Film condensation of multicomponent mixtures

The classic Nusselt model is generalized for the condensation process of a multicomponent vapor mixture. The condensed vapors may be miscible in their liquid state or contain noncondensable gases.The reduction in the condensation rate owing to the accumulation of a noncondensable gas or the more volatile components near the condensate interface is demonstrated for three component systems of methanol—water—air and acetone—methanol—water. Also the effects of interfacial suction and forced convection are included.The analytical solution incorporates Diffusion Law for a multicomponent system and both exact and approximate integral method solutions are applied. The accuracy of the integral method turns out to be remarkably good.     

Low-energy resonances in photodissociation of CH+

Close coupling calculations for the photodissociation cross sections of CH⁺+hv → C⁺(²P) + H(²S) exhibit near threshold peaks not ascribable only to quasi-bound levels in the A ¹Π potential. Our calculations demonstrate the importance of non-adiabatic transitions and thereby suggest the necessity to revise earlier predictions of the rate of radiative association of C⁺ with H.     

Disintegration of Cnoidal Waves over Smooth Topography

The transformation of cnoidal waves in a basin with smooth topography is studied in the frame of the variable-coefficient Korteweg–de Vries equation and the generalized Zakharov's system. It is shown that the cnoidal structure of the propagating nonlinear wave is destroyed if the topography contains a periodic component with a characteristic scale close to the nonlinearity length. Focusing on waves in intermediate depth, a simple analytical model based on a two-harmonic representation of the cnoidal wave demonstrates the main features of the process of disintegration of the cnoidal structure of the nonlinear wave. Numerical simulations of the interaction of several harmonics confirm the analytical conclusions.     

On uniformly accurate high‐order Boussinesq difference equations for water waves

A new accurate finite‐difference (AFD) numerical method is developed specifically for solving high‐order Boussinesq (HOB) equations. The method solves the water‐wave flow with much higher accuracy compared to the standard finite‐difference (SFD) method for the same computer resources. It is first developed for linear water waves and then for the nonlinear problem. It is presented for a horizontal bottom, but can be used for variable depth as well. The method can be developed for other equations as long as they use Padé approximation, for example extensions of the parabolic equation for acoustic wave problems. Finally, the results of the new method and the SFD method are compared with the accurate solution for nonlinear progressive waves over a horizontal bottom that is found using the stream function theory. The agreement of the AFD to the accurate solution is found to be excellent compared to the SFD solution. Copyright © 2005 John Wiley & Sons, Ltd.     

A Liouville-type theorem for the p-Laplacian with potential term

In this paper we prove a sufficient condition, in terms of the behavior of a ground state of a singular p  -Laplacian problem with a potential term, such that a nonzero subsolution of another such problem is also a ground state. Unlike in the linear case (p=2$p=2$), this condition involves comparison of both the functions and of their gradients.     

Fluorescent DNA nanotags: supramolecular fluorescent labels based on intercalating dye arrays assembled on nanostructured DNA templates

Fluorescence detection and imaging are vital technologies in the life sciences and clinical diagnostics. The key to obtaining high-resolution images and sensitive detection is to use fluorescent molecules or particles that absorb and emit visible light with high efficiency. We have synthesized supramolecular complexes consisting of a branched DNA template and fluorogenic intercalating dyes. Because dyes can intercalate up to every other base pair, high densities of fluorophores are assembled yet the DNA template keeps them far enough away from each other to prevent self-quenching. The efficiency with which these noncovalent assemblies absorb light is more than 10-fold greater than that of the individual dye molecules. F?rster resonance energy transfer from the intercalated dyes to covalently attached acceptor dyes is very efficient, allowing for wavelength shifting of the emission spectrum. Simple biotinylation of the DNA template allows for labeling of streptavidin-coated synthetic microspheres and mouse T-cells.     

A Liouville-type Theorem for Schrödinger Operators

In this paper we prove a sufficient condition, in terms of the behavior of a ground state of a symmetric critical operator P ₁, such that a nonzero subsolution of a symmetric nonnegative operator P ₀ is a ground state. Particularly, if P _j : = ?Δ + V _j , for j = 0,1, are two nonnegative Schrödinger operators defined on \(\Omega\subseteq \mathbb{R}^d\) such that P ₁ is critical in Ω with a ground state φ, the function \(\psi\nleq 0\) is a subsolution of the equation P ₀ u = 0 in Ω and satisfies \(\psi_+\leq C\varphi\) in Ω, then P ₀ is critical in Ω and \(\psi\) is its ground state. In particular, \(\psi\) is (up to a multiplicative constant) the unique positive supersolution of the equation P ₀ u = 0 in Ω. Similar results hold for general symmetric operators, and also on Riemannian manifolds.     

Frequency upshift in BO2 and CO2+ upon electronic excitation: a twin-state model rationalization

The twin-state model, previously shown to provide a simple physical rationalization for the frequency upshift (exaltation) of the Kekulé mode in benzene upon S(0) to S(1) electronic excitation, is extended to the case of the BO(2) radical and the CO(2)(+) radical cation. In the case of BO(2)/CO(2)(+), the ground and excited states are degenerate, yet the model applies to the degenerate two-state system as well. In contrast with a pseudo-Jahn-Teller model, the twin-state one can predict which frequency is exalted and also which pair of electronic states are coupled, thus explaining the specificity of the phenomenon. The frequency exaltation is a spectroscopic manifestation of the resonance between the pair of VB structures describing twin states. In analogy with the case of benzene, it is predicted that the ν(3) asymmetric stretch fundamental will be a dominant peak in the two-photon absorption spectrum of BO(2) and CO(2)(+).     

On the efficiency of water soluble antioxidants

The wide use of high intensity ultrasound (HIU) in modern medicine raises the question of bio-safety. It has been shown that the effect of HIU in biological media may have similarity to the effects of ionizing radiation. Exposure of biological media to HIU field may lead to cavitation phenomenon followed by formation of free radicals such as hydroxyl radical (OH) and the super-oxide ion (O₂-). These are highly reactive species that may cause harmful effects and induce oxidative stress. In the present study we employed electron spin resonance (ESR) spectroscopy together with spin traps to quantify the dynamics of hydroxyl radical formation during exposure to HIU field in the presence of different amounts of six antioxidants. Thus, the efficiency of water-soluble antioxidants, namely Allicin, Melatonin, Deoxyribose, Trolox, Nuphlutine and Hermidin, to suppress accumulation of OH radicals was examined. The results show that among the six, Trolox and Allicin reduce hydroxyl concentration with the highest efficiency.