Theory and experiment on the three-dimensional motion of a freely suspended spherical particle at the entrance to a pore at low Reynolds number

This paper examines the three dimensional approach of a neutrally buoyant sphere of any size to a circular hole in a plane wall at very low Reynolds number. The analysis differs from previous studies, largely applied to the multipore filter, in that the authors investigate the three dimensional hydrodynamic interaction of the sphere with the entrance geometry of the pore in the limit of zero inertia. The problem is first exactly formulated as the linear superposition of fundamental Stokes flows for rotation and translation of the sphere and flow past a stationary sphere. Approximate solutions are then obtained for the deviation of sphere trajectories from fluid stream lines and the results compared with laboratory model experiments in a low Reynolds number settling tank. The theory and experiment show that because of the hydrodynamic interaction sphere trajectories and fluid streamlines deviate significantly as the opening is approached, that all spheres eventually enter the pore regardless of their initial position, but that a non-uniform concentration profile develops with large increases in concentration near the walls of the orifice in the vicinity of the opening. The results provide a basic mechanism to explain the onset of Fahraeus phenomenon for red cells entering small blood vessels and glass tubes.     

Low-Field Nuclear Magnetic Resonance Time Domain Characterization of Polyunsaturated Fatty Acid–Rich Linseed and Fish Oil Emulsions during Thermal Air Oxidation

Linseed contains high levels of polyunsaturated fatty acids (PUFA), such as α-linolenic acid (> 50% ALA-18:3), that are naturally protected against thermal oxidation by their encapsulation within linseed oil bodies (OB) by multiple components including antioxidant proteins and mucilage emulsifying agents. Linseed OB emulsions (LSE) can be produced by grinding linseed seeds, adding water, adjusting pH, and sonication. This is a process that can encapsulate externally added PUFA to minimize their thermal oxidation, as it does for the intrinsic ALA PUFA. Fish oil (FO) encapsulation into this LSE platform to form linseed fish oil emulsions (LSFE) offers the possibility of a nutritive delivery system of the biologically essential FO PUFA eicosapentaenoic acid and docosahexaenoic acid. In this study, ¹H low-field nuclear magnetic resonance (LF-NMR) is used to characterize LSE's and LSFE's chemical and structural properties as well as their stability and changes under thermal oxidation (55 °C for 96 hours). ¹H LF-NMR data processing was developed to generate one-dimensional (1D) T₁ (spin–lattice), 1D T₂ (spin–spin), and 2D (T₁ vs. T₂) relaxation time spectra that can characterize OB emulsions and monitor their time domain fingerprints (spectrum peaks) of chemical and structural changes during the oxidation process. The ¹H LF-NMR analysis were further supported and correlated with conventional peroxide value test, self-diffusion, droplet size distribution, zeta potential estimation of surface stability, and gas chromatography–mass spectrometry analysis of fatty acid profile changes under thermal oxidation conditions. The 1D and 2D LF-NMR relaxation spectra showed that the LSE and LSFE did not suffer intense oxidation process, due to PUFA assembly in OB oxidative protection. These results were further confirmed by the supportive analytical methodologies. The results of this study demonstrate the efficacy of ¹H LF-NMR methodology to monitor PUFA's rich oil and emulsion thermal oxidation.     

Wireless network design via 3-decompositions

We consider some network design problems with applications for wireless networks. The input for these problems is a metric space (X,d) and a finite subset UX of terminals. In the Steiner Tree with Minimum Number of Steiner Points (STMSP) problem, the goal is to find a minimum size set SX−U of points so that the unit-disc graph of S+U is connected. Let Δ be the smallest integer so that for any finite VX for which the unit-disc graph is connected, this graph contains a spanning tree with maximum degree Δ. The best known approximation ratio for STMSP was Δ−1 [I.I. Măndoiu, A.Z. Zelikovsky, A note on the MST heuristic for bounded edge-length Steiner trees with minimum number of Steiner points, Information Processing Letters 75 (4) (2000) 165–167]. We improve this ratio to (Δ+1)/2+1+ε.In the Minimum Power Spanning Tree (MPST) problem, V=X is finite, and the goal is to find a “range assignment” on the nodes so that the edge set contains a spanning tree, and ∑_vVp(v) is minimized. We consider a particular case {0,1}-MPST of MPST when the distances are in {0,1}; here the goal is to find a minimum size set SV of “active” nodes so that the graph (V,E₀+E₁(S)) is connected, where , and E₁(S) is the set the edges in with both endpoints in S. We will show that the (5/3+ε)-approximation scheme for MPST of [E. Althaus, G. Calinescu, I. Măndoiu, S. Prasad, N. Tchervenski, A. Zelikovsky, Power efficient range assignment for symmetric connectivity in static ad hoc wireless networks, Wireless Networks 12 (3) (2006) 287–299] achieves a ratio 3/2 for {0,1}-distances. This answers an open question posed in [E. Lloyd, R. Liu, S. Ravi, Approximating the minimum number of maximum power users in ad hoc networks, Mobile Networks and Applications 11 (2006) 129–142].     

Computation considerations and fast algorithms for calculating the diffraction integral

Abstract

One of the most basic optical ‘components’ is free-space propagation. A common approximation used when calculating the resultant field distribution after propagation is the Fresnel integral. This integral can be evaluated in two ways: directly or by using the angular spectrum. In this paper, we estimate the regions in which each mode of evaluation is preferable according to computing efficiency and accuracy considerations. A fast numerical algorithm is introduced for each region. The result is relevant also for the evaluation of the Rayleigh-Sommerfeld diffraction formula.     

Development of Saturable Absorbers for Laser Passive Q‐Switching near 1.5 μm Based on Transparent Ceramic Co2+:MgAl2O4

We describe the development of a reasonable cost Co²⁺:MgAl₂O₄ transparent ceramic plates fabrication technology that allows the producing of parts functioning as passive laser Q‐switches in the 1.3–1.7 μm domain. The main relevant material characteristics were measured. The absorption band, positioned between 1.2 and 1.7 μm, is typical of the ⁴A₂ (⁴F) → ⁴T₁ (⁴F) transition of Co²⁺ substituting Mg²⁺ ions in their T_d symmetry sites. The measured ground‐state absorption cross section σ_gs = 2.9 × 10^?19 cm², saturation contrast γ = 0.12, and depleted ground‐state recovery time τ₂ = 110–430 ns render such parts suitable for the intended application. The radiative lifetime was estimated as . The spin‐orbit splitting constant was estimated as ξ_SL??150 cm^?1 for the ⁴F parent ground state, and ξ_SL ? –575 cm^?1 for the ⁴P parent excited state. Obtained specimens had a transmission of ~80% (t = 2 mm, λ = 600 nm) and included some opaque, white spots. Further improvement of host optical transmission and resistance to laser damage are necessary.     

Alkyl Tail Segments Mobility as a Marker for Omega-3 Polyunsaturated Fatty Acid-Rich Linseed Oil Oxidative Aging

Omega-3 polyunsaturated fatty acid (PUFA)-rich linseed oil (LSO) is an important component in biological systems, foods, and many other industrial products. In recent years, LSO has attracted increased attention in the field of functional foods, which has highlighted its facile susceptibility to aging by autoxidation. Common colorimetric and a long list of spectral methodologies have been used to follow after and predict LSO shelf life's quality, especially in regards to aging by autoxidation. These standard methodologies are nevertheless limited, because of the complexity of the LSO's chemical and physical changes. The goal of the present study is to develop a sensorial ¹H LF-NMR energy relaxation time application based on monitoring primary chemical and structural changes occurring with time and temperature during oxidative thermal stress for better and rapid evaluation of LSO's aging process. Using ¹H low-field NMR, the different T₂ times of energy relaxations due to spin–spin coupling, and proton motion/mobility of LSO molecular segments were monitored. As previously reported, we characterized the chemical and structural changes in all phases of the autoxidation aging process. Starting from the initiation phase (abstraction of hydrogen radical, fatty acid chain rearrangement, and oxygen uptake yielding hydroperoxides products), through to the propagation phase (chain reactions resulting in tail cleavage to form alkoxy radicals, and alpha, beta-unsaturated aldehydes formation), and a termination phase (cross linking and production of polymerization end products). The ¹H LF NMR transverse relaxation approach, monitors both the covalent bond's strong forces (100–400 kJ mol⁻¹) in LSO oxidative aging decomposition, as well as secondary relatively weak interactive forces by hydrogen bonds (~70 kJ mol⁻¹), and electrostatic bonds (0–50 kJ mol⁻¹) contributing to secondary crosslinking interactions leading to a LSO viscous gel of polymerized products in the termination phase. In the present paper, we show that LSO tail segments mobility in terms of T₂ multi-exponential energy relaxation time decays, generated by data reconstruction of ¹H transverse relaxation components are providing a clear, sharp, and informative understanding of LSO sample's autoxidation aging processes. To support T₂ time domain data analysis, we used data from high-field band-selective ¹H NMR pulse excitation for quantification of hydroperoxides and aldehydes of the same LSO samples treated under the same thermal conditions (25, 40, 60, 80, 100, 120 °C) with pumped air for 168 hours. Peroxide value, viscosity, and self-diffusion analyses, as well as fatty acids profile and by-products determined by GC–MS on the same samples were carried out, and correlated with the LSO tail T₂ energy relaxation time results. From these results, it is postulated that selective determination of LSO tail T₂ time domain can be used as a rapid evaluation marker for following omega-3 PUFA-rich oils oxidative aging process within industrial and commercial products.     

Luminescent CdS quantum dots as selective ion probes

Water-soluble luminescent CdS quantum dots (QDs) capped by polyphosphate, L-cysteine, and thioglycerol were synthesized in aqueous solution. The ligands were found to have a profound effect on the luminesence response of CdS QDs to physiologically important metal cations. Polyphosphate-capped CdS QDs were sensitive to nearly all mono- and divalent cations, showing no ion selectivity. Conversely, thioglycerol-capped CdS QDs were sensitive to only copper and iron ions. Similar concentrations of physiologically relevant cations, such as zinc, sodium, potassium, calcium, and magnesium ions did not affect the luminescence of thioglycerol-capped CdS QDs. On the other hand, L-cysteine-capped CdS QDs were sensitive to zinc ions and insensitive to other physiologically important cations, such as copper, calcium, and magnium ions. To demonstrate the detection capability of these new ion probes, L-cysteine and thioglycerol-capped CdS QDs were used to detect zinc and copper ions in physiological buffer samples. The detection limits were 0.8 microM for zinc (II) and 0.1 microM for copper (II) ions. The emission enhancement of the QDs by zinc (II) is attributed to activation of surface states, whereas the effective reduction of copper (II) to copper (I) may explain the emission decrease of the thioglycerol-capped CdS QDs when charged with copper ions. Unlike organic fluorescent dyes, the thioglycerol-capped luminescent CdS QDs discriminate between copper and zinc ions and are therefore suitable for the analysis of copper ions in biological samples in the presence of physiological concentrations of zinc ions. The interference of iron ions with zinc and copper ion detection is attributed to an inner filter effect, which is eliminated by adding fluoride ions to form the colorless complex FeF6(3-). To the best of our knowledge, this is first use of luminescent semiconductor quantum dots as selective ion probes in aqueous samples.     

Optical generation of fuzzy-based rules

In the last third of the 20th century, fuzzy logic has risen from a mathematical concept to an applicable approach in soft computing. Today, fuzzy logic is used in control systems for various applications, such as washing machines, train-brake systems, automobile automatic gear, and so forth. The approach of optical implementation of fuzzy inferencing was given by the authors in previous papers, giving an extra emphasis to applications with two dominant inputs. In this paper the authors introduce a real-time optical rule generator for the dual-input fuzzy-inference engine. The paper briefly goes over the dual-input optical implementation of fuzzy-logic inferencing. Then, the concept of constructing a set of rules from given data is discussed. Next, the authors show ways to implement this procedure optically. The discussion is accompanied by an example that illustrates the transformation from raw data into fuzzy set rules.     

Approximating Node Connectivity Problems via Set Covers

Given a graph (directed or undirected) with costs on the edges, and an integer $k$, we consider the problem of finding a $k$-node connected spanning subgraph of minimum cost. For the general instance of the problem (directed or undirected), there is a simple $2k$-approximation algorithm. Better algorithms are known for various ranges of $n,k$. For undirected graphs with metric costs Khuller and Raghavachari gave a $( 2+{2(k-1)}/{n})$-approximation algorithm. We obtain the following results: (i) For arbitrary costs, a $k$-approximation algorithm for undirected graphs and a $(k+1)$-approximation algorithm for directed graphs. (ii) For metric costs, a $(2+({k-1})/{n})$-approximation algorithm for undirected graphs and a $(2+{k}/{n})$-approximation algorithm for directed graphs. For undirected graphs and $k=6,7$, we further improve the approximation ratio from $k$ to $\lceil (k+1)/2 \rceil=4$; previously, $\lceil (k+1)/2 \rceil$-approximation algorithms were known only for $k \leq 5$. We also give a fast $3$-approximation algorithm for $k=4$. The multiroot problem generalizes the min-cost $k$-connected subgraph problem. In the multiroot problem, requirements $k_u$ for every node $u$ are given, and the aim is to find a minimum-cost subgraph that contains $\max\{k_u,k_v\}$ internally disjoint paths between every pair of nodes $u,v$. For the general instance of the problem, the best known algorithm has approximation ratio $2k$, where $k=\max k_u$. For metric costs there is a 3-approximation algorithm. We consider the case of metric costs, and, using our techniques, improve for $k \leq 7$ the approximation guarantee from $3$ to $2+{\lfloor (k-1)/2 \rfloor}/{k} < 2.5$.