Solutions to the ultradiscrete Toda molecule equation expressed as minimum weight flows of planar graphs

We define a function by means of the minimum weight flow on a planar graph and prove that this function solves the ultradiscrete Toda molecule equation, its B\"acklund transformation and the two dimensional Toda molecule equation. The method we employ in the proof can be considered as fundamental to the integrability of ultradiscrete soliton equations.Comment: 14 pages, 10 figures Added citations in v

Nonlinear wave propagation through cold plasma

Electromagnetic wave propagation through cold collision free plasma is studied using the nonlinear perturbation method. It is found that the equations can be reduced to the modified Kortweg-de Vries equation

Extended Quantum Dimer Model and novel valence-bond phases

We extend the quantum dimer model (QDM) introduced by Rokhsar and Kivelson so as to construct a concrete example of the model which exhibits the first-order phase transition between different valence-bond solids suggested recently by Batista and Trugman and look for the possibility of other exotic dimer states. We show that our model contains three exotic valence-bond phases (herringbone, checkerboard and dimer smectic) in the ground-state phase diagram and that it realizes the phase transition from the staggered valence-bond solid to the herringbone one. The checkerboard phase has four-fold rotational symmetry, while the dimer smectic, in the absence of quantum fluctuations, has massive degeneracy originating from partial ordering only in one of the two spatial directions. A resonance process involving three dimers resolves this massive degeneracy and dimer smectic gets ordered (order from disorder).Comment: 20 pages, 13 figures, accepted for publication in J. Stat. Mec

On the evolution and environmental dependence of the star formation rate versus stellar mass relation since z ˜ 2.

This paper discusses the evolution of the correlation between galaxy star formation rates (SFRs) and stellar mass (M*) over the last ∼10 Gyr, particularly focusing on its environmental dependence. We first present the mid-infrared (MIR) properties of the Hα-selected galaxies in a rich cluster Cl 0939+4713 at z = 0.4. We use wide-field Spitzer/MIPS 24 μm data to show that the optically red Hα emitters, which are most prevalent in group-scale environments, tend to have higher SFRs and higher dust extinction than the majority population of blue Hα sources. With an MIR stacking analysis, we find that the median SFR of Hα emitters is higher in higher density environment at z = 0.4. We also find that star-forming galaxies in high-density environment tend to have higher specific SFR (SSFR), although the trend is much less significant compared to that of SFR. This increase of SSFR in high-density environment is not visible when we consider the SFR derived from Hα alone, suggesting that the dust attenuation in galaxies depends on environment; galaxies in high-density environment tend to be dustier (by up to ∼0.5 mag), probably reflecting a higher fraction of nucleated, dusty starbursts in higher density environments at z = 0.4. We then discuss the environmental dependence of the SFR–M* relation for star-forming galaxies since z ∼ 2, by compiling our comparable, narrow-band-selected, large Hα emitter samples in both distant cluster environments and field environments. We find that the SSFR of Hα-selected galaxies (at the fixed mass of log (M*/M⊙) = 10) rapidly evolves as (1 + z)3, but the SFR–M* relation is independent of the environment since z ∼ 2, as far as we rely on the Hα-based SFRs (with M*-dependent extinction correction). Even if we consider the possible environmental variation in the dust attenuation, we conclude that the difference in the SFR–M* relation between cluster and field star-forming galaxies is always small (≲0.2 dex level) at any time in the history of the Universe since z ∼ 2

Quantum spin pumping mediated by magnon

We theoretically propose quantum spin pumping mediated by magnons, under a time-dependent transverse magnetic field, at the interface between a ferromagnetic insulator and a non-magnetic metal. The generation of a spin current under a thermal equilibrium condition is discussed by calculating the spin transfer torque, which breaks the spin conservation law for conduction electrons and operates the coherent magnon state. Localized spins lose spin angular momentum by emitting magnons and conduction electrons flip from down to up by absorbing the momentum. The spin transfer torque has a resonance structure as a function of the angular frequency of the applied transverse field. This fact is useful to enhance the spin pumping effect induced by quantum fluctuations. We also discuss the distinction between our quantum spin pumping theory and the one proposed by Tserkovnyak et al.Comment: 27 pages, 2 figures. v2; the detail of the calculation has been added in Appendix. The distinction from the spin pumping theory proposed by Tserkovnyak et al. has been clarified in section 5. v3; typos correcte

Collagen gene expression during chondrogenesis from chick periosteum-derived cells

AbstractChick periosteum-derived cells, which do not enter the chondrogenic cell lineage during normal bone development and growth, exhibit chondrogenic potential in high cell density culture conditions. In such cultures, collagen gene expression was temporally analyzed at the mRNA level by a reverse transcription PCR (RT-PCR) procedure, which showed that α1(II) and α1(IX) collagen mRNAs are coordinately increased, coincident with the onset of overt chondrogenesis, and subsequently decreased as chondrocytes exhibited hypertrophic characteristics. α1(X) collagen mRNA was detected well before the onset of chondrogenesis and markedly increased along with the hypertrophic change. For α2(I) collagen, both the bone/tendon form and the cartilage form of mRNA were detected throughout the culture period. This culture system provides an experimental vehicle capable of investigating the molecular events involved in the full range of chondrogenic differentiation starting from uncommitted periosteum-derived mesenchymal stem cells

Mixed perturbative expansion: the validity of a model for the cascading

A new type of perturbative expansion is built in order to give a rigorous derivation and to clarify the range of validity of some commonly used model equations. This model describes the evolution of the modulation of two short and localized pulses, fundamental and second harmonic, propagating together in a bulk uniaxial crystal with non-vanishing second order susceptibility $\chi^(2)$ and interacting through the nonlinear effect known as ``cascading'' in nonlinear optics. The perturbative method mixes a multi-scale expansion with a power series expansion of the susceptibility, and must be carefully adapted to the physical situation. It allows the determination of the physical conditions under which the model is valid: the order of magnitude of the walk-off, phase-mismatch,and anisotropy must have determined values.Comment: arxiv version is already officia

Speech Communication

Contains reports on seven research projects.Contract AF19(604)-2061 with Air Force Cambridge Research CenterContract N5ori-07861 with the Navy (Office of Naval Research)National Science Foundatio

Subaru Deep Survey V. A Census of Lyman Break Galaxies at z=4 and 5 in the Subaru Deep Fields: Photometric Properties

(abridged) We investigate photometric properties of Lyman Break Galaxies (LBGs) at z=3.5-5.2 based on large samples of 2,600 LBGs detected in deep (i'~27) and wide-field (1,200 arcmin^2) images taken in the Subaru Deep Field (SDF) and the Subaru/XMM Deep Field (SXDF). The selection criteria for the LBG samples are examined with 85 spectroscopically identified objects and by Monte Carlo simulations. We find in the luminosity functions of LBGs (i) that the number density of bright galaxies (M_{1700}<-22; corresponding to SFR_{corr}>100 Msolar yr^{-1}) decreases significantly from z=4 to 5 and (ii) that the faint-end slope of the luminosity function may become steeper towards higher redshifts. We estimate dust extinction of z=4 LBGs with M<M^* from UV slopes, and obtain E(B-V)=0.15+/-0.03 as the mean value. The dust extinction remains constant with apparent luminosity, but increases with intrinsic luminosity. We find no evolution in dust extinction between LBGs at z=3 and 4. We investigate the evolution of UV-luminosity density at 1700A, rho, and find that rho does not significantly change from z=3 to z=5, i.e., rho(z=4)/rho(z=3)=1.0+/-0.2 and rho(z=5)/rho(z=3)=0.8+/-0.4, thus the cosmic star-formation rate (SFR) density remains constant. We find that the stellar mass density estimated from the cosmic SFR is consistent with those derived directly from the stellar mass function at z=0-1, but exceeds those at z~3 by a factor of 3. We find that the ratio of the UV-luminosity density of Ly-a emitters (LAEs) to that of LBGs is ~60% at z=5, and thus about a half of the star formation at z=5 probably occurs in LAEs. We obtain a constraint on the escape fraction of UV-ionizing photons produced by LBGs, f_{esc}>~0.13.Comment: 41 pages, 22 figures, ApJ in press. Paper with high resolution figures is available at http://hikari.astron.s.u-tokyo.ac.jp/~ouchi/work/astroph/SDS_V_VI/SDS_V.pdf (PDF