Robert C. Hilborn

Bio: Robert C. Hilborn is an academic researcher. The author has contributed to research in topics: Synchronization of chaos. The author has an hindex of 1, co-authored 1 publications receiving 1163 citations.

The Systems View of Life: A Unifying Vision

Abstract: Over the past thirty years, a new systemic conception of life has emerged at the forefront of science. New emphasis has been given to complexity, networks, and patterns of organisation, leading to a novel kind of 'systemic' thinking. This volume integrates the ideas, models, and theories underlying the systems view of life into a single coherent framework. Taking a broad sweep through history and across scientific disciplines, the authors examine the appearance of key concepts such as autopoiesis, dissipative structures, social networks, and a systemic understanding of evolution. The implications of the systems view of life for health care, management, and our global ecological and economic crises are also discussed. Written primarily for undergraduates, it is also essential reading for graduate students and researchers interested in understanding the new systemic conception of life and its implications for a broad range of professions - from economics and politics to medicine, psychology and law.

Chaos and the quantum phase transition in the Dicke model.

Abstract: We investigate the quantum-chaotic properties of the Dicke Hamiltonian; a quantum-optical model that describes a single-mode bosonic field interacting with an ensemble of N two-level atoms. This model exhibits a zero-temperature quantum phase transition in the $\stackrel{\ensuremath{\rightarrow}}{N}\ensuremath{\infty}$ limit, which we describe exactly in an effective Hamiltonian approach. We then numerically investigate the system at finite N, and by analyzing the level statistics, we demonstrate that the system undergoes a transition from quasi-integrability to quantum chaotic, and that this transition is caused by the precursors of the quantum phase transition. Our considerations of the wave function indicate that this is connected with a delocalization of the system and the emergence of macroscopic coherence. We also derive a semiclassical Dicke model that exhibits analogues of all the important features of the quantum model, such as the phase transition and the concurrent onset of chaos.

Self-Propelled Particles with Soft-Core Interactions: Patterns, Stability, and Collapse

Abstract: Understanding collective properties of driven particle systems is significant for naturally occurring aggregates and because the knowledge gained can be used as building blocks for the design of artificial ones. We model self-propelling biological or artificial individuals interacting through pairwise attractive and repulsive forces. For the first time, we are able to predict stability and morphology of organization starting from the shape of the two-body interaction. We present a coherent theory, based on fundamental statistical mechanics, for all possible phases of collective motion.

Nonextensive statistics: theoretical, experimental and computational evidences and connections

Abstract: The domain of validity of standard thermodynamics and Boltzmann-Gibbs statistical mechanics is discussed and then formally enlarged in order to hopefully cover a variety of anomalous systems. The generalization concerns nonextensive systems, where nonextensivity is understood in the thermodynamical sense. This generalization was first proposed in 1988 inspired by the probabilistic description of multifractal geometries, and has been intensively studied during this decade. In the present effort, after introducing some historical background, we briefly describe the formalism, and then exhibit the present status in what concerns theoretical, experimental and computational evidences and connections, as well as some perspectives for the future. In addition to these, here and there we point out various (possibly) relevant questions, whose answer would certainly clarify our current understanding of the foundations of statistical mechanics and its thermodynamical implications.

Chaos theory and strategy: theory, application, and managerial implications

Abstract: This paper argues that chaos theory provides a useful theorectical framework for understanding the dynamic evolution of industries and the complex interactions among industry actors. It is argued that industries can be conceptualized and modeled as complex, dynamic systems, which exhibit both unpredictability and underlying order. The relevance of chaos theory for strategy is discussed, and a number of managerial implications are suggested. To illustrate the application of chaos theory, a simulation model is presented that depicts the interactions between a manufacturer of computers, its suppliers, and its market. The results of the simulation demonstrate how managers might underestimate the costs of international production. The paper concludes that, by understanding industries as complex systems, managers can improve decision making and search for innovative solutions.