A weight-function approach for determining watershed initial conditions for combustion waves

In many generic combustion models, one finds that a combustionwave will develop with a specific wave speed. However, thereare possible initial temperature profiles which do not evolveinto such waves, but rather die out to the ambient temperature.There can exist, in some models, a clear distinction betweenthose initial conditions that do evolve into combustion wavesand those that do not; this is sometimes referred to as thewatershed initial condition. When fuel consumption is consideredto be negligible, analytical methods can be used to obtain theexact watershed. In this paper, we consider the problem of determiningpseudo-watersheds and ascertaining the relationship betweenthese pseudo-watersheds and the exact watersheds. In the processa novel weight-function approach for infinite spatial domainsis developed.     

Synthesis of cytotoxic cyanobactin,Wewakazole B

We report herein the synthesis of cytotoxic cyanobactin, Wewakazole B through an efficient solution-phase approach. The key steps of the synthesis are the macrocyclic lactamization of linear dodecapeptide and construction of two hexapeptides with three different substituted oxazole rings.     

Self-similarity in periodically forced oscillators

Periodic stimulation of limit cycle oscillations leads to one-dimensional maps f: S¹ → S¹ with two parameters which correspond to the frequency and amplitude of the periodic forcing. Bifurcations are described for the situtation in which f is of topological degree zero. Self-similarity is found in the parameter space.     

Complex dynamics and multistability in a damped harmonic oscillator with delayed negative feedback

A center manifold reduction and numerical calculations are used to demonstrate the presence of limit cycles, two-tori, and multistability in the damped harmonic oscillator with delayed negative feedback. This model is the prototype of a mechanical system operating with delayed feedback. Complex dynamics are thus seen to arise in very plausible and commonly occurring mechanical and neuromechanical feedback systems. (c) 1995 American Institute of Physics.     

Dynamical disease: Identification,temporal aspects and treatment strategies of human illness

Dynamical diseases are characterized by sudden changes in the qualitative dynamics of physiological processes, leading to abnormal dynamics and disease. Thus, there is a natural matching between the mathematical field of nonlinear dynamics and medicine. This paper summarizes advances in the study of dynamical disease with emphasis on a NATO Advanced Research Worshop held in Mont Tremblant, Quebec, Canada in February 1994. We describe the international effort currently underway to identify dynamical diseases and to study these diseases from a perspective of nonlinear dynamics. Linear and nonlinear time series analysis combined with analysis of bifurcations in dynamics are being used to help understand mechanisms of pathological rhythms and offer the promise for better diagnostic and therapeutic techniques. (c) 1995 American Institute of Physics.     

The origin of sticking between a hydroperoxy radical and a water surface

An understanding of how gas-phase radicals in the earth's atmosphere become incorporated with liquid-phase cloud droplets is a vital part of understanding the chemical budgeting of these highly reactive species. Recent studies have suggested that hydroperoxy radicals (HO2) have an affinity for binding to a water surface. The calculations presented here are used to extricate the components of the attractive contribution of the intermolecular interactions that are responsible for the unusually strong binding between the hydroperoxy radical and a water surface. The analyses reveal that, for the binding of an HO2 radical to a water surface, the two water molecules nearest the radical are the most relevant to the bonding and the addition of other water molecules has little affect on the bonding between the radical and the two nearest waters. These results suggest that, once the HO2 is bound to the surface, the binding is a relatively local phenomenon. Identifying the properties responsible for the strong attraction is an important result that can be used to identify other radical systems whose chemistry might be impacted by the presence of water.