bluuebunny/crossref_metadata_2025 huggingface dataset:
Torsion of certain beams
Authors: Obaid Evelyn E. , Obaid S. A.
Published: July 2002

Complex variable methods are introduced to derive exact and closed expressions for the stress functions, torsional rigidities, and peripheral shearing stresses of certain isotropic cylinders under torsion. Numerical results in some special cases are presented in tabular and graphic form. The equations for the boundaries of the cross sections for these cylinders have the polar forms r2=a2(2 cos 2θ−1), a>0 (‖θ‖≤π/6), r4=2na4/(n−1+cos 4θ)(n+1+cos 4θ), a>0 (‖θ‖≤π, 2<n<∞), and rm−2=am−2 (cos2 θ−cos2δ) /sin2 δ cos mθ, a>0 (m>2, 0<δ<π/2m, ‖θ‖≤δ).
Closed formula for the product of n Dirac matrices
Authors: Moreno Matías
Published: July 2002

The product of n Dirac γ matrices is evaluated in terms of traces of at most (n+3) γ matrices. This leads to a method that can be used to generalize identities for a correlated product of γ matrices. The expression for the n γ matrix product also provides a method for the evaluation of a scalar, a pseudoscalar, a vector, an axial vector, and a second rank antisymmetric tensor associated with a one-line fermion amplitude that drastically simplifies the squaring of fermionic amplitudes. The general spin and particle–antiparticle dependence of the squared amplitude is given.
On a certain class of solutions of the Einstein–Maxwell equations
Authors: Kowalczyński Jerzy Klemens
Published: July 2002

This paper deals with exact solutions of the Einstein–Maxwell equations. The solutions belong to a metric form which is a special case of the Robinson–Trautman form. The chosen metric form admits positive, zero, and negative Gaussian curvature (labeled ε=1, 0, −1, respectively) of its two-dimensional angularlike part. Some general properties of the solutions are given for all the values of ε. All the explicit solutions for ε=±1 are presented. They are of the Petrov type II. The physical meaning of ε is discussed.
Supertwistor fiber bundles as a formalism for supergravities
Authors: Luehr C. P. , Rosenbaum M.
Published: July 2002

A gauge theory of supergravity which allows one to obtain first-order Lagrangians that are locally gauge invariant by construction is presented. The formalism makes use of supertwistors as a representation space for the construction of a typical fiber of a vector bundle associated with a principal bundle, where the structural group is the super-Poincaré group. The approach proposed provides a means of resolving one of the central problems of gauge field theories of external symmetry groups, that is the satisfactory treatment of translations.
On the general solution to equations modeling a homogeneously broadened injection laser
Authors: Lerche I.
Published: July 2002

The strongly coupled, nonlinear, differential equations which describe the amplification of modal intensities for propagation through a homogeneously broadened amplifier are shown to be generally reducible to a linear integral equation which is readily soluble by Laplace transform techniques. The mode intensities are shown to be generally expressible in terms of simple quadratures taken over the solution to the linear integral equation, which we also provide.
A generalized Molien function for field theoretical Hamiltonians
Authors: Felix Jeffrey W. , Hatch Dorian M.
Published: July 2002

A generating function, or Molien function, the coefficients of which give the number of independent polynomial invariants in G, has been useful in the Landau and renormalization group theories of phase transitions. Here a generalized Molien function for a field theoretical Hamiltonian (with short-range interactions) of the most general form invariant in a group G is derived. This form is useful for more general renormalization group calculations. Its Taylor series is calculated to low order for the FΓ−2 representation of the space group R3̄c and also for the l=1 (faithful) representation of SO(3).
Graded manifolds and vector bundles: A functorial correspondence
Authors: Batchelor M.
Published: July 2002

A functorial correspondence between the category of graded manifolds and the category of vectors bundles is given. Given a graded manifold (X,A), a vector bundle G over X is given as a subset of the product X×A0 where A0 is the dual coalgebra of A. This bundle has an obvious coalgebra structure on each fiber. The correspondence is achieved by showing that the sheaf A is isomorphic as a sheaf of algebras to the sheaf of sections of the vector bundle G′ dual to G.
Poincaré covariant infraparticle sectors
Authors: Stark Hans-Georg
Published: July 2002

Footing on the infraparticle picture of quantum electrodynamics, a Poincaré covariant description of asymptotic sectors, containing n charged particles (n≥1) and the associated radiation field, is given. The analogy of this method to Wigner’s description of elementary particles is discussed.
The Dirac wave equation in the presence of an external field
Authors: Abounadi Jinane , Darkhosh Teymour
Published: July 2002

The method of characteristics is applied to the Dirac wave equation in the presence of an external field. The retarded Green’s function for the minimal coupling to an external electromagnetic field is calculated explicitly, and a general coupling is discussed.
Spin fluids in stationary axis-symmetric space-times
Authors: Krisch J. P.
Published: July 2002

The relations establishing the equivalence of an ordinary perfect fluid stress-energy tensor and a spin fluid stress-energy tensor are derived for stationary axis-symmetric space-times in general relativity. Spin fluid sources for the Gödel cosmology and the van Stockum metric are given.
Critical exponent of susceptibility for a class of general ferromagnets in d>4 dimensions
Authors: Kondo Kei-ichi , Hara Takashi
Published: July 2002

A ‘‘rigorous proof’’ is presented that the critical exponent γ of the susceptibility χ takes its mean field value in d>4 dimensions for ferromagnets with single spin measure in the Brydges–Fröhlich–Spencer class, modulo a numerical calculation of a certain function I(d) of dimension d. This class of ferromagnets contains, for example, the Ising spin model and lattice scalar φ4 model.
Generalization of Levinson’s theorem to particle–matter interactions
Authors: Chung S. G. , George Thomas F.
Published: July 2002

It is shown that Levinson’s theorem in static potential scattering can be generalized to a particle dynamically interacting with one-dimensional matter systems (liquids or solids). A restriction on a particle–matter interaction is that it decays faster than an inverse quadratic of the particle–matter separation.
New analytical models for anisotropic spheres in general relativity
Authors: Ponce de León J.
Published: July 2002

Two new exact analytical solutions to Einstein’s field equations representing static fluid spheres with anisotropic pressures are presented. One solution has a maximum value of mass of about 0.42 times the radius of the fluid sphere, dictated by causality and the corresponding values for the surface red shift and the central red shift are 1.58 and 9.03, respectively. The other solution has a maximum mass of about 0.435 times the radius of the fluid sphere and the corresponding red shifts from the surface and from the center are 1.77 and 16.28, respectively. In the low mass limit both solutions reduce to the constant density Schwarzschild interior solution.
A few remarks on the paper ‘‘Necessary versus sufficient conditions for exact solubility of statistical models on lattices’’ [J. Math. Phys. 2
7, 593 (1986)]
Authors: Gutkin Eugene
Published: July 2002

Lochak and Maillard [J. Math. Phys. 27, 593 (1986)] claim that the Baxter condition, which was known to be sufficient for the commutativity of transfer matrices, is also necessary (under some additional technical assumptions). Although the claim is correct, the proof in that paper is false. In this paper the errors of Lochak and Maillard are pointed out and correct proofs are outlined.
Generalized Riccati equations for self-dual Yang–Mills fields
Authors: Chau L.-L. , Yen H. C.
Published: July 2002

It is shown that although no Riccati equations in the strict sense are likely to exist for the self-dual Yang–Mills fields, certain ‘‘generalized Riccati equations’’ derivable from the Bäcklund transformation do exist, and are capable of reproducing the linear system when a certain contraint is imposed.
Classical nonlinear σ models on Grassmann manifolds of compact or noncompact type
Authors: Antoine J-P. , Piette B.
Published: July 2002

Grassmannian σ models are reexamined in the light of a new geometrical result. Namely, the Cartan immersion of a Riemannian symmetric space G/H into its isometry group G is not always a diffeomorphism onto the set Mσ introduced by Eichenherr and Forger [Nucl. Phys. B 164, 528 (1980)]. This is the case, in particular, for Grassmann manifolds of all types: their set Mσ is shown to be disconnected and its structure is completely analyzed. As a consequence, a new constraint must be introduced in the Bäcklund transformation (BT) method proposed by Harnad, Saint-Aubin, and Shnider [Commun. Math. Phys. 92, 329 (1984)]. It is shown, however, to always be satisfied for Grassmann manifolds of compact type (i.e., G compact), but the problem remains open in most other cases. On the other hand, the BT method is extended to the Euclidean regime.
Four-dimensional boson field theory. III. Nontriviality
Authors: Baker George A. , Johnson J. D.
Published: July 2002

The results of numerical investigations based on series analysis indicate clearly that the method of phantom fields constructs nontrivial, self-interacting scalar Euclidean boson field theories. It is found that these continuum theories arise as the scaling limit to normal critical points of lattice statistical mechanical models. The character of these theories is numerically indistinguishable from that of a classical theory on the lambda line near the tricritical point.
Absence of phase transitions for continuum models of dimension d>1
Authors: Klein David , Yang Wei-Shih
Published: July 2002

Examples of grand canonical continuum models are given in Rd, or a suitable subset of Rd, for which no multiple phases exist.
Coherent-state path-integral S-matrix formalism applied to the Lee model
Authors: Hammer C. L. , Shrauner J. E.
Published: July 2002

In this paper we show that a coherent-state path-integral treatment significantly simplifies the analysis of the Lee model, including higher sector calculations. The method may be applicable to more general field theories. However, the special properties of the Lee model allow the results to be displayed in closed form.
Ternary composition algebras and Hurwitz’s theorem
Authors: Shaw Ronald
Published: July 2002

Axioms are proposed for a certain ‘‘alternative’’ kind of ternary composition algebra, termed a 3Cn algebra. The axioms are shown to be (for n>2) in a simple correspondence with the axioms for a ternary vector cross product algebra. The axioms imply that n=1, 2, 4, or 8 (from which the usual Hurwitz theorem is deduced). The existence of 3C8 algebras is demonstrated by an explicit construction in four-dimensional Hilbert space, without appeal to the properties of the algebra of octonions.
Representations of SL(2,R) in a Hilbert space of analytic functions and a class of associated integral transforms
Authors: Basu Debabrata
Published: July 2002

It is shown that the boson operators of SL(2,R) realized as hyperdifferential operators in Bargmann’s Hilbert space of analytic functions yield, on exponentiation, a parametrized continuum of integral transforms. Each value of the group parameters yields an integral transform pair. For the metaplectic representation the resulting integral transform is essentially the mapping of the Moshinsky–Quesne transform in Bargmann’s Hilbert space B(C). The formula for the inversion of this transform is obtained simply by replacing the group element by its inverse. The corresponding Hilbert space for arbitrary representations of the discrete series is B(C2), where C2 is the two-dimensional complex Euclidean space. To carry out the reduction of B(C2) into the eigenspaces Bk(C) (k= 1/2 ,1, (3)/(2) ,...) of irreducible representations of the positive discrete class, the complex polar coordinates (z1=z cos φ, z2=z sin φ) in C2 are introduced. The ‘‘reduced Bargmann space’’ Bk(C) has many interesting features. The elements of Bk(C) are entire functions of the complex ‘‘radius’’ z analytic in the upper half-plane. In contrast to the Gaussian measure in B(C2), the integration measure in the scalar product in Bk(C) contains a modified Bessel function of the second kind. The principal vector in Bk(C), on the other hand, is a modified Bessel function of the first kind. The resulting integral transform maps Bk(C) onto itself and the integral kernel is the product of an exponential and a modified Bessel function of the first kind. The inversion formula for this transform is obtained again by replacing the group element by its inverse.
A unitary representation of SL(2,R)
Authors: Bacry Henri
Published: July 2002

A given unitary representation of the group SL(2,R), belonging to the discrete series, is shown to involve necessarily some special functions (in particular, Laguerre and Hardy–Pollaczek polynomials). Various realizations of this representation are investigated, including the coherent states one. More generally, it is shown that the representations of the discrete series of the universal covering of SL(2,R) involves generalized Laguerre and Pollaczek polynomials. The Riemann zeta function is shown to be concerned with these representations.
Scale-invariant gravity in two dimensions
Authors: Schmidt Hans-Jürgen
Published: July 2002

The vacuum field equations are solved in a V2 following from the scale-invariant gravitational Lagrangian £=Rk+1. For £=R2, exactly six solutions exist. Just one of them breaks the scale-invariance and has indefinite signature. For k→0, nontrivial results also arise. Their relation to two-dimensional quantum gravity is discussed. For £=F(R) a Birkhoff-type theorem holds.
Clifford algebra: Notes on the spinor metric and Lorentz, Poincaré, and conformal groups
Authors: Crawford J. P.
Published: July 2002

A particular normalization for the set of basis elements {Γi} of the complex Clifford algebras C(p,q) is motivated and defined by demanding that the physical bispinor densities ρi=Ψ̄ΓiΨ be real. This condition, referred to here as Dirac normalization, also necessitates the introduction of the spinor metric γ, and the solution of the metric conditions is given for arbitrary (p,q); when N=p+q is even the metric is unique, and when N is odd there are two distinct metrics. Then the Dirac normalization preserving automorphism group of the basis is explored. This is also the group of transformations leaving the spinor metric invariant. In particular, the physically important cases of the Lorentz, Poincaré, and conformal groups are sought as subgroups of the automorphism group. As expected, it is found that the Lorentz group is always contained in the automorphism group. However, it is found that the Poincaré and conformal groups are contained only in the cases where N is even and q is odd. Furthermore, when N is odd these groups may be found in the full isomorphism group, but only for one of the two possible spinor metrics. Possible physical implications of these results are discussed.
Quantum quaternions
Authors: Marchiafava Stefano , Rembieliński Jakub
Published: July 2002

The notion of quantum quaternions is introduced as a one-parametric quantum deformation of the quaternion algebra. An appriopriate noncommutative differential calculus is developed and the quantum version of the Fueter equation is founded.
Debye potentials and Hamiltonians for magnetic field line flow
Authors: Torres del Castillo G. F.
Published: July 2002

It is shown that any divergence-free vector field invariant under a group of volume-preserving transformations can be expressed locally in terms of two scalar potentials which depend on two variables only. It is also shown that the corresponding field line equations can be written in Hamiltonian form with one of these potentials as the Hamiltonian.
Stable and unstable manifolds in a zone of instability. II
Authors: Tanikawa Kiyotaka , Yamaguchi Yoshihiro
Published: July 2002

A diffeomorphism f: R2→R2 possessing a simple heteroclinic cycle [J. Franks, Publ. Math. IHES 71, 105 (1990)] bounding a disk D is first considered. Using the Poincaré index argument, one gets an easy result that f has a fixed point in D. If f is area preserving, there is a sequence of points in each of the stable and unstable manifolds of the simple heteroclinic cycle converging to the boundary of any connected component of the maximal invariant set in D. This result is applied to an area-preserving twist map. It is shown that each of the stable and unstable manifolds of any p/q-homoclinic Birkhoff saddle in a zone of instability of the map has a sequence of points converging, for example, to the boundary of the connected invariant set containing any second p′/q′-Birkhoff point. Finally, the relation between a homoclinic Birkhoff saddle and a second Birkhoff periodic point is briefly discussed.
Spatiality of *-derivations of partial O*-algebras
Authors: Antoine J.-P. , Inoue A. , Trapani C.
Published: July 2002

The notion of *-derivation on an algebra of unbounded operators is extended to partial O*-algebras, and the corresponding notion of spatiality is investigated. Special emphasis is given to *-derivations associated to one-parameter groups of *-automorphisms and to *-derivations of partial GW*-algebras.
Ray representations of N(≤2)+1-dimensional Galilean group
Authors: Doebner H.-D. , Mann H.-J.
Published: July 2002

For a quantum mechanical system, modeled via unitary or antiunitary representations of a symmetry group G with Lie algebra g, the Hamiltonian H is of special interest. If H is an element of g or of the universal enveloping algebra U(g), a generic time dependence for any element in U(g) is given through the Heisenberg picture. As an example we consider a system with Gal(N) as symmetry group with H as one of the generators. For N≥3 one gets from ray representations the free Schrödinger equation. For N=1 a peculiarity occurs: the ‘‘free’’ equation has an interaction term, which results from the construction and parametrization of unitary ray representations. For N=2 there is another special feature: there exist ray representations of the universal covering group Gal(2)■, which induce no ray representations of Gal(2). Furthermore, for these representations it is not possible to construct a Schrödinger equation.
Statistical mechanics of the deformable droplets on Riemannian surfaces: Applications to reptation and related problems
Authors: Kholodenko Arkady L.
Published: July 2002

The statistical mechanics treatment of the Laplace–Young-type problems developed for the flat surfaces is generalized to the case of surfaces of constant negative curvature and connected with them to Riemannian surfaces. Obtained results are mainly used to supply an additional support of the quantum Hall effect (QHE) analogy employed in recent work [J. Phys. 4, 843 (1994)], which provides theoretical justification of the tube concept used in polymer reptation models. As a byproduct, close links between QHE, quantum chaos, and the non-Abelian Chern–Simons quantum mechanics are indicated.
Twisting 2-cocycles for the construction of new non-standard quantum groups
Authors: Jacobs Andrew D. , Cornwell J. F.
Published: July 2002

We introduce a new class of 2-cocycles defined explicitly on the generators of certain multiparameter standard quantum groups. These allow us, through the process of twisting the familiar standard quantum groups, to generate new as well as previously known examples of non-standard quantum groups. In particular we are able to construct generalisations of both the Cremmer-Gervais deformation of SL(3) and the so called esoteric quantum groups of Fronsdal and Galindo in an explicit and straightforward manner.
Multiperiodic coherent states and the Wentzel–Kramers–Brillouin exactness. II. Noncompact case and classical theories revisited
Authors: Fujii Kazuyuki , Funahashi Kunio
Published: July 2002

We show that the Wentzel–Kramers–Brillouin approximation gives the exact result in the trace formula of “CQN,” which is the noncompact counterpart of CPN, in terms of the “multiperiodic” coherent state. We revisit the symplectic 2-forms on CPN and CQN and, especially, construct that on CQN with the unitary form. We also revisit the exact calculation of the classical partition functions of them.
Intermediate level statistics with one-parameter random matrix ensembles
Authors: Hasegawa Hiroshi , Ma Jian-Zhong
Published: July 2002

We discuss a formulation of the level statistics for quantum systems that lie in an intermediate regime between the integrability subject to Poisson statistics and the full chaos subject to Gaussian statistics of the typical random matrix theory (RMT). It is based on the idea initiated by Yukawa and also by Nakamura and Lakshmanan, namely, to transcribe the eigenvalue statistics into statistical mechanics of the completely integrable Calogero system with internal degrees of rotation. By analyzing the previous works of Gaudin and Forrester from this viewpoint, we answer the question raised by Mehta and Dyson in early RMT concerning the expectation of compressible level gas, which is realized now in such an intermediate regime. It indicates the general absence of a fractional power dependence of the two-level correlation function under the ordinary thermodynamic-limit procedure as the manifestation that a transition between localized and delocalized states does not occur. The predictability of the transition by modifying the theory is remarked. Two applications of the present scheme are shown: the information loss per level and the correlation hole of survival probability for intermediate circular unitary ensembles.
Quantum averaging. III. Time-dependent systems
Authors: Scherer Wolfgang
Published: July 2002

We present new perturbation algorithms for time-dependent quantum systems. These new methods make use of a time-dependent averaging method and are based on analogies with the Poincaré–von Zeipel (PvZ) and Kolmogorov–Arnold–Moser (KAM) expansions. Application to a simple example shows that the PvZ as well as the KAM expansion are superior to the standard quantum mechanical time-dependent perturbation method (Dyson expansion).
Study of hydrodynamical limits in a multicollision scale Boltzmann equation for semiconductors
Authors: Montarnal Philippe
Published: July 2002

We derive in this paper a generalized hydrodynamical model for semiconductors from a multicollision scale Boltzmann equation. We apply a Chapman–Enskog method for two time-scale collisional operators. These two time scales are linked respectively with the elastic part of the electron/lattice scattering term and the electron/electron collision term. Our model has a global entropy function and a symmetric formulation. It is a generalization of the classical hydrodynamical model since we add two terms: a “thermal friction force” and a “friction heat flux.” Moreover, with some changes of parameters we obtain both the energy-transport model and the Euler–Poisson hydrodynamical model.
Nonalgebraic integrability of one reversible dynamical system of the Cremona type
Authors: Rerikh K. V.
Published: July 2002

A reversible dynamical system (RDS) and a system of nonlinear functional equations, defined by a certain rational quadratic Cremona mapping and arising from the static model of the dispersion approach in the theory of strong interactions [the Chew–Low-type equations with crossing-symmetry matrix A(l,1)], are considered. This RDS is split into one- and two-dimensional ones. An explicit Cremona transformation that completely determines the exact solution of the two-dimensional system is found. This solution depends on an odd function satisfying a nonlinear autonomous three-point functional equation. Nonalgebraic integrability of RDS under consideration is proved using the method of Poincaré normal forms and the Siegel theorem on biholomorphic linearization of a mapping at a nonresonant fixed point.
Rational conformal field theory extensions of W1+∞ in terms of bilocal fields
Authors: Georgiev L. S. , Todorov I. T.
Published: July 2002

The rational conformal field theory extensions of W1+∞ at c=1 are in one-to-one correspondence with one-dimensional integral lattices L(m). Each extension is associated with a pair of oppositely charged “vertex operators” of charge square m∈N. Their product defines a bilocal field Vm(z1,z2) whose expansion in powers of z12=z1−z2 gives rise to a series of (neutral) local quasiprimary fields Vl(z,m) (of dimension l+1). The associated bilocal exponential of a normalized current generates the W1+∞ algebra spanned by the Vl(z,1) (and the unit operator). The extension of this construction to higher (integer) values of the central charge c is also considered. Applications to a quantum Hall system require computing characters (i.e., chiral partition functions) depending not just on the modular parameter τ, but also on a chemical potential ζ. We compute such a ζ dependence of orbifold characters, thus extending the range of applications of a recent study of affine orbifolds.
Highest weight irreducible representations of the quantum algebra Uh(A∞)
Authors: Palev T. D. , Stoilova N. I.
Published: July 2002

A class of highest-weight irreducible representations of the algebra Uh(A∞), the quantum analog of the completion and central extension A∞ of the Lie algebra gl∞, is constructed. It is considerably larger than the class of representations known so far. Within each module a basis is introduced and the transformation relations of the basis under the action of the Chevalley generators are explicitly given. The verification of the quantum algebra relations is shown to reduce to a set of nontrivial q-number identities. All representations are restricted in the terminology of S. Levendorskii and Y. Soibelman [Commun. Math. Phys. 140, 399–414 (1991)].
Chaos in Robertson–Walker cosmology
Authors: Bombelli Luca , Lombardo Fernando , Castagnino Mario
Published: July 2002

Chaos in Robertson–Walker cosmological models where gravity is coupled to one or more scalar fields has been studied by a few authors, mostly using numerical simulations. In this paper we begin a systematic study of the analytical aspect. We consider one conformally coupled scalar field and, using the fact that the model is integrable when the field is massless, we show in detail how homoclinic chaos arises for nonzero masses using a perturbative method.
Calculus on the multivector manifold spin+(p,q)
Authors: Blake Stephen
Published: July 2002

Coordinate-free differential and integral calculus is formulated on the spin groups, regarded as multivector manifolds embedded in Geometric Algebra. The derivative with respect to a point on the manifold is shown to be in the tangent algebra at the inverse point. The curvature of spin(p,q) is calculated and related to the structure constants of its Lie algebra. Volume elements on spin(p,q) are introduced naturally as completely antisymmetrized geometric products of bivectors. They are left invariant like Haar measure and are elements of a multivector-valued Grassman algebra. It is shown that integration in this sense is forbidden for many spin groups. A version of Stokes’s theorem is formulated on spin(p,q).
The trace formulas yield the inverse metric formula
Authors: Silva Ronaldo Rodrigues
Published: July 2002

It is a well-known fact that the first and last nontrivial coefficients of the characteristic polynomial of a linear operator are, respectively, its trace and its determinant. This work shows how to compute recursively all the coefficients as polynomial functions in the traces of the successive powers of the operator. With the aid of Cayley–Hamilton’s theorem the trace formulas provide a rational formula for the resolvent kernel and an operator-valued null identity for each finite dimension of the underlying vector space. The four-dimensional resolvent formula allows an algebraic solution of the inverse metric problem in general relativity.
Graded differential geometry of graded matrix algebras
Authors: Grosse H. , Reiter G.
Published: July 2002

We study the graded derivation-based noncommutative differential geometry of the Z2-graded algebra M(n|m) of complex (n+m)×(n+m)-matrices with the “usual block matrix grading” (for n≠m). Beside the (infinite-dimensional) algebra of graded forms, the graded Cartan calculus, graded symplectic structure, graded vector bundles, graded connections and curvature are introduced and investigated. In particular we prove the universality of the graded derivation-based first-order differential calculus and show that M(n|m) is a “noncommutative graded manifold” in a stricter sense: There is a natural body map and the cohomologies of M(n|m) and its body coincide (as in the case of ordinary graded manifolds).
Unified Kadomtsev–Petviashvili equation
Authors: Chen Xue-Nong
Published: July 2002

The problem of shallow water waves propagating over slowly varying topography is considered. The fluid is assumed to be weakly viscous and the effects of viscosity can be considered only in the boundary layer on the bottom. By the methods of multiple scales and matched asymptotics, the Boussinesq theory is extended for this problem and a unified Kadomtsev–Petviashvili equation is obtained, in which viscous, topographic, and transverse modulational effects are incorporated.
Stability of the global Alfvén eigenmode in the presence of fusion alpha particles in an ignited tokamak plasma
Authors: Fu G. Y. , Van Dam J. W.
Published: July 2002

The stability of global Alfvén eigenmodes is investigated in the presence of super-Alfvénic energetic particles, such as fusion-product alpha particles in an ignited deuterium–tritium tokamak plasma. Alpha particles tend to destabilize these modes when ω*α>ωA, where ωA is the shear-Alfvén modal frequency and ω*α is the alpha particle diamagnetic drift frequency. This destabilization due to alpha particles is found to be significantly enhanced when the alpha particles are modeled with a slowing-down distribution function rather than with a Maxwellian distribution. However, previously neglected electron damping due to the magnetic curvature drift is found to be comparable in magnitude to the destabilizing alpha particle term. Furthermore, the effects of toroidicity are also found to be stabilizing, since the intrinsic toroidicity induces poloidal mode coupling, which enhances the parallel electron damping from the sideband shear-Alfvén Landau resonance. In particular, for typical ignition tokamak parameters, global Alfvén eigenmodes are found to be completely stabilized by either the electron damping that enters through the magnetic curvature drift or the damping introduced by finite toroidicity.
Evolution of an X-pinch plasma
Authors: Cochran F. L. , Davis J.
Published: July 2002

The evolution of a dynamic X-pinch plasma, formed by two or more intersecting crossed copper wires, is investigated theoretically and numerically in two dimensions to determine the behavior at the point of intersection. An X-pinch plasma for conditions corresponding to (a) pure hydrodynamic and (b) nonlocal thermodynamic equilibrium radiation hydrodynamic simulations are considered when driven by an externally applied current.
Hydrodynamic target response to an induced spatial incoherence-smoothed laser beam
Authors: Emery M. H. , Gardner J. H. , Lehmberg R. H. , Obenschain S. P.
Published: July 2002

One of the critical elements for high-gain target designs is the high degree of symmetry that must be maintained in the implosion process. The induced spatial incoherence (ISI) concept has some promise for reducing ablation pressure nonuniformities to ≊1%. The ISI method produces a spatial irradiance profile that undergoes large random fluctuations on picosecond time scales but is smooth on long time scales. The ability of the ISI method to produce a nearly uniform ablation pressure is contingent on both temporal smoothing and thermal diffusion. In the start-up phase of a shaped reactorlike laser pulse, the target is directly illuminated by the laser light and thermal diffusion is not effective at smoothing residual nonuniformities in the laser beam. During this period in the laser pulse, the target response is dominated by the initial shock generated by the laser pulse and the results indicate that this first shock can be the determining factor in the success or failure of the implosion process. The results of numerical simulations of several target/laser pulse designs which were investigated in an attempt to mitigate the impact of the initial shock structure stemming from the early temporal phase of an ISI-smoothed laser beam are presented. It is shown that ‘‘foamlike’’ layers, multiple laser wavelengths, and shallow angles of incidence can sharply reduce the perturbation level stemming from the first shock.
A limitation to the analogy between pure electron plasmas and two-dimensional inviscid fluids
Authors: Peurrung A. J. , Fajans J.
Published: July 2002

Thermal corrections to E×B drifts cause small structures in pure electron plasmas to smear. This smearing breaks the strict analogy between the behavior of pure electron plasmas and the behavior of two-dimensional inviscid fluids. The causes and consequences of this smearing are discussed, a criterion for the validity of the plasma/fluid analogy is constructed, and experimental examples of the failure of the analogy are presented. The criterion indicates that fluid-like behavior can persist to scale lengths far smaller than the normal ‘‘collective’’ behavior limit.
Observation of a current-limited double layer in a linear turbulent-heating device
Authors: Inuzuka Hiroshi , Torii Yutaka , Nagatsu Masaaki , Tsukishima Takashige
Published: July 2002

Time- and space-resolved measurements of strong double layers (DLs) have been carried out for the first time on a linear turbulent-heating device, together with those of fluctuation spectra and precise current measurements. A stable stong DL is formed even when the electric current through the DL is less than the so-called Bohm value. Discussion of the formation and decay processes is given, indicating a transition from an ion-acoustic DL to a monotonic DL.
Efficiency of current drive by fast waves
Authors: Karney Charles F. F. , Fisch Nathaniel J.
Published: July 2002

The Rosenbluth form for the collision operator for a weakly relativistic plasma is derived. The formalism adopted by Antonsen and Chu can then be used to calculate the efficiency of current drive by fast waves in a relativistic plasma. Accurate numerical results and analytic asymptotic limits for the efficiencies are given.
Finite orbit analysis for long wavelength modes in a plasma with a hot component
Authors: Hammer James H. , Berk H. L.
Published: July 2002

The z-pinch model is used to calculate finite Larmor radius effects of a plasma with a hot component plasma annulus. The equations are analyzed for layer modes and the finite Larmor radius stabilization condition is calculated. Stability requires k2 ρ2h Rβh/Δ≳1, where k is the wavenumber in the z direction, ρh the hot species Larmor radius, βh the hot particle beta, and Δ the thickness of the pressure profile. In addition a new instability is found, caused by the interaction of the precessional modes associated with inner and outer edges of the hot particle pressure profile.
Gas flow in vertical slots with large horizontal temperature differences
Authors: Chenoweth D. R. , Paolucci S.
Published: July 2002

Perfect gas exact solutions to the steady Navier–Stokes equations are given for laminar convective motion in open and closed vertical slots with large temperature differences using Sutherland law transport properties. The solutions are valid a few slot widths away from the ends in the asymptotic region where the opposite hot and cold wall boundary layers are fully merged. It is found that the static pressure (in the closed slot) and temperature and velocity distributions (in all cases) are very sensitive to property variations, even though the heat flux may not be. We observe the net horizontal and vertical heat fluxes to be the same as those obtained from the Boussinesq equations. Comparisons with constant property solutions and the well-known Boussinesq limiting solution for small temperature differences are given for examples using air.
The eddy viscosity in a turbulent boundary layer on a cylinder
Authors: Lueptow Richard M. , Leehey Patrick
Published: July 2002

The eddy viscosity for a turbulent boundary layer on a cylinder was measured using hot-wire anemometry. Except near the wall, the eddy viscosity is roughly constant with a value corresponding to that estimated from the slope of the mean velocity profile. These results confirm that a constant eddy viscosity closure scheme is appropriate for the boundary layer on a cylinder.
Scattering of magnetosonic waves off interchange modes in mirror plasmas
Authors: McBride J. B. , Stefan V.
Published: July 2002

Scattering of fast magnetosonic waves off interchange modes is studied using a weak coupling, mode–mode dispersion relation. This process can lead to stabilization of interchange modes if certain specified conditions on the fast wave electric field strength and on the wave vectors of the interacting modes are satisfied.
Study of the magnetic compressional mode in a hot particle plasma
Authors: Stotler D. P. , Berk H. L. , Engquist M. G.
Published: July 2002

The integral equation for the magnetic compressional mode, accounting for geometrical effects along the field line and using the eikonal approximation across the field line, is solved numerically for the eigenvalues and eigenfunctions. These results reproduce the analytic estimates when there is strong drift reversal. The representation of the eigenfunction of the form B̂∥=[C(ψ)/B] ×(dP⊥h/dψ) is found to give accurate growth rates over a large range of parameter values. For typical EBT-S [Plasma Phys. 25, 597 (1983)] parameters, instability is predicted for all pressure scale lengths just below those needed for drift reversal, i.e., ‖R ∂(Pc) +P⊥h)/2B2 ∂r‖>1 (where P is the article pressure, c and h refer to cold and hot components, B is the midplane magnetic field, and R is the midplane radius of curvature). If larger core densities are present, a wave–particle resonance arises when the particle drifts are not reversed, causing instability up to much larger pressure scale lengths. Stability for all values of the ratio of hot electron density to core density is obtained with ‖R ∂Pc/B2 ∂r‖>1+P∥h/P⊥h.
Long-wave instability of periodic flows at large Reynolds numbers
Authors: Libin A. , Sivashinsky G. , Levich E.
Published: July 2002

It is shown that simple unidirectional and helical periodic flows are unstable to long-wave perturbations at large Reynolds numbers. Consideration is given to the cases of periodic flow sustained by an applied force and periodic flow freely decaying owing to viscosity.
Spontaneous collapse of double layers in a simple mirror confinement device
Authors: Inuzuka Hiroshi , Torii Yutaka , Nagatsu Masaaki , Tsukishima Takashige
Published: July 2002

An empirical law τDIDL =const has been found for the lifetime τD of the double layers (DL) observed in a linear turbulent-heating device NU-II [Phys. Fluids 28, 703 (1985)], where IDL is the current passing through the DL.
Effect of large-amplitude perpendicularly propagating radio frequency waves on the interchange instability
Authors: Otani Niels F. , Cohen Bruce I.
Published: July 2002

Results are presented from hybrid 2-D quasineutral Darwin simulations of the interchange instability in the presence of a large rf wave in the ion-cyclotron frequency range. The simulation models the plane perpendicular to the background magnetic field using cold particle ions and a cold E×B electron fluid. Related theory is also discussed. Fluid equations appropriate to the simulation model are derived and their properties demonstrated and compared to simulation. A method for solving for the rf-modified growth rates from the fluid equations is described. It is generally expected that the current component associated with the mean, rf-induced ion drift is capable of influencing the stability of the interchange mode; however, no modification of the mean ion drift is observed in simulations in which rf is present. Instead, in both the theory and simulation, an electron rf-field oscillation current dominates the modification to the gravitational current. As a result, even in the presence of large rf fields (Brf/B0=15%), only modest corrections to the interchange growth rates are observed. The effect is stabilizing for kLn≲0.8–0.9, apparently for both signs of the square-electric-field gradient, and is destabilizing for larger values of kLn, although the credibility of the simulation begins to become suspect here. Fractional reduction of the interchange growth rate is observed to be quadratically dependent on the rf wave amplitude, independent of ion-cyclotron resonant effects, and proportional to ∇B2rf/∇B20, consistent with an eikonal theory developed for the study of stabilizing effects on perpendicularly propagating fast Alfvén waves. The results also suggest that additional gradient-independent stabilizing effects may be operative when kLn∼1. Finally, it is also observed that, while the rf wave has little effect on the interchange instability, the interchange mode strongly affects the rf wave, damping it significantly as the mode saturates.
Low Rayleigh number convection in horizontal, eccentric annuli
Authors: Wang YuZhou , Bau Haim H.
Published: July 2002

Low Rayleigh number thermal convection in a Newtonian fluid confined between two horizontal, circular cylinders is studied analytically using a regular perturbation expansion. Both cylinders are impermeable and maintained at different, uniform temperatures. The line connecting the cylinders’ centers (referred to as the intracenter line) may be inclined at an arbitrary angle with respect to the gravity vector. When the intracenter line is parallel to the gravity vector, bicellular convection is observed in the annulus and the flow is symmetrical with respect to the intracenter line. When the intracenter line is inclined with respect to the gravity vector, the flow domain is doubly connected. The flow is asymmetrical vis-à-vis the intracenter line; and, in addition to the cellular convection, there is net circulation around the inner cylinder. This circulation consists of fluid ascending on one side of the inner cylinder and descending on the other.
Self-similar oscillations of a Z pinch bounded by a magnetic multipole
Authors: Tendler M.
Published: July 2002

A new analytic, self-similar solution of the fluid equations with losses in a stabilized Z pinch is presented. A scaling is suggested for the net energy loss with plasma density and temperature typical for a Z pinch immersed in an external multipole magnetic field. The solution of the strongly nonlinear system of fluid equations is obtained by self-similar methods. Strongly aharmonic high frequency oscillations of the plasma parameters are found. It is emphasized that a static Z pinch cannot be stabilized by a stationary field of a magnetic multipole. Therefore the potentiality of these oscillations to affect the stability of Z pinches embedded in a magnetic multipole is investigated. The effect of the dynamic stabilization is considered by taking estimates.
Potential and velocity measurements in a magnetized hollow cathode discharge by means of electric probes and laser induced fluorescence
Authors: Gräfen W. , Hoesslin M. v. , Kempkens H. , Uhlenbusch J.
Published: July 2002

By means of electric probes, surfaces of equal electrical potential are measured in the plasma of a magnetized hollow cathode arc burning in argon. At moderate distances between the cathode and the anode the potential increases nearly linearly in proceeding in the axial direction from the cathode to the anode. In the radial direction a potential growth can be observed up to a plateau regime near the plasma edge. If the cathode–anode distance exceeds a critical length, the situation changes insofar as a voltage jump of nearly a factor of 2 occurs near the anode where higher voltage values are reached than on the anode surface. There the voltage drops in the radial direction to the outside plateau value. This voltage distribution is produced by a (positive) anodic space charge cloud, which accelerates the electrons. The voltage jump guarantees the transport of the arc current even in the case of a long arc. This space charge decelerates the ions flying in the axial direction and creates the possibility of ions rotating around the cathode–anode axis in the anode regime. This latter possibility was examined by monitoring the frequency resolved Doppler shift of the argon ion line at λ=611.49 nm measured by laser induced scattering. The flow field of the ions can be quantitatively understood from the spatial distribution of the electrical potential.
Undulation of a magnetized electron beam by a periodic ion channel
Authors: Bosch R. A. , Gilgenbach R. M.
Published: July 2002

Electron-beam dynamics are calculated for an electron beam propagating parallel to a uniform magnetic field through a periodic ion density channel. Results show that resonant excitation of transverse electron oscillations occurs when the wavelength of the ion density variation equals the axial distance over which an electron cyclotron orbit occurs. This indicates that a periodic ion channel behaves as an electrostatic undulator with magnetoresonance. It is found that periodic ion densities of 1011–1012 cm−3 are required to achieve transverse electron velocities comparable to those of a typical magnetostatic undulator.
Lower hybrid suppression of drift waves in a plasma cylinder
Authors: Praburam G. , Tripathi V. K. , Jain V. K.
Published: July 2002

Drift waves in a cylindrical plasma column with an exponential density profile have a Bessel function mode structure and are linearly unstable because of finite Larmor radius effects. In the presence of a lower hybrid eigenmode pump, these modes suffer a nonlinear frequency upshift because of the ponderomotive force and tend to be stabilized when k0z>kz.
The effects of inertia and interfacial shear on film flow on a rotating disk
Authors: Rehg Timothy J. , Higgins Brian G.
Published: July 2002

In this paper the issue is addressed of how a liquid film of uniform thickness thins on a rotating disk because of the action of centrifugal force. The Navier–Stokes equations in self-similar form are solved numerically by a finite-difference method. The effects of film inertia, disk acceleration protocols, and interfacial shear are studied. The numerical results show that inertia has a marked influence on the rate of thinning when the Reynolds number is large and that existing asymptotic theories are inadequate for predicting the transient film thickness. When the disk has a finite acceleration at start-up, the effects of local inertia are important even at low Reynolds numbers and the thinning rate is reduced. When the overlying phase is a gas, interfacial shear enhances the rate of thinning at sufficiently long spinning times.
Effect of local property smearing on global variables: Implication for numerical simulations of multiphase flows
Authors: Haj-Hariri H. , Shi Q. , Borhan A.
Published: July 2002

This work addresses the sensitivity of a calculated global quantity to the smoothing of discontinuous variation of properties. The analysis is based on the very simple model problem of a fully developed, thermocapillary channel flow. The predictions of this simple model are shown to be in excellent agreement with the results for the Navier–Stokes simulations of the thermocapillary migration of a spherical drop. The main conclusion is that the migration velocity depends very strongly on the smearing of the driving interfacial force whereas it is rather insensitive to the smearing of the discontinuous viscosity distribution. This hints at the indispensability of grid adaption for modeling interfacial forces.