Differentiable spaces that are subcartesian

We show that the differential structure of the orbit space of a proper action of a Lie group on a smooth manifold is weakly reflexive. This implies that the orbit space is a differentiable space in the sense of Smith, which ensures that the orbit space has an exterior algebra of differential forms, that satisfies Smith’s version of de Rham’s theorem. Because the orbit space is a locally closed subcartesian space, it has vector fields and their flows.     

Alkaline oxygen evolution: exploring synergy between fcc and hcp cobalt nanoparticles entrapped in N-doped graphene

Herein, we report a Mott-Schottky catalyst by entrapping cobalt nanoparticles inside the N-doped graphene shell (Co@NC). The Co@NC delivered excellent oxygen evolution activity with an overpotential of merely 248 mV at a current density of 10 mA cm^–2 with promising long-term stability. The importance of Co encapsulated in NC has further been demonstrated by synthesizing Co nanoparticles without NC shell. The synergy between the hexagonal close-packed (hcp) and face-centered cubic (fcc) Co plays a major role to improve the OER activity, whereas the NC shell optimizes the electronic structure, improves the electron conductivity, and offers a large number of active sites in Co@NC. The density functional theory calculations have revealed that the hcp Co has a dominant role in the surface reaction of electrocatalytic oxygen evolution, whereas the fcc phase induces the built-in electric field at the interfaces with N-doped graphene to accelerate the H⁺ ion transport.     

2.3–21 GHz broadband and high linearity distributed low noise amplifier

This paper focuses on the design of a 2.3–21 GHz Distributed Low Noise Amplifier (LNA) with low noise figure (NF), high gain (S₂₁), and high linearity (IIP3) for broadband applications. This distributed amplifier (DA) includes S/C/X/Ku/K-band, which makes it very suitable for heterodyne receivers. The proposed DA uses a 0.18 μm GaAs pHEMT process (OMMIC ED02AH) in cascade architecture with lines adaptation and equalization of phase velocity techniques, to absorb their parasitic capacitances into the gate and drain transmission lines in order to achieve wide bandwidth and to enhance gain and linearity. The proposed broadband DA achieved an excellent gain in the flatness of 13.5 ± 0.2 dB, a low noise figure of 3.44 ± 1.12 dB, and a small group delay variation of ±19.721 ps over the range of 2.3–21 GHz. The input and output reflection coefficients S₁₁ and S₂₂ are less than −10 dB. The input compression point (P_1dB) and input third-order intercept point (IIP3) are −1.5 dBm and 11.5 dBm, respectively at 13 GHz. The dissipated power is 282 mW and the core layout size is 2.2 × 0.8 mm².     

Phase transition in the one-dimensional pair-hopping model with unusual one-electron hopping

By modifying the conventional one-electron hopping behavior, we study effects of an occupation-dependent hopping on the ground state of the half-filled one-dimensional pair-hopping model. At weak coupling, the use of bosonization and renormalization-group analysis techniques helps to derive the phase diagram. Such unusual hopping is shown to drive a spin-gap transition and to introduce a new region where the triplet superconducting instability dominates for positively small pair-hopping interaction.     

Mass distribution and skewness for passive scalar transport in pipes with polygonal and smooth cross sections

We extend our previous results characterizing the loading properties of a diffusing passive scalar advected by a laminar shear flow in ducts and channels to more general cross‐sectional shapes, including regular polygons and smoothed corner ducts originating from deformations of ellipses. For the case of the triangle and localized, cross‐wise uniform initial distributions, short‐time skewness is calculated exactly to be positive, while long‐time asymptotics shows it to be negative. Monte Carlo simulations confirm these predictions, and document the timescale for sign change. The equilateral triangle appears to be the only regular polygon with this property—all others possess positive skewness at all times. Alternatively, closed‐form flow solutions can be constructed for smooth deformations of ellipses, and illustrate how both nonzero short‐time skewness and the possibility of multiple sign switching in time is unrelated to domain corners. Exact conditions relating the median and the skewness to the mean are developed which guarantee when the sign for the skewness implies front (more mass to the right of the mean) or back (more mass to the left of the mean) “loading” properties of the evolving tracer distribution along the pipe. Short‐ and long‐time asymptotics confirm this condition, and Monte Carlo simulations verify this at all times. The simulations are also used to examine the role of corners and boundaries on the distribution for short‐time evolution of point source , as opposed to cross‐wise uniform, initial data.     

Modeling the effect of deep traps on the capacitance–voltage characteristics of p-type Si-doped GaAs Schottky diodes grown on high index GaAs substrates

Numerical simulation, using SILVACO-TCAD, is carried out to explain experimentally observed effects of different types of deep levels on the capacitance–voltage characteristics of p-type Si-doped GaAs Schottky diodes grown on high index GaAs substrates. Two diodes were grown on (311)A and (211)A oriented GaAs substrates using Molecular Beam Epitaxy (MBE). Although, deep levels were observed in both structures, the measured capacitance–voltage characteristics show a negative differential capacitance (NDC) for the (311)A diodes, while the (211)A devices display a usual behaviour. The NDC is related to the nature and spatial distribution of the deep levels, which are characterized by the Deep Level Transient Spectroscopy (DLTS) technique. In the (311)A structure only majority deep levels (hole traps) were observed while both majority and minority deep levels were present in the (211)A diodes. The simulation, which calculates the capacitance–voltage characteristics in the absence and presence of different types of deep levels, agrees well with the experimentally observed behaviour.     

Properties of bounded stochastic processes employed in biophysics

Abstract

Realistic stochastic modeling is increasingly requiring the use of bounded noises. In this work, properties and relationships of commonly employed bounded stochastic processes are investigated within a solid mathematical ground. Four families are object of investigation: the Sine-Wiener (SW), the Doering–Cai–Lin (DCL), the Tsallis–Stariolo–Borland (TSB), and the Kessler–Sørensen (KS) families. We address mathematical questions on existence and uniqueness of the processes defined through Stochastic Differential Equations, which often conceal non-obvious behavior, and we explore the behavior of the solutions near the boundaries of the state space. The expression of the time-dependent probability density of the Sine-Wiener noise is provided in closed form, and a close connection with the Doering–Cai–Lin noise is shown. Further relationships among the different families are explored, pathwise and in distribution. Finally, we illustrate an analogy between the Kessler–Sørensen family and Bessel processes, which allows to relate the respective local times at the boundaries.     

Change of evaporation rate of single monocomponent droplet with temperature using time-resolved phase rainbow refractometry

Droplet evaporation characterization, although of great significance, is still challenging. The recently developed phase rainbow refractometry (PRR) is proposed as an approach to measuring the droplet temperature, size as well as evaporation rate simultaneously, and is applied to a single flowing n-heptane droplet produced by a droplet-on-demand generator. The changes of droplet temperature and evaporation rate after a transient spark heating are reflected in the time-resolved PRR image. Results show that droplet evaporation rate increases with temperature, from ?1.28$\times {10}^{?8}$ m²/s at atmospheric 293 K to a range of (?1.5, ?8)$\times {10}^{?8}$ m²/s when heated to (294, 315) K, agreeing well with the Maxwell and Stefan–Fuchs model predictions. Uncertainty analysis suggests that the main source is the indeterminate gradient inside droplet, resulting in an underestimation of droplet temperature and evaporation rate. With the demonstration on simultaneous measurements of droplet refractive index as well as droplet transient and local evaporation rate in this work, PRR is a promising tool to investigate single droplet evaporation in real engine conditions.