Littoral sea clutter returns at 94GHz

This paper reports and discusses measurements made of the returns from sea clutter in the littoral at 94GHz using the SAFIRE demonstration radar. These measurements add significantly to the limited data which is available on sea clutter at 94GHz as well as showing how a radar developed to assist the public understanding of technology can also be used for research purposes. Littoral clutter measurements are proportionately more important at 94GHz than at lower frequencies because the short range of radars at these frequencies means that they are much more likely to be operating in this environment than in the open sea. The measurements show peak backscatter levels of about -22dB (sea state 3, 2° grazing angle), but this is concentrated around the breaking wave crests, and the mean value is close to the -30dB reported by other workers. At the high range resolutions used, the resultant distributions appear very longtailed. The data also shows a useful insight into the behaviour of sea clutter when viewed with circular polarisation, for which the peak values are similar to those observed with linear polarisations, but the mean values are much lower.Postprin

The Mandelstam-Leibbrandt Prescription in Light-Cone Quantized Gauge Theories

Quantization of gauge theories on characteristic surfaces and in the light-cone gauge is discussed. Implementation of the Mandelstam-Leibbrandt prescription for the spurious singularity is shown to require two distinct null planes, with independent degrees of freedom initialized on each. The relation of this theory to the usual light-cone formulation of gauge field theory, using a single null plane, is described. A connection is established between this formalism and a recently given operator solution to the Schwinger model in the light-cone gauge.Comment: Revtex, 14 pages. One postscript figure (requires psfig). A brief discussion of necessary restrictions on the light-cone current operators has been added, and two references. Final version to appear in Z. Phys.

Parity Invariance and Effective Light-Front Hamiltonians

In the light-front form of field theory, boost invariance is a manifest symmetry. On the downside, parity and rotational invariance are not manifest, leaving the possibility that approximations or incorrect renormalization might lead to violations of these symmetries for physical observables. In this paper, it is discussed how one can turn this deficiency into an advantage and utilize parity violations (or the absence thereof) in practice for constraining effective light-front Hamiltonians. More precisely, we will identify observables that are both sensitive to parity violations and easily calculable numerically in a non-perturbative framework and we will use these observables to constrain the finite part of non-covariant counter-terms in effective light-front Hamiltonians.Comment: REVTEX, 9 page

Line-distortion, Bandwidth and Path-length of a graph

We investigate the minimum line-distortion and the minimum bandwidth problems on unweighted graphs and their relations with the minimum length of a Robertson-Seymour's path-decomposition. The length of a path-decomposition of a graph is the largest diameter of a bag in the decomposition. The path-length of a graph is the minimum length over all its path-decompositions. In particular, we show: - if a graph $G$ can be embedded into the line with distortion $k$, then $G$ admits a Robertson-Seymour's path-decomposition with bags of diameter at most $k$ in $G$; - for every class of graphs with path-length bounded by a constant, there exist an efficient constant-factor approximation algorithm for the minimum line-distortion problem and an efficient constant-factor approximation algorithm for the minimum bandwidth problem; - there is an efficient 2-approximation algorithm for computing the path-length of an arbitrary graph; - AT-free graphs and some intersection families of graphs have path-length at most 2; - for AT-free graphs, there exist a linear time 8-approximation algorithm for the minimum line-distortion problem and a linear time 4-approximation algorithm for the minimum bandwidth problem

Wavelets and graph C∗C^*-algebras

Here we give an overview on the connection between wavelet theory and representation theory for graph $C^{\ast}$-algebras, including the higher-rank graph $C^*$-algebras of A. Kumjian and D. Pask. Many authors have studied different aspects of this connection over the last 20 years, and we begin this paper with a survey of the known results. We then discuss several new ways to generalize these results and obtain wavelets associated to representations of higher-rank graphs. In \cite{FGKP}, we introduced the "cubical wavelets" associated to a higher-rank graph. Here, we generalize this construction to build wavelets of arbitrary shapes. We also present a different but related construction of wavelets associated to a higher-rank graph, which we anticipate will have applications to traffic analysis on networks. Finally, we generalize the spectral graph wavelets of \cite{hammond} to higher-rank graphs, giving a third family of wavelets associated to higher-rank graphs

Nonperturbative Renormalization and the QCD Vacuum

We present a self consistent approach to Coulomb gauge Hamiltonian QCD which allows one to relate single gluon spectral properties to the long range behavior of the confining interaction. Nonperturbative renormalization is discussed. The numerical results are in good agreement with phenomenological and lattice forms of the static potential.Comment: 23 pages in RevTex, 4 postscript figure

(Total) Vector Domination for Graphs with Bounded Branchwidth

Given a graph $G=(V,E)$ of order $n$ and an $n$-dimensional non-negative vector $d=(d(1),d(2),\ldots,d(n))$, called demand vector, the vector domination (resp., total vector domination) is the problem of finding a minimum $S\subseteq V$ such that every vertex $v$ in $V\setminus S$ (resp., in $V$) has at least $d(v)$ neighbors in $S$. The (total) vector domination is a generalization of many dominating set type problems, e.g., the dominating set problem, the $k$-tuple dominating set problem (this $k$ is different from the solution size), and so on, and its approximability and inapproximability have been studied under this general framework. In this paper, we show that a (total) vector domination of graphs with bounded branchwidth can be solved in polynomial time. This implies that the problem is polynomially solvable also for graphs with bounded treewidth. Consequently, the (total) vector domination problem for a planar graph is subexponential fixed-parameter tractable with respectto $k$, where $k$ is the size of solution.Comment: 16 page

Dynamical Chiral Symmetry Breaking on the Light Front.II. The Nambu--Jona-Lasinio Model

An investigation of dynamical chiral symmetry breaking on the light front is made in the Nambu--Jona-Lasinio model with one flavor and N colors. Analysis of the model suffers from extraordinary complexity due to the existence of a "fermionic constraint," i.e., a constraint equation for the bad spinor component. However, to solve this constraint is of special importance. In classical theory, we can exactly solve it and then explicitly check the property of ``light-front chiral transformation.'' In quantum theory, we introduce a bilocal formulation to solve the fermionic constraint by the 1/N expansion. Systematic 1/N expansion of the fermion bilocal operator is realized by the boson expansion method. The leading (bilocal) fermionic constraint becomes a gap equation for a chiral condensate and thus if we choose a nontrivial solution of the gap equation, we are in the broken phase. As a result of the nonzero chiral condensate, we find unusual chiral transformation of fields and nonvanishing of the light-front chiral charge. A leading order eigenvalue equation for a single bosonic state is equivalent to a leading order fermion-antifermion bound-state equation. We analytically solve it for scalar and pseudoscalar mesons and obtain their light-cone wavefunctions and masses. All of the results are entirely consistent with those of our previous analysis on the chiral Yukawa model.Comment: 23 pages, REVTEX, the version to be published in Phys.Rev.D; Some clarifications in discussion of the LC wavefunctions adde

Boost-Invariant Running Couplings in Effective Hamiltonians

We apply a boost-invariant similarity renormalization group procedure to a light-front Hamiltonian of a scalar field phi of bare mass mu and interaction term g phi^3 in 6 dimensions using 3rd order perturbative expansion in powers of the coupling constant g. The initial Hamiltonian is regulated using momentum dependent factors that approach 1 when a cutoff parameter Delta tends to infinity. The similarity flow of corresponding effective Hamiltonians is integrated analytically and two counterterms depending on Delta are obtained in the initial Hamiltonian: a change in mu and a change of g. In addition, the interaction vertex requires a Delta-independent counterterm that contains a boost invariant function of momenta of particles participating in the interaction. The resulting effective Hamiltonians contain a running coupling constant that exhibits asymptotic freedom. The evolution of the coupling with changing width of effective Hamiltonians agrees with results obtained using Feynman diagrams and dimensional regularization when one identifies the renormalization scale with the width. The effective light-front Schroedinger equation is equally valid in a whole class of moving frames of reference including the infinite momentum frame. Therefore, the calculation described here provides an interesting pattern one can attempt to follow in the case of Hamiltonians applicable in particle physics.Comment: 24 pages, LaTeX, included discussion of finite x-dependent counterterm

Renormalization of Hamiltonian Field Theory; a non-perturbative and non-unitarity approach

Renormalization of Hamiltonian field theory is usually a rather painful algebraic or numerical exercise. By combining a method based on the coupled cluster method, analysed in detail by Suzuki and Okamoto, with a Wilsonian approach to renormalization, we show that a powerful and elegant method exist to solve such problems. The method is in principle non-perturbative, and is not necessarily unitary.Comment: 16 pages, version shortened and improved, references added. To appear in JHE