Extension and Unification of Singular Perturbation Methods for ODEs Based on the Renormalization Group Method

The renormalization group (RG) method is one of the singular perturbation methods which is used in search for asymptotic behavior of solutions of differential equations. In this article, time-independent vector fields and time (almost) periodic vector fields are considered. Theorems on error estimates for approximate solutions, existence of approximate invariant manifolds and their stability, inheritance of symmetries from those for the original equation to those for the RG equation, are proved. Further it is proved that the RG method unifies traditional singular perturbation methods, such as the averaging method, the multiple time scale method, the (hyper-) normal forms theory, the center manifold reduction, the geometric singular perturbation method and the phase reduction. A necessary and sufficient condition for the convergence of the infinite order RG equation is also investigated.Comment: publised as SIAM j. on Appl. Dyn.Syst., Vol.8, 1066-1115 (2009

Scalar-Tensor Gravity in Two 3-brane System

We derive the low-energy effective action of four-dimensional gravity in the Randall-Sundrum scenario in which two 3-branes of opposite tension reside in a five-dimensional spacetime. The dimensional reduction with the Ansatz for the radion field by Charmousis et al., which solves five-dimensional linearized field equations, results in a class of scalar-tensor gravity theories. In the limit of vanishing radion fluctuations, the effective action reduces to the Brans-Dicke gravity in accord with the results of Garriga and Tanaka: Brans-Dicke gravity with the corresponding Brans-Dicke parameter $0< \omega < \infty$ (for positive tension brane) and $-3/2< \omega <0$ (for negative tension brane). In general the gravity induced a brane belongs to a class of scalar-tensor gravity with the Brans-Dicke parameter which is a function of the interval and the radion. In particular, gravity on a positive tension brane contains an attractor mechanism toward the Einstein gravity.Comment: 8 pages, discussion expanded, references adde

Kinematics of Nearby Subdwarf Stars

We present an analysis of the space motions of 742 subdwarf stars based on the sample of Carney et al. (1994, CLLA). Hipparcos parallaxes, TYC2+HIP proper motions and Tycho2 proper motions were combined with radial velocities and metallicities from CLLA. The kinematical behavior is discussed in particular in relation to their metallicities. The majority of these sample stars have metal abundances of [Fe/H] >-1 and represent the thick disk population. The halo component, with [Fe/H] <-1.6, is characterized by a low mean rotation velocity and a radially elongated velocity ellipsoid. In the intermediate metallicity range (-1.6 < [Fe/H] <-1), we find a significant number of subdwarfs with disklike kinematics. We interpret this population of stars as a metal-weak thick disk population.Comment: 6 pages, 7 figures, accepted by Astronomy & Astrophysic

Quintessence Models and the Cosmological Evolution of alpha

The cosmological evolution of a quintessence-like scalar field, phi, coupled to matter and gauge fields leads to effective modifications of the coupling constants and particle masses over time. We analyze a class of models where the scalar field potential V(phi) and the couplings to matter B(phi) admit common extremum in phi, as in the Damour-Polyakov ansatz. We find that even for the simplest choices of potentials and B(phi), the observational constraints on delta alpha/alpha coming from quasar absorption spectra, the Oklo phenomenon and Big Bang nucleosynthesis provide complementary constraints on the parameters of the model. We show the evolutionary history of these models in some detail and describe the effects of a varying mass for dark matter.Comment: 26 pages, 20 eps figure

Vacuum discharge as a possible source of gamma-ray bursts

We propose that spontaneous particle--anti-particle pair creations from the discharged vacuum caused by the strong interactions in dense matter are major sources of $\gamma$-ray bursts. Two neutron star collisions or black hole-neutron star mergers at cosmological distance could produce a compact object with its density exceeding the critical density for pair creations. The emitted anti-particles annihilate with corresponding particles at the ambient medium. This releases a large amount of energy. We discuss the spontaneous $p\bar{p}$ pair creations within two neutron star collision and estimate the exploded energy from $p\bar{p}$ annihilation processes. The total energy could be around $10^{51} - 10^{53}$ erg depending on the impact parameter of colliding neutron stars. This value fits well into the range of the initial energy of the most energetic $\gamma$-ray bursts.Comment: 12 pages, Latex, 2 figures included; replaced by the revised version, Int. J. Mod. Phys. E in pres

Quintessence, the Gravitational Constant, and Gravity

Dynamical vacuum energy or quintessence, a slowly varying and spatially inhomogeneous component of the energy density with negative pressure, is currently consistent with the observational data. One potential difficulty with the idea of quintessence is that couplings to ordinary matter should be strongly suppressed so as not to lead to observable time variations of the constants of nature. We further explore the possibility of an explicit coupling between the quintessence field and the curvature. Since such a scalar field gives rise to another gravity force of long range (\simg H^{-1}_0), the solar system experiments put a constraint on the non-minimal coupling: |\xi| \siml 10^{-2}.Comment: 9 pages, a version to be published in Phys.Rev.

Amino Acid and Energy Interrelationships in Pigs Weighing from 20 to 50 Kilograms: Rate and Efficiency of Protein and Fat Deposition

Two experiments were conducted to investigate the relationships between amino acids and DE for pigs weighing 20 to 50 kg. In Exp. 1, there were three dietary lysine levels that were either adjusted (1.50, 2.35 and 3.20 g/Mcal DE) for five DE levels (3.00 to 4.00 Mcal/kg) or unadjusted (.45, .71 and .%% of the diet) for three DE levels (3.50 to 4.00 Mcal/kg). In Exp. 2, diets containing six 1ysine:DE ratios (1.90 to 3.90 g/Mcal) at two DE levels (3.25 and 3.75 Mcal/kg) were fed. Pigs were housed individuiiy, and could eat and drink ad libitum. When pigs weighed 50 kg, their empty body composition was determined by the urea dilution technique in Exp. 1 and by prediction equations based on backfat in Exp. 2. For the adjusted diets in Exp. 1, protein deposition and protein deposition:DE intake increased (P \u3c .01) slightly as DE levels increased. These criteria decreased linearly (P \u3c .001), and fat deposition increased (P = .11) as DE increased when 1ysine:DE ratios were not maintained. As lysine levels increased, protein deposition and protein deposition: DE intake increased (P \u3c .001) in both the adjusted and unadjusted diets. In Exp. 2, there was no effect of DE on either the rate or efficiency of protein deposition. Both protein deposition and protein deposition: DE intake increased (P \u3c .001) and fat deposition decreased as 1ysine:DE ratios increased up to 3.00 g lysine/Mcal DE. Protein deposition: lysine intake decreased (P \u3c .01) progressively as the 1ysine:DE ratio increased. Regression analyses indicated that protein deposition increased up to 3.00 g 1ysineMcal DE. The results demonstrate the need to adjust lysine according to energy levels and indicate that the optimum ratio for protein deposition was approximately 3.00 g lysine/Mcal DE (or 49 g of balanced protein/Mcal DE)

Effects of Randomness on the Field-Induced Phase Transition in the S=1 Bond-Alternating Spin Chain NTENP

We report novel effects of randomness in the S=1 bond-alternating antiferromagnetic chain compound with a dimer-singlet ground state [Ni(N,N'-bis(3-aminopropyl)propane-1,3-diamine(mu-NO2]ClO4 abbreviated as NTENP. The 15N NMR spectra develop a continuum with sharply peaked edges at low temperatures, indicating an inhomogeneous staggered magnetization induced by magnetic field. We attribute this to random anisotropic interactions due to disorder of NO2 groups in the chains. The field-induced antiferromagnetic transition exhibits remarkably anisotropic behavior. We propose that a field-induced incoherent magnetization is transformed into a coherent antiferromagnetic moment with spatially fluctuating amplitude.Comment: 4pages, 5 figues, submitted to J. Phys. Soc. Jp