Terminal Damping of a Solitary Wave Due to Radiation in Rotational Systems

The evolution of a solitary wave under the action of rotation is considered within the framework of the rotation-modified Korteweg–de Vries equation. Using an asymptotic procedure, the solitary wave is shown to be damped due to radiation of a dispersive wave train propagating with the same phase velocity as the solitary wave. Such a synchronism is possible because of the presence of rotational dispersion. The law of damping is found to be "terminal" in the sense that the solitary wave disappears in a finite time. The radiated wave amplitude and the structure of the radiated "tail" in space–time are also found. Some numerical results, which confirm the approximate theory developed here, are given.     

Catecholase activity of a series of dicopper(II) complexes with variable Cu-OH(phenol) moieties

The catecholase activity of a series of dicopper(II) complexes containing different numbers of phenol groups coordinated to the metal centers was studied to identify functional as well as structural models for the type III copper enzymes tyrosinase and catechol oxidase. The syntheses and characterization of complexes [Cu(2)(H(2)bbppnol)(mu-OAc)(H(2)O)(2)]Cl(2).2H(2)O (1) and [Cu(2)(Hbtppnol)(mu-OAc)](ClO(4))(2) (2) were previously reported by us (Inorg. Chim. Acta 1998, 281, 111-115; Inorg. Chem. Commun. 1999, 2, 334-337), and complex [Cu(2)(P1-O(-))(OAc(-))](ClO(4))(2) (3) was previously reported by Karlin et al. (J. Am. Chem. Soc. 1997, 119, 2156-2162). The catalytic activity of the complexes 1-3 on the oxidation of 3,5-di-tert-butylcatechol was determined spectrophotometrically by monitoring the increase of the 3,5-di-tert-butyl-o-benzoquinone characteristic absorption band at about 400 nm over time in methanol saturated with O(2)/aqueous buffer pH 8 solutions at 25 degrees C. The complexes were able to oxidize 3,5-di-tert-butylcatechol to the corresponding o-quinone with distinct catalytic activity. A kinetic treatment of the data based on the Michaelis-Mentèn approach was applied. The [Cu(2)(H(2)bbppnol)(mu-OAc)(H(2)O)(2)]Cl(2) small middle dot2H(2)O complex showed the highest catalytic activity of the three complexes as a result of a high turnover rate (k(cat) = 28 h(-1)) combined with a moderate substrate-catalyst binding constant (K(ass) = 1.3 x 10(3) M(-1)). A mechanism for the oxidation reaction is proposed, and reactivity differences, k(cat)/K(M) of the complexes, were found to be dependent on (DeltaE)(1,2), the difference in the driving force for the reduction reactions Cu(II)(2)/Cu(II)Cu(I) and Cu(II)Cu(I)/Cu(I)(2).     

Optical solitons: Perspectives and applications

This article serves as an introduction to the focus issue on optical solitons. After a short review of the history of solitons and the field of integrable systems, a brief overview of the development of nonlinear optics and optical solitons is provided. Next, the various contributions to this focus issue are presented, and a few separate remarks are devoted to optical communications, where solitons promise to play a decisive role in the next generation of commercial systems. (c) 2000 American Institute of Physics.     

Maximum likelihood method in the problem of adaptive detection of signals with unknown noninformative parameters

A new algorithm of signal detection is synthesized with an estimate of signal noninformative parameters against the noise background with an arbitrary distribution law. It has been shown by a simple example of Gaussian clutter that the efficiency of the synthesized detector approaches the efficiency of deterministic signal detection. Antiaircraft Command High School of Nizhny Novgorod, Russia. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 41, No, 5, pp. 640–650, May, 1998.     

Dynamics of particles in the steady flows of an inviscid fluid

Advection of small particles with inertia in two-dimensional ideal flows is studied both numerically and analytically. It is assumed that the flow disturbance around the particle corresponds to a potential dipole, so that the motion is driven by pressure gradient, inertial, and added-mass forces. It is found that in general the motion is nonintegrable, but particular exact solutions can be obtained. The problem is then studied for the cases of axisymmetric flow, when the motion proves to be completely integrable, and of a cellular flow, for which both regular and stochastic (bounded and unbounded) trajectories are calculated. In the latter case, the unbounded stochastic motion is of Brownian-like character, and the results derived show that the particle dispersion process is generally anomalous.     

The structure of LC-continuous functions

A function f is LC-continuous if the inverse image of any open set is a locally closed set; i.e., an intersection of an open set and a closed set. The aim of this paper is to prove the following theorem: Let f: X→Y be an LC-continuous function onto a separable metric space Y. Then X can be covered by countably many subsets T _n ⊂X such that each restriction f∣T _n is continuous at all points of T _n .     

Nonlinear Dynamics of Rock: Hysteretic Behavior

We discuss the dynamics of media with hysteretic stress-strain properties. First, experimental evidence of the hysteretic behavior of rock is presented. This evidence leads to a pattern of unifying behavior whose origin is within the bond system of the material, which includes small cracks, intergrain contacts and, the cement that holds the grains in place. Nonlinear response is evident over a large frequency interval (dc to several MHz at least), and it is significant from strains of plasticity down to the smallest measurable strains (order 10^-8-10^-9). Second, some models related to such a behavior are outlined. Finally, oscillations and waves in hysteretic media are discussed.