On the existence and multiplicity of positive solutions to classes of steady state reaction diffusion systems with multiple parameters

We study positive solutions to the steady state reaction diffusion systems of the form: \begin{equation} \left\{\begin{array}{ll} -\Delta u = \lambda f(v)+\mu h(u), & \Omega,\\ -\Delta v = \lambda g(u)+\mu q(v),& \Omega,\\ \frac{\partial u}{\partial \eta}+\sqrt[]{\lambda +\mu}\, u=0,& \partial\Omega,\\ \frac{\partial v}{\partial \eta}+\sqrt[]{\lambda +\mu}\, v=0, & \partial\Omega,\\ \end{array}\right. \end{equation} where ${\lambda,\mu>0}$ are positive parameters, ${\Omega}$ is a bounded in $\mathbb{R}^{N}$$(N>1)$ with smooth boundary ${\partial \Omega}$, or ${\Omega=(0,1)}$, ${ \frac{\partial z}{\partial \eta} }$ is the outward normal derivative of $z$. Here $f, g, h, q\in C^{2} [0,r)\cap C[0,\infty)$ for some $r>0$. Further, we assume that $f, g, h$ and $q$ are increasing functions such that $f(0) = g(0) = h(0) = {q}(0) = 0$, $f^\prime(0), g^\prime(0), h^\prime(0), q^\prime(0) > 0$, and $\lim\limits_{s\to \infty}\frac{f(M g(s))}{s}=0$ for all $M>0$. Under certain additional assumptions on $f, g, h$ and $q$ we prove our existence and multiplicity results. Our existence and multiplicity results are proved using sub-super solution methods

Single-molecule super-resolution imaging of chromosomes and in situ haplotype visualization using Oligopaint FISH probes

Fluorescence in situ hybridization (FISH) is a powerful single-cell technique for studying nuclear structure and organization. Here we report two advances in FISH-based imaging. We first describe the in situ visualization of single-copy regions of the genome using two single-molecule super-resolution methodologies. We then introduce a robust and reliable system that harnesses single-nucleotide polymorphisms (SNPs) to visually distinguish the maternal and paternal homologous chromosomes in mammalian and insect systems. Both of these new technologies are enabled by renewable, bioinformatically designed, oligonucleotide-based Oligopaint probes, which we augment with a strategy that uses secondary oligonucleotides (oligos) to produce and enhance fluorescent signals. These advances should substantially expand the capability to query parent-of-origin-specific chromosome positioning and gene expression on a cell-by-cell basis

Growth of Pure Zinc-Blende GaAs(P) Core-Shell Nanowires with Highly Regular Morphology

The growth of self-catalyzed core–shell nanowires (NWs) is investigated systematically using GaAs(P) NWs. The defects in the core NW are found to be detrimental for the shell growth. These defects are effectively eliminated by introducing beryllium (Be) doping during the NW core growth and hence forming Be–Ga alloy droplets that can effectively suppress the WZ nucleation and facilitate the droplet consumption. Shells with pure zinc-blende crystal quality and highly regular morphology are successfully grown on the defect-free NW cores and demonstrated an enhancement of one order of magnitude for room-temperature emission compared to that of the defective shells. These results provide useful information on guiding the growth of high-quality shell, which can greatly enhance the NW device performance

Frequency of natural out-crossing in partially cleistogamous pigeonpea lines in diverse environments

Natural out-crossing is the major cause of loss of varietal purity in pegeonpea [Cajanus cajan (L.) Millsp.]. The frequency of natural out-crossing of partially cleistogamous mutant lines, characterized by a modified keel and filamentous anthers, was studied at two locations in Sri Lanka and three locations in India. Indeterminate growth habit and normal floral morphology were used as dominant markers and the frequency of anural out-crossing was estimated as percentage of the observed hybrid plants. Natural out-crossing in the mutant lines in Sri Lanka ranged from 0.14 to 1.33% in comparison to 6.34 to 19.64% in the controls. In the Indian environments, natural outcrossing ranged from 0.16 to 2.67%. The mutant was higly stable over diverse environments, and may be of considerable economic importance in pigeonpea improvement and seed-production programs

Multiple radial phosphorus segregations in GaAsP core-shell nanowires

Highly faceted geometries such as nanowires are prone to form self-formed features, especially those that are driven by segregation. Understanding these features is important in preventing their formation, understanding their effects on nanowire properties, or engineering them for applications. Single elemental segregation lines that run along the radii of the hexagonal cross-section have been a common observation in alloy semiconductor nanowires. Here, in GaAsP nanowires, two additional P rich bands are formed on either side of the primary band, resulting in a total of three segregation bands in the vicinity of three of the alternating radii. These bands are less intense than the primary band and their formation can be attributed to the inclined nanofacets that form in the vicinity of the vertices. The formation of the secondary bands requires a higher composition of P in the shell, and to be grown under conditions that increase the diffusivity difference between As and P. Furthermore, it is observed that the primary band can split into two narrow and parallel bands. This can take place in all six radii, making the cross sections to have up to a maximum of 18 radial segregation bands. With controlled growth, these features could be exploited to assemble multiple different quantum structures in a new dimension (circumferential direction) within nanowires

Self-Catalyzed AlGaAs Nanowires and AlGaAs/GaAs Nanowire-Quantum Dots on Si Substrates

[Image: see text] Self-catalyzed AlGaAs nanowires (NWs) and NWs with a GaAs quantum dot (QD) were monolithically grown on Si(111) substrates via solid-source molecular beam epitaxy. This growth technique is advantageous in comparison to the previously employed Au-catalyzed approach, as it removes Au contamination issues and renders the structures compatible with complementary metal–oxide–semiconductor (CMOS) technology applications. Structural studies reveal the self-formation of an Al-rich AlGaAs shell, thicker at the NW base and thinning towards the tip, with the opposite behavior observed for the NW core. Wide alloy fluctuations in the shell region are also noticed. AlGaAs NW structures with nominal Al contents of 10, 20, and 30% have strong room temperature photoluminescence, with emission in the range of 1.50–1.72 eV. Individual NWs with an embedded 4.9 nm-thick GaAs region exhibit clear QD behavior, with spatially localized emission, both exciton and biexciton recombination lines, and an exciton line width of 490 μeV at low temperature. Our results demonstrate the properties and behavior of the AlGaAs NWs and AlGaAs/GaAs NWQDs grown via the self-catalyzed approach for the first time and exhibit their potential for a range of novel applications, including nanolasers and single-photon sources

Evaluation of pigeonpea accessions and selected lines for reaction to Maruca

Maruca vitrata (Geyer) is a serious insect pest of tropical legumes. In Sri Lanka, yield losses due to Maruca damage in pigeonpea [Cajanus cajan (L.) Millsp.] range up to 100%. The development of resistant cultivars and germplasm is one of the best means of control. The objectives of this study were to screen 271 accessions for resistance to M. vitrata and evaluate reaction of lines selected from the promising accessions. The high level of natural incidence of Maruca in Sri Lanka provided an opportunity for evaluation of germplasm at Field Crops Research and Development Institute, Maha Illuppallama. Screening of the germplasm accessions revealed large variation in Maruca damage to flowers and pods. On average, the Maruca damage in determinate accessions (66–75%) was higher than that of nondeterminate accessions (41–50%). Resistant plants from four determinate and 12 nondeterminate accessions were selected. Further selection for resistance to Maruca damage among and within lines derived from the resistant plants was exercised for six generations under nonsprayed field conditions. Under insecticide-free conditions, the selections from two accessions showed significant yield advantages over controls. Data on pod damage and larval counts indicated that the resistance was conditioned through yield compensation mechanisms. In pigeonpea, this is the first report of the selection of Maruca resistant lines. Further studies showed that by using the resistant genotypes it is possible to reduce the number of insecticide sprays for economic yields

Long-term stability and optoelectronic performance enhancement of InAsP nanowires with an ultrathin InP passivation layer

The influence of nanowire (NW) surface states increases rapidly with the reduction of diameter and hence severely degrades the optoelectronic performance of narrow-diameter NWs. Surface passivation is therefore critical, but it is challenging to achieve long-term effective passivation without significantly affecting other qualities. Here, we demonstrate that an ultrathin InP passivation layer of 2–3 nm can effectively solve these challenges. For InAsP nanowires with small diameters of 30–40 nm, the ultrathin passivation layer reduces the surface recombination velocity by at least 70% and increases the charge carrier lifetime by a factor of 3. These improvements are maintained even after storing the samples in ambient atmosphere for over 3 years. This passivation also greatly improves the performance thermal tolerance of these thin NWs and extends their operating temperature from <150 K to room temperature. This study provides a new route toward high-performance room-temperature narrow-diameter NW devices with long-term stability

Highly strained III-V-V coaxial nanowire quantum wells with strong carrier confinement

Coaxial quantum wells (QWs) are ideal candidates for nanowire (NW) lasers, providing strong carrier confinement and allowing close matching of the cavity mode and gain medium. We report a detailed structural and optical study and the observation of lasing for a mixed group-V GaAsP NW with GaAs QWs. This system offers a number of potential advantages in comparison to previously studied common group-V structures (e.g., AlGaAs/GaAs) including highly strained binary GaAs QWs, the absence of a lower band gap core region, and deep carrier potential wells. Despite the large lattice mismatch (∼1.7%), it is possible to grow defect-free GaAs coaxial QWs with high optical quality. The large band gap difference results in strong carrier confinement, and the ability to apply a high degree of compressive strain to the GaAs QWs is also expected to be beneficial for laser performance. For a non-fully optimized structure containing three QWs, we achieve low-temperature lasing with a low external (internal) threshold of 20 (0.9) μJ/cm2/pulse. In addition, a very narrow lasing line width of ∼0.15 nm is observed. These results extend the NW laser structure to coaxial III–V–V QWs, which are highly suitable as the platform for NW emitters