Representations and classification of traveling wave solutions to Sinh-G{\"o}rdon equation

Two concepts named atom solution and combinatory solution are defined. The classification of all single traveling wave atom solutions to Sinh-G{\"o}rdon equation is obtained, and qualitative properties of solutions are discussed. In particular, we point out that some qualitative properties derived intuitively from dynamic system method aren't true. In final, we prove that our solutions to Sinh-G{\"o}rdon equation include all solutions obtained in the paper[Fu Z T et al, Commu. in Theor. Phys.(Beijing) 2006 45 55]. Through an example, we show how to give some new identities on Jacobian elliptic functions.Comment: 12 pages. accepted by Communications in theoretical physics (Beijing

Eliashberg theory of excitonic insulating transition in graphene

A sufficiently strong Coulomb interaction may open an excitonic fermion gap and thus drive a semimetal-insulator transition in graphene. In this paper, we study the Eliashberg theory of excitonic transition by coupling the fermion gap equation self-consistently to the equation of vacuum polarization function. Including the fermion gap into polarization function increases the effective strength of Coulomb interaction because it reduces the screening effects due to the collective particle-hole excitations. Although this procedure does not change the critical point, it leads to a significant enhancement of the dynamical fermion gap in the excitonic insulating phase. The validity of the Eliashberg theory is justified by showing that the vertex corrections are suppressed at large $N$ limit.Comment: 8 pages, 6 figure

Interactions of satellite-speed helium atoms with satellite surfaces. 2: Energy distributions of reflected helium atoms

Energy transfer in collisions of satellite-speed (7,000 m/sec) helium atoms with a cleaned 6061-T6 satellite-type aluminum surface was investigated using the molecular-beam technique. The amount of energy transferred was determined from the measured energy of the molecular-beam and the measured spatial and energy distributions of the reflected atoms. Spatial distributions of helium atoms scattered from a 6061-T6 aluminum surface were measured. The scattering pattern exhibits a prominent backscattering, probably due to the gross surface roughness and/or the relative lattice softness of the aluminum surface. Energy distributions of reflected helium atoms from the same surface were measured for six different incidence angles. For each incidence angle, distributions were measured at approximately sixty scattering positions. At a given scattering position, the energy spectra of the reflected helium atoms and the background gas were obtained using the retarding-field energy analyzer

Researches on interactions of satellite-speed helium atoms with aluminum and quartz surfaces

Three major areas were experimentally studied: (1) energy transfer in collisions of satellite-speed (700 m/sec) helium atoms with a cleaned satellite-type aluminum surface was investigated using the molecular-beam technique. Spatial and energy distributions of reflected helium atoms were measured and analyzed, (2) The gross accommodation coefficient for a satellite-speed (7000 m/sec) helium beam entering a 2-inch-diameter aluminum spherical cavity was determined by measuring the exit velocity distribution of the leaving helium atoms using a metastable time-of-flight method. Results indicate that the 7000-m/sec satellite-speed helium atoms entering the cavity gain full accommodation with the room-temperature inner surface of the sphere through a large number of collisions before leaving the spherical cavity; and (3) the feasibility of producing a satellite-speed atomic hydrogen beam by arc-heating, for use in studies of interactions of satellite-surfaces with hydrogen atoms under laboratory conditions, was investigated. It was found that a stable arc-heated molecular hydrogen beam can be obtained using the arc-heater, and that a partially dissociated hydrogen beam can be produced. Photographs of laboratory equipment are shown

Heat transport measurements in turbulent rotating Rayleigh-Benard convection

We present experimental heat transport measurements of turbulent Rayleigh-B\'{e}nard convection with rotation about a vertical axis. The fluid, water with Prandtl number ($\sigma$) about 6, was confined in a cell which had a square cross section of 7.3 cm$\times$7.3 cm and a height of 9.4 cm. Heat transport was measured for Rayleigh numbers $2\times 10^5 <$ Ra $< 5\times 10^8$ and Taylor numbers $0 <$ Ta $< 5\times 10^{9}$. We show the variation of normalized heat transport, the Nusselt number, at fixed dimensional rotation rate $\Omega_D$, at fixed Ra varying Ta, at fixed Ta varying Ra, and at fixed Rossby number Ro. The scaling of heat transport in the range $10^7$ to about $10^9$ is roughly 0.29 with a Ro dependent coefficient or equivalently is also well fit by a combination of power laws of the form $a Ra^{1/5} + b Ra^{1/3}$. The range of Ra is not sufficient to differentiate single power law or combined power law scaling. The overall impact of rotation on heat transport in turbulent convection is assessed.Comment: 16 pages, 12 figure