1980 Preface * 1999 Preface * 1999 Acknowledgements * Introduction * 1 Circular Logic * 2 Phase Singularities (Screwy Results of Circular Logic) * 3 The Rules of the Ring * 4 Ring Populations * 5 Getting Off the Ring * 6 Attracting Cycles and Isochrons * 7 Measuring the Trajectories of a Circadian Clock * 8 Populations of Attractor Cycle Oscillators * 9 Excitable Kinetics and Excitable Media * 10 The Varieties of Phaseless Experience: In Which the Geometrical Orderliness of Rhythmic Organization Breaks Down in Diverse Ways * 11 The Firefly Machine 12 Energy Metabolism in Cells * 13 The Malonic Acid Reagent ('Sodium Geometrate') * 14 Electrical Rhythmicity and Excitability in Cell Membranes * 15 The Aggregation of Slime Mold Amoebae * 16 Numerical Organizing Centers * 17 Electrical Singular Filaments in the Heart Wall * 18 Pattern Formation in the Fungi * 19 Circadian Rhythms in General * 20 The Circadian Clocks of Insect Eclosion * 21 The Flower of Kalanchoe * 22 The Cell Mitotic Cycle * 23 The Female Cycle * References * Index of Names * Index of Subjects

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/596B270197FE27DE5FABB598B6210622/S0025557200150892a.pdf/div-class-title-span-class-italic-the-geometry-of-biological-time-span-by-a-t-winfree-pp-544-dm68-corrected-second-printing-1990-isbn-3-540-52528-9-springer-div.pdf

The geometry of biological time , by A. T. Winfree. Pp 544. DM68. Corrected Second Printing 1990. ISBN 3-540-52528-9 (Springer)

A comprehensive review (ca. 230 references) is presented of the present (1983) state of knowledge of paramagnetic defects in crystalline quartz, as derived from electron paramagnetic resonance spectroscopy and related techniques. An auxiliary description of relevant concepts in solid state electron paramagnetic resonance (EPR), suitable for the non-specialist, is included. The centres described include those arising from impurity ions (Al, H, Cu, Ag, Ge, P, Ti, Fe) as well as those (E′) associated with oxygen ions missing in the quartz structure. Emphasis is placed on the structural information derivable from EPR. A brief survey of the present state of understanding of the optical bands caused by the defects is also given.

A review of electron spin spectroscopy and its application to the study of paramagnetic defects in crystalline quartz

Isostables, isochrons, and Koopman spectrum for the action-angle representation of stable fixed point dynamics

Large-scale complex eigenvalue problems

The energy, ground-state properties, polarizability and dipole shielding factor of one-electron systems confined in boxes are studied as functions of box size, R. The systems are the unbound electron, hydrogenic atom, harmonic oscillator and z 2p oscillators in various 1D and 3D boxes (cartesian and spherical). Exact polarizabilities α are compared with the variational Kirkwood, Buckingham and Unsold bounds. For all boxes with an attractive internal potential the curve α(R) has a characteristic s shape. Some discussion of α(R) for ions in crystals in given in terms of these models.

Energy, polarizability and size of confined one-electron systems

Finite element method for solving the two-dimensional schroedinger equation

A Bonhoeffer--van der Pol system is analyzed in the range of parameters where the attractor is a focus. The system's responses to a single pulse stimulus applied at different points along a ``hidden structure'' are used to construct a one-dimensional map from which the system's responses to pulse train stimulations are obtained.

Forced Bonhoeffer-van der Pol oscillator in its excited mode.

The feasibility of a spiral-type solution, periodic both in time and in space, of a reaction-diffusion equation (specifically the FitzHugh-Nagumo system) in an excitable medium is numerically demonstrated. The solution consists of arrays of interacting spiral pairs, which repeatedly create by partial annihilation a system of residual portions (RPs). The latter behaves as a source to the next generation of the spiral-pair array. If basic (highest) translational symmetry is not conserved, pointwise perturbations, above a certain threshold, are shown to be able to destroy the pattern after a certain transient time by changing its symmetry. If the basic translational symmetry is preserved, such perturbations do not cause destruction unless occurring at the nearest vicinity of the RP site. Singular value decomposition methods are used to analyze the structure of the pattern, revealing the importance of the spiral pairs and the RPs.

Time-periodic lattice of spiral pairs in excitable media.

Application of the finite-element method to the hydrogen atom in a box in an electric field

Simple cylindrical models of a hydrogen atom confined in crystalline quartz are considered. The isotropic and anisotropic components of the hyperfine splitting are evaluated by solving numerically the appropriate two‐dimensional Schrodinger equation, utilizing an adaptation of a finite element package previously described. The results show good agreement with electron paramagnetic resonance data, and given an estimate of d‐orbital admixture in the H‐atom ground state orbital.

M. Friedman

Papers

Finite element method for solving the two-dimensional schroedinger equation

Forced Bonhoeffer-van der Pol oscillator in its excited mode.

Time-periodic lattice of spiral pairs in excitable media.

Application of the finite-element method to the hydrogen atom in a box in an electric field

Models for the hydrogen atom confined within crystalline quartz