Proper Coordinate Transformation Research Articles

KUSTANNHEIMO -STIEFEI TRANSFORMATION OF BARY-ON STRUCTURE MODEL WITH A FOUR-DIMENSI-ONAL COVARIANT HARMONIC OSCILLATOR

In this paper, we assume there exist no three-body forces in a baryon. So that the constraint equations for two particles Pi2+U(x2)+mi2=0 (i=1，2 )can be applied to the SU3 model of the baryon. Next, we take U(x2) as a+bx2. By use of a proper coordinate transformation, the internal motion of the baryon can be reduced to double covariant harmonic oscillators. From the Kustannheimo-Stiefel transformation, the problem of a covariant harmonic oscillator can be transformed to that of a threedimensional hydrogen atom with constranits. On that basis, the difficulty of the excitation of the time degree of freedom can be avoided naturally and the mass-squared formula for baryons can be obtained.

EQUIVALENCE OF LIGHT-CONE AND CONFORMAL GAUGES IN TWO-DIMENSIONAL QUANTUM GRAVITY

We show that the light-cone and conformal gauges are equivalent in the sense that the well known SL (2, ℝ) current structure in the light-cone gauge is obtained from the results in the conformal one under a proper coordinate transformation. This result is due to the residual symmetry of the scalar field Φ.

Finite difference simulation for heat conduction with phase change in an irregular food domain with volumetric change

A mathematical model including the volumetric changes for food freezing or thawing is obtained by modifying the general heat conduction parabolic partial differential equation. The shape of food is assumed to be a body of rotation with an irregular cross-sectional contour. Coordinates are fixed to the initial food volume through a proper coordinate transformation. Due to the highly temperature-dependent food properties during phase change, the nodal temperatures are solved numerically by a general implicit finite difference method while a heat balance method is applied to boundary nodes with any kind of boundary conditions. A computerized numerical simulation method is developed and verified experimentally for a general heat conduction phase change (solidification/melting) problem.

A theoretical investigation of the effect of freestream turbulence on skin friction and heat transfer for a bluff body

Abstract A theoretical investigation of the effect of freestream turbulence on skin friction and heat transfer around a circular cylinder in cross flow is presented. The flow field is divided into different regions. A two-equation turbulence model together with proper coordinate transformations is used. The calculations are performed for Reynolds numbers in the range of 12500–50000 and turbulence intensities in the range of Tu∞ = 1.25–6.1% and turbulent length scales in the range of Λ f∞ D = 0.1–1.6 . Effect on skin friction and heat transfer of both turbulence intensity and turbulent length scale is found. Good agreement with experiment is achieved.

Antiplane line force in a three-phase anisotropic medium

By proper coordinate transformations, the method of images is applied to analyzing the displacement and stress fields of an antiplane line force in a three-phase anisotropic medium. The general solutions include several special cases of technological interest, such as thin plates, materials with surface film, and composite materials with lamellar structure. Application of the results to determine the elastic fields of screw dislocations is illustrated.

Aspects of the Hamiltonian dynamics of interacting gravitational gauge and Higgs fields with applications to spherical symmetry

We discuss some aspects of the Hamiltonian dynamics of interacting gravitational Yang-Mills-Higgs fields. Special attention is paid to the difference between proper and improper gauge and coordinate transformations and their relation to surface integrals in the Hamiltonian and gauge generators. The Hamiltonian formalism is specialized to spherically symmetric fields and the main points of the general theory are illustrated and discussed in detail in that case. Two kinds of spherically symmetric fields are considered: “manifest spherical symmetry” and “spherical symmetry up to a gauge”. In the former case the Yang-Mills-Higgs potentials themselves are spherically symmetric whereas in the latter (which deals with SO(3) only) a rotation in physical space is compensated for by a gauge rotation of the same magnitude. The 't Hooft-Polyakov monopole and the Julia-Zee dyon belong to the latter class.

Measurements of the Turbulent Boundary Layer under Pack Ice

Abstract The mean and turbulent flow structure under pack ice was measured during the 1972 AIDJEK pilot study with small mechanical current meter triplets at eight levels in the planetary boundary layer. CTD profiles showed a well-mixed layer of nearly neutral stability to about 35 m, bounded below by a strong pycnocline. The skin friction velocity u* was determined by measuring the Reynolds stress at 2 and 4 m below the ice (beyond the surface layer) and from consideration of other terms in the mean momentum equation. Local pressure gradients and advective acceleration due to topography could not be ignored; when an estimate of the effect was included, u* was 1.0±0.1 cm s−1 when the ice velocity relative to the ocean was 24 cm s−1. With the proper coordinate transformation, the planetary boundary layer of the ocean resembles that of the atmosphere. Composite averages of non-dimensional Reynolds stress and mean flow in the ocean, when compared with recent models of a neutrally buoyant, horizontally homoge...