Correspondence between the classical and quantum canonical transformation groups from an operator formulation of the wigner function

An explicit expression of the Wigner operator is derived, such that the Wigner function of a quantum state is equal to the expectation value of this operator with respect to the same state. This Wigner operator leads to a representation-independent procedure for establishing the correspondence between the inhomogeneous symplectic group applicable to linear canonical transformations in classical mechanics and the Weyl-metaplectic group governing the symmetry of unitary transformations in quantum mechanics.     

Mathematical simulation of the shock compression of porous molybdenum using a heterogeneous model

The shock compression of a heterogeneous material is numerically simulated. The physical model used for the simulation is based on a layered model of a porous material and consists of a set of thin matrix plates with a known equation of state that are separated by filler layers also with a known equation of state. The model is intended to calculate the parameters (pressure, temperature, mass velocity) of shock compression of the matrix and the filler of heterogeneous materials during their one-dimensional shock compression in terms of a developed hydrodynamic code. The adequacy of the proposed model is tested on porous molybdenum during shock-wave loading to a pressure of 15–70 GPa and a temperature of 4000 K.     

Normal analytic polyhedra in ℂ2 with a noncompact automorphism group

Let P be a bounded analytic polyhedron in ℂ² whose boundary is smooth except for normal crossing singularities. We show that P is a holomorphic quotient of the bidisc, if its automorphism group is noncompact.     

Simultaneous jumps in two two-level atoms

We demonstrate the importance of collective behaviour in two identical two-level atoms. When the atoms become very close together a cascade three-level atom analysis can be adopted to show the increasing possibility of simultaneous jumps. Due to the dipole-dipole interaction the intermediate one-atom excited state is detuned by a large amount when the atoms are close together but leaving the upper two-atom excited state in two-photon resonance. The relative importance of multiple jumps compared with stepwise independent jumps is then changed dramatically.     

In vivo mapping of functional domains and axonal connectivity in cat visual cortex using magnetic resonance imaging

Noninvasive cognitive neuroimaging studies based on functional magnetic resonance imaging (fMRI) are of ever-increasing importance for basic and clinical neurosciences. The explanatory power of fMRI could be greatly expanded, however, if the pattern of the neuronal circuitry underlying functional activation could be made visible in an equally noninvasive manner. In this study, blood oxygenation level-dependent (BOLD)-based fMRI and diffusion tensor imaging (DTI) were performed in the same cat visual cortex, and the foci of fMRI activation utilized as seeding points for 3D DTI fiber reconstruction algorithms, thus providing the map of the axonal circuitry underlying visual information processing. The methods developed in this study will lay the foundation for in vivo neuroanatomy and the ability for noninvasive longitudinal studies of brain development.     

Marked length rigidity of rank one symmetric spaces and their product

In this paper we show that if two Zariski dense representations, from a group G into Iso(X) where X is rank one symmetric space, have the proportional marked length spectrum, then they are conjugate. As a generalization we show that a Zariski dense representation into the isometry group of the product of rank one symmetric spaces is determined by the marked cross ratio.     

Top–bottom mass hierarchy, s-\mu puzzle and gauge coupling unification with split multiplets

Supersymmetric 5D SU(5) grand unification is considered. SU(5) is broken down to by the assignment of the bulk field(s). The matter fields are located at the fixed point(s). In the bulk, a Higgs multiplet (containing the bottom doublet ) and the SU(5) gauge multiplet are located. At one fixed point, (the top doublet) and the standard model matter multiplets are presented. Because of the difference of the locations of and , one can obtain a hierarchy between top and bottom Yukawa couplings. We also present a possible way to understand the s– mass puzzle in this framework of the split multiplet. Received: 10 December 2001 / Revised version: 22 January 2002 / Published online: 5 April 2002     

Terwilliger algebras of wreath products by quasi-thin schemes

The structure of Terwilliger algebras of wreath products by thin schemes or one-class schemes was studied in [A. Hanaki, K. Kim, Y. Maekawa, Terwilliger algebras of direct and wreath products of association schemes, J. Algebra 343 (2011) 195–200]. In this paper, we will consider the structure of Terwilliger algebras of wreath products by quasi-thin schemes. This gives a generalization of their result.     

Effects of combined dimension reduction and tabulation on the simulations of a turbulent premixed flame using a large-eddy simulation/probability density function method

A turbulent lean-premixed propane–air flame stabilised by a triangular cylinder as a flame-holder is simulated to assess the accuracy and computational efficiency of combined dimension reduction and tabulation of chemistry. The computational condition matches the Volvo rig experiments. For the reactive simulation, the Lagrangian Large-Eddy Simulation/Probability Density Function (LES/PDF) formulation is used. A novel two-way coupling approach between LES and PDF is applied to obtain resolved density to reduce its statistical fluctuations. Composition mixing is evaluated by the modified Interaction-by-Exchange with the Mean (IEM) model. A baseline case uses In Situ Adaptive Tabulation (ISAT) to calculate chemical reactions efficiently. Its results demonstrate good agreement with the experimental measurements in turbulence statistics, temperature, and minor species mass fractions. For dimension reduction, 11 and 16 represented species are chosen and a variant of Rate Controlled Constrained Equilibrium (RCCE) is applied in conjunction with ISAT to each case. All the quantities in the comparison are indistinguishable from the baseline results using ISAT only. The combined use of RCCE/ISAT reduces the computational time for chemical reaction by more than 50%. However, for the current turbulent premixed flame, chemical reaction takes only a minor portion of the overall computational cost, in contrast to non-premixed flame simulations using LES/PDF, presumably due to the restricted manifold of purely premixed flame in the composition space. Instead, composition mixing is the major contributor to cost reduction since the mean-drift term, which is computationally expensive, is computed for the reduced representation. Overall, a reduction of more than 15% in the computational cost is obtained.