Showing papers on "Antisymmetric relation published in 1997"

Mechanics of laminated composite plates : theory and analysis

Abstract: Introduction and Mathematical Preliminaries Fiber-Reinforced Composite Materials. Vectors and Tensors. Matrices. Transformation of Vector and Tensor Components. Integral Relations. Equations of Anisotropic Elasticity Classification of Equations. Kinematics. Kinetics. Constitutive Equations. Equations of Thermoelasticity and Electroelasticity. Summary. Virtual Work Principles and Variational Methods Virtual Work. The Variational Operator and Functionals. Extrema of Functionals. Virtual Work Principles. Variational Methods. Summary. Introduction to Composite Materials Basic Concepts and Terminology. Constitutive Equations of a Lamina. Transformation of Stresses and Strains. Plane Stress Constitutive Relations. Classical and First-Order Theories of Laminated Composite Plates Introduction. An Overview of ESL Laminate Theories. The Classical Laminated Plate Theory. The First-Order Laminated Plate Theory. Stiffness Characteristics for Selected Laminates. One-Dimensional Analysis of Laminated Plates Introduction. Analysis of Laminated Beams Using CLPT. Analysis of Laminated Beams Using FSDT. Cylindrical Bending Using CLPT. Cylindrical Bending Using FSDT. Closing Remarks. Analysis of Specially Orthotropic Plates Using CLPT Introduction. Bending of Simply Supported Plates. Bending of Plates with Two Opposite Edges Simply Supported. Bending of Rectangular Plates with Various Boundary Conditions. Buckling of Simply Supported Plates Under Compressive Loads. Buckling of Rectangular Plates Under Inplane Shear Load. Vibration of Simply Supported Plates. Buckling and Vibration of Plates with Two Parallel Edges Simply Supported. Closure. Analytical Solutions of Rectangular Laminates Using CLPT Governing Equations in Terms of Displacements. Admissible Boundary Conditions for the Navier Solutions. Navier Solutions of Antisymmetric Cross-Ply Laminates. The Navier Solutions of Antisymmetric Angle-Ply Laminates. The LTvy Solutions. Analysis of Midplane Symmetric Laminates. Transient Analysis. Summary. Analytical Solutions of Rectangular Laminates Using FSDT Introduction. Simply Supported Antisymmetric Cross-Ply Laminates. Simply Supported Antisymmetric Angle-Ply Laminates. Antisymmetric Cross-Ply Laminates with Two Opposite Edges Simply Supported. Antisymmetric Angle-Ply Laminates with Two Opposite Edges Simply Supported. Transient Solutions. Summary. Finite Element Analysis of Composite Laminates Introduction. Laminated Beams and Plate Strips by CLPT. Timoshenko Beam/Plate Theory. Numerical Results for Beams and Plate Strips. Finite Element Models of Laminated Plates (CLPT). Finite Element Models of Laminated Plates (FSDT). Summary. Refined Theories of Laminated Composite Plates Introduction. A Third-Order Plate Theory. Higher-Order Laminate Stiffness Characteristics. The Navier Solutions. LTvy Solutions of Cross-Ply Laminates. Displacement Finite Element Model. Layerwise Theories and Variable Kinematic Models In troduction. Development of the Theory. Finite Element Model. Variable Kinematic Formulations. Nonlinear Analysis of Composite Laminates Introduction. Nonlinear Stiffness Coefficients. Solution Methods for Nonlinear Algebraic Equations. Computational Aspects and Numerical Examples. Closure. Index Most chapters include Exercises and References for Additional Reading

Thermodynamics and Rheology

Abstract: Introduction. I. Kinematics. II. Dynamics. III. Deformation and Stress. IV. Non-Equilibrium Thermodynamics. V. Thermodynamics of Deformation. Systems Close to Equilibrium. VI. Thermodynamics of Deformation. Systems Far From Equilibrium. VII. Electric Polarization in Flowing Media. VIII. Applications of the Theory. Appendix: A.1. The Basic Operations. A.2. Symmetric and Antisymmetric Tensors. A.3. Tensor Products. A.4. Eigenvalues and Invariants. A.5. Orthogonal Tensors. A.6. Isotropic Tensors. A.7. Derivatives. A.8. Integral Theorems. References.

Sigma-model for the generalized composite p-branes

Abstract: A multidimensional gravitational model containing several dilatonic scalar fields and antisymmetric forms is considered. The manifold is chosen in the formMDM0M1 Mn , where Mi are Einstein spaces (i> 1). The block-diagonal metric is chosen and all fields and scale factors of the metric are functions of M0. For the forms composite (electromagnetic) p-brane ansatz is adopted. The model is reduced to a gravitating self-interacting sigma- model with certain constraints. In the pure electric and magnetic cases the number of these constraints is n1.n1 1/=2 where n1 is the number of one-dimensional manifolds among Mi . In the 'electromagnetic' case for dim M0 D 1; 3 additional n1 constraints appear. A family of 'Majumdar-Papapetrou-type' solutions governed by a set of harmonic functions is obtained, when all factor-spacesM are Ricci-flat. These solutions are generalized to the case of non-Ricci- flat M0 when some additional 'internal' Einstein spaces of non-zero curvature are also added to M. As an example exact solutions for DD 11 supergravity and the related 12-dimensional theory are presented.

Explicit Fermionic Tree Expansions

Abstract: We express connected Fermionic Green's functions in terms of completely explicit tree formulas. In contrast with the ordinary formulation in terms of Feynman graphs these formulas allow a completely transparent proof of convergence of the perturbative series. Indeed they are compatible with the mathematical implementation in Grassmann integrals of the Pauli principle. The first formula we give, which is the most symmetric, is compatible with Gram's inequality. The second one, the "rooted formula", respects even better the antisymmetric structure of determinants, and allows the direct comparison of rows and columns in the fermionic determinant. To illustrate the power of these formulas, we provide a ``three lines proof'' that the radius of convergence of the Gross-Neveu field theory with cutoff is independent of the number of colors. An other potential area for applications would be the study of correlated Fermions systems and superconductivity.

The Reissner-Nordström problem for intersecting electric and magnetic p-branes.

Abstract: A multidimensional model with (at most) one curved factor space and n Ricci-flat internal spaces is considered, with arbitrary numbers of dilatonic scalar fields and antisymmetric forms of both electric and magnetic types, associated with p-branes in theories like M-theory. The problem setting covers, in particular, homogeneous cosmologies, static, spherically symmetric and Euclidean models. Exact solutions are obtained when the p-brane dimensions and the dilatonic couplings obey orthogonality conditions in minisuperspace. Conditions for black hole and wormhole existence among static models are formulated. For black holes, a kind of no-hair theorem, leading to F-form selection, is obtained; it is shown that even in spaces with multiple times a black hole may only exist with its unique, one-dimensional time; infinite Hawking temperature is explicitly shown to imply a curvature singularity at an assumed horizon, and such cases among extreme black-hole solutions are indicated.

Non-extremal Intersecting p-branes in Various Dimensions

Abstract: Non-extremal intersecting p-brane solutions of gravity coupled with several antisymmetric fields and dilatons in various space-time dimensions are constructed. The construction uses the same algebraic method of finding solutions as in the extremal case and a modified "no-force" conditions. We justify the "deformation" prescription. It is shown that the non-extremal intersecting p-brane solutions satisfy harmonic superposition rule and the intersections of non-extremal p-branes are specified by the same characteristic equations for the incidence matrices as for the extremal p-branes. We show that S-duality holds for non-extremal p-brane solutions. Generalized T-duality takes place under additional restrictions to the parameters of the theory which are the same as in the extremal case.

Antisymmetric rotation measures in our Galaxy: Evidence for an A0 dynamo

Abstract: Rotationmeasuresforextragalacticsources,afterse- lection to emphasize the large-scale structure of the Galactic magnetic eld, reveal a striking antisymmetric pattern about the Galactic plane and the meridian through the Galactic Cen- tre. This pattern is also observed in the rotation measures of pulsars with jbj > 8. The symmetry of the pattern, the magni- tudeoftherotationmeasuresandthedistancedependenceofthe pulsar rotation measures show that this pattern is not the result of local perturbations, but is on a large and possibly Galactic scale. This antisymmetric pattern and the existence of magnetic elds perpendicular to the plane in the Galactic Centre region, indicate that a dynamo mode of odd symmetry, possibly of A0 type, makes a substantial contribution to the magnetic elds in the thick disk and halo of our Galaxy, at least inside the Solar circle.

Block-orthogonal brane systems, black holes and wormholes.

Abstract: Multidimensional cosmological, static spherically symmetric and Euclidean configurations are described in a unified way for gravity interacting with several dilatonic fields and antisymmetric forms, associated with electric and magnetic p -branes. Exact solutions are obtained when certain vectors, built from the input parameters of the model, are either orthogonal in the minisuperspace, or form mutually orthogonal subsystems. Some properties of black hole solutions are indicated, in particular, a no-hair-type theorem and restrictions emerging in models with multiple times. From the non-existence of Lorentzian wormholes, a universal restriction is obtained, applicable to orthogonal or block-orthogonal subsystems of any p -brane systems. Euclidean wormhole solutions are found, their actions and radii are explicitly calculated.

Block-Orthogonal Brane Systems, Black Holes and Wormholes

Abstract: Multidimensional cosmological, static spherically symmetric and Euclidean configurations are described in a unified way for gravity interacting with several dilatonic fields and antisymmetric forms, associated with electric and magnetic p-branes. Exact solutions are obtained when certain vectors, built from the input parameters of the model, are either orthogonal in the minisuperspace, or form mutually orthogonal subsystems. Some properties of black-hole solutions are indicated, in particular, a no-hair-type theorem and restrictions emerging in models with multiple times. From the non-existence of Lorentzian wormholes, a universal restriction is obtained, applicable to orthogonal or block-orthogonal subsystems of any p-brane systems. Euclidean wormhole solutions are found, their actions and radii are explicitly calculated.

Integrable multidimensional cosmology for intersecting p-branes.

Abstract: A multidimensional field model describing the behaviour of (at most) one Einstein space of non-zero curvature and n Ricci-flat internal spaces is considered. The action contains several dilatonic scalar fields and antisymmetric forms. The problem setting covers various problems with field dependence on a single space-time coordinate, in particular, isotropic and anisotropic homogeneous cosmologies. When the forms are chosen to be proportional to volume forms of p-brane factor spaces, a Toda-like Lagrange representation arises. Exact solutions are obtained when the p-brane dimensions and the dilatonic couplings obey some orthogonality conditions. General features and some special cases of cosmological solutions are discussed. It is shown, in particular, that all hyperbolic models with a 3-dimensional external space possess an asymptotic with the external scale factor a(t) is proportional to |t| (the cosmic time), while all internal scale factors and all scalar fields tend to finite limits. For D=11 a family of models with one 5-brane and three 2-branes is described.

Marginally Trapped Surfaces in the Nonsymmetric Gravitational Theory

Abstract: We consider a simple, physical approach to the problem of marginally trapped surfaces in the Nonsymmetric Gravitational Theory (NGT). We apply this approach to a particular spherically symmetric, Wyman sector gravitational field, consisting of a pulse in the antisymmetric field variable. We demonstrate that marginally trapped surfaces do exist for this choice of initial data.

Schouten–Nijenhuis brackets

Abstract: The Poisson and graded Poisson Schouten–Nijenhuis algebras of symmetric and antisymmetric contravariant tensor fields, respectively, on an n-dimensional manifold M are shown to be n-symplectic. This is accomplished by showing that both brackets may be defined in a unified way using the n-symplectic structure on the bundle of linear frames LM of M. New results in n-symplectic geometry are presented and then used to give globally defined representations of the Hamiltonian operators defined by the Schouten–Nijenhuis brackets.

Surprises in Open-String Perturbation Theory

Abstract: The perturbative analysis of models of open and closed superstrings presents a number of surprises. For instance, variable numbers of antisymmetric tensors ensure their consistency via generalized Green-Schwarz cancellations and a novel type of singularity occurs in their moduli spaces. All these features are related, in one way or another, to the presence of boundaries on the world sheet or, equivalently, of extended objects (branes) interacting with the bulk theory in space time. String dualities have largely widened the interest in these models, that exhibit a wealth of generic non-perturbative features of String Theory.

Atomic Wave Function Forms

Abstract: Using variational Monte Carlo, we compare the features of 118 trial wave function forms for selected ground and excited states of helium, lithium, and beryllium in order to determine which characteristics give the most rapid convergence toward the exact nonrelativistic energy. We find that fully antisymmetric functions are more accurate than are those which use determinants, that exponential functions are more accurate than are linear function, and that the Pade function is anomalously ´ accurate for the two-electron atom. We also find that the asymptotic and nodal behavior of the atomic wave function is best described by a minimal set of functions. Q 1997 John Wiley & Sons, Inc. Int J Quant Chem 63: 1001)1022, 1997

Free totally (anti)symmetric massless fermionic fields in d-dimensional anti-de Sitter space

Abstract: Free massless fermionic fields of arbitrary spins s>0 corresponding to totally (anti)symmetric tensor - spinor representations of the SO(d-1) compact subgroup and in d-dimensional anti-de Sitter space are investigated. We propose the free equations of motion, subsidiary conditions and corresponding gauge transformations for such fields. The equations obtained are used to derive the lowest energy values for the above-mentioned representations. A new representation for equations of motion and gauge transformations in terms of generators of the anti-de Sitter group SO(d-1,2) is found. It is demonstrated that in contrast to the symmetric case the gauge parameter of the antisymmetric massless field is also a massless field.

p-brane solutions in diverse dimensions

Abstract: A generic Lagrangian, in arbitrary spacetime dimension, describing the interaction of a graviton, a dilaton, and two antisymmetric tensors is considered. An isotropic $p$-brane solution consisting of three blocks and depending on four parameters in the Lagrangian and two arbitrary harmonic functions is obtained. For specific values of parameters in the Lagrangian the solution may be identified with previously known superstring solutions.

Edge and strip plasmons in a two-dimensional electron fluid

Abstract: We study plasma oscillations in a bounded two-dimensional electron fluid. The use of a variational method allows a simple analysis of plasma modes in a strip of finite width. For the exactly solvable model that neglects the pressure gradient in a plasma confined to a semi-infinite plane a simple one-parameter variational function gives the edge plasmon frequency reasonably close to the exact value. In the case of the semi-infinite plane we also incorporate the effects of the pressure gradient in our variational solution. In a two-dimensional strip of finite width we find the symmetric and antisymmetric plasma modes of different frequencies. The method used here can be readily extended to include the effects of applied magnetic fields and different confinement geometries.

Transition between two oscillation modes

Abstract: A model for the symmetric coupling of two self-oscillators is presented. The nonlinearities cause the system to vibrate in two modes of different symmetries. The transition between these two regimes of oscillation can occur by two different scenarios. This might model the release of vortices behind circular cylinders with a possible transition from a symmetric to an antisymmetric B\'enard\char21{}von Karman vortex street.

Composite p-branes in various dimensions

Abstract: We review an algebraic method of finding the composite p-brane solutions for a generic Lagrangian, in arbitrary spacetime dimension, describing an interaction of a graviton, a dilaton and one or two antisymmetric tensors. We set the Fock-De Donder harmonic gauge for the metric and the “no-force” condition for the matter fields. Then equations for the antisymmetric field are reduced to the Laplace equation and the equation of motion for the dilaton and the Einstein equations for the metric are reduced to an algebraic equation. Solutions composed of n constituent p-branes with n independent harmonic functions are given. Relations with known solutions in D = 10 and D = 11 dimensions are discussed.

Average energy of an n-electron system in a finite-dimensional and spin-adapted model space

Abstract: An expression for the average energy of an N-electron system in a finite-dimensional, antisymmetric, and spin-adapted model space (as, e.g., a full-configuration interaction space) is derived using elementary properties of the Hamiltonian in the Fock space. © 1997 John Wiley & Sons, Inc.

Higher Dimensional Yang-Mills Theories and Topological Terms

Abstract: Higher dimensional generalisations of self-duality conditions and of theta angle terms are analysed in Yang-Mills theories. For the theory on a torus, the torus metric and various antisymmetric tensors are viewed as coupling constants related by U-duality, arising from background expectation values of supergravity fields for D-brane or matrix theories. At certain special points in the moduli space of coupling constants certain branes or instantons are found to dominate the functional integral. The possibility of lifting chiral or supersymmetric theories to higher dimensions is discussed.

Structure of the electromagnetic field in a slab of photonic crystal

Abstract: We simulate the s-polarized electromagnetic field diffracted by a truncated two-dimensional lattice. We observe strong decay of the transmittivity for frequencies lying in the gaps displayed by the dispersion relation of the infinite crystal and find regular oscillations outside these gaps. The structure of the field in the lattice is explained in terms of modes of its infinite counterpart. In particular, the oscillations are related to the resonance in the layer of propagating Bloch waves, just as in a Fabry–Perot interferometer. This interpretation enables us to retrieve the dispersion relation. Finally, we study the symmetry properties of the modes and show that for certain frequencies the transmissivity of the system is null under symmetric illumination but nonzero under antisymmetric lighting or vice versa.

On the Reality of Antisymmetric Stresses in Fast Granular Flows

Abstract: Starting from the virtual power expression for fast flow of dense assemblies of rough, slightly inelastic spheres, we derive expressions for the average stress tensor, momentum and angular momentum balances and corresponding variational boundary conditions. We show that the stress tensor can be decomposed into two parts with distinct physical significance. The first part can be interpreted as an area averaged stress tensor, which is nonsymmetric in general. The second part is obtained as the divergence of a third order tensor which can be interpreted as the difference between the area and the volume averages of the stress tensor. Accordingly, the stress tensor is symmetric for quasistatic flow.