Approximating geometric bottleneck shortest paths

In a geometric bottleneck shortest path problem, we are given a set S of n points in the plane, and want to answer queries of the following type: given two points p and q of S and a real number L, compute (or approximate) a shortest path between p and q in the subgraph of the complete graph on S consisting of all edges whose lengths are less than or equal to L. We present efficient algorithms for answering several query problems of this type. Our solutions are based on Euclidean minimum spanning trees, spanners, and the Delaunay triangulation. A result of independent interest is the following. For any two points p and q of S, there is a path between p and q in the Delaunay triangulation, whose length is less than or equal to 2π/(3cos(π/6)) times the Euclidean distance |pq| between p and q, and all of whose edges have length at most |pq|.     

Elastic waves in a fiber-reinforced composite

The propagation of time-harmonic elastic waves in a fiber-reinforced composite is studied. The circular fibers are assumed to be parallel to each other and randomly distributed with a statistically uniform distribution. The direction of propagation and the associated particle motion are considered to be normal to the fibers. It is shown that the average waves in the composite separate into compressional and shear types. General formulae for the complex wave number giving the phase velocity and the damping are obtained. It is shown that these formulae lead to the Hashin-Rosen expressions for the transverse bulk modulus and the lower bound for the transverse rigidity, if the correlation in the positions of the fibers can be ignored. The correlation terms, for exponential correlation, are shown to have a significant effect on the damping property of the composite, especially at high frequencies and concentrations.     

Interaction of RuIII(EDTA) with cellular thiols and O2: biological implications thereof

Reaction of [Ru^III(EDTA)(CyS)]^2? (edta^4? = ethylenediaminetetraacetate; CySH = cysteine) with molecular oxygen (O₂) has been studied as a function of pH (4.0–8.0) and cysteine concentration (0.2–2.0 mM) at room temperature (25 °C). Biological activities of the [Ru(EDTA)]/CySH/O₂ system pertaining to cleavage of supercoiled plasmid DNA to its nicked open circular form has been explored in this work. Results are discussed in regard to the reaction of the ruthenium(III)-complex with molecular oxygen) and a working mechanism is proposed for the biological activities of the ruthenium(III)-complex in the presence of O₂.     

Planar solidification of a warm flowing-liquid under different boundary conditions

Planar solidification of a warm flowing liquid with the convective heat transfer to the growing solid layer, has been analysed for the boundary conditions of constant temperature, constant heat flux and convective heat flux at the surface respectively. The mathematical formulation of the problem resulted in a coupled set of two differential equations in temperature and solid thickness as function of position, time and the problem parameters. Analytical expressions for the temperature distribution within the growing solid layer, the rate of solidification and the solidification time are obtained. The perturbation techniques employed here is simple and straight forward in contrast with the earlier techniques. Good agreement between the experimental results and the present solutions is obtained for the convective heat flux boundary condition. The results of this analysis are useful in the design and analysis of experiments dealing with freezing/melting in one dimension. The role of the parameter Stefan number which is small for phase change materials, is discussed in context with the storage of thermal energy.     

Examining the lateral displacement of HL60 cells rolling on asymmetric P-selectin patterns

The lateral displacement of cells orthogonal to a flow stream by rolling on asymmetrical receptor patterns presents a new opportunity for the label-free separation and analysis of cells. Understanding the nature of cell rolling trajectories on such substrates is necessary to the engineering of substrates and the design of devices for cell separation and analysis. Here, we investigate the statistical nature of cell rolling and the effect of pattern geometry and flow shear stress on cell rolling trajectories using micrometer-scale patterns of biomolecular receptors with well-defined edges. Leukemic myeloid HL60 cells expressing the PSGL-1 ligand were allowed to flow across a field of patterned lines fabricated using microcontact printing and functionalized with the P-selectin receptor, leveraging both the specific adhesion of this ligand-receptor pair and the asymmetry of the receptor pattern inclination angle with respect to the fluid shear flow direction (α = 5, 10, 15, and 20°). The effects of the fluid shear stress magnitude (τ = 0.5, 1, 1.5, and 2.0 dyn/cm(2)), α, and P-selectin incubation concentration were quantified in terms of the rolling velocity and edge tracking length. Rolling cells tracked along the inclined edges of the patterned lines before detaching and reattaching on another line. The detachment of rolling cells after tracking along the edge was consistent with a Poisson process of history-independent interactions. Increasing the edge inclination angle decreased the edge tracking length in an exponential manner, contrary to the shear stress magnitude and P-selectin incubation concentration, which did not have a significant effect. On the basis of these experimental data, we constructed an empirical model that predicted the occurrence of the maximum lateral displacement at an edge angle of 7.5°. We also used these findings to construct a Monte Carlo simulation for the prediction of rolling trajectories of HL60 cells on P-selectin-patterned substrates with a specified edge inclination angle. The prediction of lateral displacement in the range of 200 μm within a 1 cm separation length supports the feasibility of label-free cell separation via asymmetric receptor patterns in microfluidic devices.     

Every Large Point Set contains Many Collinear Points or an Empty Pentagon

We prove the following generalised empty pentagon theorem for every integer ℓ ≥ 2, every sufficiently large set of points in the plane contains ℓ collinear points or an empty pentagon. As an application, we settle the next open case of the “big line or big clique” conjecture of Kára, Pór, and Wood [Discrete Comput. Geom. 34(3):497–506, 2005].     

Anion binding in the C3v-symmetric cavity of a protonated tripodal amine receptor: potentiometric and single crystal X-ray studies

Tris(2-aminoethyl)amine (tren) based pentafluorophenyl-substituted tripodal L, tris[[(2,3,4,5,6-pentafluorobenzyl)amino]ethyl]amine receptor is synthesized in good yield and characterized by single crystal X-ray diffraction analysis. Detailed structural aspects of binding of different anionic guests toward L in its triprotonated form are examined thoroughly. Crystallographic results show binding of fluoride in the C(3v)-symmetric cavity of [H(3)L](3+) where spherical anion fluoride is in tricoordinated geometry via (N-H)(+)···F interaction in the complex [H(3)L(F)]·[F](2)·2H(2)O, (3). In the case of complexes [H(3)L(OTs)]·[OTs](2), (4) and [H(3)L(OTs)]·[NO(3)]·[OTs], (5), tetrahedral p-toluenesulphonate ion is engulfed in the cavity of [H(3)L](3+) via (N-H)(+)···O interactions. Interestingly, complex [(H(3)L)(2)(SiF(6))]·[BF(4)](4)·CH(3)OH·H(2)O, (6) shows encapsulation of octahedral hexafluorosilicate in the dimeric capsular assembly of two [H(3)L](3+) units, via a number of (N-H)(+)···F interactions. The kinetic parameters of L upon binding with different anions are evaluated using a potentiometric study in solution state. The potentiometric titration experiments in a polar protic methanol/water (1:1 v/v) binary solvent system show high affinity of the receptor toward more basic fluoride and acetate anions, with a lesser affinity for other inorganic anions (e.g., chloride, bromide, nitrate, sulfate, dihydrogenphosphate, and p-toluenesulphonate).     

Synthesis, characterization, and electronic structure of new type of heterometallic boride clusters

The reaction of [Cp*TaCl(4)], 1 (Cp* = η(5)-C(5)Me(5)), with [LiBH(4)·THF] at -78 °C, followed by thermolysis in the presence of excess [BH(3)·THF], results in the formation of the oxatantalaborane cluster [(Cp*Ta)(2)B(4)H(10)O], 2 in moderate yield. Compound 2 is a notable example of an oxatantalaborane cluster where oxygen is contiguously bound to both the metal and boron. Upon availability of 2, a room temperature reaction was performed with [Fe(2)(CO)(9)], which led to the isolation of [(Cp*Ta)(2)B(2)H(4)O{H(2)Fe(2)(CO)(6)BH}], 3. Compound 3 is an unusual heterometallic boride cluster in which the [Ta(2)Fe(2)] atoms define a butterfly framework with one boron atom lying in a semi-interstitial position. Likewise, the diselenamolybdaborane, [(Cp*Mo)(2)B(4)H(4)Se(2)], 4 was treated with an excess of [Fe(2)(CO)(9)] to afford the heterometallic boride cluster [(Cp*MoSe)(2)Fe(6)(CO)(13)B(2)(BH)(2)], 5. The cluster core of 5 consists of a cubane [Mo(2)Se(2)Fe(2)B(2)] and a tricapped trigonal prism [Fe(6)B(3)] fused together with four atoms held in common between the two subclusters. In the tricapped trigonal prism subunit, one of the boron atoms is completely encapsulated and bonded to six iron and two boron atoms. Compounds 2, 3, and 5 have been characterized by mass spectrometry, IR, (1)H, (11)B, (13)C NMR spectroscopy, and the geometric structures were unequivocally established by crystallographic analysis. The density functional theory calculations yielded geometries that are in close agreement with the observed structures. Furthermore, the calculated (11)B NMR chemical shifts also support the structural characterization of the compounds. Natural bond order analysis and Wiberg bond indices are used to gain insight into the bonding patterns of the observed geometries of 2, 3, and 5.