An exact solution of linearized flow of an emitting, absorbing and scattering grey gas

The governing equations for the problem of linearized flow through a normal shock wave in an emitting, absorbing, and scattering grey gas are reduced to two linear coupled integro-differential equations. By separation of variables, these equations are further reduced to an integral equation similar to that which arises in neutron-transport theory. It is shown that this integral equation admits both regular (associated with discrete eigenfunctions) and singular (associated with continuum eigenfunctions) solutions to form a complete set. The exact closed-form solution is obtained by superposition of these eigen-functions. If the gas downstream of a strong shock is absorption–emission dominated, the discrete mode of the solution disappears downstream. The effects of isotropic scattering are discussed. Quantitative comparison between the numerical results based on the exact solution and on the differential approximation are presented

Critical couplings and string tensions via lattice matching of RG decimations

We calculate critical couplings and string tensions in SU(2) and SU(3) pure lattice gauge theory by a simple and inexpensive technique of two-lattice matching of RG block transformations. The transformations are potential moving decimations generating plaquette actions with large number of group characters and exhibit rapid approach to a unique renormalized trajectory. Fixing the critical coupling $\beta_c(N_\tau)$ at one value of temporal lattice length $N_\tau$ by MC simulation, the critical couplings for any other value of $N_\tau$ are then obtained by lattice matching of the block decimations. We obtain $\beta_c(N_\tau)$ values over the range $N_\tau = 3 - 32$ and find agreement with MC simulation results to within a few percent in all cases. A similar procedure allows the calculation of string tensions with similarly good agreement with MC data.Comment: 12 pages, Latex, 1 figur

Fabrication of photonic band-gap crystals

We describe the fabrication of three-dimensional photonic crystals using a reproducible and reliable procedure consisting of electron beam lithography followed by a sequence of dry etching steps. Careful fabrication has enabled us to define photonic crystals with 280 nm holes defined with 350 nm center to center spacings in GaAsP and GaAs epilayers. We construct these photonic crystals by transferring a submicron pattern of holes from 70-nm-thick polymethylmethacrylate resist layers into 300-nm-thick silicon dioxide ion etch masks, and then anisotropically angle etching the III-V semiconductor material using this mask. Here, we show the procedure used to generate photonic crystals with up to four lattice periods depth

Renormalization in Coulomb gauge QCD

In the Coulomb gauge of QCD, the Hamiltonian contains a non-linear Christ-Lee term, which may alternatively be derived from a careful treatment of ambiguous Feynman integrals at 2-loop order. We investigate how and if UV divergences from higher order graphs can be consistently absorbed by renormalization of the Christ-Lee term. We find that they cannot.Comment: 23 pages, 26 figure