Effects of fin pitch and tube diameter on the air-side performance of tube bank fin heat exchanger with the fins punched plane and curved rectangular vortex generators

Tube bank fin heat exchangers with vortex generators are widely used in the field of industrial applications. The effects of the fin pitch and the tube diameter on the air-side performance of the tube bank fin heat exchanger with plane rectangular vortex generators (PRVG) and curved rectangular vortex generators (CRVG) are experimentally studied in this paper. Performance comparison is carried out between the fins with PRVG and CRVG. The experimental results show that both PRVG and CRVG can effectively enhance heat transfer performance compared with the plain fin. Both the fin pitch and the tube diameter have obvious effect on f compared with the effect on Nu, especially for the fin with PRVG. The characteristics of Nu, f, and Nu/f^1/3 are different for the fins with PRVG and CRVG. The fin with CRVG has a better heat transfer performance than the fin with PRVG for all the cases studied in this paper.     

Grassmann variables on quantum spaces

Attention is focused on antisymmetrized versions of quantum spaces that are of particular importance in physics, i.e. two-dimensional quantum plane, q-deformed Euclidean space in three or four dimensions as well as q-deformed Minkowski space. For each case standard techniques for dealing with q-deformed Grassmann variables are developed. Formulae for multiplying supernumbers are given. The actions of symmetry generators and fermionic derivatives upon antisymmetrized quantum spaces are calculated. The complete Hopf structure for all types of quantum space generators is written down. From the formulae for the coproduct a realization of the L-matrices in terms of symmetry generators can be read off. The L-matrices together with the action of symmetry generators determine how quantum spaces of different type have to be fused together. Arrival of the final proofs: 6 December 2005     

Chern-Simons theory,coloured-oriented braids and link invariants

A method to obtain explicit and complete topological solution of SU(2) Chern-Simons theory onS ³ is developed. To this effect the necessary aspects of the theory of coloured-oriented braids and duality properties of conformal blocks for the correlators ofSU(2) _k Wess-Zumino conformal field theory are presented. A large class of representations of the generators of the groupoid of coloured-oriented braids are obtained. These provide a whole lot of new link invariants of which Jones polynomials are the simplest examples. These new invariants are explicity calculated as illustrations for knots up to eight crossings and twocomponent multicoloured links up to seven crossings.     

Fusion rings and geometry

The algebraic structure of fusion rings in rational conformal field theories is analyzed in detail in this paper. A formalism which closely parallels classical tools in the study of the cohomology of homogeneous spaces is developed for fusion rings, in general, and for current algebra theories, in particular. It is shown that fusion rings lead to a natural orthogonal polynomial structure. The rings are expressed through generators and relations. The relations are then derived from some potentials leading to an identification of the fusion rings with deformations of affine varieties. In general, the fusion algebras are mapped to affine varieties which are the locus of the relations. The connection with modular transformations is investigated in this picture. It is explained how chiral algebras, arising inN=2 superconformal field theory, can be derived from fusion rings. In particular, it is argued that theories of the typeSU(N) _k /SU(n–1) are theN=2 counterparts of Grassmann manifolds and that there is a natural identification of the chiral fields with Schubert varieties, which is a graded algebra isomorphism.Supported in part by NSF grant PHY 89-04035 supplemented by funds from NASA     

The jordanian deformation of Su(2) and clebsch-gordan coefficients

Representation theory for the Jordanian quantum algebraU _h (sl(2)) is developed using a nonlinear relation between its generators and those of sl(2). Closed form expressions are given for the action of the generators ofU _h (sl(2)) on the basis vectors of finite dimensional irreducible representations. In the tensor product of two such representations, a new basis is constructed on which the generators ofU _h (sl(2)) have a simple action. Using this basis, a general formula is obtained for the Clebsch-Gordan coefficients ofU _h (sl(2)). Some remarkable properties of these Clebsch-Gordan coefficients are derived. Presented at the 6th International Colloquium on Quantum Groups: “Quantum Groups and Integrable Systems”, Prague, 19–21 June 1997.     

Reflections on the evolution of physical theories

Conclusion Let me come back to the successes of the Poincaré group in particle physics. This is a group with ten generators. The translation generators are responsible for the energy-momentum conservation laws, the rotation generators of the conservation of angular momentum, and the boost generators of the conservation ofinitial position. If positions are slightly different from the ones described by Minkowski space, it means that we have to change slightly the notion of boosts. If we remember that boosts were questionable in Minkowski space (see Section 9), we are not surprised. We are naturally led to a deformation of the Poincaré group which would preserve translations and rotations [such a deformation has been proposed by Lukierskiet al. (n.d.)]. By duality, small changes at short distances must correspond to small changes in large momenta. The fact that cutoffs for momenta are involved in QED is perhaps related to a noncommutative structure for our space. With such a structure, making the size of an electron go to zero is meaningless and consequently the difficulty of an electron with infinite energy also becomes meaningless. A noncommutative space is probably a way to solve the difficulties mentioned in the epigraphs to this paper.     

Teleparallelism as a universal connection on null hypersurfaces in general relativity

We show that there exists a close relationship between inner geometry of a null hypersurfaceN ₃ and the Newman-Penrose (NP) spin coefficient formalism. Projecting the null complexNP tetrad ontoN ₃ we get two triads of basis vectors inN ₃. Inner geometry ofN ₃ is based on the assumption that these vectors are parallelly transported along the surface; this gives rise to the teleparallel connection as a metric nonsymmetric affine connection. The gauge freedom for the choice of the basis triads is given by the isotropy subgroup of the local Lorentz group leaving invariant the direction of the null generators ofN ₃, and teleparallelism is determined by the equivalence class of the basis triads with respect to the global gauge group. Nine of the twelve NP coefficients are identified as the triad components of the torsion and the second fundamental form ofN ₃. The resulting generalized Gauss-Codazzi equations are identical to 9 of the NP equations, i.e., to the half of the Ricci identities. This result gives a geometrical meaning to the entire formalism. Finally we present a general proof of Penrose's theorem that the shear of the null generators ofN ₃ is the only initial null datum for a gravitational field onN ₃.     

Scaling properties of ℤ k- 1 actions on the circle

We derive universal scaling properties for ^k–1 actions on the circle whose generators have rotation numbers algebraic of degreek. As fork=2 these properties can be explained for arbitraryk in terms of a renormalization group transformation. It has at least one trivial fixed point corresponding to an action whose generators are pure rotations. The spectrum of the linearized transformation in this fixed point is analyzed completely. The fixed point is hyperbolic with a (k–1)-dimensional unstable manifold. In the casek=2 the known results are therefore recovered.     

Polynomial relations in the centre ofU q (sl(N))

When the parameter of deformationq is a root of unity, the centre ofU _q (sl(N)) contains, besides the usualq-deformed Casimirs, a set of new generators, which are basically themth powers of all the Cartan generators ofU _q (sl(N)). All these central elements are, however, not independent. In this Letter, generalizing the well-known case ofU _q (sl(2)), we explicitly write polynomial relations satisfied by the generators of the centre. Application to the parametrization of irreducible representations and to fusion rules are sketched.On leave from SPht, CE Saclay, 91191 Gif-sur-Yvette Cedex, France.     

Dynamical symmetry breaking of lambda- and vee-type three-level systems on quantization of the field modes

We develop a scheme to construct the Hamiltonians of the lambda-, vee- and cascade-type three-level configurations using the generators of SU(3) group. It turns out that this approach provides a well-defined selection rule to give different Hamiltonians for each configuration. The lambda- and vee-type configurations are exactly solved with different initial conditions while taking the two-mode classical and quantized fields. For the classical field, it is shown that the Rabi oscillation of the lambda model is similar to that of the vee model and the dynamics of the vee model can be recovered from lambda model and vice versa simply by inversion. We then proceed to solve the quantized version of both models by introducing a novel Euler matrix formalism. It is shown that this dynamical symmetry exhibited in the Rabi oscillation of two configurations for the semiclassical models is completely destroyed on quantization of the field modes. The symmetry can be restored within the quantized models when both field modes are in the coherent states with large average photon number which is depicted through the collapse and revival of the Rabi oscillations.      

Parton-hadron duality in event generators

The validity of local parton-hadron duality within the framework of HERWIG and JETSET event generators is investigated. We concentrate one ⁺ e ^– annihilations in LEP 2 energy range as these interactions provide theoretically the cleanest condition for the discussion of this concept. We conclude that the concept of local parton-hadron duality is not valid in either of the two generators considered.     

YangianY(sl(2)) in hydrogen atom

The YangianY(sl(2)) is studied in the usual hydrogen atom. Its generators are expressed in terms of the angular momentum operators and the so-called Runge-Lenz vector. The energy is found to play the role of the deformation parameter. At the critical point from the bound state to the free state, the YangianY(sl(2)) reduces to the loop algebraL(sl(2)). The corresponding matrix elements of theY(sl(2)) generators are also discussed for the energy eigenstates.     

The Hamiltonian in relativistic systems of interacting particles

The dynamics of a system of relativistically interacting particles is determined by a set of constraints, some combination of which has been frequently identified with the Hamiltonian. These constraints differ from the generators of the Poincaré transformations, among whichp ₀ generates translations along the time axis and hence is to be considered as the energy of the system. There are thus grounds for consideringP ₀ as the appropriate Hamiltonian. In this paper we establish a close relationship between transformations generated by the constraints and those generated by the Poincaré generators. In particular we find that the true Hamiltonian is a rather complicated but well-defined function ofp ₀ and all the constraints. We show that the generators of the entire algebra of the Poincaré group can be realized in such a fashion that the Hamiltonian is correctly included among them, and such that particle world lines in Minkowski space-time generated by this Hamiltonian transform correctly under the Poincaré group.This work was partially supported by the National Science Foundation Grant No. PHY 79-0887 to Syracuse University and by Grant No. PHY 79-09405 to Yeshiva University.     

The q-boson operator algebra and q-Hermite polynomials

The q-boson algebra is defined as an associative algebra with generators and relations. Some examples are given, and then the q-boson algebra is extended such that the roots of the diagonal generators are also defined. It is shown that a family of transformations exist mapping one set of standard generators of the q-boson algebra to another set of standard generators. Using such a transformation, one obtains expressions for q-bosons for which the kth q-boson state is expressed in terms of a q-Hermite polynomial p _k (x; q) which reduces to the ordinary Hermite polynomial of degree k when q=1.     

Wavelet multi-resolution analysis of initial condition effects on near-wake turbulent structures

The effects of initial conditions on turbulence structures of various scales in a near wake have been investigated for two wake generators with the same characteristic dimension, i.e., a circular cylinder and a screen of 50% solidity, based on the wavelet multi-resolution analysis. The experimental investigation used two orthogonal arrays of sixteen X-wires, eight in the (x, y)-plane, and eight in the (x, z)-plane. Measurements were made atx/h (x is the streamwise distance downstream of the cylinder andh is the height of the wake generator) = 20. The wavelet multi-resolution technique was applied to decomposing the velocity data, obtained in the wakes generated by the two generators, into a number of wavelet components based on the central frequencies. The instantaneous sectional streamlines and vorticity field were thus ‘visualized’ for each wavelet component or central frequency. It was found that the behavior of large- and intermediate-scale structures depend on the initial conditions and the small-scale structures are independent of the initial conditions. The contributions from the wavelet components to the time-averaged Reynolds stresses and vorticity were estimated. Both the large-scale and intermediate longitudinal structures make the most significant contributions to Reynolds stresses in the circular cylinder wake, but the contribution from the large-scale structures appears dominating in the screen wake. The relatively small scale structures of the circular cylinder wake contribute most to the total rms spanwise vorticity.     

Polarization-Free Quantum Fields and Interaction

A new approach to the inverse scattering problem proposed by Schroer, is applied to two-dimensional integrable quantum field theories. For any two-particle S-matrix S ₂ which is analytic in the physical sheet, quantum fields are constructed which are localizable in wedge-shaped regions of Minkowski space and whose two-particle scattering is described by the given S ₂. These fields are polarization-free in the sense that they create one-particle states from the vacuum without polarization clouds. Thus they provide examples of temperate polarization-free generators in the presence of nontrivial interaction.     

Operator coproduct-realization of quantum group transformations in two-dimensional gravity I

A simple connection between the universalR matrix ofU _q(sl(2)) (for spins 1/2 andJ) and the required form of the coproduct action of the Hilbert space generators of the quantum group symmetry is put forward. This leads us to an explicit operator realization of the coproduct action on the covariant operators. It allows us to derive the expected quantum group covariance of the fusion and braiding matrices, although it is of a new type: the generators depend upon worldsheet variables, and obey a new central extension of theU _q(sl(2)) algebra realized by (what we call) fixed point commutation relations. This is explained by showing on a general ground that the link between the algebra of field transformations and that of the coproduct generators is much weaker than previously thought. The central charges of our extendedU _q(sl(2)) algebra, which includes the Liouville zero-mode momentum in a non-trivial way, are related to Virasoro-descendants of unity. We also show how our approach can be used to derive the Hopf algebra structure of the extended quantum-group symmetry related to the presence of both of the screening charges of 2D gravity.Partially supported by the EC contracts CHRXCT920069 and CHRXCT920035.Unité Propre du Centre National de la Recherche Scientifique, associée à l'École Normale Supérieure et à l'Université de Paris-Sud.     

Convergence of local charges and continuity properties ofW*-inclusions

The local generators of symmetry transformations which have recently been constructed from a quantum field theoretical version of Noether's theorem are shown to converge to the global ones as the volume tends to the whole space. The proof relies on the continuous volume dependence of the universal localizing maps which are associated to the local splitW*-inclusions.Research supported by Ministero della Pubblica Istruzione and CNR-GNAFA     

The universalR-matrix forU q sl(3) and beyond!

TheR-matrices for the quantised Lie algebrasA _n are constructed through the quantum double procedure given by Drinfel'd [6]. The case ofU _q sl(3) is thoroughly analysed initially to demonstrate the more subtle points of the calculation. The ease of the calculation forA _n is very dependent on a choice of generators for the Borel subalgebraU _q b ₊ and its dual, and a certain ordering imposed on these generators which is related to the length of a certain word in the Weyl group.Supported by a SERC studentship     

Periodic and partially periodic representations ofSU(N) q

The Gelfand-Zetlin basis is adapted toSU(N) _q forq a root of unit. Extra parameters are incorporated in the matrix elements of the generators to obtain all the invariants corresponding to the augmented center. A crucial identity is derived and proved, which guarantees the periodicity of the action of the generators. Full periodicity is relaxed by stages, some raising and lowering operators remaining injective while others become nilpotent with corresponding changes in the dimension of the representation. In the extreme case of highest weight representations. all the raising and lowering operators are nilpotent. As an alternative approach an auxiliary algebra giving all the periodic representations is presented. An explicit solution of this system forN=3, while fully equivalent to the G.-Z. basis, turns out to be much simpler.