Formal Languages in Dynamical Systems

We treat here the interrelation between formal languages and those dynamical systems that can be described by cellular automata (CA). There is a well-known injective map which identifies any CA-invariant subshift with a central formal language. However, in the special case of a symbolic dynamics, i.e. where the CA is just the shift map, one gets a stronger result: the identification map can be extended to a functor between the categories of symbolic dynamics and formal languages. This functor additionally maps topological conjugacies between subshifts to empty-string-limited generalized sequential machines between languages. If the periodic points form a dense set, a case which arises in a commonly used notion of chaotic dynamics, then an even more natural map to assign a formal language to a subshift is offered. This map extends to a functor, too. The Chomsky hierarchy measuring the complexity of formal languages can be transferred via either of these functors from formal languages to symbolic dynamics and proves to be a conjugacy invariant there. In this way it acquires a dynamical meaning. After reviewing some results of the complexity of CA-invariant subshifts, special attention is given to a new kind of invariant subshift: the trapped set, which originates from the theory of chaotic scattering and for which one can study complexity transitions.Comment: 23 pages, LaTe

Truncated horseshoes and formal languages in chaotic scattering

In this paper we study parameter families of truncated horseshoes as models of multiscattering systems which show a transition to chaos without losing hyperbolicity, so that the topological features of the transition are completely describable by a parameterized family of symbolic dynamics. At a fixed parameter value the corresponding horseshoe represents the set of orbits trapped in the scattering region. The bifurcations are a pure boundary effect and no other bifurcations such as saddle center bifurcations occur in this transition scenario. Truncated horseshoes actually arise in concrete potential scattering under suitable conditions. It is shown that a simple scattering model introduced earlier can realize this scenario in a certain parameter range (the "truncated sawshoe") . For this purpose, we solve the inverse scattering problem of finding the central potential associated to the sawshoe model. Furthermore, we review classification schemes for the transition to chaos of truncated horseshoes originating from symbolic dynamics and formal language theory and apply them to the truncated double horseshoe and the truncated sawshoe.Comment: 39 pages postscript; use uudecode and uncompress ! 4 figures available as hardcopies on reques

Extraversion and adaptive performance: Integrating trait activation and socioanalytic personality theories at work

This is the author accepted manuscript. The final version is available from the publisher via the DOI in this recordBoth trait activation and socioanalytic personality theories clarify the personality – performance relationship at work. We argue that extraversion needs to be interactively combined with both social competency (socioanalytic theory) and an activating context (trait activation theory) to demonstrate effects on a relevant type of work performance. Specifically, the aim of the present study was to examine extraversion's association with adaptive performance when combined with social competency and context (i.e., climate for personal initiative). Our results demonstrate that the three-way interaction (i.e., extraversion × social competency × climate for initiative) has a significant relationship with adaptive performance, such that the extraversion–performance association is strengthened when both social competency and climate for initiative are heightened. Our findings suggest that personality scholars should consider both socioanalytic and trait activation perspectives when investigating performance prediction. We discuss implications, strengths, limitations, and directions for future research

Summer 1976

The Superintendents\u27s Obligation (page 3) Farm Machinery Noise can Damage Hearing (9) Back and Beyond (10) Tolerance to Benzimidazole-Derivative Fungacides by Fusarium Roseum on Kentucky Bluegrass Turf (13) Biological Pest Control Gaining Acceptance (16) Compare Fertilizer Values Before Buying (18) UMass Turfgrass Research Fund (19

Summer 1975

Getting Back to Basics--Turfgrass Fertilization (page 3) Carefree Herbaceous Perennials For Gardens and Borders (9) Back and Beyond (10) Turf News--New Lifting Technique accepted (14) Vandalism on Golf Courses (15) UMass Turfgrass Research Fund (20

Controlled Irradiative Formation of Penitentes

Spike-shaped structures are produced by light-driven ablation in very different contexts. Penitentes 1-4 m high are common on Andean glaciers, where their formation changes glacier dynamics and hydrology. Laser ablation can produce cones 10-100 microns high with a variety of proposed applications in materials science. We report the first laboratory generation of centimeter-scale snow and ice penitentes. Systematically varying conditions allows identification of the essential parameters controlling the formation of ablation structures. We demonstrate that penitente initiation and coarsening requires cold temperatures, so that ablation leads to sublimation rather than melting. Once penitentes have formed, further growth of height can occur by melting. The penitentes intially appear as small structures (3 mm high) and grow by coarsening to 1-5 cm high. Our results are an important step towards understanding and controlling ablation morphologies.Comment: Accepted for publication in Physical Review Letter

Spring 1983 Conference Issue

Chemical Retardation of Grass Growth (page 3) Cultivar Trials - 1982 (5) Fifty-second Annual Turf Conference and Seventh Industrial Show (10) Dollar Spot Fungicide Control Trials - 1982 (13) Winter Protection of Herbaceous Perennials (14) Control of Annual Bluegrass in Golf Tees Using Perennial Ryegrass and Ethofumesate (15

Scattering map for two black holes

We study the motion of light in the gravitational field of two Schwarzschild black holes, making the approximation that they are far apart, so that the motion of light rays in the neighborhood of one black hole can be considered to be the result of the action of each black hole separately. Using this approximation, the dynamics is reduced to a 2-dimensional map, which we study both numerically and analytically. The map is found to be chaotic, with a fractal basin boundary separating the possible outcomes of the orbits (escape or falling into one of the black holes). In the limit of large separation distances, the basin boundary becomes a self-similar Cantor set, and we find that the box-counting dimension decays slowly with the separation distance, following a logarithmic decay law.Comment: 20 pages, 5 figures, uses REVTE

Spring 1975 Conference Issue

Professionalism (page 3) Back and Beyond (4) Kentucky Bluegrass Variety Trial (5) Perennial Ryegrass Variety Trial (7) Tall and Hard Fescue Variety Trial (9) Red Fescue Variety Trial (9) Turf Conference Program (10) Turf News (14) You Can Make It Easier to Collect Soil Samples (15

Dissipative chaotic scattering

We show that weak dissipation, typical in realistic situations, can have a metamorphic consequence on nonhyperbolic chaotic scattering in the sense that the physically important particle-decay law is altered, no matter how small the amount of dissipation. As a result, the previous conclusion about the unity of the fractal dimension of the set of singularities in scattering functions, a major claim about nonhyperbolic chaotic scattering, may not be observable.Comment: 4 pages, 2 figures, revte