Is the number of species on earth increasing or decreasing? Time, chaos and the origin of species

Darwin's On the Origin of Species has led to a theory of evolution with a mass of empirical detail on population genetics below species level, together with heated debate on the details of macroevolutionary patterns above species level. Most of the main principles are clear and generally accepted, notably that life originated once and has evolved over time by descent with modification. Here, I review the fossil and molecular phylogenetic records of the response of life on Earth to Quaternary climatic changes. I suggest that the record can be best understood in terms of the nonlinear dynamics of the relationship between genotype and phenotype, and between climate and environments. 'The origin of species' is essentially unpredictable, but is nevertheless an inevitable consequence of the way that organisms reproduce through time. The process is 'chaotic', but not 'random'. I suggest that biodiversity is best considered as continuously branching systems of lineages, where 'species' are the branch tips. The Earth's biodiversity should thus (1) be in a state of continuous increase and (2) show continuous discrepancies between genetic and morphological data in time and space. © The Palaeontological Association.

Time operator for diffusion

Volume: 11 Issue: 4 Pages: 465-477 Published: MAR 2000 Times Cited: 9 References: 15 Citation MapCitation Map beta Abstract: We extend the concept of time operator for general semigroups and construct a non-self-adjoint time operator for the diffusion equation which is intertwined with the unilateral shift. We obtain the spectral resolution, the age eigenstates and a new shift representation of the solution of the diffusion equation. Based on previous work we obtain similarly a self-adjoint time operator for Relativistic Diffusion. (C) 2000 Elsevier Science Ltd. All rights reserved.

Extended spectral decompositions of the Renyi map

We present new general methods to obtain spectral decompositions of dynamical systems in rigged Hilbert spaces and investigate the existence of resonances and the completeness of the associated eigenfunctions. The results are illustrated explicitly for the simplest chaotic endomorphism, namely the Renyi map.

The Disrupted Space: Safety and Security in traditional contexts

One of the core elements of successful planning is the individuals’ experience of their shared open spaces. This paper attributes to the relationship between safety and urban design by means of natural surveillance and security in the city’s shared spaces. It examines how political claims over space reassembled alternative definitions of security in one of Cairo’s oldest quarters, and how ambitious planning schemes were mostly driven by problems of insecurity, chaos and disorder. The main crux to this account is based on original documents, interviews and maps which reveals considerable insights and accounts of how this vision affected the quarter’s spatial quality and the user’s reactions to his new spatial formula. It also reveals conflicting conceptions of safety and security between the planning ambitions and the users experiences, which not only lacked reliable visions for securing the quarter, but also resulted further disruption to their everyday living spaces.

Intermittency, quasiperiodicity and chaos in probe-induced ferroelectric domain switching

Memristive materials and devices, which enable information storage and processing on one and the same physical platform, offer an alternative to conventional von Neumann computation architectures. Their continuous spectra of states with intricate field-history dependence give rise to complex dynamics, the spatial aspect of which has not been studied in detail yet. Here, we demonstrate that ferroelectric domain switching induced by a scanning probe microscopy tip exhibits rich pattern dynamics, including intermittency, quasiperiodicity and chaos. These effects are due to the interplay between tip-induced polarization switching and screening charge dynamics, and can be mapped onto the logistic map. Our findings may have implications for ferroelectric storage, nanostructure fabrication and transistor-less logic.

Quantum chaos in ultracold collisions between Yb(¹S0) and Yb(³P2)

We calculate and analyze Feshbach resonance spectra for ultracold Yb(1S0)+Yb(3P2) collisions as a function of an interatomic potential scaling factor λ and external magnetic field. We show that, at zero field, the resonances are distributed randomly in λ, but that signatures of quantum chaos emerge as a field is applied. The random zero-field distribution arises from superposition of structured spectra associated with individual total angular momenta. In addition, we show that the resonances with respect to magnetic field in the experimentally accessible range of 400 to 2000 G are chaotically distributed, with strong level repulsion that is characteristic of quantum chaos.

Approach to chaos in ultracold atomic and molecular physics: Statistics of near-threshold bound states for Li+CaH and Li+CaF

We calculate near-threshold bound states and Feshbach resonance positions for atom–rigid-rotor models of the highly anisotropic systems Li+CaH and Li+CaF. We perform statistical analysis on the resonance positions to compare with the predictions of random matrix theory. For Li+CaH with total angular momentum J=0 we find fully chaotic behavior in both the nearest-neighbor spacing distribution and the level number variance. However, for J>0 we find different behavior due to the presence of a nearly conserved quantum number. Li+CaF (J=0) also shows apparently reduced levels of chaotic behavior despite its stronger effective coupling. This may indicate the development of another good quantum number relating to a bending motion of the complex. However, continuously varying the rotational constant over a wide range shows unexpected structure in the degree of chaotic behavior, including a dramatic reduction around the rotational constant of CaF. This demonstrates the complexity of the relationship between coupling and chaotic behavior.

Nonlinear excitations in strongly-coupled plasma lattices: envelope solitons, kinks and intrinsic localized modes

Ensembles of charged particles (plasmas) are a highly complex form of matter, most often modeled as a many-body system characterized by weak inter-particle interactions (electrostatic coupling). However, strongly-coupled plasma configurations have recently been produced in laboratory, either by creating ultra-cold plasmas confined in a trap or by manipulating dusty plasmas in discharge experiments. In this paper, the nonlinear aspects involved in the motion of charged dust grains in a one-dimensional plasma monolayer (crystal) are discussed. Different types of collective excitations are reviewed, and characteristics and conditions for their occurrence in dusty plasma crystals are discussed, in a quasi-continuum approximation. Dust crystals are shown to support nonlinear kink-shaped supersonic solitary longitudinal excitations, as well as modulated envelope localized modes associated with longitudinal and transverse vibrations. Furthermore, the possibility for intrinsic localized modes (ILMs) — Discrete Breathers (DBs) — to occur is investigated, from first principles. The effect of mode-coupling is also briefly considered. The relation to previous results on atomic chains, and also to experimental results on strongly-coupled dust layers in gas discharge plasmas, is briefly discussed.