An Extremal Problem Arising in the Dynamics of Two-Phase Materials That Directly Reveals Information about the Internal Geometry

In two-phase materials, each phase having a non-local response in time, it has been found that for some driving fields the response somehow untangles at specific times, and allows one to directly infer useful information about the geometry of the material, such as the volume fractions of the phases. Motivated by this, and to obtain an algorithm for designing appropriate driving fields, we find approximate, measure independent, linear relations between the values that Markov functions take at a given set of possibly complex points, not belonging to the interval [-1,1] where the measure is supported. The problem is reduced to simply one of polynomial approximation of a given function on the interval [-1,1] and, to simplify the analysis, Chebyshev approximation is used. This allows one to obtain explicit estimates of the error of the approximation, in terms of the number of points and the minimum distance of the points to the interval [-1,1]. Assuming this minimum distance is bounded below by a number greater than 1/2, the error converges exponentially to zero as the number of points is increased. Approximate linear relations are also obtained that incorporate a set of moments of the measure. In the context of the motivating problem, the analysis also yields bounds on the response at any particular time for any driving field, and allows one to estimate the response at a given frequency using an appropriately designed driving field that effectively is turned on only for a fixed interval of time. The approximation extends directly to Markov-type functions with a positive semidefinite operator valued measure, and this has applications to determining the shape of an inclusion in a body from boundary flux measurements at a specific time, when the time-dependent boundary potentials are suitably tailored. © 2022 Wiley Periodicals, Inc.     

Computational study of shock wave focusing in a log-spiral duct

The mechanism of shock wave focusing in a two-dimensional log-spiral duct has been investigated here numerically using a finite volume method. This approach is based on a MUSCL TVD scheme with flux-vector splitting applied to the Euler equations. The isopycnics determined from the calculations are compared with the experimental results obtained by use of holographic interferometric photography and are found to be in excellent qualitative agreement with the experiments. The computational results clarify the details of the wave interactions very near to the focus. In particular, phenomena such as the formation of secondary shock waves prior to the implosion, their interaction with the reflected shock and the formation of vortices after the implosion have been examined.     

The Mach reflection of shock waves in converging,cylindrical channels

Shock waves impinging on axisymmetric converging passages of moderate wall angle undergo cyclical Mach reflection processes which are generally not self-similar during progression through the contraction. This paper presents the results of shock tube experiments in air where shocks of moderate strength are incident on cones having a range of wall angles of 10° to 30°. Mach reflection is maintained as the dominant reflection process throughout this range but the number of cycles decreases as wall angle increases. A ray-shock approach, used to calculate the triple-point trajectories gives good agreement with the experimental locations of their intersections with the centreline and wall.     

Synthesis of C-9 oxidised N-acetylneuraminic acid derivatives as biological probes

Sialic acids are 9-carbon acidic sugars involved in a number of important biological processes and human diseases. As part of our ongoing interest in the development of novel sialic acids as biological probes, we have developed an efficient and simple synthesis of C-9 oxidised sialic acid derivatives. The key oxidative step involves the use of TEMPO under carefully controlled aqueous pH conditions.     

Synthesis of simple heparanase substrates

Heparanase degrades heparan sulfate (HS) chains on proteoglycans; elevated levels of heparanase expression correlate with tumour cell metastatic potential and vascularity, and reduced post-operative survival of cancer patients. Consequently, heparanase expression is considered a biomarker for cancer detection. Although several heparanase assays have been developed, most require the preparation of heterogeneous, (radio)labelled HS substrates and rely on the separation of enzymatically-degraded products on the basis of molecular size. In studies directed towards the development of a more direct heparanase assay, a series of glucuronides and glycosyl glucuronides were synthesised as putative heparanase substrates. These compounds were designed with various aryl aglycones that could be measured spectrophotometrically upon hydrolysis of the glycosidic linkage by heparanase. It was found that the N-sulfated 4-nitrophenyl glycosyl glucuronide 24 and the N-sulfated methylumbelliferyl glycosyl glucuronide 26 were hydrolysed by recombinant human heparanase. These compounds represent the simplest substrates of heparanase reported to date.     

Existence of a Weak Solution in L p to the Vortex-Wave System

The vortex-wave system is a coupling of the two-dimensional vorticity equation with the point-vortex system. It is a model for the motion of a finite number of concentrated vortices moving in a distributed vorticity background. In this article, we prove existence of a weak solution to this system with an initial background vorticity in L ^p , p>2, up to the time of first collision of point vortices.     

Surfactant addition and alternating current electrophoretic oscillation during size fractionation of nanoparticles in channels with two or three different height segments

An array of parallel planar nanochannels containing two or three segments with varying inner heights was fabricated and used for size fractionation of inorganic and biological nanoparticles. A liquid suspension of the particles was simply drawn through the nanochannels via capillary action. Using fluorescently labeled 30 nm polyacrylonitrile beads, different trapping behaviors were compared using nanochannels with 200-45 nm and 208-54-30 nm height segments. Addition of sodium dodecyl sulfate (SDS) surfactant to the liquid suspension and application of an AC electric field were shown to aid in the prevention of channel clogging. After initial particle trapping at the segment interfaces, significant particle redistribution occurred when applying a sinusoidal 8V peak-to-peak oscillating voltage with a frequency of 150 Hz and DC offset of 4V. Using the 208-54-30 nm channels, 30 nm hepatitis B virus (HBV) capsids were divided into three fractions. When the AC electric field was applied to this trapped sample, all of the virus particles passed through the interfaces and accumulated at the channel ends.     

Exterior cloaking with active sources in two dimensional acoustics

We cloak a region from a known incident wave by surrounding the region with three or more devices that cancel out the field in the cloaked region without significantly radiating waves. Since very little waves reach scatterers within the cloaked region, the scattered field is small and the scatterers are for all practical purposes undetectable. The devices are multipolar point sources that can be determined from Green's formula and an addition theorem for Hankel functions. The cloaking devices are exterior to the cloaked region.