Existence of global weak solutions for a phase–field model of a vesicle moving into a viscous incompressible fluid

We consider in this article a model of vesicle moving into a viscous incompressible fluid. The vesicle is described through a phase–field equation and through a transport equation modeling the local incompressibility of its membrane. The equations for the fluid are the classical Navier–Stokes equations with a force resulting from the presence of the vesicle. Our main result states the existence of weak solutions for the corresponding system. The proof is based on compactness/monotonicity arguments. Copyright © 2013 John Wiley & Sons, Ltd.     

Tree metrics and edge-disjoint S-paths

Given an undirected graph \(G=(V,E)\) with a terminal set \(S \subseteq V\) , a weight function on terminal pairs, and an edge-cost \(a: E \rightarrow \mathbf{Z}_+\) , the \(\mu \) -weighted minimum-cost edge-disjoint \(S\) -paths problem ( \(\mu \) -CEDP) is to maximize \(\sum \nolimits _{P \in \mathcal{P}} \mu (s_P,t_P) - a(P)\) over all edge-disjoint sets \(\mathcal{P}\) of \(S\) -paths, where \(s_P,t_P\) denote the ends of \(P\) and \(a(P)\) is the sum of edge-cost \(a(e)\) over edges \(e\) in \(P\) . Our main result is a complete characterization of terminal weights \(\mu \) for which \(\mu \) -CEDP is tractable and admits a combinatorial min–max theorem. We prove that if \(\mu \) is a tree metric, then \(\mu \) -CEDP is solvable in polynomial time and has a combinatorial min–max formula, which extends Mader’s edge-disjoint \(S\) -paths theorem and its minimum-cost generalization by Karzanov. Our min–max theorem includes the dual half-integrality, which was earlier conjectured by Karzanov for a special case. We also prove that \(\mu \) -EDP, which is \(\mu \) -CEDP with \(a = 0\) , is NP-hard if \(\mu \) is not a truncated tree metric, where a truncated tree metric is a weight function represented as pairwise distances between balls in a tree. On the other hand, \(\mu \) -CEDP for a truncated tree metric \(\mu \) reduces to \(\mu '\) -CEDP for a tree metric \(\mu '\) . Thus our result is best possible unless P = NP. As an application, we obtain a good approximation algorithm for \(\mu \) -EDP with “near” tree metric \(\mu \) by utilizing results from the theory of low-distortion embedding.     

A parametric successive underestimation method for convex multiplicative programming problems

This paper addresses itself to the algorithm for minimizing the product of two nonnegative convex functions over a convex set. It is shown that the global minimum of this nonconvex problem can be obtained by solving a sequence of convex programming problems. The basic idea of this algorithm is to embed the original problem into a problem in a higher dimensional space and to apply a branch-and-bound algorithm using an underestimating function. Computational results indicate that our algorithm is efficient when the objective function is the product of a linear and a quadratic functions and the constraints are linear. An extension of our algorithm for minimizing the sum of a convex function and a product of two convex functions is also discussed.     

A new water‐soluble branched poly(ethylene imine) derivative having hydrolyzable imidazolidine moieties and its application to long‐lasting release of aldehyde

A new water‐soluble poly(ethylene imine)‐derivative having imidazolidine moieties was developed. With using branched poly(ethylene imine) (BPEI) as a precursor, it was modified by Michael addition reaction of its primary amino group to an acrylate having poly(ethylene glycol) (PEG) chain. The modified BPEI was reacted with octanal to give the corresponding BPEI derivative having octanal‐derived imidazolidine moieties. The obtained polymer inherited the high hydrophilicity of the attached PEG chains to allow hydrolysis of the imidazolidine moieties under homogeneous conditions in aqueous media, leading to long‐lasting release of octanal. © 2010 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2010     

Radiochemical study of fast fission mechanism

The reaction of²³⁸U with¹²C was studied radiochemically with the purpose of elucidating fast fission characteristics. Fast fission component was extracted in far-asymmetric mass region and interpreted as the mass diffusion following the Fokker-Planck equation. Anomalous charge dispersion widths in the corresponding mass region and a sudden increase of the whole mass distribution width at the critical energy were also observed to support the above interpretation. The reaction time of fast fission was determined to be 5·10⁻²¹ s from the width and position of the mass distribution.     

Magnetically-driven heat transport device using a binary temperature-sensitive magnetic fluid

The magnetic body force in boiling two-phase temperature-sensitive magnetic fluid (TSMF) flow is known to effectively increase the driving force of magnetic fluid in a non-uniform magnetic field. Based on this mechanism, in the present study, a binary TSMF, which is a mixture of the TSMF and a low-boiling-saturation-temperature organic solution, is proposed to be used in a heat transport device to enhance its circulation. In order to see its performance in the heat transport device, the pressure difference at different heated temperatures, magnetic fields and inclination angles of the heating section are investigated experimentally and theoretically. Results showed that the driving force increases remarkably due to more gas phase appearing in the test fluid and the magnetization of it decreasing. At low magnetic field the driving force is enhanced greatly when the inclination angle is close to 60°, while at high magnetic field the driving force is remarkably enhanced due to the effect of the magnetic force in the inclination angle range from 0° to 30° and 60° to 90°.     

Resistivity control of sputtered amorphous-silicon by ion-implantation

The resistivity of a hydrogenated sputtered amorphous-silicon is controlled by using room temperature implantation of P⁺. It is found that the defects produced by implantation can be minimized by annealing at 300°C in an H₂ atmosphere, and also found that there is a threshold implanted dose, beyond which the resistivity begins to be controlled by changing the dose.     

Some Regularity Criteria for Affine Semilocal Rings

The purpose of this article is to study an existence of p-bases and mainly to give some regularity criteria for semilocal rings essentially of finite type over fields.     

Large-scale forcing with less communication in finite-difference simulations of stationary isotropic turbulence

This study proposes a new forcing scheme suitable for massively-parallel finite-difference simulations of stationary isotropic turbulence. The proposed forcing scheme, named reduced-communication forcing (RCF), is based on the same idea as the conventional large-scale forcing scheme, but requires much less data communication, leading to a high parallel efficiency. It has been confirmed that the RCF scheme works intrinsically in the same manner as the conventional large-scale forcing scheme. Comparisons have revealed that a fourth-order finite-difference model run in combination with the RCF scheme (FDM-RCF) is as good as a spectral model, while requiring less computational costs. For the range 80 < Re_λ < 540, where Re_λ is the Taylor microscale-based Reynolds number, large computations using the FDM-RCF scheme show that the Reynolds dependences of skewness and flatness factors have similar power-laws as found in previous studies.