Small coupling limit and multiple solutions to the Dirichlet Problem for Yang Mills connections in 4 dimensions - Part I

In this paper (Part I) and its sequels (Part II and Part III), we analyze the structure of the space of solutions to the epsilon-Dirichlet problem for the Yang-Mills equations on the 4-dimensional disk, for small values of the coupling constant epsilon. These are in one-to-one correspondence with solutions to the Dirichlet problem for the Yang Mills equations, for small boundary data. We prove the existence of multiple solutions, and, in particular, non minimal ones, and establish a Morse Theory for this non-compact variational problem. In part I, we describe the problem, state the main theorems and do the first part of the proof. This consists in transforming the problem into a finite dimensional problem, by seeking solutions that are approximated by the connected sum of a minimal solution with an instanton, plus a correction term due to the boundary. An auxiliary equation is introduced that allows us to solve the problem orthogonally to the tangent space to the space of approximate solutions. In Part II, the finite dimensional problem is solved via the Ljusternik-Schirelman theory, and the existence proofs are completed. In Part III, we prove that the space of gauge equivalence classes of Sobolev connections with prescribed boundary value is a smooth manifold, as well as some technical lemmas used in Part I. The methods employed still work when the 4-dimensional disk is replaced by a more general compact manifold with boundary, and SU(2) is replaced by any compact Lie group

A one dimensional model for the prediction of extraction yields in a two phases modified twin-screw extruder

Solid/liquid extraction is performed on raw plant substrate with a modified twin-screw extruder (TSE) used as a thermo-mecanochemical reactor. Visual observations and experimental residence time distributions (RTD) are used to develop a solid transport model based on classical chemical engineering method. Modeled and experimental residence times are compared. The transport model is then coupled with a reactive extraction model in order to predict extraction yields

Optical properties of NaxV2O5

The optical properties of sodium-deficient NaxV2O5 (0.85 < x <1) single crystals are analyzed in the wide energy range, from 0.012 to 4.5 eV, using ellipsometry, infrared reflectivity, and Raman scattering techniques. The material remains insulating up to the maximal achieved hole concentration of about 15%. In sodium deficient samples the optical absorption peak associated to the fundamental electronic gap develops at about 0.44 eV. It corresponds to the transition between vanadium dxy and the impurity band, which forms in the middle of the pure NaV2O5 gap. Raman spectra measured with incident photon energy larger then 2 eV show strong resonant behavior, due to the presence of the hole-doping activated optical transitions, peaked at 2.8 eV.Comment: 7 pages, 4 fugures, to be published in PR

A Search for Active Galactic Nuclei in Sc Galaxies with H II Spectra

(Abridged) We have searched for nuclear radio emission from a statistically complete sample of 40 Sc galaxies within 30 Mpc that are optically classified as star-forming objects, in order to determine whether weak AGNs might be present. Only three nuclear radio sources were detected, in NGC 864, NGC 4123, and NGC 4535. These galaxies have peak 6-cm radio powers of 10^{20} W/Hz at arcsecond resolution, while upper limits of the non-detected galaxies typically range from 10^{18.4} to 10^{20} W/Hz. The three nuclear radio sources all are resolved and appear to have diffuse morphologies, with linear sizes of ~300 pc. This strongly indicates that circumnuclear star formation has been detected in these three H II galaxies. Comparison with previous 20-cm VLA results for the detected galaxies shows that the extended nuclear radio emission has a flat spectrum in two objects, and almost certainly is generated by thermal emission from gas ionized by young stars in the centers of those galaxies. The 6-cm radio powers are comparable to predictions for thermal emission that are based on the nuclear H-alpha luminosities, and imply nuclear star formation rates of 0.08-0.8 solar masses/yr, while the low-resolution NRAO VLA Sky Survey implies galaxy-wide star formation rates of 0.3-1.0 solar masses/yr in stars above 5 solar masses. Although the presence of active nuclei powered by massive black holes cannot be definitively ruled out, the present results suggest that they are likely to be rare in these late-type galaxies with H II spectra.Comment: To appear in ApJ. 7 page

Two phase residence time distribution in a modified twin screw extruder

Biomass fractionation is performed with a modified Clextral twin-screw extruder used as a thermo-mechano-chemical reactor. This new process is firstly analyzed. Visual observations, residence time distributions, and global mass balances are used to obtain information about the process phenomena and their coupling. Residence time distributions (RTD) classical models are adopted to represent the experimental plots. The influence of continuous and discrete process parameters upon the RTD of the solid and liquid phases is analyzed

Effects of Velocity Correlation on Early Stage of Free Cooling Process of Inelastic Hard Sphere System

The free cooling process in the inelastic hard sphere system is studied by analysing the data from large scale molecular dynamics simulations on a three dimensional system. The initial energy decay, the velocity distribution function, and the velocity correlation functions are calculated to be compared with theoretical predictions. The energy decay rate in the homogeneous cooling state is slightly but distinctively smaller than that expected from the independent collision assumption. The form of the one particle velocity distribution is found not to be stationary. These contradict to the predictions of the kinetic theory based on the Enskog-Boltzmann equation and suggest that the velocity correlation is already important in the early stage of homogeneous cooling state. The energy decay rate is analysed in terms of the velocity correlation.Comment: 9 pages (figures included). To be published in J. Phys. Soc. Jpn. Vol. 73 No. 1 (2004) Added two references and removed one. Changed the name of T_{L}. Added unit constants in Sec. 5 and

Finite Temperature Effects in One-dimensional Mott-Hubbard Insulator: Angle-Resolved Photoemission Study of Na_{0.96}V_{2}O_{5}

We have made an angle-resolved photoemission study of a one-dimensional (1D) Mott-Hubbard insulator Na_{0.96}V_{2}O_{5} and found that the spectra of the V 3d lower Hubbard band are strongly dependent on the temperature. We have calculated the one-particle spectral function of the one-dimensional t-J model at finite temperatures by exact diagonalization and compared them with the experimental results. Good overall agreement is obtained between experiment and theory. The strong finite temperature effects are discussed in terms of the existence of the ``Fermi surface'' of the spinon band.Comment: 4 pages, 3 figure

Investigation of thermal and magnetic properties of defects in a spin-gap compound NaV2O5

The specific heat, magnetic susceptibility and ESR signals of a Na-deficient vanadate Na_xV_2O_5 (x=1.00 - 0.90) were studied in the temperature range 0.07 - 10 K, well below the transition point to a spin-gap state. The contribution of defects provided by sodium vacancies to the specific heat was observed. It has a low temperature part which does not tend to zero till at least 0.3 K and a high temperature power-like tail appears above 2 K. Such dependence may correspond to the existence of local modes and correlations between defects in V-O layers. The magnetic measurements and ESR data reveal S=1/2 degrees of freedom for the defects, with their effective number increasing in temperature and under magnetic field. The latter results in the nonsaturating magnetization at low temperature. No long-range magnetic ordering in the system of defects was found. A model for the defects based on electron jumps near vacancies is proposed to explain the observed effects. The concept of a frustrated two-dimensional correlated magnet induced by the defects is considered to be responsible for the absence of magnetic ordering.Comment: 6 pages, 8 figure