We investigate the oscillatory chemical dynamics in a closed isothermal reaction system described by the reversible Lotka-Volterra model. This is a three-dimensional, dissipative, singular perturbation to the conservative Lotka-Volterra model, with the free energy serving as a global Lyapunov function. We will show that there is a natural distinction between oscillatory and non-oscillatory regi...

1. The central ganglia of a number of gastropod molluscs (including the marine snail Aplysia californica and the terrestrial snail Helix pomatia) contain neurones which exhibit endogenous patterns of oscillatory activity. 2. This oscillatory activity can be modulated for long periods of time by synaptic and hormonal stimulation. 3. Stimulation of appropriate pre-synaptic nerves causes long-last...

Colloidal particles adjacent to electrodes have been observed to exhibit drastically different aggregation behavior depending on the identity of the suspending electrolyte. For example, particles suspended in potassium chloride aggregate laterally near the electrode upon application of a low-frequency (∼100 Hz) oscillatory electric field, but the same particles suspended in potassium hydroxide ...

A non-trivial solution of (1) is called oscillatory if for every N > 0 there exists an n > N such that X,X n + , 6 0. If one non-trivial solution of (1) is oscillatory then, by virtue of Sturm’s separation theorem for difference equations (see, e.g., [S]), all non-trivial solutions are oscillatory, so, in studying the question of whether a solution {x,> of (1) is oscillatory, it is no restricti...

A novel apparatus for detecting a subtle decrease in erythrocyte deformability was developed. The oscillatory shape change of erythrocytes was monitored under an oscillatory shear stress (modulating the oscillation frequency in the range of 9-90 dyn/cm2). The ellipsoidal deformation of intact erythrocytes perfectly followed the oscillatory force of up to about 2 Hz, but the diamide-treated cell...

This paper surveys recent advances in the allied challenges of discretizing highly oscillatory ordinary differential equations and computing numerical quadrature of highly oscillatory integrals, and attempts to sketch the mathematical foundations of a general approach to these issues. Having described the Magnus, Cayley and Neumann methods for highly oscillatory ordinary differential equations ...

The long-range entropic forces that arise between two micrometer-sized colloidal spheres in a fluid of much smaller colloidal spheres were directly measured using a line-scanned optical tweezer. This new technique allowed us to measure the functional form of the potential with sub-kBT energy and 15 nm spatial resolution. At the lowest small sphere concentrations, the potential was monotonically...

We study quantum mechanics problem described by the Schrödinger equation with Kapitza pendulum potential, that is asymmetric double-well potential on circle. For oscillatory states spatially localize around two stable saddle positions of we obtain perturbative eigenvalues and corresponding piecewise wavefunctions. The spectrum computed extending angle coordinate to complex plane so quantization...

Oscillatory afterpotentials in cardiac tissues are believed to result from an activation of calcium-operated cation channels of mixed selectivity (sodium, potassium), or perturbation of an electrogenic sodium-calcium exchange carrier, by an oscillatory release of calcium from sarcoplasmic reticulum. In the present experiments, the presence and properties of ouabain-induced oscillatory afterpote...

despite improvement of mechanical ventilation devices for infants, lung injury still causes morbidity and mortality in many cases. to determine the effect of high frequency oscillatory ventilation (hfov) in infants with severe respiratory failure, 10 neonates were evaluated prospectively. mean gestational age of these patients was 35 weeks and alveolar-arterial oxygen gradient (a-ado2) and the ...