Optimization of heat transfer and pressure drop in a tube with loose-fit perforated twisted tapes by Taguchi method and grey relational analysis

Journal of Thermal Analysis and Calorimetry - This work introduces the determination of the optimum values of the design parameters in a tube with loose-fit perforated twisted tapes. The effects of...     

Synthesis of linear and starlike polymers from poly(propylene glycol) methacrylate using controlled radical polymerization

The copper‐catalyzed atom transfer radical polymerization (ATRP) of poly(propylene glycol) methacrylate (PPGM) in solution to produce linear and starlike polymers is reported, using methylethyl ketone as the solvent and a temperature of 80 °C. The ATRP system used was efficient for polymerization of the functionalized monomer without protecting hydroxyl end groups of monomer. The polymerizations were consistent with “living” or controlled processes, as revealed by the linear evolution of molecular weight with conversion. Increasing the [M]₀:[I]₀ ratio resulted in increasing molecular weights, whereas the polydispersity indices remained low (M_w/M_n < 1.4) even at high conversion. Decreasing the [CuBr]₀:[I]₀ ratio resulted in lower conversions, slightly larger polydispersities, and decreased molecular weights, likely resulting from a lower initiation efficiency. Polymers were characterized by ¹H and ¹³C NMR; molecular weights of polymers with low degrees of polymerization were estimated by end‐group analysis from ¹³C NMR spectra obtained using distortionless enhancement by polarization transfer and the gated decoupling techniques. © 2001 John Wiley & Sons, Inc. J Polym Sci Part A: Polym Chem 40: 334–343, 2002     

SU(2) instantons with boundary jumps and spin tunneling in magnetic molecules

Coherent state path integrals are shown in general to contain instantons with jumps at the boundaries, i.e., boundary points lying outside classical phase space. Inclusion of these instantons is shown to resolve the "missing quench paradox" in the magnetic molecule Fe8, i.e., the fact that the tunneling between the ground Zeeman states of this molecule is quenched at only four magnetic field values, instead of the ten that would be expected from the topological Berry phase between interfering instantons. An approximate formula is found for the location of the four remaining quenches.     

Stacking of triphenylene: characterization of the potential energy surface

The interaction potential energy of triphenylene dimer has been calculated with Møller–Plesset second-order perturbation theory for various geometrical configurations. Different types of geometrical perturbations such as rotation, displacements and their combinations are studied in terms of their effects on the stability of the dimer. Minimum energy conformers for face to face, rotated, parallel displaced and T-shape structures are obtained. For the unsubstituted triphenylene, the 35° rotation of one of the monomers results in the global minimum. However, the dimer is still very flexible in terms of displacements. A helical structure seems to be the most stable form for the trimer. For large stacked clusters, the two body forces dominate the interactions while at small monomer–monomer separation, three body terms behave like z ^?9 where z is the vertical distance between two adjacent monomers.     

The investigation of complexation properties and synthesis of the (salen and salophen)-bridged Fe/Cr(III) capped complexes of novel Schiff bases

This article describes synthesis of novel Schiff base and its complexation properties with Fe(III) and Cr(III). Firstly 1,3,5-tris (formylphenoxymethyl)benzene (1, TRIPOD) with tris aldehyde groups were synthesized using the 1,3,5-trisbromomethylbenzene and 4-hydroxybezaldehyde. The compound 1 was converted to the Schiff base derivative (2, TCPIM-TRIPOD) with p-aminobenzoic acid. The prepared TCPIM-TRIPOD were reacted with four new trinuclear Fe(III) and Cr(III) complexes involving tetradenta Schiff bases N,N-bis(salicylidene)ethylenediamine-(salenH₂) or bis(salicylidene)-o-phenylenediamine-(salophenH₂) and characterized by means of elemental analysis carrying out infrared spectroscopy (IR), thermogravimetric analysis (TG), nuclear magnetic resonance (¹H-NMR), elemental analysis and magnetic susceptibility measurement. The complexes can also be characterized as low-spin distorted octahedral Fe(III) and Cr(III) bridged by carboxylic acids. The tricarboxylic acids play a role as bridges for weak antiferromagnetic intramolecular exchange.     

Interferometry with entangled atoms

A quantum gravity-gradiometer consists of two spatially separated ensembles of atoms interrogated by pulses of a common laser beam. The laser pulses cause the probability amplitudes of atomic ground-state hyperfine levels to interfere, producing two, motion-sensitive, phase shifts, which allow the measurement of the average acceleration of each ensemble, and, via simple differencing, of the acceleration gradient. Here we propose entangling the quantum states of atoms from the two ensembles prior to the pulse sequence, and show that entanglement encodes their relative acceleration in a single interference phase which can be measured directly, with no need for differencing. Received 6 June 2002 / Received in final form 25 October 2002 Published online 28 January 2003     

Oscillation of holomorphic Bergman–Besov kernels on the ball

We estimate the oscillation of holomorphic Bergman–Besov reproducing kernels on the unit ball of \(\mathbb {C}^n\). As an application of this estimate we characterize holomorphic Bergman–Besov spaces \(A_\alpha ^p\,(\alpha \in \mathbb {R})\) in terms of double integrals of the fractions \(|f(z)-f(w)|/|z-w|\) and \(|f(z)-f(w)|/|1-\langle z,w \rangle |\) and complete the earlier works done on this subject. Our results provide, when \(\alpha \le -1\), a derivative-free characterization of \(A_\alpha ^p\).     

Comments on “A more precise statement of Hamilton's principle”

Among the problems C. D. Bailey has questioned in a recent paper (Ref. 1) are a precise and general formulation of Hamilton's variational principle and the establishment of a sufficiency criterion for this to be a minimum principle. In this paper, we will try to answer these questions using the geometric theory of classical mechanics.