A methodology for designing aircraft to low sonic boom constraints

A method for designing conceptual supersonic cruise aircraft to meet low sonic boom requirements is outlined and described. The aircraft design is guided through a systematic evolution from initial three view drawing to a final numerical model description, while the designer using the method controls the integration of low sonic boom, high supersonic aerodynamic efficiency, adequate low speed handling, and reasonable structure and materials technologies. Some experience in preliminary aircraft design and in the use of various analytical and numerical codes is required for integrating the volume and lift requirements throughout the design process

Vortices and confinement at weak coupling

We discuss the physical picture of thick vortices as the mechanism responsible for confinement at arbitrarily weak coupling in SU(2) gauge theory. By introducing appropriate variables on the lattice we distinguish between thin, thick and `hybrid' vortices, the latter involving Z(2) monopole loop boundaries. We present numerical lattice simulation results that demonstrate that the full SU(2) string tension at weak coupling arises from the presence of vortices linked to the Wilson loop. Conversely, excluding linked vortices eliminates the confining potential. The numerical results are stable under alternate choice of lattice action as well as a smoothing procedure which removes short distance fluctuations while preserving long distance physics.Comment: 21 pages, LaTe

Investigation of warm fog properties and fog modification concepts

Warm fog seeding to determine potential of various sized and unsized hygroscopic chemicals for fog dissipatio

Construction of Field Algebras with Quantum Symmetry from Local Observables

It has been discussed earlier that ( weak quasi-) quantum groups allow for conventional interpretation as internal symmetries in local quantum theory. From general arguments and explicit examples their consistency with (braid-) statistics and locality was established. This work addresses to the reconstruction of quantum symmetries and algebras of field operators. For every algebra \A of observables satisfying certain standard assumptions, an appropriate quantum symmetry is found. Field operators are obtained which act on a positive definite Hilbert space of states and transform covariantly under the quantum symmetry. As a substitute for Bose/Fermi (anti-) commutation relations, these fields are demonstrated to obey local braid relation.Comment: 50 pages, HUTMP 93-B33

Nexus solitons in the center vortex picture of QCD

It is very plausible that confinement in QCD comes from linking of Wilson loops to finite-thickness vortices with magnetic fluxes corresponding to the center of the gauge group. The vortices are solitons of a gauge-invariant QCD action representing the generation of gluon mass. There are a number of other solitonic states of this action. We discuss here what we call nexus solitons, in which for gauge group SU(N), up to N vortices meet a a center, or nexus, provided that the total flux of the vortices adds to zero (mod N). There are fundamentally two kinds of nexuses: Quasi-Abelian, which can be described as composites of Abelian imbedded monopoles, whose Dirac strings are cancelled by the flux condition; and fully non-Abelian, resembling a deformed sphaleron. Analytic solutions are available for the quasi-Abelian case, and we discuss variational estimates of the action of the fully non-Abelian nexus solitons in SU(2). The non-Abelian nexuses carry Chern-Simons number (or topological charge in four dimensions). Their presence does not change the fundamentals of confinement in the center-vortex picture, but they may lead to a modified picture of the QCD vacuum.Comment: LateX, 24 pages, 2 .eps figure

Coherent Patterning of Matter Waves with Subwavelength Localization

We propose the Subwavelength Localization via Adiabatic Passage (SLAP) technique to coherently achieve state-selective patterning of matter waves well beyond the diffraction limit. The SLAP technique consists in coupling two partially overlapping and spatially structured laser fields to three internal levels of the matter wave yielding state-selective localization at those positions where the adiabatic passage process does not occur. We show that by means of this technique matter wave localization down to the single nanometer scale can be achieved. We analyze in detail the potential implementation of the SLAP technique for nano-lithography with an atomic beam of metastable Ne* and for coherent patterning of a two-component 87Rb Bose-Einstein condensate.Comment: 6 pages, 5 figure

Combinatorial quantization of the Hamiltonian Chern-Simons theory I

Motivated by a recent paper of Fock and Rosly \cite{FoRo} we describe a mathematically precise quantization of the Hamiltonian Chern-Simons theory. We introduce the Chern-Simons theory on the lattice which is expected to reproduce the results of the continuous theory exactly. The lattice model enjoys the symmetry with respect to a quantum gauge group. Using this fact we construct the algebra of observables of the Hamiltonian Chern-Simons theory equipped with a *-operation and a positive inner product.Comment: 49 pages. Some minor corrections, discussion of positivity improved, a number of remarks and a reference added

Center vortices and confinement vs. screening

We study adjoint and fundamental Wilson loops in the center-vortex picture of confinement, for gauge group SU(N) with general N. There are N-1 distinct vortices, whose properties, including collective coordinates and actions, we study. In d=2 we construct a center-vortex model by hand so that it has a smooth large-N limit of fundamental-representation Wilson loops and find, as expected, confinement. Extending an earlier work by the author, we construct the adjoint Wilson-loop potential in this d=2 model for all N, as an expansion in powers of $\rho/M^2$, where $\rho$ is the vortex density per unit area and M is the vortex inverse size, and find, as expected, screening. The leading term of the adjoint potential shows a roughly linear regime followed by string breaking when the potential energy is about 2M. This leading potential is a universal (N-independent at fixed fundamental string tension $K_F$) of the form $(K_F/M)U(MR)$, where R is the spacelike dimension of a rectangular Wilson loop. The linear-regime slope is not necessarily related to $K_F$ by Casimir scaling. We show that in d=2 the dilute vortex model is essentially equivalent to true d=2 QCD, but that this is not so for adjoint representations; arguments to the contrary are based on illegal cumulant expansions which fail to represent the necessary periodicity of the Wilson loop in the vortex flux. Most of our arguments are expected to hold in d=3,4 also.Comment: 29 pages, LaTex, 1 figure. Minor changes; references added; discussion of factorization sharpened. Major conclusions unchange

Remarks on Finite W Algebras

The property of some finite W algebras to be the commutant of a particular subalgebra of a simple Lie algebra G is used to construct realizations of G. When G=so(4,2), unitary representations of the conformal and Poincare algebras are recognized in this approach, which can be compared to the usual induced representation technique. When G=sp(2,R) or sp(4,R), the anyonic parameter can be seen as the eigenvalue of a W generator in such W representations of G. The generalization of such properties to the affine case is also discussed in the conclusion, where an alternative of the Wakimoto construction for sl(2) level k is briefly presented. This mini review is based on invited talks presented by P. Sorba at the ``Vth International Colloquium on Quantum Groups and Integrable Systems'', Prague (Czech Republic), June 1996; ``Extended and Quantum Algebras and their Applications to Physics'', Tianjin (China), August 1996; ``Selected Topics of Theoretical and Modern Mathematical Physics'', Tbilisi (Georgia), September 1996; to be published in the Proceedings.Comment: LaTeX, 16 pages, references adde

Multivalued Fields on the Complex Plane and Conformal Field Theories

In this paper a class of conformal field theories with nonabelian and discrete group of symmetry is investigated. These theories are realized in terms of free scalar fields starting from the simple $b-c$ systems and scalar fields on algebraic curves. The Knizhnik-Zamolodchikov equations for the conformal blocks can be explicitly solved. Besides of the fact that one obtains in this way an entire class of theories in which the operators obey a nonstandard statistics, these systems are interesting in exploring the connection between statistics and curved space-times, at least in the two dimensional case.Comment: (revised version), 30 pages + one figure (not included), (requires harvmac.tex), LMU-TPW 92-1