bluuebunny/crossref_metadata_2025 huggingface dataset:
CALCULATION OF THE K-MESON FORM FACTOR BY MEANS OF THE PRINCIPAL VALUE METHOD
Authors: AGAEV SHAHIN S.
Published: November 2004

The K-meson electromagnetic form factor FK(Q2) is calculated by using the principal value method, which allows one to regulate endpoint ir singularities of QCD running coupling constant αS(Q2xy) (αS(Q2(1−x)(1−y))) in the soft x→0, y→0(x→1, y→1) region by expressing it in terms of the αS(Q2). In calculations the K-meson sum rules wave function is used.
BI-HAMILTONIAN STRUCTURE OF THE SUPERSYMMETRIC NONLINEAR SCHRÖDINGER EQUATION
Authors: BRUNELLI J.C. , DAS ASHOK
Published: November 2004

We show that the supersymmetric nonlinear Schrödinger equation is a bi-Hamiltonian integrable system. We obtain the two Hamiltonian structures of the theory from the ones of the supersymmetric two-boson hierarchy through a field redefinition. We also show how the two Hamiltonian structures of the supersymmetric KdV equation can also be derived from a Hamiltonian reduction of the supersymmetric two-boson hierarchy.
ASYMPTOTIC SYMMETRY GROUPS OF LONG-RANGED GAUGE CONFIGURATIONS
Authors: GIULINI DOMENICO
Published: November 2004

We make some general remarks on long-ranged configurations in gauge or diffeomorphism invariant theories where the fields are allowed to assume some nonvanishing values at spatial infinity. In this case the Gauss constraint only eliminates those gauge degrees of freedom which lie in the connected component of asymptotically trivial gauge transformations. This implies that proper physical symmetries arise either from gauge transformations that reach to infinity or those that are asymptotically trivial but do not lie in the connected component of transformations within that class. The latter transformations form a discrete subgroup of all symmetries whose position in the ambient group has proven to have interesting implications. We explain this for the dyon configuration in the SO(3) Yang-Mills-Higgs theory, where we prove that the asymptotic symmetry group is Z|m|×ℝ where m is the monopole number. We also discuss the application of the general setting to general relativity and show that here the only implication of discrete symmetries for the continuous part is a possible extension of the rotation group SO(3) to SU(2).
ON HIGHER DERIVATIVE DILATONIC GRAVITY IN TWO DIMENSIONS
Authors: NAFTULIN S. , ODINTSOV S.D.
Published: November 2004

We discuss lowering the order of the two-dimensional scalar-tensor R2 quantum gravity, by mapping the most general version of the model to a multi-dilaton gravity, which is essentially the sigma-model coupled with the Jackiw-Teitelboim-like gravity. In the continuation of our previous research, we calculate the divergent part of the one-loop effective action in a 2-D scalar-tensor (dilatonic) gravity with the R2-term, which belongs to a specific degenerate case and cannot be obtained from the general expression. The corresponding finiteness conditions are found.
STRONG COUPLING AND THE COSMOLOGICAL CONSTANT
Authors: WITTEN EDWARD
Published: November 2004

The vanishing of the cosmological constant and the absence of a massless dilaton might be explained by a duality between a supersymmetric string vacuum in three dimensions and a nonsupersymmetric string vacuum in four dimensions.
ON THE REALIZATION OF THE DEFORMED CENTERLESS VIRASORO ALGEBRA ON THE QUANTUM PLANE
Authors: EL HASSOUNI A. , HASSOUNI Y. , TAHRI E.H. , ZAKKARI M.
Published: November 2004

By using two types of differential structures on the quantum plane, we give two different ways to realize the deformed centerless Virasoro algebra.
PERTURBING CONFORMAL TURBULENCE
Authors: COCEAL OMDUTH , THOMAS STEVEN
Published: November 2004

We consider perturbations of the nonunitary minimal model solutions of two-dimensional conformal turbulence proposed by Polyakov. Demanding the absence of nonintegrable singularities in the resulting theories leads to constraints on the dimension of the perturbing operator. We give some general solutions of these constraints, illustrating with examples of specific models. We also examine the effect of such perturbations on the Hopf equation and derive the interesting result that the latter is invariant under a certain class of perturbations, to first-order in perturbation theory, examples of which are given in specific cases.
PHASE-INTEGRAL APPROACH TO THE WAVE EQUATION OF THE UNIVERSE
Authors: DALARSSON NILS
Published: November 2004

We apply the phase-integral method to the Wheeler-DeWitt equation in a closed Friedmann-Robertson-Walker (FRW) model for the simple minisuperspace, where the only degree of freedom is that of the scale factor R of the closed homogeneous and isotropic universe, in which the vacuum energy density is provided by a homogeneous massive scalar field ϕ, with all its degrees of freedom “frozen-out”. We calculate the wave function of the universe and the tunneling probability for the universe to make the transition from R=0 to the transition point R=R0, up to the fifth-order of phase-integral approximation. Thus we show that the phase-integral method provides a tool for the more systematic and accurate treatment of the wave equation of the universe and includes the first-order JWKB results obtained by Hartle and Hawking as the special case.
CONFINEMENT, QUARK MATTER EQUATION OF STATE AND HYBRID STARS
Authors: KHADKIKAR S.B. , MISHRA A. , MISHRA H.
Published: November 2004

We consider here quark matter equation of state in a relativistic harmonic confinement model at zero temperature. The same is considered to study phase transition of neutron matter to quark matter at high densities. This, along with a phenomenological equation of state in the neutron matter sector is used to study hybrid stars. Using Tolman-Oppenheimer-Volkoff equations, stable solutions for hybrid stars are obtained with a maximum mass of 1.98 Mʘ and radii around 10 km with a quark core of about 1 to 2 km.
POISSON LIE GROUPS AND THE MIURA TRANSFORMATION
Authors: FIGUEROA-O’FARRILL JOSÉ M. , STANCIU SONIA
Published: November 2004

We point out that the recent proof of the Kupershmidt-Wilson theorem by Cheng and Mas-Ramos is underpinned by the Poisson Lie property of the second Gel’fand-Dickey bracket. The supersymmetric Kupershmidt-Wilson theorem is also proved along the same lines.
RELAXATION MECHANISMS: FROM STRING MODULI TO AXIONS
Authors: VAYONAKIS C.E.
Published: November 2004

The relaxation mechanism of Damour-Polyakov for fixing the vacuum expectation value of certain scalar fields (moduli) in string theory could provide a convenient framework for the Peccei- Quinn relaxation mechanism and remove the narrow “axion window”.
LIMITING TEMPERATURE, LIMITING CURVATURE AND THE CYCLIC UNIVERSE
Authors: FUKUMA MASAFUMI , KAWAI HIKARU , NINOMIYA MASAO
Published: November 2004

We propose a new type of cosmological model in which it is postulated that not only the temperature but also the curvature is limited by the mass scale of the Hagedorn temperature. We find that the big bang of this universe is smoothly connected to the big crunch of the previous universe through a Hagedorn universe, in which the temperature and curvature remain very close to their limiting values. In this way, we obtain the picture of a cyclic universe. By estimating the entropy gained in each big crunch and big bang, we reach the conclusion that our universe has repeated this process about forty times after it was created at the Planck scale. We also show that the model gives a scale-invariant spectrum of curvature perturbations.
SUPERCONDUCTIVITY IN FERROMAGNETIC METALS AND IN COMPOUNDS WITHOUT INVERSION CENTRE
Authors: MINEEV V. P.
Published: November 2004

The symmetry properties and the general overview of the superconductivity theory in the itinerant ferromagnets and in materials without space parity are presented. The basic notions of unconventional superconductivity are introduced in broad context of multiband superconductivity which is an inherent property of ferromagnetic metals or metals without centre of inversion.
BATH PARAMETER DEPENDENCE OF CHEMICALLY-DEPOSITED COPPER SELENIDE THIN FILM
Authors: AL-MAMUN  , ISLAM A. B. M. O.
Published: November 2004

In this article, a low cost chemical bath deposition (CBD) technique has been used for the preparation of Cu 2-x Se thin films on to glass substrate. Different thin films (0.2–0.6 μm) were prepared by adjusting the bath parameter like concentration of ammonia, deposition time, temperature of the solution, and the ratios of the mixing composition between copper and selenium in the reaction bath. From these studies, it reveals that at low concentration of ammonia or TEA, the terminal thicknesses of the films are less, which gradually increases with the increase of concentrations and then drop down at still higher concentrations. It has been found that complexing the Cu 2+ ions with TEA first, and then addition of ammonia yields better results than the reverse process. The film thickness increases with the decrease of value x of Cu 2-x Se .
A DYNAMICAL SYSTEMS APPROACH TO MEMBRANE PHENOMENA UNDERLYING CARDIAC ARRHYTHMIAS
Authors: KLINE RICHARD P. , BAKER B. MITCHELL
Published: November 2004

A model is constructed for cardiac rhythmic response to stimulation via a family of continuous time dynamical systems. Starting with experimentally observed properties common to the kinetics of both repolarizing membrane currents and cardiac action potential responses to sudden changes in cycle length, extremely elementary dynamical assumptions are made concerning current activation and decay, and repolarization threshold. A two-parameter family of one-dimensional dynamical systems emerges. The resulting systems are analytically tractable in considerable detail generating restitution curves, bifurcation schemes, rhythmic responses and chaotic behavior for a representative cardiac cell. The excellent qualitative and quantitative agreement with experimental data reported for several cardiac preparations is discussed. The two-dimensional analog produces unexpected basin behavior which could be of clinical significance in explaining how a single extra beat or a pause could alter subsequent action potential behavior and cause dispersion of refractoriness across the ventricle increasing the risks for arrhythmias. By having a manageable number of parameters, analytically defined patterns of behavior, and computational ease, this dynamical system has the potential to be used in computer simulations to study the effects of antiarrhythmic drugs on complex two- and three-dimensional reentrant substrates, or used on line by an interactive pacemaker.
ROUTE TO CHAOS VIA INVERSE CASCADE OF CONTINUOUS BIFURCATIONS
Authors: GUTMAN M. , GONTAR V.
Published: November 2004

A route to chaos via an inverse cascade of continuous bifurcations that arithmetically reduce the period of successive orbits has been obtained for piecewise continuous one-dimensional maps. We have studied the mechanism of these bifurcations and established that their scaling behavior is governed by constants with new universal properties. The possibility of obtaining discontinuous bifurcation from any selected orbit of a cascade of period-doubling to any orbit of inverse cascade has been demonstrated.
CHAOTIC MIXING IN RIGID, PERFECTLY PLASTIC MATERIAL
Authors: FEENY B.F. , MOON F.C. , CHEN P.Y. , MUKHERJEE S.
Published: November 2004

An example of Lagrangian chaos or mixing in a solid material is presented here. The mixing due to cyclic torques of rigid, perfectly plastic sheet is simulated. The plastic flow results in an area-preserving map. Results are displayed as Poincaré maps, the stretching and folding of an initial line of material points, the mixing of initial regions, and the eigenvalues about initial points during one mixing cycle. The Poincaré sections show iterates of sets of points after each cycle of deformation. The mixing diagrams provide evidence for horseshoe-like processes in the dynamics. Single-cycle eigenvalues exhibit self similarity in the spatial structure.
A SIMPLE TEST FOR HIDDEN PERIODICITY IN TIME SERIES DATA
Authors: ROSENBLUM MICHAEL , KURTHS JÜRGEN
Published: November 2004

We would like to draw the attention of specialists in time series analysis to a simple but efficient algorithm for the determination of hidden periodic regimes in complex time series. The algorithm is stable towards additive noise and allows one to detect periodicity even if the examined data set contains only a few periods. In such cases it is more suitable than other techniques, such as spectral analysis or recurrence map. We recommend the use of this test prior to the evaluation of attractor dimensions and other dynamical characteristics from experimental data.
ROTATION VECTORS FOR TORAL MAPS AND FLOWS: A TUTORIAL
Authors: WALSH JAMES A.
Published: November 2004

This paper is an introduction to the concept of rotation vector defined for maps and flows on the m-torus. The rotation vector plays an important role in understanding mode locking and chaos in dissipative dynamical systems, and in understanding the transition from quasiperiodic motion on attracting invariant tori in phase space to chaotic behavior on strange attractors. Throughout this article the connection between the rotation vector and the dynamics of the map or flow is emphasized. We begin with a brief introduction to the dimension one setting, in which case the rotation vector reduces to the well known rotation number of H. Poincaré. A survey of the main results concerning the rotation number and bifurcations of circle maps is presented. The various definitions of rotation vector in the higher dimensional setting are then introduced with emphasis again placed on how certain properties of the rotation set relate to the dynamics of the map or flow. The dramatic differences between results in dimension two and results in higher dimensions are also presented. The tutorial concludes with a brief introduction to extensions of the concept of rotation vector to the setting of dynamical systems defined on surfaces of higher genus.
CHAOTIC RAMSEY EQUILIBRIUM
Authors: SORGER GERHARD
Published: November 2004

We consider an economy in which a single commodity is produced by a large number of competitive firms. The economy is inhabited by a finite number of heterogeneous and infinitely lived agents who supply the factor inputs labor and capital to the firms and use the resulting factor income to finance their consumption. Their objective is to maximize the discounted stream of utility derived from consumption subject to the constraint that their wealth is non-negative at each point in time. We derive a system of two difference equations that describes the dynamic evolution of capital stocks and show by means of a robust example that this system can have a snap-back repeller and, consequently, can generate chaotic dynamics.
MAP DYNAMICS OF REPRODUCTION
Authors: PHILLIPSON PAUL E. , SCHUSTER PETER
Published: November 2004

One-dimensional return maps characterized by one critical point produce a universal sequence of periodic orbits, the Metropolis, Stein & Stein (MSS) sequence. Iterates of such maps can be regarded as an object whose structure is defined by the MSS sequence. The two critical point mapping [Formula: see text] as the control parameter b varies between [Formula: see text] and 1 is shown to display evolution from a single MSS structure to two identical MSS structures, suggestive of reproduction. The process of reproduction connotes a causal relationship whereby an original structure provides the blueprint for a copy. Here causality is replaced by an omniscient instruction, the mapping, and reproduction is achieved by progressively changing the instruction through variation of the control parameter. Bistability plays a crucial role in map dynamics of reproduction, which is viewed as a holistic process providing an alternative mechanism to digital replication.
MIXING STUDIES USING HORSESHOES
Authors: CHAKRAVARTHY V.S. , OTTINO J.M.
Published: November 2004

The ability to recognize and classify horseshoe generated structures is important in mixing problems. In this paper, we develop techniques to study higher iterations of horseshoe maps, by exploiting a method for representing them in a convenient mathematical notation. We show how to keep track of mixing of various blob segments over a number of iterations. Multiple iterations are investigated and an algorithm is developed in order to compute the higher iterations of the original horseshoe. Using similar ideas we present a method to keep track of thicknesses of the various blob striations. In a chaotic flow, complicated patterns can develop due to rapid stretching and folding. The tools developed in this paper would help determine the underlying cause of these patterns, i.e., identify the generating horseshoe.
CONTROLLING AND SYNCHRONIZATION OF CHAOS IN THE SIMPLEST DISSIPATIVE NON-AUTONOMOUS CIRCUIT
Authors: MURALI K. , LAKSHMANAN M. , CHUA L.O.
Published: November 2004

Several recent studies have focussed on the feasibility of controlling and synchronization of chaotic systems. Recently we have proposed a very simple nonlinear chaotic circuit consisting of only three linear circuit elements and a Chua’s diode. This paper examines a simple way of controlling chaos in this nonlinear electronic circuit both experimentally and numerically. Also, synchronization of chaos in this circuit has been studied numerically.
DIRECTING ORBITS OF CHAOTIC DYNAMICAL SYSTEMS
Authors: PASKOTA M. , MEES A.I. , TEO K.L.
Published: November 2004

In this paper, we consider the directing of orbits of discrete chaotic dynamical systems towards desired targets. Our aim is to significantly reduce the time needed to reach a target region by applying only small, bounded perturbations. We derive an open-loop control from methods of optimal control theory, and we discuss the effects of random dynamical noise on the open-loop control.
BIFURCATIONS OF ATTRACTING CYCLES FROM TIME-DELAYED CHUA’S CIRCUIT
Authors: MAISTRENKO Yu. L. , MAISTRENKO V.L. , VIKUL S.I. , CHUA L.O.
Published: November 2004

We study the bifurcations of attracting cycles for a three-segment (bimodal) piecewise-linear continuous one-dimensional map. Exact formulas for the regions of periodicity of any rational rotation number (Arnold’s tongues) are obtained in the associated three-dimensional parameter space. It is shown that the destruction of any Arnold’s tongue is a result of a border-collision bifurcation, and is followed by the appearance of a cycle of intervals with the same rotation number, whose dynamics is determined by a skew tent map. Finally, for the interval cycle the merging bifurcation corresponds to a homoclinic bifurcation of some point cycle.
BIFURCATION AND CHAOS IN ITERATED MAPS WITH O(2) SYMMETRY
Authors: ASTON P.J.
Published: November 2004

Iterated maps with O(2) symmetry are considered with a view to understanding transitions which occur as a parameter is varied. Bifurcations from the trivial solution are first considered followed by secondary bifurcations from nontrivial solutions. This is achieved by the derivation of a new system of equations in the orbit space. A transition in which a symmetric chaotic attractor starts drifting round the group orbit is also considered and it is shown that a single antisymmetric Lyapunov exponent determines whether or not a symmetric attractor is stable to nonsymmetric perturbations.
BIFURCATION SETS AND DISTRIBUTIONS OF LIMIT CYCLES IN A HAMILTONIAN SYSTEM APPROACHING THE PRINCIPAL DEFORMATION OF A Z4-FIELD
Authors: LIU ZHENGRONG , HU BAMBI , LI JIBIN
Published: November 2004

We consider a perturbed Hamiltonian system approaching the principal deformation of a Z4-equivariant principal singular field. By studying global and local bifurcations of this system, nine limit cycles with the distribution [Formula: see text] and five limit cycles with the II′jasenko distribution [Formula: see text] are found. Explicit formulas for the bifurcation sets and their phase portraits have also been obtained.
ON GEOMETRICAL PROPERTIES OF TWO-DIMENSIONAL DIFFEOMORPHISMS WITH HOMOCLINIC TANGENCIES
Authors: GONCHENKO S.V. , SHIL’NIKOV L.P.
Published: November 2004

Two-dimensional diffeomorphisms with a quadratic tangency of invariant manifolds of a saddle fixed point are considered in the cases where the saddle value σ is either less than 1 or equal to it. A description of the structure of hyperbolic subsets is given. In the case σ=1, it is shown that almost all such diffeomorphisms admit the complete description in distinction with the case σ<1.
FURTHER RESULTS ON THE EVOLUTION OF SOLITARY WAVES AND THEIR BOUND STATES OF A DISSIPATIVE KORTEWEG-DE VRIES EQUATION
Authors: VELARDE MANUEL G. , NEKORKIN VLADIMIR I. , MAKSIMOV ANDREY G.
Published: November 2004

Numerical evidence is provided of (long lasting) solitary waves (traveling localized dissipative structures) and their bound states as well as periodic and “chaotic”, erratic wave trains of a dissipation-modified Korteweg-de Vries equation originally derived to account for long wavelength oscillatory Bénard-Marangoni convection.
MAPS, PDE'S AND SOLITARY WAVES
Authors: SHINBROT TROY , OTTINO J. M.
Published: November 2004

We describe a map-based model which reproduces many of the behaviors seen in partial differential equations (PDE's). Like PDE's, we show that this model can support an infinite number of stationary solutions, traveling solutions, breathing solutions, and elastically colliding solutions. Unlike PDE's, the model can be applied with minimal computational machinery, and few sources of numerical error. Moreover, this model clarifies possible mechanisms by which various coherent solutions are maintained in the face of diffusion.
ON A CLASS OF FRACTAL MATRICES III: LIMIT STRUCTURES AND HIERARCHICAL ITERATED FUNCTION SYSTEMS
Authors: BARBÉ ANDRÉ M.
Published: November 2004

Fractrices (fractal matrices, excess-matrices) were defined in an earlier paper, Part I, as a special class of integer matrices with multifractal features. In contrast with Part II where a quantitative analysis of these objects was performed from a finitist constructivist point of view, the present Part III discusses the corresponding genuine limit fractal version. First this is done by a standard limit analysis which eventually leads to a (nonstandard) hyperreal-number view on this limit. Then a related hierarchical iterated function system is constructed whose attractor is the very same limit. This limit is either a hierarchical Zeno or Cantor set, or a space filling set. Its fractal dimension function is investigated.
GEOMETRY OF TARGETING OF CHAOTIC SYSTEMS
Authors: PASKOTA M. , MEES A. I. , TEO K. L.
Published: November 2004

In this paper, we analyze the geometry of directing of orbits of chaotic dynamical systems. The geometric approach enables us to interpret the obtained results so as to complement some of the existing ideas about minimum-time targeting. The analysis is illustrated by an example.
UNIVERSAL PHENOMENA IN SOME INFINITE-DIMENSIONAL DYNAMICAL SYSTEMS
Authors: SHARKOVSKY A. N.
Published: November 2004

Qualitative and quantitative "universalities" known for one-dimensional dynamical systems are transferred to some infinite-dimensional dynamical systems given by difference and differential-difference equations, and also by boundary value problems for equations with partial derivatives.
ON TOPOLOGICAL DYNAMICS OF SEQUENCES OF CONTINUOUS MAPS
Authors: KOLYADA SERGIĬ , SNOHA LUBOMÍR
Published: November 2004

We define and study ω-limit sets and topological entropy for a nonautonomous discrete dynamical system given by a sequence [Formula: see text] of continuous selfmaps of a compact topological space. A special attention is paid to the case when the space is metric and the sequence [Formula: see text] either forms an equicontinuous family of maps or is uniformly convergent. We also show that for any continuous maps f and g from a compact topological space into itself the topological entropies h(f ◦ g) and h(g ◦ f) are equal.
PARAMETER DOMAINS FOR GENERATING SPATIAL PATTERN: A COMPARISON OF REACTION–DIFFUSION AND CELL-CHEMOTAXIS MODELS
Authors: ZHU MEI , MURRAY J. D.
Published: November 2004

Reaction–diffusion and cell-chemotaxis mechanisms have been widely used as models for biological pattern formation. Applications require the formation of specific patterns. Both mechanisms involve local reaction dynamics and diffusion. In addition, the cell-chemotaxis mechanism involves chemotactic movement in response to an external gradient. It has been considered that chemotaxis is like negative diffusion which has a destabilizing effect. In this paper, we use a general weakly nonlinear analysis and numerical simulations to divide the parameter space into different domains giving rise to specific classes of spatial patterns, namely, spots and stripes, compare the robustness and sensitivity of the different models, and discuss spatial patterns intermediate between stripes and spots. We show that chemotaxis is not always a destabilizing factor — it can also have positive diffusion effect.
A CONTRACTION-MAPPING-BASED CONTROL APPROACH TO STABILIZE CHAOTIC SYSTEMS
Authors: XU DAOLIN , BISHOP STEVEN R.
Published: November 2004

Stabilization of chaotic dynamical systems onto periodic orbits is considered via a control approach based on the contraction-mapping theorem. The convergence of the control scheme is guaranteed by the construction of a contraction map. The control time required to reach within a finite precision of the desired state is in a logarithmic form, which can be adjusted by setting the convergence rate. The effects of noise on the control process are investigated; in particular (a) the effect on the magnitude of control inputs, which determines the condition of a controllable noise level, and (b) the effect on the robustness of the control process. The Cubic map is used to numerically demonstrate the control process.
DISCRETIZATION CHAOS IN THE SWITCHING CONTROL SYSTEM WITH FINITE SWITCHING VALUES
Authors: YU XING HUO
Published: November 2004

A case study is presented to demonstrate the discretization chaos in the switching control system with only finite switching values. It is proved that for the second order oscillator, with several classes of sampling periods, discrete switching control enables periodic motions around the desired equilibrium. The pattern of the discretized system is determined by the initial conditions as well as the sampling periods. Simulation results are presented to confirm the theoretical investigations.
THE FRACTAL GEOMETRY OF THE MANDELBROT SET 2: HOW TO COUNT AND HOW TO ADD
Authors: DEVANEY ROBERT L.
Published: November 2004

In a previous paper in this series,1 we showed how one may read off dynamical information about orbits of Fc(x)=x2+c from the geometry of the Mandelbrot set. In this paper we extend these ideas to show further relations between the dynamics of x2+c and the Mandelbrot set. In particular, we show that Mandelbrot set may be used as a vehicle to show students how to “count” and how to “add” geometrically.

The ideas in this paper arose from a series of experiments conducted by high school students in “chaos clubs” organized in the Boston public schools by Jonathan Choate, Mary Corkery, Beverly Mawn, and the author. The goal of these clubs was to expose young students to contemporary ideas in mathematics. Students discovered various facts about the Mandelbrot set using a combination of computer experiments and group projects. This paper presents a summary of some of the students’ findings.
THE AVERAGE FRACTAL DIMENSION AND PROJECTIONS OF MEASURES AND SETS IN Rn
Authors: ZÄHLE M.
Published: November 2004

In this note we introduce the concept of local average dimension of a measure µ, at x∈ℝn as the unique exponent where the lower average density of µ, at x jumps from zero to infinity. Taking the essential infimum or supremum over x we obtain the lower and upper average dimensions of µ, respectively. The average dimension of an analytic set E is defined as the supremum over the upper average dimensions of all measures supported by E. These average dimensions lie between the corresponding Hausdorff and packing dimensions and the inequalities can be strict.

We prove that the local Hausdorff dimensions and the local average dimensions of µ at almost all x are invariant under orthogonal projections onto almost all m- dimensional linear subspaces of higher dimension. The corresponding global results for µ and E (which are known for Hausdorff dimension) follow immediately.
ESTIMATORS FOR LONG-RANGE DEPENDENCE: AN EMPIRICAL STUDY
Authors: TAQQU MURAD S. , TEVEROVSKY VADIM , WILLINGER WALTER
Published: November 2004

Various methods for estimating the self-similarity parameter and/or the intensity of long-range dependence in a time series are available. Some are more reliable than others. To discover the ones that work best, we apply the different methods to simulated sequences of fractional Gaussian noise and fractional ARIMA (0, d, 0). We also provide here a theoretical justification for the method of residuals of regression.
THE DEFORMATION OF ROCKS: FRACTALS EVERYWHERE
Authors: HERRMANN HANS J. , POLIAKOV ALEXEI N.B. , TZSCHICHHOLZ FRANK
Published: November 2004

When rocks are sheared very strongly they either fracture or flow plastically if the hydrostatic pressures are strong enough. Both cases have been studied extensively in geophysical examples and in laboratory experiments. The faults in the brittle case and the shear bands in the plastic case form fractal networks that reflect the detailed stress field and the history of the deformation. Origin of the fractal patterns are instabilities due to the non-linearity in the constitutive behavior. In both cases an internal fractal structure is also found: power-law distributed gouge in faults and multifractal strain rate distributions in shear bands. We show examples illustrating the important consequences of fractal concepts to the understanding of this field.
RECOVERING THE GRADIENTS OF THE SOLUTIONS OF SECOND ORDER HYPERBOLIC EQUATIONS BY INTERPOLATING THE FINITE ELEMENT SOLUTIONS
Authors: LIN TAO , WANG HONG
Published: November 2004

We present a technique to generate better approximations to the gradients of the solutions of the second order hyperbolic (acoustic wave) equations by postprocessing finite element solutions with higher degree polynomial interpolation. The postprocessing procedure is inexpensive, local, vectorizable, and parallelizable. In addition, the postprocessing procedure is independent of the computation of the finite element solution; therefore it can be easily incorporated with the existing finite element codes to efficiently generate globally better approximations to the gradients or first order partial derivatives of the main quantities of the acoustic field modeled by the acoustic wave equation.
MODEL CATALYSTS: FROM EXTENDED SINGLE CRYSTALS TO SUPPORTED PARTICLES
Authors: GOODMAN D.W.
Published: November 2004

Model oxide-supported metal catalysts have been prepared by evaporating a metal (e.g., Cu, Pd) onto an oxide ( SiO 2, Al 2 O 3) thin film (~100 Å) which, in turn, is supported on a refractory metal (Mo, W, Ta) surface. The deposited metal films, upon annealing, form small metallic clusters on the oxide surface whose sizes are dependent upon the initial metal film thickness. The surface structures and particle morphologies have been characterized using scanning probe microscopies, temperature programed desorption, X-ray and ultraviolet photoemission, and high-resolution electron energy-loss spectroscopy/infrared reflection-absorption spectroscopy of adsorbed carbon monoxide. The catalytic properties of these particles have also been investigated with respect to several reactions including CO/O 2 and CO/NO. The chemical and electronic properties of the metal particles with respect to size are compared to the analogous properties of extended single-crystal surfaces.
MODIFICATION OF SURFACE STRUCTURE BY SPILLOVER SPECIES: CONSEQUENCES IN THE REACTION OF SOLIDS AND CATALYSIS
Authors: DELMON BERNARD
Published: November 2004

Transition metals can dissociate hydrogen to a surface mobile species called spillover hydrogen ( H so ). Similarly, oxides like α- Sb 2 O 4, BiPO 4, Bi 2 O 3 (donors) can dissociate molecular oxygen to a mobile surface species ( O so ). These metals or oxides are conveniently called donors. This article reviews effects which are due to spillover species when reacting with the surface of a solid distinct from the donors: (i) acceleration of the nucleation steps in the reduction of oxides, (ii) control of the nature of active sites on sulfides (e.g., MoS 2), and (iii) control of the adequate oxido-reduction state of the surface of the oxides active in selective oxidation. Atomic interpretations of the surface reactions explaining these effects will be given. It will be shown that all these phenomena are caused by the special reactivity of spillover species. Fundamental questions which could be solved by surface science approaches will be outlined.
WAVES ON A METAL SURFACE AND QUANTUM CORRALS
Authors: CROMMIE M.F. , LUTZ C.P. , EIGLER D.M. , HELLER E.J.
Published: November 2004

Electrons occupying surface states on the close-packed faces of noble metals form a two-dimensional (2-d) nearly free electron gas. Because this system is accessible to the scanning tunneling microscope (STM), it provides a unique opportunity to study the local properties of low-dimensional electrons. On Cu (111) we have observed standing wave patterns in the surface local density of states due to the quantum mechanical interference of surface state electrons scattering off of step edges and adsorbates. We find that Fe adatoms strongly scatter the surface state and, as a result, are good building blocks for constructing atomic-scale barriers (“quantum corrals”) to confine the surface state electrons. The barriers are constructed by individually positioning Fe adatoms using the tip of a cold (4 K) STM. Tunneling spectroscopy performed inside of the corrals reveals discrete resonances, consistent with size quantization. A more quantitative understanding is obtained by accounting for the multiple scattering of surface state electrons with the corrals’ constituent adatoms. This scattering is characterized by a complex phase shift which can be extracted from the electronic density pattern inside a quantum corral.
CHEMISORPTION SITE DETERMINATION OF HYDROGEN IN THE SYSTEM c(1×1)H/Rh(311) EMPLOYING He-DIFFRACTION
Authors: APEL R. , FARÍAS D. , RIEDER K.H.
Published: November 2004

He-beam diffraction data evaluated for clean Rh (311) yield a best-fit corrugation, which shows a pronounced corrugation amplitude along the (100)-microfacets and a practically vanishing amplitude along the (111)-microfacets in agreement with expectation, but in contrast to Ni (311) where the reverse situation was found. Hydrogen adsorption leads to a sequence of c(1×1), c(1×3), p(1×1), c(1×3), and p(1×1) REC phases. The fact that the c(1×1) phase was observed with He-diffraction, but not in previous LEED studies, again proves the exceptional sensitivity of He scattering for adsorbed hydrogen. Surface charge density calculations were performed to reproduce the shape and amplitude of the best-fit corrugation function of the c(1×1)H-phase. In this way we found that the H atoms occupy places between the topmost bridge sites and the adjacent threefold hollow sites on the (111)-microfacets; the H-Rh bond length amounts to 1.92±0.1 Å.
POLARIZATION OF DIFFERENT INTERFACES OF Rh AND Ag STUDIED BY RECURSION TECHNIQUES
Authors: HERGERT W. , RENNERT P. , DEMANGEAT C. , DREYSSÉ H.
Published: November 2004

We investigate the reasons for the discrepancy between experimental and theoretical findings concerning the onset of magnetic moment when Rh , which is nonmagnetic in the bulk form, is coated on Ag (001). To perform the calculation we use a recently developed recursion method in the reciprocal space for the derivation of the density of states of multilayered systems. The local magnetic moments are deduced versus the exchange integral J. We found that a single-monolayer of Rh epitaxially grown on Ag (001) presents a high magnetic moment. This magnetic moment decreases when the Rh monolayer is covered by a Ag overlayer. However, the magnetic moment is not entirely killed as obtained also previously by recent full-potential linearized-augmented-plane-wave calculations. Therefore, there seems to be, discrepancy with recent surface-magneto-optic-Kerr effect experiments which have not detected any long-range order in the case of a monolayer of Rh on Ag (001). We study intermixing effects between Rh and Ag using different model structures containing ordered Ag .50 Rh .50 layers. The disappearance of magnetism in experimentally studied samples can be explained by such intermixing effects.
ON THE DISSOCIATION OF O2 ON ALKALI METALS
Authors: GREBER T. , MORGANTE A. , FICHTNER-ENDRUSCHAT S. , ERTL G.
Published: November 2004

The reaction of O 2 with Li and Cs films is accompanied by the emission of electrons. The variations of the initial yields with the velocity of the impinging molecules is exploited to access the dynamics of the adsorption process. The data are analyzed in terms of a model where chemisorption proceeds via an intermediate [Formula: see text] species. This [Formula: see text] state readily dissociates while the de-excitation of the resulting O − into O 2− may cause electron emission. From a comparison with experimentally observed electron yields the reaction time and velocity uptake of the products is accessed.
XPS STUDIES OF THE STABILITY OF A ZIRCONIUM CARBIDE FILM IN THE PRESENCE OF ZIRCONIUM OXIDE AND HYDROGEN
Authors: WONG P.C. , LI Y.S. , MITCHELL K.A.R.
Published: November 2004

X-ray photoelectron spectroscopy (XPS) has been used to study the interfacial chemistries of a 65-Å film prepared by depositing zirconium in an oxidizing environment onto a methane-pretreated 11-Å thick zirconium oxide film, which initially was deposited onto a gold substrate. The second metal deposition results in an outermost region composed of a mixed zirconium oxide, while below there is metallic zirconium followed by zirconium carbide and carbon on top of the first zirconium oxide film, which is itself in contact with the gold. The carbide component showed no changes on heating to 425°C, on treating with a hydrogen plasma at room temperature, or on heating the resulting film to 425°C. The oxide layers do show characteristic changes, and this also contrasts with earlier observations for a zirconium sulphide film. The zirconium carbide Zr3d 5/2 component has a binding energy of 180.6 eV.
THEORY OF ALKALI-METAL ADSORPTION ON CLOSE-PACKED METAL SURFACES
Authors: STAMPFL CATHERINE , SCHEFFLER MATTHIAS
Published: November 2004

Results of recent density-functional-theory calculations for alkali-metal adsorbates on close-packed metal surfaces are discussed. Single adatoms on the (111) surface of Al and Cu are studied with the self-consistent surface Green-function method by which the pure adsorbate-substrate interaction may be analyzed. Higher coverage ordered adlayers of K on Al(111) , Na on Al(111) , and Na on Al(001) are treated using the ab initio pseudopotential plane-wave method which affords the prediction of coverage-dependent stable and metastable adsorbate geometries and phase transitions of the adsorbate layers. Together, these studies give insight and understanding into current key issues in alkali-metal adsorption, namely, the nature of the adsorbate-substrate bond at low coverage and the occurrence of hitherto unanticipated adsorbate geometries, and the associated electronic properties.
STRUCTURAL AND MAGNETIC PROPERTIES OF EPITAXIAL Ni80Fe20 THIN FILMS ON Cu/Si
Authors: HASHIM I. , JOO H.S. , ATWATER H.A.
Published: November 2004

Single-crystal films of permalloy ( Ni 80 Fe 20) were grown on Cu (001) seed layers oriented epitaxially with Si (001). The microstructural properties were measured using in-situ reflection high-energy electron diffraction, and ex-situ transmission electron microscopy, x-ray diffraction, and atomic force microscopy, whereas the magnetic properties were probed using in-situ magneto-optic Kerr effect and ex-situ vibrating sample magnetometry. Anisotropic magnetoresistance and resistivity for some of the samples were also measured. The coercivity for thinner (≤5 nm) Ni 80 Fe 20 was significantly higher (10–20 Oersteds) than polycrystalline films deposited on SiO 2/ Si , and was also higher than films deposited on lattice-matched Cu x Ni 1–x alloys. These magnetic properties were explained using a theoretical model involving interaction of domain walls with defects such as misfit dislocations and coherent islands, due to the mismatch between Ni 80 Fe 20 and Cu .
REFINEMENT OF THE ${\rm{Si}}(111) \mbox{-}
(\surd{3} \times \surd{3}){\rm{R30}}^\circ - {\rm{Ag}}$ STRUCTURE BY LOW-ENERGY ELECTRON DIFFRACTION
Authors: OVER H. , TONG S.Y. , QUINN J. , JONA F.
Published: November 2004

We have reinvestigated the bond geometry of the [Formula: see text] surface by means of low-energy electron diffraction using a much larger experimental data set than that previously used. The [Formula: see text] surface consists of a [Formula: see text] lattice of Ag atoms which replaces the topmost Si atoms, and forces the remaining Si atoms to form trimers. The Ag-Ag bond length turned out to be 3.47±0.12 Å. The Ag atoms are laterally displaced from the bulk positions of the Si atoms which they have replaced by 0.53 Å resulting in a Ag-Si bond length of 2.36±0.17 Å. The missing top Si layer and the formation of Si trimers lead to strong distortions in deeper Si layers, most notably a buckling in the third and fourth Si layer with a magnitude of about 0.35 Å and 0.2 Å, respectively. Applying the concept of ‘split positions’, the low Debye temperature of Ag has been interpreted as being caused by strong in-plane (either static or dynamic) movements of the Ag atoms perpendicular to the Ag-Si bonding.
ALKALI-ATOM ADSORPTION ON SEMICONDUCTOR SURFACES: METALLIZATION AND SCHOTTKY-BARRIER FORMATION
Authors: FLORES F.
Published: November 2004

Alkali metals deposited on weakly ionic semiconductors are neither reactive nor form large three-dimensional islands, offering an ideal system in which Schottky junctions can be analyzed. In this paper, the alkali-metal-semiconductor interface is reviewed with a special emphasis on the formation of the Schottky barrier. Two regimes are clearly differentiated for the deposition of AMs on a semiconductor: in the high-coverage limit the Schottky barrier is shown to depend, for not very defective interfaces, on the semiconductor charge neutrality level. For low coverages, different one- and two-dimensional structures appear on the semiconductor surface presenting an insulating behavior. For depositions around a metal monolayer, a Mott metal-insulator transition appears; then, the interface Fermi energy is pinned by the metallic density of states at the position determined by the semiconductor charge neutrality level. This situation defines the Schottky barrier height of a thick-metal overlayer.
XPS CHEMICAL SHIFTS FOR CO ADSORBED ON Ni(100): A THEORETICAL STUDY
Authors: PEDOCCHI L. , ROVIDA G. , RUSSO N.
Published: November 2004

Starting from the observed chemical shift of C-1s and O-1s ionization potentials (IP), reported in the literature for the adsorption of CO on Ni (100), and correlated to the different CO adsorption sites at different coverages, we have carried out a theoretical investigation, using a first-principle density-functional method, to calculate ionization energies for adsorbed CO in the atop and bridge sites. In our approach, the Ni (100) surface was simulated with clusters of up to nine metal atoms of different geometry, in order to test the two adsorption sites. For each cluster, the CO adsorption geometry was optimized and the O-1s and C-1s ionizations were calculated. The main result was that the (O-1s–C-1s) difference was very well reproduced even with clusters of modest size, thus confirming the possibility to use this value as a structure-sensitive parameter.
BIMODAL ANGULAR AND VELOCITY DISTRIBUTIONS OF CO2 DESORBING AFTER OXIDATION OF CO ON Pt(111)
Authors: POEHLMANN E. , SCHMITT M. , HOINKES H. , WILSCH H.
Published: November 2004

Time-of-flight (TOF) distributions of CO 2 molecules desorbing after the oxidation of CO on Pt (111) were investigated at various desorption angles ϑ for surface temperatures Ts in the range 550–800 K. The Pt (111) surface was exposed to a continuous flow of O 2 from a doser and to a chopped CO nozzle beam. Surface residence-time effects proved to be unimportant or were elucidated. Bimodal TOF distributions composed of two parts were obtained: molecules with a Maxwellian velocity distribution corresponding to Ts appeared in a cosine-shaped angular distribution and molecules with appreciably higher kinetic energies (mean kinetic energy normal to the surface ⊥≈9kTs) were observed in a narrow angular distribution proportional to cos 8 ϑ. The partition of the total desorbing CO 2 flux to these two channels depended on Ts and ϑ and the total oxygen dose d0 accumulated during an experiment. With increasing d0 the Maxwellian component markedly increased at the expense of the fast component. The observed trends suggest almost only fast desorption from clean Pt (111). We therefore assume Maxwellian desorption to occur mainly from surface sites gradually produced under the influence of oxygen.
SHARP POINCARÉ–SOBOLEV INEQUALITIES AND THE SHORTEST LENGTH OF SIMPLE CLOSED GEODESICS ON A TOPOLOGICAL TWO SPHERE
Authors: ZHU MEIJUN
Published: November 2004

We show that the sharp constants of Poincaré–Sobolev inequalities for any smooth two dimensional Riemannian manifold are less than or equal to [Formula: see text]. For a smooth topological two sphere M2, the sharp constants are [Formula: see text] if and only if M2is isometric to two sphere S2with the standard metric. In the same spirit, we show that for certain special smooth topological sphere the ratio between the shortest length of simple closed geodesics and the square root of its area is less than or equals to [Formula: see text].
Electrophysiological characterization of volume-activated chloride currents in mouse cholangiocyte cell line
Authors: Chen Biyi , Nicol Grant , Cho Won Kyoo
Published: November 2004

Recent electrophysiological and radioisotope efflux studies have demonstrated various Cl− channels in cholangiocytes including volume-activated Cl− channels (VACC). Because VACCs play prominent roles in many vital cellular functions and physiology in cholangiocytes, we have examined their electrophysiological characteristics in mouse cholangiocytes to provide an important framework for studying in the future. The present study is to characterize VACCs expressed in the mouse bile duct cell (MBDC) line, conditionally immortalized by SV40 virus. Conventional whole cell patch-clamp techniques were used to study the electrophysiological characteristics of VACC in MBDC. When the MBDCs were exposed to hypotonic solution, they exhibited an outwardly rectified current, which was significantly inhibited by replacing chloride in the bath solution with gluconate or glutamate and by administration of classic chloride channel inhibitors 5-nitro-2-(3-phenylpropylamino)-benzoate, glybenclamide, DIDS, and tamoxifen. These inhibitory effects were reversible with washing them out from the bath solution. Moreover, the ion selectivity of the volume-activated channel to different anions indicates that it is more permeable to SCN− > I− ≥ Cl− > F− ≥ acetate ≥ glutamate ≥ gluconate. These electrophysiological characteristics demonstrate that the volume-activated current observed is a VACC. In addition, the VACC in MBDC has electrophysiological characteristics similar to those of the VACC in human cholangiocarcinoma cell line. The present study is the first to characterize the VACC in mouse cholangiocyte and will provide an important framework for further studies to examine and understand the role of the VACC in biliary secretion and ion-transport physiology.