Infinite Configurations Research Articles

Thermo-capillary convection in various infinite rectangular container configurations

The thermo-capillary behavior or a viscous liquid in rectangular container configuration has been investigated for various liquid height ratios h/l. Streamlines and velocity distributions have been presented. The effect of a partial rigid surface cover has also been determined. With the increase of the liquid height ratio more vortices develop and exhibit decreasing strength towards the bottom of the container. An obstruction of the free liquid surface moves the vortices in the direction of the free liquid surface, exhibiting decreased strengths.

5.6.2 Decision Making in Modular Product Platform Development

AbstractIn order to achieve larger market share and address individual customer needs, firms are challenged to manage the seemingly contradictory existence of internally low variety and a maximum external variety. One very powerful approach is to use modular product architectures (PA). This permits one to establish product families based on platforms.Using platforms is a common strategy in diverse industries. For development of platform architectures, there are almost infinite possible configurations. There is a need for a framework for evaluation and selection of possible concepts. By evaluating design concepts one is faced with decision‐making. To do this, one must make choices over a distinct evaluation method and effective metrics. In this choice, the quality of information is the limiting and determining factor, it is the differentiating characteristic among methods. To show this, diverse methods will be presented and their characteristics and benefits will be discussed.

Connections and Curvature in the Riemannian Geometry of Configuration Spaces

Torsion free connections and a notion of curvature are introduced on the infinite dimensional nonlinear configuration space Γ of a Riemannian manifold M under a Poisson measure. This allows us to state identities of Weitzenböck type and energy identities for anticipating stochastic integral operators. The one-dimensional Poisson case itself gives rise to a non-trivial geometry, a de Rham–Hodge–Kodaira operator, and a notion of Ricci tensor under the Poisson measure. The methods used in this paper have been thus far applied to d-dimensional Brownian path groups and rely on the introduction of a particular tangent bundle and associated damped gradient.

Representing Reversible Cellular Automata with Reversible Block Cellular Automata

Cellular automata are mappings over infinite lattices such that each cell is updated according tothe states around it and a unique local function.Block permutations are mappings that generalize a given permutation of blocks (finite arrays of fixed size) to a given partition of the lattice in blocks.We prove that any d-dimensional reversible cellular automaton can be exp ressed as thecomposition of d+1 block permutations.We built a simulation in linear time of reversible cellular automata by reversible block cellular automata (also known as partitioning CA and CA with the Margolus neighborhood) which is valid for both finite and infinite configurations. This proves a 1990 conjecture by Toffoli and Margolus <i>(Physica D 45)</i> improved by Kari in 1996 <i>(Mathematical System Theory 29)</i>.

Meron pairs and fermion zero modes

Merons, conjectured as a semiclassical mechanism for color confinement in QCD, have been described analytically by either infinite action configurations or an Ansatz with discontinuous action. We construct a smooth, finite action, stationary lattice solution corresponding to a meron pair. We also derive an analytical solution for the zero mode of the meron pair Ansatz, show that it has the qualitative behavior of the exact zero mode of the lattice solution, and propose the use of zero modes to identify meron gauge field configurations in stochastic evaluations of the lattice QCD path integral.

Experimental Investigation of Adaptive Control Applied to HSFD Supported Rotors

This paper describes the experimental application of adaptive control to Hybrid Squeeze Film Damper (HSFD) supported rotors. The HSFD has been shown to be an adaptive damper capable of providing infinite damper configurations between short and long damper configurations. Previously, theoretical investigations of the adaptive control of HSFD concentrated on the development of the model reference adaptive control (MRAC) method, as well as development of a nonlinear reference model. Simulations of the performance of the adaptive controller during run-up and coast-down indicated the superior performance of the adaptive controller. In this paper, the adaptive controller is tested on a multi-mode rotor. A test rig is designed and developed using computer control. A simple reference model is investigated consisting of a second order system. Three forms for adaptation gain are studied. The results of the experimental investigation illustrated the performance capabilities of the adaptive controller applied to the HSFD, and moreover indicated the possibility of simple design for the adaptive controller. [S0742-4795(00)01603-3]

A truncated Floquet wave diffraction method for the full wave analysis of large phased arrays. I. Basic principles and 2-D cases

This two-part sequence deals with the formulation of an efficient method for the full wave analysis of large phased array antennas. This is based on the method of moments (MoM) solution of a fringe integral equation (IE) in which the unknown function is the difference between the exact solution of the finite array and that of the associated infinite array. The unknown currents can be interpreted as produced by the field diffracted at the array edge, which is excited by the Floquet waves (FWs) pertinent to the infinite configuration. Following this physical interpretation, the unknown in the IE is efficiently represented by a very small number of basis functions with domain on the entire array aperture. In order to illustrate the basic concepts, the first part of this sequence deals with the two-dimensional example of a linearly phased slit array. It is shown that the dominant phenomenon fur describing the current perturbation with respect to the infinite array is accurately represented in most cases by only three diffracted-ray-shaped unknown functions. This also permits a simple interpretation of the element-by-element current oscillation, which was described by other authors.

Slot jet impingement heat transfer from circular cylinders

The heat transfer characteristics of circular cylinders exposed to slot jet impingement of air has been studied experimentally. The study focused on Reynolds numbers (based on nozzle average exit velocity and cylinder diameter) in the range 600–8000. Both contoured orifice and sharp-edged orifice jet configurations were investigated for cylinder diameter-to-jet width spacings of 0.66, 1.0 and 2.0, and for jet exit-to-nozzle width spacings in the range 1< z/ w<11. Reference measurements were made with the same cylinder in infinite parallel flow in a wind tunnel. The results reveal that the slot jet yields considerably higher average heat transfer from the cylinder when compared to the infinite parallel flow case on the basis of identical average velocity in the slot jet and infinite flow configurations. As with slot jet impingement heat transfer from flat surfaces, there appears to be a nozzle-to-cylinder spacing, scaled by nozzle width, which exhibits a maximum in heat transfer. The average heat transfer characteristics of the cylinder are correlated empirically.

Exact results for deterministic cellular automata traffic models

We present a rigorous derivation of the flow at arbitrary time in a deterministic cellular automaton model of traffic flow. The derivation employs regularities in preimages of blocks of zeros, reducing the problem of preimage enumeration to a well-known lattice path counting problem. Assuming infinite lattice size and random initial configuration, the flow can be expressed in terms of generalized hypergeometric function. We show that the steady-state limit agrees with previously published results.

Order by thermal disorder in 2D planar rotator model with dipolar interactions

The energy of a square planar rotator model of spins interacting via dipolar forces is minimized by infinite inequivalent configurations corresponding to spins arranged on four interpenetrating sublattices making angles , with a reference axis, being arbitrary. This infinite degeneracy of the ground state is accidental in nature and one expects that it is removed by thermal fluctuations in agreement with Monte Carlo simulation. Indeed we find that the elementary excitation energies which depend on lead to a free energy which is a function of with minima at and corresponding to columnar configurations. This selection of columnar configurations out of the infinite ground state manifold is an example of order by thermal disorder.

Syntheses and crystal structures of cdta ( trans-cyclohexane-1,2-diamine– N, N, N′, N′-tetra-acetate)-based copper(II) dimers and polymers

Four cdta ( trans-cyclohexane-1,2-diamine– N, N, N′, N′-tetra-acetate)-based copper(II) compounds, [(H 2cdta)Cu(4,4′-bpy)Cu(H 2cdta)]·4,4′-bpy·2H 2O ( 1), [(H 2cdta)Cu(pyz)–Cu(H 2cdta)]·14H 2O ( 2), [Cu(cdta)Cu(H 2O) 3(4,4′-bpy)] n ·8 nH 2O ( 3) and [{Cu(cdta)(H 2O) 2} 2–(pyz)] n ·4 nH 2O ( 4), were obtained from a Cu 2+–diimine–cdta system (4,4′-bpy=4,4′-bipyridine and pyz=pyrazine). The X-ray crystallography analysis shows that 1 and 2 are diimine-bridged dimers, 3 has an infinite zigzag configuration and 4 contains a `step ladder'-like structure.

Dirichlet forms and Dirichlet operators for infinite particle systems: Essential self-adjointness

We study the Dirichlet forms and the associated Dirichlet operators for Gibbs measures on infinite particle configuration space. The Dirichlet forms are defined to be “gradient-type” forms by introducing a measurable field of rigged Hilbert spaces on the configuration space. Under mild conditions on the interaction including singular potentials, we show that the pre-Dirichlet operator is symmetric and that the closure of the pre-Dirichlet form satisfies the Markovian property. When the interaction is three times differentiable and decreasing sub-exponentially, we show that the Dirichlet operator is essentially self-adjoint on a domain consisting of bounded smooth local functions.

Elastic neutron scattering and rhombohedral antiferromagnets

Infinite isoenergetic helix spin configurations minimize the energy of the classical Heisenberg rhombohedral antiferromagnet with nearest neighbor interactions. We comment about elastic neutron scattering data on ACrO2 (A=Cu, Ag, Pd) compounds which seem to support the degenerate helix scenario modified by quantum fluctuations in agreement with the theoretical expectation. We investigate by a microscopic approach the existence of static short range order in β-oxygen as suggested on the basis of recent elastic neutron scattering experiment.

SEIBERG-WITTEN-FLOER HOMOLOGY AND HEEGAARD SPLITTINGS

The dimensional reduction of Seiberg-Witten theory defines a gauge theory of compact connected three-manifolds. Solutions of the equations modulo gauge symmetries on a three-manifold Y can be interpreted as the critical points of a functional defined on an infinite dimensional configuration space of U(1)-connections and spinors. The original Seiberg-Witten equations on the infinite cylinder Y × IR are the downward gradient flow of the functional. Thus, it is possible to construct an infinite dimensional Morse theory. The associated Morse homology is the analogue in the context of Seiberg-Witten theory of Floer’s instanton homology constructed using Yang-Mills gauge theory. The construction and the properties of this Seiberg-Witten Floer homology are essentially different according to whether the three-manifold Y is a homology sphere or has non-trivial rational homology. In this work we construct the Seiberg-Witten Floer homology for three-manifolds with b^1(Y ) > 0. We define an associated Casson-like invariant and we prove that it satisfies the expected intersection formula under a Heegaard splitting of the three-manifold.

Quantum fluctuations in antiferromagnets of the BX2 family (abstract)

The hexagonal antiferromagnets of the BX2 family, where B is a magnetic ion, and X a halogen, are characterized by an in plane exchange interaction J much stronger than the exchange interaction J′ along the c axis, so that some features of the triangular antiferromagnet (TA) could survive in these real compounds. In particular we are interested to investigate a possible ‘‘planar’’ phase with the spins lying in the c plane supported by quantum fluctuations when an external magnetic field H is applied perpendicular to the c axis. We find that such a phase is stable for sufficiently small interplane coupling owing to the zero point motion energy, whereas an ‘‘umbrella’’ phase would be expected on the basis of the classical approximation for any nonzero interplane coupling. Notice that for the TA model the planar and umbrella configurations are degenerate in classical approximation for any H and infinite isoenergetic planar configurations exist. Quantum fluctuations select a planar configuration with a spin over three opposite to the field. We find that the classical scenario itself is substantially different for any j=J′/J≠0, because only a planar configuration with a spin over three nearly perpendicular to the field and the umbrella configuration minimize the energy of the model and the umbrella is stable. However, quantum fluctuations stabilize the planar configuration for any H below a critical interplane coupling j*. For intermediate j the planar configuration is stable for low and high fields, whereas only the umbrella phase is stable of j large enough.

Cellular automata with almost periodic initial conditions

Cellular automata are dynamical systems on the compact metric space of subshifts. They leave many classes of subshifts invariant. Here we show that cellular automata leave 'circle subshifts' invariant. These are the strictly ergodic subshifts of (0,1)(Zd) obtained by a circle sequence xn=1J(n. alpha ) where J is a finite union of half-open intervals. For such initial conditions, the evolution of the whole infinite configuration can be computed by evolving the finitely many parameters defining the set J. Moreover, many macroscopic quantities can be computed exactly for the infinite system. We illustrate that in one dimension by rule 18 and in two dimensions by the Game of Life. The ideas also apply to cellular automata acting on (0, ..., N-1)(Zd). This we illustrate by the HPP model, a lattice gas automaton with N=16.

Finite-volume statistical mechanics of two-component Coulomb-like systems and the principle of macroscopic equivalence

Classical stable charge-symmetric two-component systems are discussed in a fixed domainΛ⊂ℝd. The limitN→∞ of the finite-N canonical Gibbs ensemble is compared with the results obtained from a discussion of the Gibbs measures on the space of infinite configurations (the states). A first-order phase transition in the Gibbs states is proved for a large class of interactions, including regularized Coulomb interactions ford≧3. In the latter case the transition is isomorphic to an implosion/explosion transition in regularized gravitational systems. Spherical symmetry is not assumed. A transition occurs for certain largedomain/low-temperature pairs (Λ,β∓1), but ceases to exist in the infinite-volume ensemble. The phase transition supports the conjecture that the standard thermodynamic-limit sequence can be nonuniform even for standardH-stable Hamiltonians. The results about the limit of the finite-N ensemble are less complete due to lack of sufficient control of the correlations. However, some notable differences between both descriptions are shown, which are cuased by noncommuting limits. Possible physical consequences and open questions are pointed out.

Boundary integral equation using a three-dimensional thick-plate fundamental solution

The fundamental solution of a Green's function for a point-load acting in the interior of an unbounded, homogeneous, isotropic, thick layer is used in connection with the boundary integral equations technique in order to obtain a formulation for the stress and displacement fields concerning three-dimensional plate problems with traction-free surfaces. This new formulation is based on the Green's function obtained by the author and defined in Appendix A. The formulation may analogously be applied to other three-dimensional cracked finite or infinite configurations.

Frustration and zero-point motion in Heisenberg body-centred tetragonal antiferromagnets

Body-centred tetragonal (BCT) antiferromagnets are a central topic of both theoretical and experimental research. The Heisenberg BCT antiferromagnet shows full frustration induced by the lattice structure for all physically meaningful values of the exchange parameters. A previous analysis of the minimum-energy configuration indicated full frustration only if no coupling between next-nearest-neighbour planes is present. However, the analysis was restricted to a classical helix configuration whereas infinite non-helical configurations characterized by an arbitrary angle between the spin at the centre and the spins at the corner minimize the classical energy of the model in a substantial part of the parameter space. In any case the relevance of quantum fluctuations in solving the infinite degeneracy is confirmed. The first quantum correction to the magnon energy spectrum is shown to lift the degeneracy of the soft lines which are present in the classical approximation.

Formal languages and global cellular automaton behavior

A connection is made between the description of one-dimensional cellular automata as dynamical systems acting on a compact metric space, and as computational systems acting on strings. Operators are defined which determine a bijective correspondence between subshifts of infinite configurations and languages of finite strings. Under this correspondence, families of languages give rise to families of subshifts. Regular languages correspond to sofic subshifts. Families of subshifts corresponding to context-free, context-sensitive, and recursively enumerable languages are introduced and their closure properties under forward and backward cellular automaton images studied.