Comment on: “Confined states in two-dimensional flat elliptic quantum dots and elliptic quantum wires” [Physica E 11 (2001) 345]

We argue that the two-dimensional elliptic quantum dot problem with finite barrier cannot be exactly solved, contrary to a recent assertion (van den Broek and Peeters, Physica E 11 (2001) 345. We also prove it explicitly by numerically calculating the correct energy spectrum.     

Immuno-affinity columns versus conventional clean-up: a method-comparison study for the determination of zearalenone in corn

The efficiency of a modern analytical method employing immuno-affinity columns (IACs) is compared to a well established traditional technique with respect to the determination of zearalenone (ZON) in corn in the μg/kg range. Despite of a constant error of about 4 μg/kg in the examined working range of 10–200 μg/kg, analytical data obtained from the analysis of spiked and naturally contaminated samples showed good correspondence for the compared methods. The performance characteristics of immuno-affinity-chromatography as a new clean-up technique for the determination of ZON in corn is reported for the first time and compared to a conventional clean-up procedure     

Interference of a four-hole aperture for on-chip quantitative two-dimensional differential phase imaging

We present a novel on-chip method for quantitative two-dimensional differential phase imaging. This technique uses four circular holes (600 nm diameter, 1.2 mum spacing) arranged in a 'plus' pattern that are fabricated in a layer of metal above a complementary metal-oxide semiconductor (CMOS) imaging sensor. The interference pattern of the aperture shifts position with respect to the differential phase of the incident light. By imaging the interference pattern with the CMOS sensor, this method measures amplitude and differential phase (1 degrees /microm sensitivity for signal-to-noise ratio >/=16 dB) of the incident light field simultaneously. An application to optical beam profiling is presented; we show the amplitude and differential phase profiles of a Gaussian laser beam and an optical vortex.     

Fe2+ and Cu2+ Increase the Production of Hyaluronic Acid by Lactobacilli via Affecting Different Stages of the Pentose Phosphate Pathway

This study aimed at optimizing the production of hyaluronic acid by Lactobacillus acidophilus FTDC 1231 using response surface methodology and evaluating the effects of divalent metal ions along the production pathway using molecular docking. Among different divalent metal ions that were screened, only iron (II) sulphate and copper (II) sulphate significantly (P?<?0.05) affected the production of hyaluronic acid. Subsequent optimization yielded hyaluronic acid at concentration of 0.6152?mg/mL in the presence of 1.24 mol L^?1 iron (II) sulphate and 0.16 mol L^?1 of copper (II) sulphate (103 % increase compared to absence of divalent metal ions). Data from molecular docking showed Fe²⁺ improved the binding affinity of UDP-pyrophophorylase towards glucose-1-phosphate, while Cu²⁺ contributed towards the interaction between UDP-glucose dehydrogenase and UDP-glucose. We have demonstrated that lactobacilli could produce hyaluronic acid at increased concentration upon facilitation by specific divalent metal ions, via specific targets of enzymes and substrates along pentose phosphate pathway.     

Eigenmodes of triaxial ellipsoidal acoustical cavities with mixed boundary conditions

The linear acoustics problem of resonant vibrational modes in a triaxial ellipsoidal acoustic cavity with walls of arbitrary acoustic impedance has been quasi-analytically solved using the Frobenius power-series expansion method. Eigenmode results are presented for the lowest two eigenmodes in cases with pressure-release, rigid-wall, and lossy-wall boundary conditions. A mode crossing is obtained as a function of the specific acoustic impedance of the wall; the degeneracy is not symmetry related. Furthermore, the damping of the wave is found to be maximal near the crossing.     

The dynamics of Charles Taylor’s remarkable one-wheeled vehicle

In the 1950s and 1960s, Charles F. Taylor designed and tested various prototype one-wheeled vehicles. These machines were stabilized and steered using gyroscopes. In this paper, a simple model of a one-wheeled vehicle is presented and analyzed. This analysis explains the ability of these machines to exhibit stable steady motions.      

Effective Cohesive Behavior of Layers of Interatomic Planes

A simple model of cleavage in brittle crystals consists of a layer of material containing N atomic planes separating in accordance with an interplanar potential under the action of an opening displacement δ prescribed on the boundary of the layer. The problem addressed in this work concerns the characterization of the constrained minima of the energy E_N of the layer as a function of δ as N becomes large. These minima determine the effective or macroscopic cohesive law of the crystal. The main results presented in this communication are: (i) the computation of the Γ limit E₀ of E_N as N → ∞; (ii) the characterization of the minimum values of E₀ as a function of the macroscopic opening displacement; (iii) a proof of uniform convergence of the minima of E_N for the case of nearest-neighbor interactions; and (iv) a proof of uniform convergence of the derivatives of E_N, or tractions, in the same case. The scaling on which the present Γ-convergence analysis is based has the effect of separating the bulk and surface contributions to the energy. It differs crucially from other scalings employed in the past in that it renders both contributions of the same order.     

Effective macroscopic adhesive contact behavior induced by small surface roughness

In this paper we study a model contact problem involving adhesive elastic frictionless contact between rough surfaces. The problem's most notable feature is that it captures the phenomenon of depth-dependent-hysteresis (DDH) (e.g., see Kesari et al., 2010), which refers to the observation of different contact forces during the loading and unloading stages of a contact experiment. We specifically study contact between a rigid axi-symmetric punch and an elastic half-space. The roughness is represented as arbitrary periodic undulations in the punch's radial profile. These undulations induce multiple equilibrium contact regions between the bodies at each indentation-depth. Assuming that the system evolves so as to minimize its potential energy, we show that different equilibrium contact regions are selected during the loading and unloading stages at each indentation-depth, giving rise to DDH. When the period and amplitude of our model's roughness is reduced, we show that the evolution of the contact force and radius with the indentation-depth can be approximated with simpler curves, the effective macroscopic behavior, which we compute. Remarkably, the effective behavior depends solely on the amplitude and period of the model's roughness. The effective behavior is useful for estimating material properties from contact experiments displaying DDH. We show one such example here. Using the effective behavior for a particular roughness model (sinusoidal) we analyze the energy loss during a loading/unloading cycle, finding that roughness can toughen the interface. We also estimate the energy barriers between the different equilibrium contact regions at a fixed indentation-depth, which can be used to assess the importance of ambient energy fluctuations on DDH.