Beta Epsilon Research Articles

Scaling law and asymptotic distribution of Lyapunov exponents in conservative dynamical systems with many degrees of freedom

The authors study by numerical means the infinite product of 2N*2N conservative random matrices which mimics the chaotic behaviour of Hamiltonian systems with N+1 degrees of freedom made of weakly nearest-neighbour coupled oscillators. The maximum Lyapunov exponent lambda 1 exhibits a power-law behaviour as a function of the coupling constant epsilon : lambda 1 approximately epsilon beta with either beta =1/2 or beta =2/3, depending on the probability distribution of the matrix elements. These power laws do not depend on N and moreover increasing N, lambda 1 rapidly tends to an asymptotic value lambda *1 which only depends on epsilon and on the kind of probability distribution chosen for building up the matrices. They also compute the spectrum of the Lyapunov exponents and show that is has a thermodynamic limit of large N. This suggests the existence of a Kolmogorov entropy per degree of freedom proportional to lambda *1.

Scaling law for the maximum Lyapunov characteristic exponent of infinite product of random matrices

The authors present a simple derivation for the scaling behaviour of the maximum Lyapunov characteristic exponent lambda of infinite product of symplectic random matrices. The considered random matrices depend on a parameter epsilon and lambda =0 for epsilon =0. They obtain lambda varies as epsilon beta with either beta =1/2 or beta =2/3 depending on the probability distribution of the matrix elements. The results are in agreement with a previous numerical simulation.

Diffusion tensor of electron or light ion swarm in electric fields in gases

The diffusion tensor in an isolated electron or light ion swarm subject only to elastic collisions with molecules has been formulated from the multiterm expansion of the Boltzmann equation in the hydrodynamic description. Derived diffusion coefficients for the transverse and longitudinal directions include the additional terms representative of the curvature effect under the action of an electric field besides the usual two-term expressions. Discussion is, particularly, focused on the relation between the transverse diffusion coefficient DT and its conventional expression DV. Numerical calculations have been made for the electron swarm in a model gas having a momentum transfer cross-section, Qm( epsilon )=Q0 epsilon beta ( beta =0, 1/2, 1), with isotropic scattering. It will be recognised that an appreciable degree of discrepancy occurs between DT and DV with the increase of the power beta , i.e. of the cross-sectional dependence on energy.

Energy loss by electric and magnetic charges in matter

Exact expressions for the electromagnetic fields of a charged particle through a dispersive and dissipative medium have been used to calculate exact expressions for the energy loss due to distant collisions. These are evaluated using Fermi's one-oscillator approximation to the dielectric constant. For particle velocities with beta epsilon 0-1/2 the present results differ from those of these authors. It is shown that this is due to their incomplete treatment of the conditions imposed by the model for the dielectric constant. The relevance of these results to the detection of magnetic monopoles and of dyons is also discussed.

Myocardial hydroxyproline and mechanical response to prolonged pressure loading followed by unloading in the cat.

To determine the myocardial response to prolonged pressure-loading and unloading, kittens weighing 0.8-1.2 kg underwent pulmonary artery banding, which initially elevated right ventricular (RV) systolic pressure by 10-15 mm Hg. 52 and 76 wk later; RV weight/body weight had increased by approximately 80%. Total RV hydroxyproline had increased significantly, whereas hydroxyproline concentration was unchanged from that of nonbanded animals of comparable age. In isometrically contracting RV papillary muscles, peak active force was significantly less at 76 wk (3.3 +/- 0.8 [SD] g/mm2 than at 52 wk (5.1 +/- 0.8 g/mm2) or in nonbanded animals (4.8 +/- 0.8 g/mm2). Velocity of muscle shortening at comparable loads was unchanged after 52 wk but was significantly less after 76 wk. In nonstimulated, slowly stretched muscles, passive stiffness constants, alpha and beta, derived from delta = alpha(e beta epsilon - 1), where delta is instantaneous stress and epsilon is Lagrangian strain, were unchanged by banding. The band was removed after 52 wk in additional animals that were studied 24 wk later. In those animals with normal RV pressures at death, hypertrophy had regressed and hydroxyproline concentration was comparable to that of nonbanded and banded animals; Active and passive mechanical function remained normal. In this model, changes in hydroxyproline parallel changes in muscle mass, and passive stiffness remains normal during development and regression of hypertrophy. Removal of the pressure load after prolonged hypertrophy prevents or retards the late development of myocardial dysfunction.

Hydroxyproline and passive stiffness of pressure-induced hypertrophied kitten myocardium.

Passive stiffness and hydroxyproline content of myocardium hypertrophied by pressure-loading were determined in kittens 2, 8-16, and 24-52 wk after pulmonary artery banding, which initially elevated right ventricular systolic pressure by 10-15 mm Hg. Right ventricular mass increased by approximately 75%, three-quarters of which occurred during the first 2 wk after banding. Passive stiffness was assessed from resting length-tension relations of isometrically contracting isolated right ventricular papillary muscles. Stiffness constants, alpha and beta were determined from the relationship sigma = alpha (e beta epsilon - 1) where sigma = stress and epsilon = Lagrangian strain. Elastic stiffness (d sigma/d epsilon) was derived from: d sigma/d epsilon = beta sigma + beta alpha. Right ventricular hydroxyproline increased in proportion to muscle mass so that hydroxyproline concentration remained unchanged after banding. Both alpha, beta, and elastic stiffness-stress relations were similar to values in nonbanded controls. Thus, we did not observe an increase in passive stiffness or hydroxyproline concentration of pressure-stiffness or hydroxyproline concentration of pressure-induced hypertrophied myocardium in contrast to most previous studies.

A cross-linking study of the Ca2+, Mg2+-activated adenosine triphosphatase of Escherichia coli.

The solubilized Ca2+,Mg2+-activated adenosine triphosphatase of Escherichia coli is composed of five subunits designated alpha, beta, gamma, delta and epsilon in order of decreasing molecular weight. The subunit structure of the enzyme has been investigated by the use of the cleavable cross-linking agents dithiobis(succinimidyl propionate), methyl-4-mercaptobutyrimidate, dimethyl-3,3'-dithiobispropionimidate, disuccinimidyl tartarate, and cupric 1,10-phenanthrolinate. The products of cross-linking were analyzed by two different two-dimensional gel electrophoresis systems. The following cross-linked subunit dimers were observed: alpha 2, beta 2, alpha beta, alpha delta, beta gamma, beta delta, beta epsilon and gamma epsilon. These results, together with other published data, are discussed in relation to a model of the arrangement of the subunits in the ATPase molecule.

Phase transitions in lattice fluids. I. Short-range interactions

The phase transitions of lattice fluids with molecules defined by first-neighbour exclusion, and interacting at short range, are considered using extended Kikuchi approximations. On the square lattice, a second-neighbour interaction does not produce a disordered low-density transition, but does make the packing transition first order below a critical temperature epsilon beta =-1.05. The resulting phase diagram therefore has only generalized fluid and solid regions. In a Kikuchi double- square calculation with third-neighbour interaction a disordered transition is produced, but this overlaps with the ordered state and again there is no stable intermediate liquid phase. Short-range interactions produce qualitatively the same effect on the triangular and simple cubic lattices. Particularly for the ordered state, the large set of non-linear equations produced by an analytical treatment of extended Kikuchi approximations have limited the range of possible calculations.