Involutivity of integrals for sine-Gordon, modified KdV and potential KdV maps

Closed form expressions in terms of multi-sums of products have been given in \cite{Tranclosedform, KRQ} of integrals of sine-Gordon, modified Korteweg-de Vries and potential Korteweg-de Vries maps obtained as so-called $(p,-1)$-traveling wave reductions of the corresponding partial difference equations. We prove the involutivity of these integrals with respect to recently found symplectic structures for those maps. The proof is based on explicit formulae for the Poisson brackets between multi-sums of products.Comment: 24 page

Geometrically nonlinear isogeometric analysis of laminated composite plates based on higher-order shear deformation theory

In this paper, we present an effectively numerical approach based on isogeometric analysis (IGA) and higher-order shear deformation theory (HSDT) for geometrically nonlinear analysis of laminated composite plates. The HSDT allows us to approximate displacement field that ensures by itself the realistic shear strain energy part without shear correction factors. IGA utilizing basis functions namely B-splines or non-uniform rational B-splines (NURBS) enables to satisfy easily the stringent continuity requirement of the HSDT model without any additional variables. The nonlinearity of the plates is formed in the total Lagrange approach based on the von-Karman strain assumptions. Numerous numerical validations for the isotropic, orthotropic, cross-ply and angle-ply laminated plates are provided to demonstrate the effectiveness of the proposed method

Transport properties in Simplified Double Exchange model

Transport properties of the manganites by the double-exchange mechanism are considered. The system is modeled by a simplified double-exchange model, i.e. the Hund coupling of the itinerant electron spins and local spins is simplified to the Ising-type one. The transport properties such as the electronic resistivity, the thermal conductivity, and the thermal power are calculated by using Dynamical mean-field theory. The transport quantities obtained qualitatively reproduce the ones observed in the manganites. The results suggest that the Simplified double exchange model underlies the key properties of the manganites.Comment: 5 pages, 5 eps figure

Spectroscopic Confirmation of Multiple Red Galaxy-Galaxy Mergers in MS1054-03 (z=0.83)

We present follow-up spectroscopy of the galaxy cluster MS1054-03 (z=0.83) confirming that at least six of the nine merging galaxy pairs identified by van Dokkum et al. (1999) are indeed bound systems: they have projected separations of R_s<10 kpc and relative line-of sight velocities of dv<165 km/s. For the remaining three pairs, we were unable to obtain redshifts of both constituent galaxies. To identify a more objective sample of merging systems, we select bound red galaxy pairs (R_s<=30 kpc, dv<=300 km/s) from our sample of 121 confirmed cluster members: galaxies in bound red pairs make up 15.7+/-3.6% of the cluster population. The (B-K_s) color-magnitude diagram shows that the pair galaxies are as red as the E/S0 members and have a homogeneous stellar population. The red pair galaxies span a large range in luminosity and internal velocity dispersion to include some of the brightest, most massive members (L>L*, sigma>200 km/s); these bound galaxy pairs must evolve into E/S0 members by z~0.7. These results combined with MS1054's high merger fraction and reservoir of likely future mergers indicates that most, if not all, of its early-type members evolved from (passive) galaxy-galaxy mergers at z<~1.Comment: accepted by ApJ Letters; high resolution version of Fig. 2 available at http://www.exp-astro.phys.ethz.ch/tran/outgoing/ms1054mgrs.ps.g

Infall, the Butcher-Oemler Effect, and the Descendants of Blue Cluster Galaxies at z~0.6

Using wide-field HST/WFPC2 imaging and extensive Keck/LRIS spectroscopy, we present a detailed study of the galaxy populations in MS2053--04, a massive, X-ray luminous cluster at z=0.5866. Analysis of 149 confirmed cluster members shows that MS2053 is composed of two structures that are gravitationally bound to each other; their respective velocity dispersions are 865 km/s (113 members) and 282 km/s (36 members). MS2053's total dynamical mass is 1.2x10^15 Msun. MS2053 is a classic Butcher-Oemler cluster with a high fraction of blue members (24%) and an even higher fraction of star-forming members (44%), as determined from their [OII] emission. The number fraction of blue/star-forming galaxies is much higher in the infalling structure than in the main cluster. This result is the most direct evidence to date that the Butcher-Oemler effect is linked to galaxy infall. In terms of their colors, luminosities, estimated internal velocity dispersions, and [OII] equivalent widths, the infalling galaxies are indistinguishable from the field population. MS2053's deficit of S0 galaxies combined with its overabundance of blue spirals implies that many of these late-types will evolve into S0 members. The properties of the blue cluster members in both the main cluster and infalling structure indicate they will evolve into low mass, L<L* galaxies with extended star formation histories like that of low mass S0's in Coma. Our observations show that most of MS2053's blue cluster members, and ultimately most of its low mass S0's, originate in the field. Finally, we measure the redshift of the giant arc in MS2053 to be z=3.1462; this object is one in only a small set of known strongly lensed galaxies at z>3.Comment: Accepted by ApJ. Version with full resolution figures available at http://www.exp-astro.phys.ethz.ch/tran/outgoing/ms2053.ps.g

Integrable and superintegrable systems associated with multi-sums of products

We construct and study certain Liouville integrable, superintegrable, and non-commutative integrable systems, which are associated with multi-sums of products.Comment: 26 pages, submitted to Proceedings of the royal society

The staircase method: integrals for periodic reductions of integrable lattice equations

We show, in full generality, that the staircase method provides integrals for mappings, and correspondences, obtained as traveling wave reductions of (systems of) integrable partial difference equations. We apply the staircase method to a variety of equations, including the Korteweg-De Vries equation, the five-point Bruschi-Calogero-Droghei equation, the QD-algorithm, and the Boussinesq system. We show that, in all these cases, if the staircase method provides r integrals for an n-dimensional mapping, with 2r<n, then one can introduce q<= 2r variables, which reduce the dimension of the mapping from n to q. These dimension-reducing variables are obtained as joint invariants of k-symmetries of the mappings. Our results support the idea that often the staircase method provides sufficiently many integrals for the periodic reductions of integrable lattice equations to be completely integrable. We also study reductions on other quad-graphs than the regular 2D lattice, and we prove linear growth of the multi-valuedness of iterates of high-dimensional correspondences obtained as reductions of the QD-algorithm.Comment: 40 pages, 23 Figure