined sewer overflow (CSO) in drainage systems are associated with large uncertainties. Especially on rainfall inputs, parameters, and assessment of return periods. This paper proposes a Monte Carlo based methodology for stochastic prediction of...... both maximum water levels as well as CSO volumes based on operations of the urban drainage model MOUSE (Lindberg and Joergensen 1986) in a single catchment case study. Results show quite a wide confidence interval of the model predictions especially on the large return periods. Traditionally, return...... periods of drainage system predictions are based on ranking, but this paper proposes a new methodology for the assessment of return periods. Based on statistics of characteristic rainfall parameters and correlation with drainage system predictions, it is possible to predict return periods more reliably...
The effect of short recovery period investment on least-cost generation system expansion
The effect of the short recovery period of private investment on least-cost generation system expansion is analysed, and a trade-off method for generation system expansion, which gives consideration to both the least-cost strategy and the short recovery period of private investment, is presented. First, the optimal mix of generation units under a standard recovery period for all units is established, and then the surcharge, due to the difference between the short recovery period and the standard recovery period, is calculated and shared between all units. The former is an optimization to make best use of natural resources, and the latter is a trade-off method to spread the surcharge throughout the system. (Author)
Self-similarities of periodic structures for a discrete model of a two-gene system
Souza, S.L.T. de, E-mail: thomaz@ufsj.edu.br [Departamento de Física e Matemática, Universidade Federal de São João del-Rei, Ouro Branco, MG (Brazil); Lima, A.A. [Escola de Farmácia, Universidade Federal de Ouro Preto, Ouro Preto, MG (Brazil); Caldas, I.L. [Instituto de Física, Universidade de São Paulo, São Paulo, SP (Brazil); Medrano-T, R.O. [Departamento de Ciências Exatas e da Terra, Universidade Federal de São Paulo, Diadema, SP (Brazil); Guimarães-Filho, Z.O. [Aix-Marseille Univ., CNRS PIIM UMR6633, International Institute for Fusion Science, Marseille (France)
2012-03-12
We report self-similar properties of periodic structures remarkably organized in the two-parameter space for a two-gene system, described by two-dimensional symmetric map. The map consists of difference equations derived from the chemical reactions for gene expression and regulation. We characterize the system by using Lyapunov exponents and isoperiodic diagrams identifying periodic windows, denominated Arnold tongues and shrimp-shaped structures. Period-adding sequences are observed for both periodic windows. We also identify Fibonacci-type series and Golden ratio for Arnold tongues, and period multiple-of-three windows for shrimps. -- Highlights: ► The existence of noticeable periodic windows has been reported recently for several nonlinear systems. ► The periodic window distributions appear highly organized in two-parameter space. ► We characterize self-similar properties of Arnold tongues and shrimps for a two-gene model. ► We determine the period of the Arnold tongues recognizing a Fibonacci-type sequence. ► We explore self-similar features of the shrimps identifying multiple period-three structures.
Hopf-pitchfork bifurcation and periodic phenomena in nonlinear financial system with delay
Highlights: ► We derive the unfolding of a financial system with Hopf-pitchfork bifurcation. ► We show the coexistence of a pair of stable small amplitudes periodic solutions. ► At the same time, also there is a pair of stable large amplitudes periodic solutions. ► Chaos can appear by period-doubling bifurcation far away from Hopf-pitchfork value. ► The study will be useful for interpreting economics phenomena in theory. - Abstract: In this paper, we identify the critical point for a Hopf-pitchfork bifurcation in a nonlinear financial system with delay, and derive the normal form up to third order with their unfolding in original system parameters near the bifurcation point by normal form method and center manifold theory. Furthermore, we analyze its local dynamical behaviors, and show the coexistence of a pair of stable periodic solutions. We also show that there coexist a pair of stable small-amplitude periodic solutions and a pair of stable large-amplitude periodic solutions for different initial values. Finally, we give the bifurcation diagram with numerical illustration, showing that the pair of stable small-amplitude periodic solutions can also exist in a large region of unfolding parameters, and the financial system with delay can exhibit chaos via period-doubling bifurcations as the unfolding parameter values are far away from the critical point of the Hopf-pitchfork bifurcation.
Positive Periodic Solutions of Cooperative Systems with Delays and Feedback Controls
Tursuneli Niyaz
2013-01-01
Full Text Available This paper studies a class of periodic n species cooperative Lotka-Volterra systems with continuous time delays and feedback controls. Based on the continuation theorem of the coincidence degree theory developed by Gaines and Mawhin, some new sufficient conditions on the existence of positive periodic solutions are established.
Single rub-impacting periodic motions of a rigid constrained rotor system
QunhongLI; QishaoLU
2000-01-01
This paper discusses the existence of single rub-impacting period-n motions for a kind of rotor systems with rigid constraints. The ranges of parameters for period-2 motions are also given. An example of this method is given.
PERIODIC SOLUTIONS TO A KIND OF NEUTRAL DIFFERENTIAL SYSTEM:VIA (h,k)-DICHOTOMY
无
2012-01-01
In this paper, based on the theory of (h, k)-Dichotomy of linear system and Kras-noselskii's fixed point theorem, we study the existence of periodic solutions to a neutral differential equation. Some new sufficient conditions are obtained to guarantee the existence and uniqueness of T-periodic solution to the equation.
ON THE EXISTENCE OF PERIODIC SOLUTIONS FOR NONLINEAR SYSTEM WITH MULTIPLE DELAYS
曹显兵
2003-01-01
The existence of T-periodic solutions of the nonlinear system with multiple delaysis studied. By using the topological degree method, sufficient conditions are obtained forthe existence of T-periodic solutions. As an application, the existence of positive periodicsolution for a logarithmic population model is established under some conditions.
RESEARCH OF THE PERIODIC MOTION AND STABILITY OF TWO-DEGREE-OF-FREEDOM NONLINEAR OSCILLATING SYSTEMS
刘俊
2002-01-01
The periodic motion and stability for a class of two-degree-of freedom nonlinear oscillating systems are studied by using the method of Liapunov function.The sufficient conditions which guarantee the existence, uniqueness and asymptotic stability of the periodic solutions are obtained.
Theoretical Basis and Correct Explanation of the Periodic System: Review and Update
Schwarz, W. H. Eugen; Rich, Ronald L.
2010-01-01
Long-standing questions on the theoretical basis of the periodic system have been answered in recent years. A specific type of periodicity is imposed on all elements by the main groups just before and after the noble gasses. The upper "n"p shells of these elements are unique because of their stabilized energies and the large gaps to the next…
ALMOST PERIODIC SOLUTION OF A NONAUTONOMOUS DIFFUSIVE FOOD CHAIN SYSTEM OF THREE SPECIES
LuoGuilie
1999-01-01
In this paper,the almost periodic nonautonomous diffusive food chain system of threespecies is discussed. By using the comparison theorem and V-function method,the author provesthe existence and uniqueness of a positive almost periodic solution,and its stability under disturbances from the hull.
Stochastic period-doubling bifurcation in biharmonic driven Duffing system with random parameter
Stochastic period-doubling bifurcation is explored in a forced Duffing system with a bounded random parameter as an additional weak harmonic perturbation added to the system. Firstly, the biharmonic driven Duffing system with a random parameter is reduced to its equivalent deterministic one, and then the responses of the stochastic system can be obtained by available effective numerical methods. Finally, numerical simulations show that the phase of the additional weak harmonic perturbation has great influence on the stochastic period-doubling bifurcation in the biharmonic driven Duffing system. It is emphasized that, different from the deterministic biharmonic driven Duffing system, the intensity of random parameter in the Duffing system can also be taken as a bifurcation parameter, which can lead to the stochastic period-doubling bifurcations
Periodic orbits and non-integrability of Henon-Heiles systems
Llibre, Jaume [Departament de Matematiques, Universitat Autonoma de Barcelona, 08193 Bellaterra, Barcelona, Catalonia (Spain); Jimenez-Lara, Lidia, E-mail: jllibre@mat.uab.cat, E-mail: lidia@xanum.uam.mx [Departamento de Fisica, Universidad Autonoma Metropolitana-Iztapalapa, PO Box 55-534, Mexico, DF, 09340 Mexico (Mexico)
2011-05-20
We apply the averaging theory of second order to study the periodic orbits for a generalized Henon-Heiles system with two parameters, which contains the classical Henon-Heiles system. Two main results are shown. The first result provides sufficient conditions on the two parameters of these generalized systems, which guarantee that at any positive energy level, the Hamiltonian system has periodic orbits. These periodic orbits form in the whole phase space a continuous family of periodic orbits parameterized by the energy. The second result shows that for the non-integrable Henon-Heiles systems in the sense of Liouville-Arnol'd, which have the periodic orbits analytically found with averaging theory, cannot exist any second first integral of class C{sup 1}. In particular, for any second first integral of class C{sup 1}, we prove that the classical Henon-Heiles system and many generalizations of it are not integrable in the sense of Liouville-Arnol'd. Moreover, the tools we use for studying the periodic orbits and the non-Liouville-Arnol'd integrability can be applied to Hamiltonian systems with an arbitrary number of degrees of freedom.
Periodic orbits in non-integrable hamiltoniam systems with two degrees of freedom
We present extensive numerical data concerning the periodics orbits of a non integrable two degrees of freedom hamiltoniam system. These periodics orbits form a one-parameter family and the data are displayed in a plot of energy x period. These orbits exhibit several kinds of bifurcations not predicted in the generic study by K.R. Meyer (Trans. Am. Math. Soc., 1970) due to the existence of symmetries in the hamiltonian. Using a perturbative treatment in the neighbourhood of the periodic trajectories, we analytically compute the effect of these symmetries in the bifurcations. These results are in perfect agreement with those obtained numerically. (author)
External Periodic Force Control of a Single-Degree-of-Freedom Vibroimpact System
Jingyue Wang
2013-01-01
Full Text Available A single-degree-of-freedom mechanical model of vibro-impact system is established. Bifurcation and chaos in the system are revealed with the time history diagram, phase trajectory map, and Poincaré map. According to the bifurcation and chaos of the actual vibro-impact system, the paper puts forward external periodic force control strategy. The method of controlling chaos by external periodic force feedback controller is developed to guide chaotic motions towards regular motions. The stability of the control system is also analyzed especially by theory. By selecting appropriate feedback coefficients, the unstable periodic orbits of the original chaotic orbit can be stabilized to the stable periodic orbits. The effectiveness of this control method is verified by numerical simulation.
Existence of infinitely many periodic solutions for second-order nonautonomous Hamiltonian systems
Wen Guan
2015-04-01
Full Text Available By using minimax methods and critical point theory, we obtain infinitely many periodic solutions for a second-order nonautonomous Hamiltonian systems, when the gradient of potential energy does not exceed linear growth.
Scaling of Moon Masses and Orbital Periods in the Systems of Saturn, Jupiter and Uranus
Müller H
2015-01-01
The paper shows, that the sequence of sorted by value masses of the largest moons in the systems of Saturn, Jupiter and Uranus is connected by constant scaling exponents with the sequence of their sorted by value orbital periods.
Evolution with size in a locally periodic system: scattering and deterministic maps
In this paper, we study the evolution of the wavefunction with the system size in a locally periodic structure. In particular, we analyse the dependence of the wavefunction with the number of unit cells, which also reflects information about its spatial behaviour in the system. We reduce the problem to a nonlinear map and find an equivalence of its energy regions of single periodicity and weak chaos, with the forbidden and allowed bands of the fully periodic system, respectively. At finite size the wavefunction decays exponentially with the system size, as well as in space, when the energy lies inside a region of single periodicity, while for energies in the weak chaotic region it never decays. At the transition between those regions the wavefunction still decays but in a q-exponential form; we find that the decay length is a half of the mean free path, which is larger than the lattice constant. (paper)
Mirus, K.A.
1998-06-01
In this thesis, the possibility of controlling low- and high-dimensional chaotic systems by periodically driving an accessible system parameter is examined. This method has been carried out on several numerical systems and the MST Reversed Field Pinch. The numerical systems investigated include the logistic equation, the Lorenz equations, the Roessler equations, a coupled lattice of logistic equations, a coupled lattice of Lorenz equations, the Yoshida equations, which model tearing mode fluctuations in a plasma, and a neural net model for magnetic fluctuations on MST. This method was tested on the MST by sinusoidally driving a magnetic flux through the toroidal gap of the device. Numerically, periodic drives were found to be most effective at producing limit cycle behavior or significantly reducing the dimension of the system when the perturbation frequency was near natural frequencies of unstable periodic orbits embedded in the attractor of the unperturbed system. Several different unstable periodic orbits have been stabilized in this way for the low-dimensional numerical systems, sometimes with perturbation amplitudes that were less than 5% of the nominal value of the parameter being perturbed. In high-dimensional systems, limit cycle behavior and significant decreases in the system dimension were also achieved using perturbations with frequencies near the natural unstable periodic orbit frequencies. Results for the MST were not this encouraging, most likely because of an insufficient drive amplitude, the extremely high dimension of the plasma behavior, large amounts of noise, and a lack of stationarity in the transient plasma pulses.
In this thesis, the possibility of controlling low- and high-dimensional chaotic systems by periodically driving an accessible system parameter is examined. This method has been carried out on several numerical systems and the MST Reversed Field Pinch. The numerical systems investigated include the logistic equation, the Lorenz equations, the Roessler equations, a coupled lattice of logistic equations, a coupled lattice of Lorenz equations, the Yoshida equations, which model tearing mode fluctuations in a plasma, and a neural net model for magnetic fluctuations on MST. This method was tested on the MST by sinusoidally driving a magnetic flux through the toroidal gap of the device. Numerically, periodic drives were found to be most effective at producing limit cycle behavior or significantly reducing the dimension of the system when the perturbation frequency was near natural frequencies of unstable periodic orbits embedded in the attractor of the unperturbed system. Several different unstable periodic orbits have been stabilized in this way for the low-dimensional numerical systems, sometimes with perturbation amplitudes that were less than 5% of the nominal value of the parameter being perturbed. In high-dimensional systems, limit cycle behavior and significant decreases in the system dimension were also achieved using perturbations with frequencies near the natural unstable periodic orbit frequencies. Results for the MST were not this encouraging, most likely because of an insufficient drive amplitude, the extremely high dimension of the plasma behavior, large amounts of noise, and a lack of stationarity in the transient plasma pulses
The quasi-periodic stability condition (the KAM theorem) for partially-integrable systems
Sardanashvily, G.
2003-01-01
Written with respect to an appropriate Poisson structure, a partially integrable Hamiltonian system is viewed as a completely integrable system with parameters. Then, the theorem on quasi-periodic stability in Ref. [1] (the KAM theorem) can be applied to this system.
Cauchy problem for a generalized weakly dissipative periodic two-component Camassa-Holm system
Wenxia Chen
2014-05-01
Full Text Available In this article, we study a generalized weakly dissipative periodic two-component Camassa-Holm system. We show that this system can exhibit the wave-breaking phenomenon and determine the exact blow-up rate of strong solution to the system. In addition, we establish a sufficient condition for having a global solution.
Almost Periodic Solution of a Multispecies Discrete Mutualism System with Feedback Controls
Hui Zhang
2015-01-01
Full Text Available We consider an almost periodic multispecies discrete Lotka-Volterra mutualism system with feedback controls. We firstly obtain the permanence of the system by utilizing the theory of difference equation. By means of constructing a suitable Lyapunov function, sufficient conditions are obtained for the existence of a unique positive almost periodic solution which is uniformly asymptotically stable. An example together with numerical simulation indicates the feasibility of the main result.
KONG, LIANG; Rawal, Nar; Shen, Wenxian
2014-01-01
The current paper is concerned with the existence of spreading speeds and linear determinacy for two species competition systems with nonlocal dispersal in time and space periodic habitats. The notion of spreading speed intervals for such a system is first introduced via the natural features of spreading speeds. The existence and lower bounds of spreading speed intervals are then established. When the periodic dependence of the habitat is only on the time variable, the existence of a single s...
Condition for emergence of the Floquet-Gibbs state in periodically driven open systems
Shirai, Tatsuhiko; Mori, Takashi; MIYASHITA, Seiji
2014-01-01
We study probability distribution of a steady state of a periodically driven system coupled to a thermal bath by using a quantum master equation in the weak coupling limit. It is proved that, even when the external field is strong, the probability distribution is independent of the detailed nature of the thermal bath under the following conditions: (i) the Hamiltonian of the relevant system is bounded and the period of the driving field is short, (ii) the Hamiltonians for the driving field at...
Modal Vibration Control in Periodic Time-Varying Structures with Focus on Rotor Blade Systems
Christensen, Rene Hardam; Santos, Ilmar
2004-01-01
overcome. Among others it is necessary, that the control scheme is capable to cope with non-linear time-varying dynamical system behaviour. However, rotating at constant speed the mathematical model becomes periodic time-variant. In this framework the present paper gives a contribution to design procedures...... results are provided to demonstrate the applicability and effectiveness of the technique. The results obtained shows that the control design technique is capable to cope with the time periodicity of this class of systems....
Modal Vibration Control in Periodic Time-Varying Structures with Focus on Rotor-Blade Systems
Christensen, Rene Hardam; Santos, Ilmar
2003-01-01
overcome. Among others it is necessary, that the control scheme is capable to cope with non-linear time-varying dynamical system behaviour. However, rotating at constant speed the mathematical model becomes periodic time-variant. In this framework the present paper gives a contribution to design procedures...... results are provided to demonstrate the applicability and effectiveness of the technique. The results obtained shows that the control design technique is capable to cope with the time periodicity of this class of systems....
Periodic functions with variable period
Pryjmak, M. V
2010-01-01
The examples of rhythmical signals with variable period are considered. The definition of periodic function with the variable period is given as a model of such signals. The examples of such functions are given and their variable periods are written in the explicit form. The system of trigonometric functions with the variable period is considered and its orthogonality is proved. The generalized system of trigonometric functions with the variable period is also suggested; some conditions of it...
The Period-Ratio and Mass-Ratio Correlation in Extra-Solar Multiple Planetary Systems
Jiang, Ing-Guey; Hung, Wen-Liang
2015-01-01
Employing the data from orbital periods and masses of extra-solar planets in 166 multiple planetary systems, the period-ratio and mass-ratio of adjacent planet pairs are studied. The correlation between the period-ratio and mass-ratio is confirmed and found to have a correlation coefficient of 0.5303 with a 99% confidence interval (0.3807, 0.6528). A comparison with the distribution of synthetic samples from a Monte Carlo simulation reveals the imprint of planet-planet interactions on the formation of adjacent planet pairs in multiple planetary systems.
A study of the entanglement in systems with periodic boundary conditions
Panagiotou, E.; Tzoumanekas, C.; Lambropoulou, S.; Millett, K. C.; Theodorou, D. N.
2010-01-01
We define the local periodic linking number, LK, between two oriented closed or open chains in a system with three-dimensional periodic boundary conditions. The properties of LK indicate that it is an appropriate measure of entanglement between a collection of chains in a periodic system. Using this measure of linking to assess the extent of entanglement in a polymer melt we study the effect of CReTA algorithm on the entanglement of polyethylene chains. Our numerical results show that the sta...
Relative equailibria and relative periodic solutions in systems with time-delay and $S^{1}$ symmetry
Yanchuk, Serhiy
2013-01-01
We study properties of basic solutions in systems with dime delays and $S^1$-symmetry. Such basic solutions are relative equilibria (CW solutions) and relative periodic solutions (MW solutions). It follows from the previous theory that the number of CW solutions grows generically linearly with time delay $\\tau$. Here we show, in particular, that the number of relative periodic solutions grows generically as $\\tau^2$ when delay increases. Thus, in such systems, the relative periodic solutions are more abundant than relative equilibria. The results are directly applicable to, e.g., Lang-Kobayashi model for the lasers with delayed feedback. We also study stability properties of the solutions for large delays.
Periodic solutions for a two-species nonautonomous competition system with diffusion and impulses
Dong Lingzhen [Department of Mathematics, Taiyuan University of Technology, Taiyuan 030024 (China)]. E-mail: linzhen_dong@yahoo.com.cn; Chen Lansun [Department of Applied Mathematics, Dalian University of Technology, Dalian 116023 (China); Shi Peilin [Department of Mathematics, Taiyuan University of Technology, Taiyuan 030024 (China)
2007-06-15
By re-estimating the upper bound of {integral}{sub 0}{sup {omega}}e{sup u{sub i}}{sup (t)}dt (i=1,2), we generalize a result about the existence of a positive periodic solution for a two-species nonautonomous patchy competition system with time delay. Based on that system, we consider the impulsive harvesting and stocking, and establish a two-species nonautonomous competition Lotka-Volterra system with diffusion and impulsive effects. With the continuation theorem of coincidence degree theory, we obtain the existence of a positive periodic solution for such a system. At last, two examples are given to demonstrate our results.
New Light Curves and Period Studies of V502 OPH W UMA System
Awadalla, Nabil S.
NEW LIGHT CURVES AND PERIOD STUDIES OF V502 OPH W UMa SYSTEM N.S.Awadalla National Research Institute of Astronomy and Geophysics( NRIAG ) Helwan Cairo EGYPT New BVR photoelectric observations of the W UMa eclipsing binary system V502 Oph have been presented and analyzed. The geometric and physical elements of the system have been obtained and compared to the previous results. The classification of the system concerning the sub-type of the W UMa binary has been studied as well as its evolution stage. Its period variation in a view of the light time effect has been examin
Localization of periodic orbits of the Roessler system under variation of its parameters
Starkov, Konstantin E. [CITEDI-IPN, Av. del Parque 1310, Mesa de Otay, Tijuana, BC (Mexico)]. E-mail: konst@citedi.mx; Starkov, Konstantin K. [UABC - Campus Tijuana, Facultad de Ciencias Quimicas e Ingenieria, Calzada Tecnologico, Mesa de Otay, Tijuana, BC (Mexico)
2007-08-15
The localization problem of compact invariant sets of the Roessler system is considered in this paper. The main interest is attracted to a localization of periodic orbits. We establish a number of algebraic conditions imposed on parameters under which the Roessler system has no compact invariant sets contained in half-spaces z > 0; z < 0 and in some others. We prove that if parameters (a, b, c) of the Roessler system are such that this system has no equilibrium points then it has no periodic orbits as well. In addition, we give localization conditions of compact invariant sets by using linear functions and one quadratic function.
Periodic orbits and their stability in the Rössler prototype-4 system
For the Rössler prototype-4 system x.=−y−z, y.=x, z.=αy(1−y)−βz we prove the existence of periodic orbits and study their stability or instability. The main tool for proving these results is the averaging theory. Recently the existence of some of these periodic orbits were detected numerically. -- Highlights: ► We deal with the Rössler prototype-4 system x.=−y−z, y.=x, z.=αy(1−y)−βz. ► It is one of the simplest autonomous differential equations exhibiting chaos. ► Recently some periodic orbits for this system has been detected numerically. ► We provide an analytical proof of these orbits and study their stability. ► Also we prove the existence of periodic orbits not detected numerically.
Periodic orbits and their stability in the Rössler prototype-4 system
García, Isaac A., E-mail: garcia@matematica.udl.cat [Departament de Matemàtica, Universitat de Lleida, Avda. Jaume II, 69, 25001 Lleida, Catalonia (Spain); Llibre, Jaume, E-mail: jllibre@mat.uab.cat [Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193 Bellaterra, Barcelona, Catalonia (Spain); Maza, Susanna, E-mail: smaza@matematica.udl.cat [Departament de Matemàtica, Universitat de Lleida, Avda. Jaume II, 69, 25001 Lleida, Catalonia (Spain)
2012-07-02
For the Rössler prototype-4 system x{sup .}=−y−z, y{sup .}=x, z{sup .}=αy(1−y)−βz we prove the existence of periodic orbits and study their stability or instability. The main tool for proving these results is the averaging theory. Recently the existence of some of these periodic orbits were detected numerically. -- Highlights: ► We deal with the Rössler prototype-4 system x{sup .}=−y−z, y{sup .}=x, z{sup .}=αy(1−y)−βz. ► It is one of the simplest autonomous differential equations exhibiting chaos. ► Recently some periodic orbits for this system has been detected numerically. ► We provide an analytical proof of these orbits and study their stability. ► Also we prove the existence of periodic orbits not detected numerically.
Bifurcation for Second-Order Hamiltonian Systems with Periodic Boundary Conditions
Francesca Faraci; Antonio Iannizzotto
2008-01-01
Through variational methods, we study nonautonomous systems of second-order ordinary differential equations with periodic boundary conditions. First, we deal with a nonlinear system, depending on a function $u$ , and prove that the set of bifurcation points for the solutions of the system is not ${\\sigma{}} $ -compact. Then, we deal with a linear system depending on a real parameter ${\\lambda{}}>0$ and on a function $u$ , and prove that there exists ${{\\lambda{}}}^{{_\\ast}} $ such that the se...
Ying, Lexing
2014-01-01
This paper introduces the sparsifying preconditioner for the pseudospectral approximation of highly indefinite systems on periodic structures, which include the frequency-domain response problems of the Helmholtz equation and the Schr\\"odinger equation as examples. This approach transforms the dense system of the pseudospectral discretization approximately into an sparse system via an equivalent integral reformulation and a specially-designed sparsifying operator. The resulting sparse system ...
Xiang X; Wei W; Wang JinRong
2008-01-01
Global behaviors and optimal harvesting of a class of impulsive periodic logistic single-species system with continuous periodic control strategy is investigated. Four new sufficient conditions that guarantee the exponential stability of the impulsive evolution operator introduced by us are given. By virtue of exponential stability of the impulsive evolution operator, we present the existence, uniqueness and global asymptotical stability of periodic solutions. Further, the existence result o...
H2 OPTIMAL CONTROLLERS FOR A LARGE CLASS OF LINEAR STOCHASTIC SYSTEMS WITH PERIODIC COEFFICIENTS
Adrian-Mihail Stoica
2011-07-01
Full Text Available In this paper the H2 type optimization problem for a class of timevarying linear stochastic systems modeled by Ito differential equations and Markovian jumping with periodic coefficients is considered. The main goal of such an optimization problem is to minimize the effect of additive white noise perturbations on a suitable output of the controlled system. It is assumed that only an output is available for measurements.The solution of the considered optimization problem is constructed via the stabilizing solutions of some suitable systems of generalized Riccati differential equations with periodic coefficients.
Implementing Multi-Periodic Critical Systems: from Design to Code Generation
Forget, Julien; Lesens, David; Pagetti, Claire
2010-01-01
This article presents a complete scheme for the development of Critical Embedded Systems with Multiple Real-Time Constraints. The system is programmed with a language that extends the synchronous approach with high-level real-time primitives. It enables to assemble in a modular and hierarchical manner several locally mono-periodic synchronous systems into a globally multi-periodic synchronous system. It also allows to specify flow latency constraints. A program is translated into a set of real-time tasks. The generated code (\\C\\ code) can be executed on a simple real-time platform with a dynamic-priority scheduler (EDF). The compilation process (each algorithm of the process, not the compiler itself) is formally proved correct, meaning that the generated code respects the real-time semantics of the original program (respect of periods, deadlines, release dates and precedences) as well as its functional semantics (respect of variable consumption).
Existence of positive periodic solution of mutualism system with several delays
Wu Haihui [College of Mathematics and Computer Science, Fuzhou University, Fuzhou 350002 (China); Department of Computer Science and Technology, Sunshine College, Fuzhou University, Fuzhou 350002 (China); Xia Yonghui [College of Mathematics and Computer Science, Fuzhou University, Fuzhou 350002 (China)], E-mail: yhxia@fzu.edu.cn; Lin Muren [College of Mathematics and Computer Science, Fuzhou University, Fuzhou 350002 (China)
2008-04-15
In this paper, by using Mawhin coincidence degree, some sufficient conditions are obtained for the global existence of positive periodic solutions of a mutualism systems with bounded and unbounded delays. Our results generalize significantly improve those of Gopalsamy and He [Gopalsamy K, He XZ. Persistence, attractivity, and delay in facultative mutualism. J Math Anal Appl 1997;215:154-73], Yang et al. [Yang F, Jiang D, Ying A. Existence of positive solution of multidelays facultative mutualism system. J Eng Math 2002;3:64-8], Chen et al. [Chen FD, Shi JL, Chen XX. Periodicity in Lotka-Volterra facultative mutualism system with several delays. J Eng Math 2004;21(3)] and Xia and Lin [Xia YH, Lin M, Existence of positive periodic solution of mutualism system with infinite delays. Ann Diff Eqs 2005;21(3):448-53].
Comment on the three-body theory for period changes in RS CVn systems
Van Buren, D.
1986-01-01
In the three-body theory for period variations in RS CVn systems, the timing residuals are interpreted as light-travel time differences as the eclipsing system moves about the barycenter of the triple. These residuals can require a larger orbit than Kepler's law allows, given the time scale of the period variations. For only two of eight systems investigated, SV Cam and V471 Tau, is the theory plausible in that the inferred barycentric motion of the binary is smaller than the orbit of the third body, and the inferred properties of the third body are both reasonable and consistent with its remaining hidden. The theory is thus not a general theory for period changes. Observational testing of the theory is straightforward and may lead to the detection of 'brown dwarfs' associated with eclipsing systems through their kinematic effects.
Local electric dipole moments for periodic systems via density functional theory embedding
Luber, Sandra, E-mail: sandra.luber@chem.uzh.ch [Institut für Chemie, Universität Zürich, Winterthurerstrasse 190, 8057 Zürich (Switzerland)
2014-12-21
We describe a novel approach for the calculation of local electric dipole moments for periodic systems. Since the position operator is ill-defined in periodic systems, maximally localized Wannier functions based on the Berry-phase approach are usually employed for the evaluation of local contributions to the total electric dipole moment of the system. We propose an alternative approach: within a subsystem-density functional theory based embedding scheme, subset electric dipole moments are derived without any additional localization procedure, both for hybrid and non-hybrid exchange–correlation functionals. This opens the way to a computationally efficient evaluation of local electric dipole moments in (molecular) periodic systems as well as their rigorous splitting into atomic electric dipole moments. As examples, Infrared spectra of liquid ethylene carbonate and dimethyl carbonate are presented, which are commonly employed as solvents in Lithium ion batteries.
Fast computation of the Maslov index for hyperbolic linear systems with periodic coefficients
The Maslov index is a topological property of periodic orbits of finite-dimensional Hamiltonian systems that is widely used in semiclassical quantization, quantum chaology, stability of waves and classical mechanics. The Maslov index is determined from the analysis of a linear Hamiltonian system with periodic coefficients. In this paper, a numerical scheme is devised to compute the Maslov index for hyperbolic linear systems when the phase space has a low dimension. The idea is to compute on the exterior algebra of the ambient vector space, where the Lagrangian subspace representing the unstable subspace is reduced to a line. When the exterior algebra is projectified the Lagrangian subspace always forms a closed loop. The idea is illustrated by application to Hamiltonian systems on a phase space of dimension 4. The theory is used to compute the Maslov index for the spectral problem associated with periodic solutions of the fifth-order Korteweg de Vries equation
Implementing Multi-Periodic Critical Systems: from Design to Code Generation
Julien Forget
2010-03-01
Full Text Available This article presents a complete scheme for the development of Critical Embedded Systems with Multiple Real-Time Constraints. The system is programmed with a language that extends the synchronous approach with high-level real-time primitives. It enables to assemble in a modular and hierarchical manner several locally mono-periodic synchronous systems into a globally multi-periodic synchronous system. It also allows to specify flow latency constraints. A program is translated into a set of real-time tasks. The generated code (C code can be executed on a simple real-time platform with a dynamic-priority scheduler (EDF. The compilation process (each algorithm of the process, not the compiler itself is formally proved correct, meaning that the generated code respects the real-time semantics of the original program (respect of periods, deadlines, release dates and precedences as well as its functional semantics (respect of variable consumption.
Local electric dipole moments for periodic systems via density functional theory embedding
We describe a novel approach for the calculation of local electric dipole moments for periodic systems. Since the position operator is ill-defined in periodic systems, maximally localized Wannier functions based on the Berry-phase approach are usually employed for the evaluation of local contributions to the total electric dipole moment of the system. We propose an alternative approach: within a subsystem-density functional theory based embedding scheme, subset electric dipole moments are derived without any additional localization procedure, both for hybrid and non-hybrid exchange–correlation functionals. This opens the way to a computationally efficient evaluation of local electric dipole moments in (molecular) periodic systems as well as their rigorous splitting into atomic electric dipole moments. As examples, Infrared spectra of liquid ethylene carbonate and dimethyl carbonate are presented, which are commonly employed as solvents in Lithium ion batteries
Zhao Hongyong [Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing 210016 (China)]. E-mail: hongyongz@126.com; Ding Nan [Department of Mathematics, Xinjiang Normal University, Urumqi 830054 (China)
2006-07-15
In this paper, Lotka-Volterra competition-predator system with variable delays is considered. Some sufficient conditions ensuring the existence and global attractivity of periodic solution for this system are obtained by using coincidence degree theory and Lyapunov functional method. An example is also worked out to demonstrate the advantages of our results.
Periodic solutions of certain third order nonlinear differential systems with delay
This paper investigates the existence of 2π-periodic solutions of systems of third-order nonlinear differential equations, with delay, under varied assumptions. The results obtained extend earlier works of Tejumola and generalize to third order systems those of Conti, Iannacci and Nkashama as well as DePascale and Iannacci and Iannacci and Nkashama. 16 refs
2006-01-01
Full Text Available The method of generalized quasilinearization for the system of nonlinear impulsive differential equations with periodic boundary conditions is studied. As a byproduct, the result for the system without impulses can be obtained, which is a new result as well.
E.A. Koopman; C.P. Lowe
2014-01-01
We consider the problem of detecting a percolating structure in an off-lattice model polymer system when periodic boundary conditions are used. Physically, with increasing polymer density, the point at which this first occurs is the gel point. A connected structure spans all space and the system bec
The cyclicity of period annulus of a quadratic reversible Lotka-Volterra system
Li, Chengzhi; Llibre, Jaume
2009-12-01
We prove that by perturbing the periodic annulus of the quadratic polynomial reversible Lotka-Volterra differential system \\dot x=y+\\case{3}{2}(x^2-y^2) , \\dot y=-x(1-y) , inside the class of all quadratic polynomial differential systems we can obtain at most two limit cycles.
PERIODIC SOLUTION TO A DELAYED PREDATOR-PREY SYSTEM WITH STAGE STRUCTURE AND DISPERSION
无
2011-01-01
In this paper,a delayed two-species predator-prey system with stage structure and diffiusion is investigated. Based on the continuation theorem of coincidence degree theory,the suficient conditions for the existence of positive ω-periodic solution to the system are derived. The numerical simulation of an example verifies our main result.
Sign reversal of drag in bilayer systems with in-plane periodic potential modulation
Alkauskas, A.; Flensberg, Karsten; Hu, Ben Yu-Kuang; Jauho, Antti-Pekka
2002-01-01
We develop a theory for describing frictional drag in bilayer systems with in-plane periodic potential modulations, and use it to investigate the drag between bilayer systems in which one of the layers is modulated in one direction. At low temperatures, as the density of carriers in the modulated...
Near Periodic solution of the Elliptic RTBP for the Jupiter Sun system
Perdomo, Oscar M
2016-01-01
Let us consider the elliptic restricted three body problem (Elliptic RTBP) for the Jupiter Sun system with eccentricity $e=0.048$ and $\\mu=0.000953339$. Let us denote by $T$ the period of their orbits. In this paper we provide initial conditions for the position and velocity for a spacecraft such that after one period $T$ the spacecraft comes back to the same place, with the same velocity, within an error of 4 meters for the position and 0.2 meters per second for the velocity. Taking this solution as periodic, we present numerical evidence showing that this solution is stable. In order to compare this periodic solution with the motion of celestial bodies in our solar system, we end this paper by providing an ephemeris of the spacecraft motion from February 17, 2017 to December 28, 2028.
Stochastic resonance in a periodic potential system under a constant force
An overdamped particle moving in a periodic potential, and subject to a constant force and a stochastic force (i.e., χ = -sin(2πχ) + B + Γ(t),Γ(t) is a white noise) is considered. The mobility of the particle, d/dt, is investigated. The stochastic resonance type of behaviour is revealed. The study of the SR problem can thus be extended to systems with periodic force. (author). 13 refs
Multi-period Congestion Pricing Models and Efficient Tolls in Urban Road Systems
Liu Louie Nan
2004-01-01
This paper reviews recent advances in multi-period congestion pricing models in urban road system. Mathematical formulations of various congestion pricing problems for two time periods (peak and off-peak) and for a simple road network are presented. A procedure is provided for conducting a simulation study of the peak and off-peak congestion pricing models to examine congestion tolls and their effects on traffic allocations and social welfares. Major findings from the analysis results are sum...
Periodic Solutions of the Vlasov-Poisson System with Boundary Conditions
Bostan, Mihai; Poupaud, Frédéric
1998-01-01
We study the Vlasov-Poisson system with time periodic boundary conditions. For small data we prove existence of weak periodic solutions in any space dimension. In the one dimensional case the result is stronger: we obtain existence of mild solution and uniqueness of this solution when the data are smooth. It is necessary to impose a non vanishing condition for the incoming velocities in order to control the life-time of particles in the domain.
Jung, Soyeun
2012-01-01
In the previous paper \\cite{J1}, we established pointwise bounds for the Green function of the linearized equation associated with spatially periodic traveling waves $\\bar u$ of a system of reaction diffusion equations, and also obtained pointwise nonlinear stability and behavior of $\\bar u$ under small perturbations. In this paper, using periodic resolvent kernels and the Bloch-decomposition, we establish pointwise bounds for the Green function of the linearized equation associated with peri...