499 research outputs found
Floer cohomology of Lagrangian intersections and pseudo-holomorphic disks. I.Addendum
No full textThis is an addendum to the author's earlier paper ''Floer Cohomology of Lagrangian Intersection and Pseudo-Holomorphic Discs, I,'' Comm. Pure Appl. Math. 46, 1993, pp. 949-993. The main result of this addendum extends the definition of the Fleer cohomology of Lagrangian intersection to the case where the minimal Maslov number is equal to 2. (C) 1996 John Wiley & Sons, Inc.X1145sciescopu
Spectral invariants and the length minimizing property of Hamiltonian paths
No full textIn this paper we provide a criterion for the quasi-autonomous Hamiltonian path ("Hofer's geodesic") on arbitrary closed symplectic manifolds (M, omega) to be length minimizing in its homotopy class in terms of the spectral invariants rho(G; 1) that the author has recently constructed. As an application, we prove that any autonomous Hamiltonian path on arbitrary closed symplectic manifolds is length minimizing in its homotopy class with fixed ends, as long as it has no contractible periodic orbits of period one and it has a maximum and a minimum that are generically under-twisted, and all of its critical points are non-degenerate in the Floer theoretic sense.X1110sci
Floer mini-max theory, the Cerf diagram, and the spectral invariants
No full textThe author previously defined the spectral invariants, denoted by rho(H; a), of a Hamiltonian function H as the mini-max value of the action functional A(H) over the Novikov Floer cycles in the Floer homology class dual to the quantum cohomology class a. The spectrality axiom of the invariant rho(H; a) states that the mini-max value is a critical value of the action functional AH. The main purpose of the present paper is to prove this axiom for nondegenerate Hamiltonian functions in irrational symplectic manifolds (M, omega). We also prove that the spectral invariant function rho(a) : H (sic) rho(H; a) can be pushed down to a continuous function defined on the universal (etale) covering space (sic)(M,omega) of the group Ham(M,omega) of Hamiltonian diffeomorphisms on general (M, omega). For a certain generic homotopy, which we call a Cerf homotopy H = {H(s)}(0 <= s <= 1) of Hamiltonians, the function rho(a) circle H : s (sic) rho(H(s); a) is piecewise smooth away from a countable subset of [0,1] for each non-zero quantum cohomology class a. The proof of this nondegenerate spectrality relies on several new ingredients in the chain level Floer theory, which have their own independent interest: a structure theorem on the Cerf bifurcation diagram of the critical values of the action functionals associated to a generic one-parameter family of Hamiltonian functions, a general structure theorem and the handle sliding lemma of Novikov Floer cycles over such a family and a family version. of new transversality statements involving the Floer chain map, and many others. We call this chain level Floer theory as a whole the Floer mini-max theory.X118sciescopuskc
Continuous Hamiltonian dynamics and area-preserving homeomorphism group of D2
Get PDFThe main purpose of this paper is to propose a scheme of a proof of the nonsimpleness of the group {\rm Homeo}^\Omega(D^2,\del D^2) of area preserving homeomorphisms of the 2-disc . We first establish the existence of Alexander isotopy in the category of Hamiltonian homeomorphisms. This reduces the question of extendability of the well-known Calabi homomorphism \Cal: {\rm Diff}^\Omega(D^1,\del D^2) \to \R to a homomorphism \overline \Cal: {\rm Hameo(}D^2,\del D^2) \to \R to that of the vanishing of the basic phase function , a Floer theoretic graph selector constructed in \cite{oh:jdg}, that is associated to the graph of the topological Hamiltonian loop and its normalized Hamiltonian on that is obtained via the natural embedding . Here {\rm Hameo(}D^2,\del D^2) is the group of Hamiltonian homeomorphisms introduced by M\"uller and the author \cite{oh:hameo1}. We then provide an evidence of this vanishing conjecture by proving the conjecture for the special class of \emph{weakly graphical} topological Hamiltonian loops on via a study of the associated Hamiton-Jacobi equation.1111Ysciescopuskc
The distribution of two-dimensional eccentricity of Sunyaev-Zel'dovich effect and X-ray surface brightness profiles
No full textWith the triaxial density profile of dark matter halos and the corresponding equilibrium gas distribution, we derive two-dimensional Sunyaev-Zel'dovich (SZ) effect and X-ray surface brightness profiles for clusters of galaxies. It is found that the contour map of these observables can be well approximated by a series of concentric ellipses with scale-dependent eccentricities. The statistical distribution of their eccentricities ( or, equivalently, axial ratios) is analyzed by taking into account the orientation of clusters with respect to the line of sight and the distribution of the axial ratios and the concentration parameters of dark matter halos. For clusters of mass 10(13) h(-1) M-. at redshift z = 0, the axial ratio is peaked at eta similar to 0.9 for both SZ and X-ray profiles. For larger clusters, the deviation from circular distributions is more apparent, with eta peaked at eta similar to 0.85 for M = 10(15) h(-1) M-.. To be closer to observations, we further study the axial-ratio distribution for mass-limited cluster samples with the number distribution of clusters at different redshifts described by a modified Press-Schechter model. For a mass limit of value M-lim = 10(14) h(-1) M-., the average axial ratio is [eta] similar to 0.84, with a tail extended to eta similar to 0.6. With the fast advance of high-quality imaging observations of both SZ effect and X-ray emissions, our analyses provide a useful way to probe cluster halo profiles and therefore to test theoretical halo formation models.Astronomy & AstrophysicsSCI(E)15ARTICLE2847-85961
On additive properties of two special sequences
Get PDFhttp://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000220072200007&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=8e1609b174ce4e31116a60747a720701MathematicsSCI(E)14ARTICLE3299-30311
Systematic errors in the determination of Hubble constant due to the asphericity and nonisothermality of clusters of galaxies
No full textWe present statistical studies on the systematic errors in the determination of the Hubble constant H-0 from joint analyses of X-ray and the Sunyaev-Zel'dovich (SZ) effect of clusters of galaxies. We focus on the effects of their triaxiality and nonisothermality. From the triaxial model of dark matter halos obtained from numerical simulations, we derive the distribution of the intracluster gas under the assumption of the hydrodynamic equilibrium. Both the isothermal and the polytropic gases are investigated. We run Monte Carlo simulations to generate samples of clusters according to the distributions of their masses, axial ratios, concentration parameters, and line-of-sight directions. The estimation of H0 is done by fitting X-ray and SZ profiles of a triaxial cluster with the isothermal and spherical beta model. We find that for a sample of clusters with M = 10(14) h(-1) M-. and z = 0.1, the estimated H-0 is positively biased with H-0(peak) (estimated) approximate to 1.05H(0)(true) and H-0(ave) (estimated) approximate to 1.05H(0)(true) for the isothermal case. For the polytropic case with gamma = 1.15, the bias is large with H-0(peak) (estimated) approximate to 1.35H(0)( true) and H-0(ave) (estimated) approximate to 3H(0)(true). For a mass-limited sample of clusters with M-lim = 10(13) h(-1) M-., the results are similar. On the other hand, such a large overestimation has not been seen in real observations. It is noticed that the beta-value for observed clusters is within the range of 0.5 - 0.8. Considering only the subsample in Monte Carlo simulations with beta in the range of 0.5 - 0.8, we have H-0(ave) (estimated) = 1.002H(0)(true) and H-0(ave) (estimated) = 0.994H(0)(true) for the isothermal and polytropic cases, respectively. We further find that the value of beta is more sensitive to the intrinsic asphericity of clusters than the axial ratio of two-dimensional X-ray images eta is. Limiting to clusters with beta >= 0.5 essentially excludes highly aspherical clusters from the sample. From this subsample of clusters, we can get a fair estimate on H-0.Astronomy & AstrophysicsSCI(E)5ARTICLE2630-64064
Thin Layer Splitting Along the Elastic-Plastic Solid Surface
No full textThin layer splitting along the elastic-plastic solid surface is studied based on the elastic-plastic fracture mechanics method. In the splitting process, since the split arm does not undergo the reversed plastic bending, comparing with the conventional peel test method, the split test has remarkable advantages in measuring the material fracture behavior and is recommended as a new test method. Moreover, besides the driving force parameter, the split test method provides an additional measurable parameter, a residual curvature (or curvature radius) of the split arm. Comparing with the peeling force, the split force also has the connection with the total energy release rate, which is related with the crack tip separation energy (or material fracture toughness), separation strength, and the plastic dissipation work. Through measuring the driving force and the residual curvature, the fracture toughness and separation strength can be obtained. The primary objective of the present research is to develop a series of relations of the split force, the residual curvature, as well as the crack tip slope angle, respectively with the split layer thickness and material parameters, when crack tip advances steadily. Frictionless (or smooth) contact between splitter head and split arm surface is assumed. Another objective of the present research is to explore a connection between the split test solutions and the peel test solutions. Finally, the split test analysis is applied to a wedge-loaded double-cantilever beam experiment for Al-alloy material, a considerably similar test method with the split test, conducted by Thouless and his collaborators, and the fracture parameters from both test systems are correlated
Modelling the recruitment of tiger prawns Penaeus esculentus and P. semisulcatus to nursery grounds in the Gulf of Carpentaria, northern Australia: Implications for assessing stock-recruitment relationships
Get PDFA prawn larval behavioural model was coupled to a hydrodynamic model of the Gulf of Carpentaria in northern Australia to provide estimates of the size of the spawning area from which nursery ground populations are drawn, referred to here as the advection envelope. We have assumed that, during the first 8 d after the nauplii hatch, the larvae undergo a diel vertical migration in the water column, without spending any time on the bottom. After 8 d, larvae in waters shallower than a preset transition depth were assumed to switch to vertical migration cued by the tidal cycles-remaining on the bottom during outgoing tides, and swimming into the water column during flood tides. This tidal behaviour generated a net advection of postlarvae into the coastal zone and local estuaries. The model demonstrated that this mechanism is very efficient at accumulating larvae along the coastal zone. Changes in the timing and magnitude of the tides through the year generated a strong seasonal signal in the size and shape of the advection envelope, with typically a 2-fold difference in the size of the envelope between October and March. However, winds had little effect on the size of the advection envelopes, and interannual variation in the size and shape of the advection envelopes was small (<10%). The model also demonstrated that advection envelopes are very sensitive to the postlarval transition depth, which has not yet been adequately constrained by either field or laboratory studies. For example, changing the transition depth from 7 to 30 m typically resulted in a 2-fold increase in the size of the advection envelope. The results of the model may also have significant implications for the management of the prawn fishery. Comparisons of the advection envelopes with the distribution of tiger prawn catches indicate regions where fishing is most likely to have an impact on the spawning stock and subsequent recruitment to the fishery. The results also suggest that there are 3 discrete sub-stocks of Penaeus esculentus and P. semisulcatus in the Gulf of Carpentaria and, therefore, challenge the assumption that there is a single tiger prawn stock covering the entire region
Rigidity of asymptotically hyperbolic manifolds
No full textIn this paper, we prove a rigidity theorem of asymptotically hyperbolic manifolds only under the assumptions on curvature. Its proof is based on analyzing asymptotic structures of such manifolds at infinity and a volume comparison theorem.Physics, MathematicalSCI(E)12ARTICLE3545-55925
- …
