Boundary critical behaviour at mm-axial Lifshitz points: the special transition for the case of a surface plane parallel to the modulation axes

The critical behaviour of $d$-dimensional semi-infinite systems with $n$-component order parameter $\bm{\phi}$ is studied at an $m$-axial bulk Lifshitz point whose wave-vector instability is isotropic in an $m$-dimensional subspace of $\mathbb{R}^d$. Field-theoretic renormalization group methods are utilised to examine the special surface transition in the case where the $m$ potential modulation axes, with $0\leq m\leq d-1$, are parallel to the surface. The resulting scaling laws for the surface critical indices are given. The surface critical exponent $\eta_\|^{\rm sp}$, the surface crossover exponent $\Phi$ and related ones are determined to first order in \epsilon=4+\case{m}{2}-d. Unlike the bulk critical exponents and the surface critical exponents of the ordinary transition, $\Phi$ is $m$-dependent already at first order in $\epsilon$. The \Or(\epsilon) term of $\eta_\|^{\rm sp}$ is found to vanish, which implies that the difference of $\beta_1^{\rm sp}$ and the bulk exponent $\beta$ is of order $\epsilon^2$.Comment: 21 pages, one figure included as eps file, uses IOP style file

Statistical Physics and Light-Front Quantization

Light-front quantization has important advantages for describing relativistic statistical systems, particularly systems for which boost invariance is essential, such as the fireball created in a heavy ion collisions. In this paper we develop light-front field theory at finite temperature and density with special attention to quantum chromodynamics. We construct the most general form of the statistical operator allowed by the Poincare algebra and show that there are no zero-mode related problems when describing phase transitions. We then demonstrate a direct connection between densities in light-front thermal field theory and the parton distributions measured in hard scattering experiments. Our approach thus generalizes the concept of a parton distribution to finite temperature. In light-front quantization, the gauge-invariant Green's functions of a quark in a medium can be defined in terms of just 2-component spinors and have a much simpler spinor structure than the equal-time fermion propagator. From the Green's function, we introduce the new concept of a light-front density matrix, whose matrix elements are related to forward and to off-diagonal parton distributions. Furthermore, we explain how thermodynamic quantities can be calculated in discretized light-cone quantization, which is applicable at high chemical potential and is not plagued by the fermion-doubling problem.Comment: 30 pages, 3 figures; v2: Refs. added, minor changes, accepted for publication in PR

Generalized parton distributions in the deuteron

We introduce generalized quark and gluon distributions in the deuteron, which can be measured in exclusive processes like deeply virtual Compton scattering and meson electroproduction. We discuss the basic properties of these distributions, and point out how they probe the interplay of nucleon and parton degrees of freedom in the deuteron wave function

Results and status of the NASA aircraft engine emission reduction technology programs

The results of an aircraft engine emission reduction study are reviewed in detail. The capability of combustor concepts to produce significantly lower levels of exhaust emissions than present production combustors was evaluated. The development status of each combustor concept is discussed relative to its potential for implementation in aircraft engines. Also, the ability of these combustor concepts to achieve proposed NME and NCE EPA standards is discussed

Crossover from Attractive to Repulsive Casimir Forces and Vice Versa

Systems described by an O(n) symmetrical $\phi^4$ Hamiltonian are considered in a $d$-dimensional film geometry at their bulk critical points. The critical Casimir forces between the film's boundary planes $\mathfrak{B}_j, j=1,2$, are investigated as functions of film thickness $L$ for generic symmetry-preserving boundary conditions $\partial_n\bm{\phi}=\mathring{c}_j\bm{\phi}$. The $L$-dependent part of the reduced excess free energy per cross-sectional area takes the scaling form $f_{\text{res}}\approx D(c_1L^{\Phi/\nu},c_2L^{\Phi/\nu})/L^{d-1}$ when $d<4$, where $c_i$ are scaling fields associated with the variables $\mathring{c}_i$, and $\Phi$ is a surface crossover exponent. Explicit two-loop renormalization group results for the function $D(\mathsf{c}_1,\mathsf{c}_2)$ at $d=4-\epsilon$ dimensions are presented. These show that (i) the Casimir force can have either sign, depending on $\mathsf{c}_1$ and $\mathsf{c}_2$, and (ii) for appropriate choices of the enhancements $\mathring{c}_j$, crossovers from attraction to repulsion and vice versa occur as $L$ increases.Comment: 4 RevTeX pages, 2 eps figures; minor misprints corrected and 3 references adde

Reaction Diffusion and Ballistic Annihilation Near an Impenetrable Boundary

The behavior of the single-species reaction process $A+A\to O$ is examined near an impenetrable boundary, representing the flask containing the reactants. Two types of dynamics are considered for the reactants: diffusive and ballistic propagation. It is shown that the effect of the boundary is quite different in both cases: diffusion-reaction leads to a density excess, whereas ballistic annihilation exhibits a density deficit, and in both cases the effect is not localized at the boundary but penetrates into the system. The field-theoretic renormalization group is used to obtain the universal properties of the density excess in two dimensions and below for the reaction-diffusion system. In one dimension the excess decays with the same exponent as the bulk and is found by an exact solution. In two dimensions the excess is marginally less relevant than the bulk decay and the density profile is again found exactly for late times from the RG-improved field theory. The results obtained for the diffusive case are relevant for Mg$^{2+}$ or Cd$^{2+}$ doping in the TMMC crystal's exciton coalescence process and also imply a surprising result for the dynamic magnetization in the critical one-dimensional Ising model with a fixed spin. For the case of ballistic reactants, a model is introduced and solved exactly in one dimension. The density-deficit profile is obtained, as is the density of left and right moving reactants near the impenetrable boundary.Comment: to appear in J. Phys.

Distribution of ions near a charged selective surface in critical binary solvents

Near-critical binary mixtures containing ionic solutes near a charged wall preferentially adsorbing one component of the solvent are studied. Within the Landau-Ginzburg approach extended to include electrostatic interactions and the chemical preference of ions for one component of the solvent, we obtain a simple form for the leading-order correction to the Debye-Huckel theory result for the charge density profile. Our result shows that critical adsorption influences significantly distribution of ions near the wall. This effect may have important implications for the screening of electrostatic interactions between charged surfaces immersed in binary near-critical solvents.Comment: 24 pages, 3 figure

The Hot Interstellar Medium in Normal Elliptical Galaxies III: The Thermal Structure of the Gas

This is the third paper in a series analyzing X-ray emission from the hot interstellar medium in a sample of 54 normal elliptical galaxies observed by Chandra, focusing on 36 galaxies with sufficient signal to compute radial temperature profiles. We distinguish four qualitatively different types of profile: positive gradient (outwardly rising), negative gradients (falling), quasi-isothermal (flat) and hybrid (falling at small radii, then rising). We measure the mean logarithmic temperature gradients in two radial regions: from 0--2 $J$-band effective radii $R_J$ (excluding the central point source), and from 2--$4R_J$. We find the outer gradient to be uncorrelated with intrinsic host galaxy properties, but strongly influenced by the environment: galaxies in low-density environments tend to show negative outer gradients, while those in high-density environments show positive outer gradients, suggesting influence of circumgalactic hot gas. The inner temperature gradient is unaffected by the environment but strongly correlated with intrinsic host galaxy characteristics: negative inner gradients are more common for smaller, optically faint, low radio-luminosity galaxies, whereas positive gradients are found in bright galaxies with stronger radio sources. There is no evidence for bimodality in the distribution of inner or outer gradients. We propose three scenarios to explain the inner temperature gradients: (1) Weak AGN heat the ISM locally, higher-luminosity AGN heat the system globally through jets inflating cavities at larger radii; (2) The onset of negative inner gradients indicates a declining importance of AGN heating relative to other sources, such as compressional heating or supernovae; (3) The variety of temperature profiles are snapshots of different stages of a time-dependent flow.Comment: 18 pages, emulateapj, 55 figures (36 online-only figures included in astro-ph version), submitted to Ap