Peter Kleban

Chaos, complexity and community management of fisheries

For several decades, fisheries management has been based on stock recruitment models, leading to policies designed to control the amount of effort and the quantity of fish caught. This approach has not been notably successful. In this paper we take the view that this problem arises from the complex and likely chaotic nature of fisheries. This attribute of fisheries creates a very difficult and costly information problem, which renders attempts to control the long term numerical abundance of individual species virtually impossible. We argue that feasible management must address the relatively stable parameters of fisheries systems habitat and basic biological processes, and that this demands management attention to the fine as well as the broad scale attributes of the system. Attention to detail at these differing scales implies the need for a layered or hierarchical management structure. The need to minimize Information costs also suggests an emphasis on decentrallzed, community-based approaches to management. A review of the anthropological literature shows that such approaches are common in many societies.

XPS identification of the chemical state of subsurface oxygen in the OPd(110) system

Abstract Adsorbed oxygen at room temperatures exists on Pd(110) in two states, a surface state ( β 2 ) and a more weakly bound state ( β 1 ), previously designated as “subsurface” oxygen. The “subsurface” state was postulated as responsible for the oscillations in the kinetics of catalytic CO oxidation observed on this surface. However, previous studies have cast doubt on this explanation. We have investigated the interaction of oxygen on Pd(110) by temperature programmed desorption (TPD), ultraviolet photoemission spectroscopy (UPS) and x-ray photoelectron spectroscopy (XPS). The XPS combines conventional UHV with in-situ surface analysis in controlled atmospheres of up to 1 mbar. UPS work function measurements show a decrease with oxygen adsorption, coinciding with β 1 formation observed in TPD as reported previously. XPS measurements of the Pd 3 d 5 2 line show only oxyg induced surface core-level shifts (SCLS) for oxygen exposures as high as 22 800 L ( p o 2 = 1.0 × 10 −4 mbar and T = 400 K). surface-sensitive XPS measurements and TPD for higher oxygen exposures ( p o 2 = 4.0 × 10 −2 mbar for 20 min at T = 400 K) s oxide formation coinciding with a corresponding high increase in β 1 formation. These results for oxygen pressures and temperatures in the oscillation regime, suggest that the oscillatory behavior on this surface may be due to an oxidation and reduction mechanism.

Crossing Probabilities and Modular Forms

We examine crossing probabilities and free energies for conformally invariant critical 2-D systems in rectangular geometries, derived via conformal field theory and Stochastic Löwner Evolution methods. These quantities are shown to exhibit interesting modular behavior, although the physical meaning of modular transformations in this context is not clear. We show that in many cases these functions are completely characterized by very simple transformation properties. In particular, Cardys function for the percolation crossing probability (including the conformal dimension 1/3), follows from a simple modular argument. A new type of “higher-order modular form” arises and its properties are discussed briefly.

Kinetics of PdO formation and CO reduction on Pd(110)

Abstract Recent studies have identified the ‘subsurface’ oxygen on Pd(110) as a nucleation of an oxide phase. This species has been postulated as responsible for oscillations in the catalytic CO oxidation on this surface. We have investigated the kinetics of this oxide formation and its reduction by CO on Pd(110) at temperatures and pressures where oscillations occur, using temperature-programmed desorption and X-ray photoelectron spectroscopy. The rate of oxide reduction measured was found to agree approximately with previously measured values for chemisorbed oxygen, indicating that the oxide species are weakly bound or unstable. However, we find significant qualitative and quantitative differences in the kinetics of oxide formation and other mechanisms assumed in previous studies.

Chaotic dynamics in a multiple species fishery: a model of community predation

Abstract This paper summarizes a dynamic model of a multiple species fishery that incorporates a community level phenomenon — community predation or the tendency of big fish of almost any species to eat little fish of almost any species. The model is used to explore the conditions under which the dynamic behavior of a multiple species complex characterized by community predation qualitatively conforms with the observed dynamic processes of real fisheries systems. The specifications necessary to replicate qualitatively the dynamic behavior of such system lead to the chaotic behavior of individual populations but stability of the entire system. The presence of chaos may explain why the dynamic path of individual populations in real fisheries has been so resistant to prediction, but more important, indicates that predictable order, the basis of management control of these kinds of multiple species systems, may be found at the system rather than at the individual population level.

A Farey Fraction Spin Chain

Abstract:We introduce a new number-theoretic spin chain and explore its thermodynamics and connections with number theory. The energy of each spin configuration is defined in a translation-invariant manner in terms of the Farey fractions, and is also expressed using Pauli matrices. We prove that the free energy exists and a phase transition occurs for positive inverse temperature β= 2. The free energy is the same as that of related, non-translation-invariant number-theoretic spin chain. Using a number-theoretic argument, the low-temperature (β > 3) state is shown to be completely magnetized for long chains. The number of states of energy E= log(n) summed over chain length is expressed in terms of a restricted divisor problem. We conjecture that its asymptotic form is (n log n), consistent with the phase transition at β= 2, and suggesting a possible connection with the Riemann ζ-function. The spin interaction coefficients include all even many-body terms and are translation invariant. Computer results indicate that all the interaction coefficients, except the constant term, are ferromagnetic.

The phase transition in statistical models defined on Farey fractions

We consider several statistical models defined on the Farey fractions. Two of these models may be regarded as “spin chains,” with long-range interactions, while another arises in the study of multifractals associated with chaotic maps exhibiting intermittency. We prove that these models all have the same free energy. Their thermodynamic behavior is determined by the spectrum of the transfer operator (Ruelle–Perron–Frobenius operator), which is defined using the maps (presentation functions) generating the Farey “tree.” The spectrum of this operator was completely determined by Prellberg. It follows that these models have a second-order phase transition with a specific heat divergence of the form C ∼ [∈ ln2∈]−1. The spin chain models are also rigorously known to have a discontinuity in the magnetization at the phase transition.

Free energy of rectangular domains at criticality

The authors calculate the universal part F of the free energy of rectangular domains at critical points by use of conformal field theory. F includes a term logarithmic in the size (or area), due to the corners. In addition, there is a term F0 depending on the aspect ratio, which they determine by integrating the stress tensor (T) over the rectangle. This term involves complete elliptic integrals, but may be more simply expressed in terms of the Dedekind eta -function. For central charge c>0, they find that F0 is maximal for squares, providing a thermodynamic driving force for the elongation of small domains, and argue that this should be a general tendency.

Shape-dependent universality in percolation

The shape-dependent universality of the excess percolation cluster number and cross-configuration probability on a torus is examined. Besides the aspect ratio of the torus, the universality class depends upon the twist in the periodic boundary conditions, which may be introduced when triangular lattices are used in simulations.

Anchored Critical Percolation Clusters and 2D Electrostatics

We consider the densities of clusters, at the percolation point of a two-dimensional system, which are anchored in various ways to an edge. These quantities are calculated by use of conformal field theory and computer simulations. We find that they are given by simple functions of the potentials of 2D electrostatic dipoles and that a kind of superposition cum factorization applies. Our results broaden this connection, already known from previous studies, and we present evidence that it is more generally valid. An exact result similar to the Kirkwood superposition approximation emerges.