Strong Solutions for a Phase Field Navier–Stokes Vesicle–Fluid Interaction Model

In this paper we study a mathematical model for the dynamics of vesicle membranes in a 3D incompressible viscous fluid. The system is in the Eulerian formulation, involving the coupling of the incompressible Navier–Stokes system with a phase field equation. This equation models the vesicle deformations under external flow fields. We prove the local in time existence and uniqueness of strong solutions. Moreover, we show that, given T > 0, for initial data which are small (in terms of T), these solutions are defined on [0, T] (almost global existence).     

Multiphoton Phosphorescence of Simple Ketones by Visible-light Excitation and Its Consideration for Active Sensing in Space

Journal of Fluorescence - Acetone and butanone were seen to emit blue light around 450 nm when excited in the green by a high intensity pulsed laser. The pathway of this anti-Stokes...     

Analysis of wastewater samples by direct combination of thin-film microextraction and desorption electrospray ionization mass spectrometry

An analysis method for aqueous samples by the direct combination of C18/SCX mixed mode thin-film microextraction (TFME) and desorption electrospray ionization mass spectrometry (DESI-MS) was developed. Both techniques make analytical workflow simpler and faster, hence the combination of the two techniques enables considerably shorter analysis time compared to the traditional liquid chromatography mass spectrometry (LC-MS) approach. The method was characterized using carbamazepine and triclosan as typical examples for pharmaceuticals and personal care product (PPCP) components which draw increasing attention as wastewater-derived environmental contaminants. Both model compounds were successfully detected in real wastewater samples and their concentrations determined using external calibration with isotope labeled standards. Effects of temperature, agitation, sample volume, and exposure time were investigated in the case of spiked aqueous samples. Results were compared to those of parallel HPLC-MS determinations and good agreement was found through a three orders of magnitude wide concentration range. Serious matrix effects were observed in treated wastewater, but lower limits of detection were still found to be in the low ng L(-1) range. Using an Orbitrap mass spectrometer, the technique was found to be ideal for screening purposes and led to the detection of various different PPCP components in wastewater treatment plant effluents, including beta-blockers, nonsteroidal anti-inflammatory drugs, and UV filters.     

Improvement of pesticide adsorption capacity of cellulose fibre by high-energy irradiation-initiated grafting of glycidyl methacrylate

Cellulose as a renewable raw material was used for preparation of adsorbent of organic impurities in wastewater treatment. Hydrophobic surface of cellulose substrate was developed by grafting glycidyl methacrylate in simultaneous grafting using gamma irradiation initiation. Water uptake of cellulose significantly decreased while adsorption of phenol and a pesticide molecule (2,4-dichlorophenoxyacetic acid: 2,4-D) increased upon grafting. Adsorption equilibrium data fitted the Freundlich isotherm for both solutes.     

Optimal Wloc2,2-regularity,Pohozhaevʼs identity,and nonexistence of weak solutions to some quasilinear elliptic equations

We begin by establishing a sharp (optimal) $W_{\mathrm{loc}}^{2,2}$-regularity result for bounded weak solutions to a nonlinear elliptic equation with the p-Laplacian, ${\mathrm{\Delta }}_{p}u\stackrel{\mathrm{def}}{=}\mathrm{div}({|\mathrm{?}u|}^{p?2}\mathrm{?}u)$, $1<p<\infty$. We develop very precise, optimal regularity estimates on the ellipticity of this degenerate (for $2<p<\infty$) or singular (for $1<p<2$) problem. We apply this regularity result to prove Pohozhaev?s identity for a weak solution $u\in W^{1,p}(\Omega )$ of the elliptic Neumann problem(P)$?{\mathrm{\Delta }}_{p}u+W^{\prime }(u)=f(x)\text{in}\Omega ;?u/?\nu =0\text{on}?\Omega .$ Here, Ω is a bounded domain in ${\mathbb{R}}^N$ whose boundary ?Ω is a $C^2$-manifold, $\nu \equiv \nu (x_0)$ denotes the outer unit normal to ?Ω at $x_0\in ?\Omega$, $x=(x_1,\dots ,x_N)$ is a generic point in Ω, and $f\in L^{\infty }(\Omega )\cap W^{1,1}(\Omega )$. The potential $W:\mathbb{R}\to \mathbb{R}$ is assumed to be of class $C^1$ and of the typical double-well shape of type $W(s)={|1?{|s|}^{\beta }|}^{\alpha }$ for $s\in \mathbb{R}$, where $\alpha ,\beta >1$ are some constants. Finally, we take an advantage of the Pohozhaev identity to show that problem (P) with $f\equiv 0$ in Ω has no phase transition solution $u\in W^{1,p}(\Omega )$ ($1<p?N$), such that $?1?u?1$ in Ω with $u\equiv ?1$ in ${\Omega }_{?1}$ and $u\equiv 1$ in ${\Omega }_1$, where both ${\Omega }_{?1}$ and ${\Omega }_1$ are some nonempty subdomains of Ω. Such a scenario for u is possible only if $N=1$ and ${\Omega }_{?1}$, ${\Omega }_1$ are finite unions of suitable subintervals of the open interval $\Omega ?{\mathbb{R}}^1$.     

A BSDE approach to risk-based asset allocation of pension funds with regime switching

An asset allocation problem of a member of a defined contribution (DC) pension fund is discussed in a hidden, Markov regime-switching, economy using backward stochastic differential equations, (BSDEs). A risk-based approach is considered, where the member selects an optimal asset mix with a view to minimizing the risk described by a convex risk measure of his/her terminal wealth. Firstly, filtering theory is adopted to transform the hidden, Markov regime-switching, economy into one with complete observations and to develop, (robust), filters for the hidden Markov chain. Then the optimal asset allocation problem of the member is formulated as a two-person, zero-sum stochastic differential game between the member and the market in the economy with complete observations. The BSDE approach is then used to solve the game problem and to characterize the saddle point of the game problem. An explicit expression for the optimal asset mix is obtained in the case of a convex risk measure with quadratic penalty and it can be considered a generalized version of the Merton ratio. An explicit expression for the optimal strategy of the market is also obtained, which leads to a risk-neutral wealth dynamic and may provide some insights into asset pricing in the economy with inflation risk and regime-switching risk. Numerical examples are provided to illustrate financial implications of the BSDE solution.     

Bonding and impedance matching of acoustic transducers using silver epoxy

Silver epoxy was selected to bond transducer plates on glass substrates. The properties and thickness of the bonding medium affect the electrical input impedance of the transducer. Thus, the thickness of the silver epoxy bonding layer was used as a design parameter to optimize the structure for the transducer input impedance to match the 50 Ω output impedance of most radio frequency (RF) generators. Simulation and experimental results show that nearly perfect matching is achieved without using any matching circuit. At the matching condition, the transducer operates at a frequency band a little bit below the half-wavelength resonant frequency of the piezoelectric plate. In experiments, lead titanate (PT) piezoelectric plates were employed. Both full-size, 11.5 mm × 2 mm × 0.4 mm, and half-size, 5.75 mm × 2 mm × 0.4 mm, can be well matched using optimal silver epoxy thickness. The transducer assemblies demonstrate high efficiency. The conversion loss from electrical power to acoustic power in soda-lime glass is 4.3 dB. This loss is low considering the fact that the transducers operate at off-resonance by 12%. With proper choice of silver epoxy thickness, the transducer can be matched at the fundamental, the 3rd and 5th harmonic frequencies. This leads to the possible realization of triple-band transducers. Reliability was assessed with thermal cycling test according to Telcordia GR-468-Core recommendation. Of the 30 transducer assemblies tested, none broke until 2900 cycles and 27 have sustained beyond 4050 cycles.     

Functionalization of the pyridazin-3(2H)-one ring via palladium-catalysed aminocarbonylation

5-Iodo- and 4,5-dibromo-2-methylpyridazin-3(2H)-ones were aminocarbonylated in the presence of various amines including amino acid methyl esters in a palladium-catalysed reaction. The iodo derivative afforded the corresponding amides with complete conversion and high isolated yields. The dibromo derivative has shown unexpectedly high reactivity in this reaction, resulting in 4,5-dicarboxamides using primary amines as N-nucleophiles. Monoaminocarbonylation has not been observed, i.e., neither 4-bromo-5-carboxamide nor 4-carboxamido-5-bromo derivatives have been formed. However, the use of secondary amines such as piperidine and morpholine resulted in the formations of mixtures of amino-substituted bromopyridazinones. That is, no carbon monoxide insertion took place in these cases. Some mechanistic details of the formation of aminocarbonylation and amination products are also discussed.     

Highly selective palladium-catalyzed aminocarbonylation and cross-coupling reactions on a cavitand scaffold

Palladium-catalyzed aminocarbonylation and cross-coupling reactions (Suzuki-, Sonogashira-, Stille-coupling) served as highly efficient synthetic tools for the synthesis of novel, functionalized deepened cavitands. Unexpectedly high chemoselectivities towards tetrafunctionalized cavitands have been observed for all of these reactions even using coupling partners much below the stoichiometric amount. No significant formation of either the mono-, di- or trifunctionalized products was observed.