Analysis of heat conduction in a rarefied gas at rest with a temperature jump at the boundary by consistent-order extended thermodynamics

In the context of the first- and second-order theories of consistent-order extended thermodynamics, a systematic approach is established for analyzing the temperature jump at the boundary through studying one-dimensional stationary heat conduction in a rarefied gas at rest. Thereby an approach to the free boundary-value problem in general is explored. Boundary values of temperature are assumed to be in the form of power expansion with respect to the Knudsen number, based on which analytical expressions of the temperature jump aswell as entropy production at the boundary are derived explicitly. Dependencies of these two boundary quantities on both the Knudsen number and accommodation factor are also extensively discussed. The present analysis is expected to be the basis for the study of higher-order theories of consistent-order extended thermodynamics.      

Propagation of Regularity and Persistence of Decay for Fifth Order Dispersive Models

This paper considers the initial value problem for a class of fifth order dispersive models containing the fifth order KdV equation

$$\begin{aligned} \partial _tu - \partial _x^5u -30u^2\partial _xu + 20\partial _xu\partial _x^2u + 10u\partial _x^3u = 0. \end{aligned}$$

The main results show that regularity or polynomial decay of the data on the positive half-line yields regularity in the solution for positive times.

     

Viscosity change in aqueous hectorite suspension activated by DC electric field

The change in the viscosity of deionized aqueous hectorite suspensions by applying an electric field was investigated. The deionized suspensions had low viscosity, which was almost the same as that of its solvent, water. Upon applying a DC electric field of the order of a few volt per millimeter to the deionized suspension, the viscosity started to increase gradually and reached a constant value that was high enough relative to the original value. Regarding the mechanism of the electrically induced stress increase, it is highly plausible that a three-dimensional network structure formed under the electric field due to a deformation of the electrical double layer.     

Numerical convergence of finite element solutions of nonrational B-spline element and absolute nodal coordinate formulation

In this investigation, numerical convergence of finite element solutions obtained using the B-spline approach and the absolute nodal coordinate formulation (ANCF) is discussed. Furthermore, equivalence of the two formulations with different orders of polynomials and degrees of continuity is demonstrated by several numerical examples. The degree of continuity can be easily controlled in B-spline elements by changing knot multiplicities, while continuity conditions associated with higher order derivatives need to be imposed to achieve C ² and higher continuities in ANCF elements. In order to compare element performances of the third and quartic B-spline and ANCF elements, the three-node quartic ANCF beam element is developed. It is demonstrated in several numerical examples that use of B-spline and ANCF elements with same orders and continuities leads to identical results. Furthermore, effects of polynomial orders and continuities on the accuracy and numerical convergence are demonstrated.     

Measure Valued Solutions of the 2D Keller–Segel System

We develop a theory of global measure-valued solutions for the classical Keller–Segel model. These solutions are obtained considering the limit of solutions of a regularized problem. We also prove that different regularizations yield different limit measures in the case in which classical solutions of the Keller–Segel system are not globally defined in time.     

Rapid Microwave‐Promoted Synthesis of Polyurethanes from a Fluorene Unit‐Containing Diol and Diisocyanates

A fluorene diol derivative, 9,9‐bis[4‐(2‐hydroxyethoxy)phenyl]fluorene ( 1 ), reacted with diisocyanates such as 1,3‐bis(isocyanatomethyl)cyclohexane ( 2a ), 1,6‐diisocyanatohexane ( 2b ), and 1,3‐bis(isocyanatomethyl)benzene ( 2c ) under temperature‐controlled microwave irradiation to form the corresponding polyurethanes with being 30 000 to 60 000, measured by GPC with reference to polystyrene standards within 5 to 10 min at 160 to 200 °C. In the reactions of 2a and b , the molecular weights were 15 to 20 times higher than those obtained by conventional oil bath heating. For a solvent of the microwave‐promoted reaction, a hydrocarbon compound, decalin, is preferably used to undergo the polymerization cleanly without unfavorable coloration and/or gelation.

     

High-energy diode-pumped picosecond regenerative amplification at 999 nm in wavelength with a cryogenically cooled Yb:LuLiF(4) crystal

A diode-pumped, cryogenically cooled Yb:LuLiF(4) regenerative amplifier has been developed for the first time to our knowledge. A chirped-seed pulse was amplified and compressed in the regenerative amplifier, simultaneously, which generated approximately 6 mJ, 13 ps pulses at 999 nm in wavelength without a pulse compressor. Simultaneous lasing at 999 and 1024 nm, respectively, was demonstrated, which could be used for different frequency generation in the terahertz region.     

Cp(*)RuCl-catalyzed formal intermolecular cyclotrimerization of three unsymmetrical alkynes through a boron temporary tether: regioselective four-component coupling synthesis of phthalides

Highly substituted phthalides were efficiently synthesized by sequential Cp(*)RuCl-catalyzed cyclotrimerization of alkynylboronates, propargyl alcohols, and terminal alkynes and palladium(II)-catalyzed carbonylation of the resultant arylboronates. The intermediate arylboronate was isolated and unambiguously characterized by X-ray crystallography. The perfect regioselectivity of the ruthenium-catalyzed formal intermolecular cyclotrimerization was discussed on the basis of the density functional calculations of a boraruthenacycle intermediate.     

One-pot beta-substitution of enones with alkyl groups to beta-alkyl enones

Vinylic hydrogens at the beta-position of enones were effectively substituted with alkyl groups in a one-pot procedure to afford beta-alkyl enones in good to high isolated yields by conjugate addition of higher-order dialkyl cyanocuprates to enones, followed by a reaction with N-tert-butylbenzenesulfinimidoyl chloride at -78 degree C.