Analytic solutions of initial-boundary-value problems of transient conduction using symmetries

Lie symmetry method is applied to find analytic solutions of initial-boundary-value problems of transient conduction in semi-infinite solid with constant surface temperature or constant heat flux condition. The solutions are obtained in a manner highlighting the systematic procedure of extending the symmetry method for a PDE to investigate BVPs of the PDE. A comparative analysis of numerical and closed form solutions is carried out for a physical problem of heat conduction in a semi-infinite solid bar made of AISI 304 stainless steel.     

A note on the tangent bundle of <Emphasis Type="Italic">G/P</Emphasis>

Let P be a parabolic subgroup of a complex simple linear algebraic groupG. We prove that the tangent bundle T (G/P) is stable.     

Effect of dielectric properties of metals on terahertz transmission subwavelength hole arrays

We study the influence of dielectric function of metals on the transmission properties of terahertz pulses through periodically patterned subwavelength holes. Because of a drastic increase in the value of dielectric constants, most metals become highly conductive at terahertz frequencies. Extraordinary terahertz transmission is observed in subwavelength hole arrays made from both good and poor electrical conductors. The measured transmittance of terahertz pulses is found to be enhanced with increasing ratio of the real to the imaginary dielectric constant of the constituent metals, for which the dielectric function follows the Drude model.     

1,3-Dibromo 5,5-dimethylhydantoin (DBH):A novel and efficient catalyst for the synthesis of 14-aryl-14H-dibenzo[a,j] xanthenes under solvent-free conditions

An atom-efficient and environment-friendly approach for the synthesis of aryl-14H-dibenzo[a,j]xanthenes (3a–o) via the one-pot reaction of β-naphthol and aryl aldehydes (1) catalyzed by DBH has been developed. The present approach offers several advantages such as reduced reaction times, moderate temperature, higher yields, solvent free, eco-friendly reaction condition, easy purification and economic availability of the catalyst.     

Interference of ATP with the fluorescent probes YOYO-1 and YOYO-3 modifies the mechanical properties of intercalator-stained DNA confined in nanochannels

Intercalating fluorescent probes are widely used to visualize DNA in studies on DNA-protein interactions. Some require the presence of adenosine triphosphate (ATP). We have investigated the mechanical properties of DNA stained with the fluorescent intercalating dyes YOYO-1 and YOYO-3 as a function of ATP concentrations (up to 2 mM) by stretching single molecules in nanofluidic channels with a channel cross-section as small as roughly 100?×?100 nm². The presence of ATP reduces the length of the DNA by up to 11 %. On the other hand, negligible effects are found if DNA is visualized with the minor groove-binding probe 4′,6-diamidino-2-phenylindole. The apparent drop in extension under nanoconfinement is attributed to an interaction of the dye and ATP, and the resulting expulsion of YOYO-1 from the double helix.

Open image in new window

Graphical Abstract Nanochannel-stretched DNA (48.5 kbp) stained with YOYO-1 is sensitive to ATP concentration in buffer. Nanochannels with a cross-section of 80?×?80 nm² were used to stretch DNA.

     

K5CoW12O40 · 3H2O: Heterogeneous Catalyst for the Strecker‐Type Aminative Cyanation of Aldehydes and Ketones

One‐step synthesis of α‐aminonitriles was successfully carried out by a three‐component condensation of aldehydes or ketones, amines, and potassium cyanide in the presence of a catalytic amount of K₅CoW₁₂O₄₀·3H₂O as an efficient, reusable, and nontoxic catalyst.     

Heat transfer characteristics of developing gaseous slip-flow in rectangular microchannels with variable physical properties

The effects of variable physical properties on the flow and heat transfer characteristics of simultaneously developing slip-flow in rectangular microchannels with constant wall temperature are numerically investigated. A colocated finite-volume method is used in order to solve the mass, momentum and energy equations in their most general form. Various channel aspect ratios are studied at different Knudsen numbers. Simulations indicate that the constant physical property assumption can result in under/over-prediction of the local friction and heat transfer coefficients depending on the problem configuration. Density and thermo-physical property variations have significant effects on predicting flow and heat transfer characteristics in the developing and fully-developed regions. The degree of discrepancy varies for different cases depending on Knudsen number, aspect ratio and the temperature difference between the channel inlet and the wall. The results suggest that even low temperature differences can alter the friction and heat transfer coefficients considerably.     

Charged anisotropic matter with quadratic equation of state

We extend the work of Thirukkanesh and Maharaj (Class Quantum Gravity 25:235001, 2007) by considering quadratic equation of state for the matter distribution to study the general situation of a compact relativistic body. Presence of electromagnetic field and anisotropy in the pressure are also assumed. Some new classes of static spherically symmetrical models of relativistic stars are obtained. All the results given in Thirukkanesh and Maharaj (Class Quantum Gravity 25:235001, 2007) and there in can also be recovered as a particular case of our work.     

Harmonic morphisms of warped product type from Einstein manifolds

Weitzenb?ck type identities for harmonic morphisms of warped product type are developed which lead to some necessary conditions for their existence. These necessary conditions are further studied to obtain many nonexistence results for harmonic morphisms of warped product type from Einstein manifolds. Received: 14 March 2006