Citations

It has previously been shown that acoustic ray paths in range-dependent ocean models exhibit chaotic behavior. Most of the investigations into the ray chaos phenomenon have been primarily numerical in nature. The objective of this report is to study theoretically the existence of ray chaos in a parabolic ray system with an analytically prescribed sound-speed model consisting of a double-channel profile perturbed by a typical periodic range-dependent disturbance. The perturbed Hamiltonian ray system is studied analytically via Melnikov’s method. It is shown that, under certain conditions, ray trajectories in some regions of the Poincaré section are equivalent to trajectories of the horseshoe map no matter how small the corresponding perturbation is. These conditions are sufficient for ray chaos and easily satisfied, thus explaining why double-channel propagation is very likely to exhibit chaotic behavior. [Work supported by CA43920 NIH.]

Earlier studies [P. J. Westervelt, J. Acoust. Soc. Am. 29, 199–203, 934–935 (1957)] of the mutual nonlinear interaction of two plane waves of sound with each other are extended to include the viscous effect. The viscous effect is considered both from the equations of motion and the equation of state of the medium. An analytical solution to the lowest order scattering process is obtained if the viscous effect of second order and higher can be neglected. In fact, it is shown that the scattered density ρs of two interacting plane waves having the frequencies ω1 and ω2, respectively, satisfies the following equation: ⧠2vρs=⧠2v{c0−2E12+[(2cosθ +B/A)/2ω1ω2 (1−cosθ)]∇2W12 +[DB(c20ω1ω2)−1 / 4A ×(1−cosθ)2]∇2(∂W12/∂t)+[DB(3+cosθ)/2Ac40 (1−cosθ)](∂V12/∂t)}, where E12, V12, and W12 are, respectively, the total, potential, and special defined energy densities, D is the sound diffusivity, B and A are nonlinearity parameters, θ is the intersecting angle, and ⧠2v is a modified d’Alembertian operator. [Work supported by CA43920 NIH.]

Earlier studies [P. J. Westervelt, J. Acoust. Soc. Am. 29, 199–203, 934–935 (1957)] of the mutual nonlinear interaction of two plane waves of sound with each other are extended to include the viscous effect. The viscous effect is considered both from the equations of motion and the equation of state of the medium. An analytical solution to the lowest-order scattering process is obtained if the viscous effect of second order and higher can be neglected.

Acoustic radiation pressure exerted by an arbitrary acoustic wave in a three-dimensional lossy medium is calculated by extending an indirect approach developed by Chu and Apfel [B-T. Chu and R. E. Apfel, ‘‘Acoustic radiation pressure produced by a beam of sound,’’ J. Acoust. Soc. Am. 72, 1673–1687 (1982)]. Without appealing to the detailed solutions of equations governing fluid motion, a general analytic expression for the radiation pressure in lossy media with arbitrary waves is obtained. When an infinite lossy medium is considered, the expression states that the radiation pressure, to the lowest order of approximation (i.e., second order), is equal to corresponding total energy density. For a special class of confined spaces, the expression leads to a rather general formula for the radiation pressure, in which the radiation pressure is given in terms of various energy densities in the field. Furthermore, a relationship among these energy densities is generalized to the case of lossy media, which enables one to compute the radiation pressure in the class of spaces with the knowledge of the first-order perturbation solution only.

Theories on acoustic radiation pressure associated with plane acoustic waves and lossless media have been examined extensively. The radiation pressure produced by a non-plane wave in a lossy unbounded medium was analyzed. The distinction between Lagrangian and Eulerian pressure was used to clarify the understanding of radiation pressure. The radiation pressure exerted on a perfectly absorbing pointwise target by an arbitrary acoustic wave in an unbounded lossy medium was then considered. By using an indirect approach developed in Chu and Apfel [B.-T. Chu and R. E. Apfel, 1673–1687 (1982)], the radiation pressure was analyzed without appealing to the detailed solutions of the governing fluid dynamic equations. It was shown that even in lossy media with arbitrary waves, the radiation pressure experienced by a pointwise target is equal to the Langevin pressure which is the time average energy density at that point. The radiation pressure exerted on a specific target by an arbitrary acoustic wave in an infinite lossy medium was studied and a concise theoretical result was obtained. [The work was supported by grants CA 43920 and HL 41046 from the National Institutes of Health.]

Abstract It is well known that the histone deacetylase (HDAC) inhibitor trichostatin A (TSA) acts synergistically with the DNA methyltransferase (DNMT) inhibitor 5-aza-2′-deoxycytidine (ADC) to reactivate DNA methylation-silenced genes. Moreover, in several studies, TSA was capable of inducing DNA demethylation even in the absence of ADC. Here we describe a mechanism by which HDAC inhibitors affect DNA methylation through their regulation on DNMT3B, a methyltransferase responsible for de novo DNA methylation. Using quantitative real-time PCR and Western blot analysis, we show that TSA down-regulates DNMT3B mRNA and protein expression in human endometrial cancer cells. This decrease in DNMT3B mRNA results in a significant reduction in de novo methylation activities. Further experiments indicated that TSA decreases DNMT3B mRNA stability and reduces its half-life from ∼4 to 2.5 hours. We established that protein synthesis is required for posttranscriptional regulation, suggesting the involvement of an RNase and/or key mRNA stabilization factor(s) controlling the DNMT3B mRNA stability. Therefore, TSA may not only modify histone acetylation, but also potentially alter DNA methylation. Since the HDAC inhibitors are frequently used in epigenetic studies and are considered to be promising anticancer drugs, these new findings will have implications in both laboratory and clinical settings.

AbstractAlthough hyperhomocysteinemia is an independent risk factor for cardiovascular disease, a direct role for homocysteine (Hcy) in this disease remains to be shown. Whereas diet-induced hyperhomocysteinemia promotes atherosclerosis in animal models, the effects of Hcy on atherogenesis in the absence of dietary perturbations is not known. We have generated double knock-out mice with targeted deletions of the genes for apolipoprotein E (apoE) and cystathionine β-synthase (CBS), which converts Hcy to cystathionine. ApoE−/−/CBS−/− mice developed aortic lesions even in the absence of dietary manipulation; lesion area and lesion cholesteryl ester (CE) and triglyceride (TG) contents increased with animal age and plasma Hcy levels. Plasma total cholesterol was significantly increased, whereas high density lipoprotein (HDL) cholesterol and TG concentrations of apoE−/−/CBS−/− mice were decreased. Cholesterol esterification and activities of enzymes catalyzing CE or TG formation in the vessel wall and in peritoneal macrophages were not changed by hyperhomocysteinemia. However, uptake of human acetyl-LDL, but not native low density lipoprotein (LDL), by mouse peritoneal macrophages was higher in the presence of hyperhomocysteinemia. These results suggest that isolated hyperhomocysteinemia is atherogenic and alters hepatic and macrophage lipoprotein metabolism, in part, by enhancing uptake of modified LDL.

It has been shown that acoustic ray paths in range-dependent ocean models exhibit chaotic behavior. Most of the investigations into the ray chaos phenomenon have been primarily numerical in nature. Analytical derivation of sufficient conditions for chaos in acoustic systems has been restricted to inherently discrete problems. This article reports a theoretical study of the existence of ray chaos in a class of continuous parabolic ray systems. This class of ray systems is indexed by a family of analytically prescribed double-channel sound-speed profiles perturbed by periodic range-dependent disturbances. The perturbed Hamiltonian ray systems are studied analytically via the Melnikov method. It is shown that, under certain conditions, ray trajectories of the systems are equivalent to trajectories of a classic chaotic system known as the horseshoe map when the perturbation is periodic and small. These conditions are sufficient for ray chaos and easily satisfied, thus explaining why double-channel propagation is very likely to exhibit chaotic behavior.