Influence of the bottom undulation on surface waves in thin film flow

We study gravity-driven viscous thin films flowing down an undulated plane. Applying the integral boundary-layer method we derive a set of two coupled PDEs for the film thickness and the flow rate. The steady state solution shows linear and nonlinear resonance. Based on this analytical solution we carry out a stability analysis with respect to surface waves and study wave generation and annihilation for time dependent flow. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Starting solutions for some unsteady unidirectional flows of Oldroyd-B fluids

Analytical expressions for the velocity fields corresponding to the motions of an Oldroyd-B fluid due to oscillations of an infinite flat plate as well as those induced by an oscillating pressure gradient and pressure jumps are determined by means of the Fourier sine transform. The corresponding solutions for a Maxwell and a Newtonian fluid appear as limiting cases of the solutions established here. Relevant physical properties of the flows and their dependence on material and geometry parameters are discussed. (Received: August 16, 2005; revised: December 19, 2005)     

Starting solutions for some unsteady unidirectional flows of Oldroyd-B fluids

Analytical expressions for the velocity fields corresponding to the motions of an Oldroyd-B fluid due to oscillations of an infinite flat plate as well as those induced by an oscillating pressure gradient and pressure jumps are determined by means of the Fourier sine transform. The corresponding solutions for a Maxwell and a Newtonian fluid appear as limiting cases of the solutions established here. Relevant physical properties of the flows and their dependence on material and geometry parameters are discussed.     

Callable risky perpetual debt with protection period

Issuances in the USD 260 Bn global market of perpetual risky debt are often motivated by capital requirements for financial institutions. We analyze callable risky perpetual debt emphasizing an initial protection (‘grace’) period before the debt may be called. The total market value of debt including the call option is expressed as a portfolio of perpetual debt and barrier options with a time dependent barrier. We also analyze how an issuer’s optimal bankruptcy decision is affected by the existence of the call option by using closed-form approximations. The model quantifies the increased coupon and the decreased initial bankruptcy level caused by the embedded option. Examples indicate that our closed form model produces reasonably precise coupon rates compared to numerical solutions. The credit-spread produced by our model is in a realistic order of magnitude compared to market data.     

Potential for Using Negative Spin Components in Neutron Polarizers. First Results

Technical Physics - The results of experimental verification of the feasibility of enhancing the efficiency of neutron-beam polarizers based on magnetized supermirrors are presented. The idea is to...     

Reflectometer for studying the surface of liquid systems

To study the free surface of liquids, a Reverans reflectometer with a vertical neutron scattering plane has been designed and is fabricated at Petersburg Nuclear Physics Institute. This reflectometer is intended to investigate surfaces and interfaces in liquid magnetic or nonmagnetic systems. The principles of reflectometer operation are described. The general view of the reflectometer with ready units is presented and its main technical parameters are given. The results of preliminary tests are reported.     

A Bodipy-bearing pillar[5]arene for mimicking photosynthesis: Multi-fluorophoric light harvesting system

Herein, we submitted to the original synthesis, characterization, energy transfer mechanism of the Bodipy-bearing pillar[5]arene Bodipy and its reactants by employing of infrared, ¹H, ¹¹B, ¹³C, ¹⁹F-NMRs, UV–vis, fluorescence spectroscopy, melting point apparatus, CHN elemental analysis and mass spectroscopy. Preliminary UV–vis, fluorescence and excitation measurements were carried out in CH₂Cl₂ and the results revealed an effective fluorescence resonance energy transfer (FRET) system based on the interaction of pillar[5]arene and Bodipy derivative. ε_max of target molecule reached to a maximum value and it was found as 955 000?M^?1?cm^?1. This fluorescent macromolecule worked well for mimicking a light harvesting system with an energy transfer efficiency up to 92%.     

Convergence rate of block-coordinate maximization Burer–Monteiro method for solving large SDPs

Mathematical Programming - Semidefinite programming (SDP) with diagonal constraints arise in many optimization problems, such as Max-Cut, community detection and group synchronization. Although...     

Dipotassium maleate with boric acid

In the title compound, poly[(μ₃‐boric acid)‐μ₄‐maleato‐dipotassium], [K₂(C₄H₂O₄){B(OH)₃}]_n, there are two independent K⁺ cations, one bonded to seven O atoms (three from boric acid and four from maleate), and the other eight‐coordinate via three boric acid and four maleate O atoms and a weak η¹‐type coordination to the C=C bond of the maleate central C atoms. Hydrogen bonding links the boric acid ligands and maleate dianions, completing the packing structure.     

Uniform convergence and numerical computation of the Hubbell radiation rectangular source integral

In this paper, we investigate uniform convergence of the improper Hubbell radiation rectangular source (HRS) integral H(a,b). We prove that HRS integral H(a,b) is uniform convergent in the domain D?{(a,b)∈[0,A]×[0,∞)} for any positive finite number A. Then we give an accurate and efficient computation algorithm for the HRS integral.