Low temperature electronic transports in the presence of a density gradient

In this paper, we review low temperature electronic transport results in high quality two-dimensional electron systems. We discuss the quantization of the diagonal resistance, R_xx, at the edges of several quantum Hall states. Each quantized R_xx value turns out to be close to the difference between the two adjacent Hall plateaus in the off-diagonal resistance, R_xy. Moreover, peaks in R_xx occur at different positions in positive and negative magnetic fields. All three R_xx features can be explained quantitatively by a ∼1% cm electron density gradient. Furthermore, based on this observation, the well known but still enigmatic resistivity rule, relating R_xx to , finds a simple interpretation in terms of this gradient. In another sample, at 1.2 K, R_xx we observe a strongly linear magnetic field dependence. Surprisingly, this linear magnetoresistance also originates from the density gradient. Our findings throw an unexpected light on the relationship between the experimentally measured R_xx and the diagonal resistivity ρ_xx.     

Flexible sliced designs for computer experiments

Sliced Latin hypercube designs are popularly adopted for computer experiments with qualitative factors. Previous constructions require the sizes of different slices to be identical. Here we construct sliced designs with flexible sizes of slices. Besides achieving desirable one-dimensional uniformity, flexible sliced designs (FSDs) constructed in this paper accommodate arbitrary sizes for different slices and cover ordinary sliced Latin hypercube designs as special cases. The sampling properties of FSDs are derived and a central limit theorem is established. It shows that any linear combination of the sample means from different models on slices follows an asymptotic normal distribution. Some simulations compare FSDs with other sliced designs in collective evaluations of multiple computer models.     

Determinant Forms for Extended Heat Functions and Expansions of Solutions of Associated Cauchy Problems

We briefly review series solutions of differential equations problems of the second order that lead to coefficients expressed in terms of determinants. Derivative type formulas involving a generating function with several parameters are developed for these determinant coefficients in first order problems. These permit constructing determinant forms for the heat polynomials and their Appell transforms. Hadamard's theorem for bounding determinants and conical regions are used to deduce simplified versions of expansion theorems involving these polynomials and associated Appell transforms. Extended versions of the heat equation are also considered.     

Observation of pinning mode of stripe phases of 2D systems in high Landau levels

We study the radio-frequency diagonal conductivities of the anisotropic stripe phases of higher Landau levels near half-integer fillings. In the hard direction, in which larger dc resistivity occurs, the spectrum exhibits a striking resonance, while in the orthogonal, easy direction, no resonance is discernible. The resonance is interpreted as a pinning mode of the stripe phase.     

Catalytic Hydroetherification of Unactivated Alkenes Enabled by Proton-Coupled Electron Transfer

We report a catalytic, light-driven method for the intramolecular hydroetherification of unactivated alkenols to furnish cyclic ether products. These reactions occur under visible-light irradiation in the presence of an Ir^III-based photoredox catalyst, a Brønsted base catalyst, and a hydrogen-atom transfer (HAT) co-catalyst. Reactive alkoxy radicals are proposed as key intermediates, generated by direct homolytic activation of alcohol O−H bonds through a proton-coupled electron-transfer mechanism. This method exhibits a broad substrate scope and high functional-group tolerance, and it accommodates a diverse range of alkene substitution patterns. Results demonstrating the extension of this catalytic system to carboetherification reactions are also presented.     

Strongly anisotropic electronic transport in higher Landau levels

Low-temperature, electronic transport in higher Landau levels (N>1) in a two-dimensional electron system is strongly anisotropic. At half-filling of either spin level of such Landau levels ( etc.) the magnetoresistance either collapses to form a deep minimum or is peaked in a sharp maximum, depending on the in-plane current direction. The anisotropic axis can be reoriented by applying an in-plane magnetic field of 1–2 T strength. The magnetoresistance at and (N=1) is initially isotropic but an in-plane field induces a strong anisotropy. Our observations are strong evidence for a new many-electron phase in higher Landau levels, which forms spontaneously or can be induced by an in-plane field.     

Window-modulated compounding Nakagami imaging for ultrasound tissue characterization

Ultrasound Nakagami parametric imaging is a useful tool for tissue characterization. Previous literature has suggested using a square with side lengths corresponding to 3 times the transducer pulse length as the minimum window for constructing the Nakagami image. This criterion does not produce sufficiently smooth images for the Nakagami image to characterize homogeneous tissues. To improve image smoothness, we proposed window-modulated compounding (WMC) Nakagami imaging based on summing and averaging the Nakagami images formed using sliding windows with varying window side lengths from 1 to N times the transducer pulse length in 1 pulse length step. Simulations (the number densities of scatterers: 2–16 scatterers/mm²) and experiments on fully developed speckle phantoms (the scatterer diameters: 20–106 μm) were conducted to suggest an appropriate number of frames N and to evaluate the image smoothness and resolution by analyzing the full width at half maximum (FWHM) of the parameter distribution and the widths of the image autocorrelation function (ACF), respectively. In vivo ultrasound measurements on rat livers without and with cirrhosis were performed to validate the practical performance of the WMC Nakagami image in tissue characterization. The simulation results showed that using a range of N from 7 to 10 as the number of frames for image compounding reduces the estimation error to less than 5%. Based on this criterion, the Nakagami parameter obtained from the WMC Nakagami image increased from 0.45 to 0.95 after increasing the number densities of scatterers from 2 to 16 scatterers/mm². The FWHM of the parameter distribution (bins = 40) was 13.5 ± 1.4 for the Nakagami image and 9.1 ± 1.43 for the WMC Nakagami image, respectively (p-value < .05). The widths of the ACF for the Nakagami and WMC Nakagami images were 454 ± 5.36 and 458 ± 4.33, respectively (p-value > .05). In the phantom experiments, we also found that the FWHM of the parameter distribution for the WMC Nakagami image was smaller than that of the conventional Nakagami image (p-value < .05), and there was no significant difference of the ACF width between the Nakagami and WMC Nakagami images (p-value > .05). In the animal experiments, the Nakagami parameters obtained from the WMC Nakagami image for normal and cirrhotic rat livers were 0.62 ± 0.08 and 0.92 ± 0.07, respectively (p-value < .05). The results demonstrated that the WMC technique significantly improved the image smoothness of Nakagami imaging without resolution degradation, giving Nakagami model-based imaging the ability to visualize scatterer properties with enhanced image quality.     

Linear-Eddy Model Formulated Probability Density Function and Scalar Dissipation Rate Models for Premixed Combustion

A tabulated, pseudo-turbulent Probability Density Function (PDF) model for premixed combustion is proposed. The Linear-Eddy Model (LEM) is used to construct the PDFs for a temperature-based progress variable in a premixed, turbulent methane/air V-flame produced by the Cambridge slot burner. As a second case study, the LEM PDFs are similarly compared to PDFs extracted from Direct Numerical Simulations (DNS) of a turbulent premixed flame. LEM demonstrates the ability to reproduce the salient features from experimental and DNS PDFs; moreover, it is able to better capture turbulent effects than previously suggested laminar flamelet PDF models. The Scalar Dissipation Rate (SDR) for premixed combustion is likewise investigated. The stochastic nature of LEM enables it to mimic the overall behaviors of turbulent reactions inexpensively and qualitatively. Crucially, LEM appears to be well suited for the preprocessing tabulation of PDF and SDR models for a number of premixed combustion simulation strategies.     

Preparation and Application of Immobilized Fullerene C60‐Heparin for Anticoagulation of Blood

The interaction between fullerene C60 and heparin was studied using a fullerene C60‐coated piezoelectric quartz crystal sensor. The irreversible response of the piezoelectric quartz crystal was found which could be attributed to the quite strong adsorption of heparin onto the C60 molecule. Immobilized fullerene C60‐Heparin was prepared and successfully applied as a good inhibitor for blood clotting. Like solvated heparin, both wet and dry C60‐heparin solid all demonstrated excellent ability of anticoagulation of blood. The blood clotting time with C60‐heparin solid was found to be > 7 days, while only 17.9 min required for blood clotting time in the absence of C60‐heparin solid. Furthermore, the C60‐heparin coated artificial PVC blood vessels were prepared by coating fullerene C60 onto the surface of artificial PVC blood vessels, followed by the adsorption of water solvated heparin onto the fullerene C60 molecule to form C60‐heparin coating. The blood clotting time of blood in artificial PVC blood vessels with C60‐heparin coating was found to be > 30 days, while only ≤ 30 min. of blood clotting time without the C60‐Heparin coating was observed. The C60‐heparin coated artificial PVC blood vessels can be expected to be employed in human body for the anticoagulation of blood.