Persistence of Hyperbolic Tori in Generalized Hamiltonian Systems

In this paper we prove the persistence of hyperbolic invariant tori in generalized Hamiltonian systems, which may admit a distinct number of action and angle variables. The systems under consideration can be odd dimensional in tangent direction. Our results generalize the well-known results of Graft and Zehnder in standard Hamiltonians. In our case the unperturbed Hamiltonian systems may be degenerate. We also consider the persistence problem of hyperbolic tori on submanifolds.

Effects of Sheared Flow on Microinstabilities and Transport in Plasmas

Theoretical and experimental studies associated with electric field effectson the stability and transport are briefly surveyed. The effects of radial electric field on thesuppression and/or enhancement of various microinstabilities such as drift waves, flute mode andtemperature gradient modes are discussed. The suppression of flow shear on the electron temperaturegradient mode in plasmas with slightly hollow density profiles is investigated by solving thegyrokinetic integral eigenvalue equation. Comparison between theoretical predictions andexperimental observations based on the HIBP measurements with high temporal and spatial resolutionsis made in bumpy tori and heliotron (CHS) devices.

PERSISTENCE OF RESONANT INVARIANT TORI WITH NON-HAMILTONIAN PERTURBATION

A persistence theorem for resonant invariant tori with non-Hamiltonian perturbation is proved. The method is a combination of the theory of normally hyperbolic invariant manifolds and an appropriate continuation method. The results obtained are extensions of Chicone’s for the three dimensional non-Hamiltonian systems.

Nonlinear dynamics analysis of cluster-shaped conservative flows generated from a generalized thermostatted system

The thermostatted system is a conservative system different from Hamiltonian systems,and has attracted much attention because of its rich and different nonlinear dynamics.We report and analyze the multiple equilibria and curve axes of the cluster-shaped conservative flows generated from a generalized thermostatted system.It is found that the cluster-shaped structure is reflected in the geometry of the Hamiltonian,such as isosurfaces and local centers,and the shapes of cluster-shaped chaotic flows and invariant tori rely on the isosurfaces determined by initial conditions,while the numbers of clusters are subject to the local centers solved by the Hessian matrix of the Hamiltonian.Moreover,the study shows that the cluster-shaped chaotic flows and invariant tori are chained together by curve axes,which are the segments of equilibrium curves of the generalized thermostatted system.Furthermore,the interesting results are vividly demonstrated by the numerical simulations.

Energy behavior of Boris algorithm

Boris numerical scheme due to its long-time stability,accuracy and conservative properties has been widely applied in many studies of magnetized plasmas.Such algorithms conserve the phase space volume and hence provide accurate charge particle orbits.However,this algorithm does not conserve the energy in some special electromagnetic configurations,particularly for long simulation times.Here,we empirically analyze the energy behavior of Boris algorithm by applying it to a 2D autonomous Hamiltonian.The energy behavior of the Boris method is found to be strongly related to the integrability of our Hamiltonian system.We find that if the invariant tori is preserved under Boris discretization,the energy error can be bounded for an exponentially long time,otherwise the said error will show a linear growth.On the contrary,for a non-integrable Hamiltonian system,a random walk pattern has been observed in the energy error.

The Study on the Phase Structure of the Paul Trap System

In this article, the classic dynamic of Paul trap problem is investigated. We give a complete description of the topological structure of Hamiltonian flows on the real phase space. Using the surgery’s theory of Fomenko Liouville tori, all generic bifurcations of the common level sets of the first integrals were described theoretically. We give also an explicit periodic solution for singular values of the first integrals. Numerical investigations are carried out for all generic bifurcations and we observe order-chaos transition when the critical value of a control parameter is varied.

A KAM-type Theorem for Generalized Hamiltonian Systems

In this paper we mainly concern the persistence of invariant tori in generalized Hamiltonian systems. Here the generalized Hamiltonian systems refer to the systems which may admit a distinct number of action and angle variables. In particular, system under consideration can be odd dimensional. Under the Riissmann type non-degenerate condition, we proved that the majority of the lower-dimension invariant tori of the integrable systems in generalized Hamiltonian system are persistent under small perturbation. The surviving lower-dimensional tori might be elliptic, hyperbolic, or of mixed type.

KAM Type-Theorem for Lower Dimensional Tori in Random Hamiltonian Systems

In this paper, we study the persistence of lower dimensional tori for random Hamiltonian systems, which shows that majority of the unperturbed tori persist as Cantor fragments of lower dimensional ones under small perturbation. Using this result, we can describe the stability of the non-autonomous dynamic systems.

HOPE-LANDAU BIFURCATIONS OF HIGHER DIMENSIONAL TORI

The existence of degenerate bifurcations from Tm to Pm+1 is provedunder the condition of quasi-periodic critical points.

KAM-type Theorem for Nearly Integrable Hamiltonian with a Quasiperiodic Perturbation

In this paper we consider the persistence of invariant tori of an integrable Hamiltonian system with a quasiperiodic perturbation. It is proved that if the unperturbed system satisfies the Rtissmann non-degenerate condition and the perturbed system satisfies the co-linked non-resonant condition, then the majority of invariant tori is persistent under the perturbation.

Polysurfacic Tori or Kideas Inspired by the Möbius Strip Topology

Polysurfacic tori or kideas are three-dimensional objects formed by rotating a regular polygon around a central axis. These toric shapes are referred to as “polysurfacic” because their characteristics, such as the number of sides or surfaces separated by edges, can vary in a non-trivial manner depending on the degree of twisting during the revolution. We use the term “Kideas” to specifically denote these polysurfacic tori, and we represent the number of sides (referred to as “facets”) of the original polygon followed by a point, while the number of facets from which the torus is twisted during its revolution is indicated. We then explore the use of concave regular polygons to generate Kideas. We finally give acceleration for the algorithm for calculating the set of prime numbers.

The Persistence of Invariant Tori in Nearly Small Twist Mappings with Intersection Property

In this paper we investigate the nearly small twist mappings with intersection property. With a certain non-degenerate condition, we proved that the most of invariant tori of the original small twist mappings will survive afer small perturtations. The persisted invariant tori are close to the unperturbed ones when the perturbation are small. The orbits reduced by those mappings are quasi-periodic in the invariant tori with the frequences closing to the original ones.

Tori Amos 《American Doll Posse》闪亮出炉

最近,Tori Amos的新专辑《American Doll Posse》问世。虽然她去年发行了精选集,但这张专辑是2005年《the Beekeeper》以来的首张录音室作品。专辑发行的同时,Amos将踏上世界巡演的路程,5月28日的巡演第一站设在罗马。

The KAM theorem on the modulus of continuity about parameters

In this paper,we study the Hamiltonian systems H(y,x,ξ,ε)=〈ω(ξ),y〉+εP(y,x,ξ,ε),where ω and P are continuous about ξ.We prove that persistent invariant tori possess the same frequency as the unperturbed tori,under a certain transversality condition and a weak convexity condition for the frequency mapping ω.As a direct application,we prove a Kolmogorov-Arnold-Moser(KAM) theorem when the perturbation P holds arbitrary Holder continuity with respect to the parameter ξ.The infinite-dimensional case is also considered.To our knowledge,this is the first approach to the systems with the only continuity in the parameter beyond H?lder's type.

A KAM theorem for 2-dimensional nonlinear Schrodinger equations with forcing terms and(2p+1)-nonlinearities

In this paper,we prove an infinite dimensional KAM theorem and apply it to study 2-dimensional nonlinear Schrodinger equations with different large forcing terms and(2p+1)-nonlinearities iu_(t)-Δu+φ_(1)(ω_(1)+t)u+φ_(2)(ω_(2)+t)|u|^(2p)u=0,t∈R,x∈T^(2) under periodic boundary conditions. As a result, the existence of a Whitneysmooth family of small-amplitude reducible quasi-periodic solutions is obtained.

Screening of potential aquatic probiotics from the major microflora of guppies （Poecilia reticulata）

The fish （Poecilia reticulata） was used as the source for probiotics. 46 bacterial isolates were obtained from the skin, gills, guts and intestines of the guppy, Poecilia reticulata （collected from a government model fish farm in Kottayam, India）. Of the above isolated strains, four isolates were selected based on their inhibitory spectrum against five indicator strains, Aeromonas hydro- phila 1739, Vibrio cholerae 3906, Flavobacterium 2495, Acinetobacter 1271 and Alcaligenes 1424 （standard cultures collected from Microbial Type Culture Collection （MTCC） Chandigarh, India）. Among the resulting isolates, two were gram-positive cocci, namely MBTU-PB2 and MBTU-PB3 and belong to the genus Staphylococcus. The other two were gram-negative rods, namely MBTU-PB1 and MBTU-PB4, of the genera Enterobacter and Acine- tobacter, respectively. The basic probiotic characteristics of these isolates such as the production of bacteriocin like inhibitory substances （BLIS）, antibiotic sensitivities and growth profiles were also determined. The above four isolated strains exhibited different antagonisms than the five indicator strains. During incubation, the antibacterial activity gradually increased in the inhibition zone and was influenced by the lag period （λ） and doubling time. The lag periods for most of the four selected strains were shorter than those of the indicator strains and the isolates had different growth rates （μ） than the indicator strains. All four isolates produced BLIS, however, the strains had different BLIS activities against the indicator strains. Treatment of the neutralized cell free supematants of the selected isolates with proteases eliminated or reduced the BLIS activity, suggesting a proteinaceous nature of the inhibitory compounds. Further, the optimum BLIS activity was observed at neutral pH after 18 h of incubation. The antibiotic sensitivity assay revealed that the isolates were susceptible to routinely used antibiotics, whereas the plasmid profiles showed that the plasmids had no role in the antagonistic properties of the four isolated strains. The results showed that the isolates could be a promising source for biocontrol agents in aquacultures.

Spatial structure and scale feature of the atmospheric pollution source impact of city agglomeration

The spatial structure and multi-scale feature of the atmospheric pollution influence domain of Beijing and its peripheral areas (a rapidly developed city agglomeration) is dissected and analyzed in this paper on the basis of the atmospheric pollution dynamic-chemical process observation data of the urban building ensemble boundary layer of the Beijing City Air Pollution Observation Experiment (BECAPEX) in winter (February) and summer (August) 2003, and relevant meteorological elements and satellite retrieval aerosol optical depth (AOD), etc. comprehensive data with the dynamic-statistical integrated analysis of 'point-surface' spatial structure. Results show that there existed significant difference in the contribution of winter/summer different pollution emission sources to the component character of atmospheric pollution, and the principal component analysis (PCA) results of statistical model also indicate that SO2 and NOx dominated in the component structure of winter aerosol particle; instead, CO and NOxdominated in summer. Surface layer atmospheric dynamic and thermal structures and various pollutant species at the upper boundary of building ensembles at urban different observational sites of Beijing in winter and summer showed an 'in-phase' variation and its spatial scale feature of 'influence domain'. The power spectrum analysis (PSA) shows that the period spectrum of winter/summer particle concentration accorded with those of atmospheric wind field: the longer period was dominative in winter, but the shorter period in summer, revealing the impact of the seasonal scale feature of winter/summer atmospheric general circulation on the period of atmospheric pollution variations. It is found that from analyzing urban area thermal heterogeneity that the multi-scale effect of Beijing region urban heat island (UHI) was associated with the heterogeneous expansion of tall buildings area. In urban atmospheric dynamical and thermal characteristic spatial structures, the turbulent scale feature of the urban boundary layer (UBL) of architectural complexes had important impact on the multi-scale feature of urban atmospheric pollution. The comprehensive analyses of the variational analysis field of Moderate Resolution Imaging Spectroradiometer (MODIS) AOD-surface PM10 under the condition of clear sky and the correlation resultant wind vector field for pollution source-tracing suggest that the emission sources for winter Beijing atmospheric pollution aerosols particle might be remotely traced to the south peripheral greater-Scale spatial range of Hebei, Shandong, Tianjin, etc., and the spatial distribution of the high value area of AOD was associated with that of the high value area of resident family number (heating surface source). The backward trajectory feature of winter/ summer air particles exhibits analogous multi-scale feature, and depicts the difference in the scale feature of the pollution sources spatial distribution in different seasons. The peripheral source trajectory paths of urban atmospheric pollution (UAP) mainly come from the fixed industrial surface source or heating surface source in the outskirt of Beijing, and the diffusion and transport distance of peripheral sources in winter is larger than one in summer. The above conclusions depict the multi-scale spatial influence domain and seasonal features caused by UAP source influence and atmospheric dynamical structure. The high value area of the winter Total Ozone Mapping Spectrometer (TOMS) AOD lay in the Beijing region and its south peripheral area, an S-N zonal pattern, which reflects the dynamical effect of peripheral topographic pattern on the diffusion of regional scale atmospheric pollution sources. Study suggests that the extent of winter atmospheric pollution within the 'valley' megarelief in Beijing and periphery was close related with the pollution emission sources of the south peripheral area; and the significant 'anti-phase' variation feature of winter AOD and sunshine duration in Beijing and its peripheral areas, and the regional scale correlation of low cloud cover, fog days, and aerosols reflects the local climatic effect of aerosol influence in this region. Besides, analysis of the impacts of atmospheric dry/wet deposition distributions within a valley-scale on the regional water body of Miyun reservoir also reveals the possible influence of the multi-scale spatial structure of summer water, soil and atmospheric pollution sources on the water quality of Miyun reservoir.

BOUNDEDNESS FOR SOLUTIONS OF SUPERLINEAR DUFFING EQUATIONS VIA THE TWIST THEOREM

A class of functions {g(x)} will be provided, such that the differential equation d^2x/dt^2+ g(x) = p(t) possesses an infinitely many number of invariant tori in the orbit space(t, x,dx/dt)∈S^1×R^2. Moreover, each solution of the equation is bounded. The proof is basedon the twist theorem.

Invariant tori for asymptotically linear impact oscillators

The existence of invariant tori and quasi-periodic solutions for asymptotically linear impact oscillators is proved by using the successor map and some generalized versions of the Moser's twist theorem.

Totally real conformal minimal tori in the hyperquadric Q_2

Our purpose is to study the minimal tori in the hyperquadric Q2. Firstly, we obtain a necessary and sufficient condition for the minimal surface in Qn which is also minimal in CPn＋1. Next, we show that this kind of minimal surface （neither holomorphic nor anti-holomorphic） with constant curvature in Q2 is part of a flat totally real torus. Finally, we prove that totally real minimal fiat tori in Q2 must be totally geodesic, and we classify all the totally geodesic closed surfaces in Q2.