Diameter dependence of SiGe nanowire thermal conductivity

We theoretically compute the thermal conductivity of SiGe alloy nanowires as a function of nanowire diameter, alloy concentration, and temperature, obtaining a satisfactory quantitative agreement with experimental results. Our results account for the weaker diameter dependence of the thermal conductivity recently observed in Si$_{1-x}$Ge$_x$ nanowires ($x<0.1$), as compared to pure Si nanowires. We also present calculations in the full range of alloy concentrations, $0 \leq x \leq 1$, which may serve as a basis for comparison with future experiments on high alloy concentration nanowires.Comment: 3 fig

The number of independent sets in a graph with small maximum degree

Let ${\rm ind}(G)$ be the number of independent sets in a graph $G$. We show that if $G$ has maximum degree at most $5$ then $${\rm ind}(G) \leq 2^{{\rm iso}(G)} \prod_{uv \in E(G)} {\rm ind}(K_{d(u),d(v)})^{\frac{1}{d(u)d(v)}}$$ (where $d(\cdot)$ is vertex degree, ${\rm iso}(G)$ is the number of isolated vertices in $G$ and $K_{a,b}$ is the complete bipartite graph with $a$ vertices in one partition class and $b$ in the other), with equality if and only if each connected component of $G$ is either a complete bipartite graph or a single vertex. This bound (for all $G$) was conjectured by Kahn. A corollary of our result is that if $G$ is $d$-regular with $1 \leq d \leq 5$ then $${\rm ind}(G) \leq \left(2^{d+1}-1\right)^\frac{|V(G)|}{2d},$$ with equality if and only if $G$ is a disjoint union of $V(G)/2d$ copies of $K_{d,d}$. This bound (for all $d$) was conjectured by Alon and Kahn and recently proved for all $d$ by the second author, without the characterization of the extreme cases. Our proof involves a reduction to a finite search. For graphs with maximum degree at most $3$ the search could be done by hand, but for the case of maximum degree $4$ or $5$, a computer is needed.Comment: Article will appear in {\em Graphs and Combinatorics

Investigation of transition between spark ignition and controlled auto-ignition combustion in a V6 direct-injection engine with cam profile switching

Controlled auto-ignition (CAI) combustion, also known as Homogeneous Charge Compression Ignition (HCCI) can be achieved by trapping residuals with early exhaust valve closure in a direct fuel injection in-cylinder four-stroke gasoline engines (through the employment of low-lift cam profiles). Due to the operating region being limited to low and mid-load operation for CAI combustion with a low-lift cam profile, it is important to be able to operate SI combustion at high-load with a normal cam profile. A 3.0L prototype engine was modified to achieve CAI combustion, using a Cam Profile Switching mechanism which has the capability to switch between high and low-lift cam-profiles. A strategy was used where a high-profile could be used for SI combustion and a low-lift profile was used for CAI combustion. Initial analysis showed that for transitioning from SI to CAI combustion, misfire occurred on the first CAI transitional cycle. Subsequent experiments showed that the throttle opening position and switching time could be controlled avoiding misfire. Further work investigated transitioning at different loads and from CAI to SI combustion

Visualization of the homogeneous charge compression ignition/controlled autoignition combustion process using two-dimensional planar laser-induced fluorescence imaging of formaldehyde

The paper reports an investigation into the HCCI/CAI combustion process using the two-dimensional PLIF technique. The PLIF of formaldehyde formed during the low-temperature reactions of HCCI/CAI combustion was exciting by a tunable dye laser at 355nm wavelength and detected by a gated ICCD camera. Times and locations of the two-stage autoignition of HCCI/CAI combustion were observed in a single cylinder optical engine for several fuel blends mixed with n-heptane and iso-octane. The results show, when pure n-heptane was used, the initial formation of formaldehyde and its subsequent burning were closely related to the start of the low temperature heat release stage and the start of the main heat release stage of HCCI combustion respectively. Meanwhile, it was found that the formation of formaldehyde was more affected by the charge temperature than by the fuel concentration. But its subsequent burning or the start of main heat release combustion toke place at those areas where both the fuel concentration and the charge temperature were sufficient high. As a result, it was found that the presence of stratified residual gases affected both the spatial location and the temporal site of autoignition in a HCCI/CAI combustion engine. All studied fuels were found having similar formaldehyde formation timings with n-heptane. This means that the presence of iso-octane did not affect the start of low temperature reactions apparently. However, the heat release during low temperature reaction was significantly reduced with the presence of iso-octane in the studied fuels. In addition, the presence of iso-octane retarded the start of the main combustion stage

Fluorine Abundances of Galactic Low-Metallicity Giants

With abundances and 2{\sigma} upper limits of fluorine (F) in seven metal-poor field giants, nucleosynthesis of stellar F at low metallicity is discussed. The measurements are derived from the HF(1-0) R9 line at 23358{\AA} using nearinfrared K-band high-resolution spectra obtained with CRIRES at the Very Large Telescope. The sample reaches lower metallicities than previous studies on F of field giants, ranging from [Fe/H] = -1.56 down to -2.13. Effects of three-dimensional model atmospheres on the derived F and O abundances are quantitatively estimated and shown to be insignificant for the program stars. The observed F yield in the form of [F/O] is compared with two sets of Galactic chemical evolution models, which quantitatively demonstrate the contribution of Type II supernova (SN II) {\nu}-process and asymptotic giant branch/Wolf-Rayet stars. It is found that at this low-metallicity region, models cannot well predict the observed distribution of [F/O], while the observations are better fit by models considering an SN II {\nu}-process with a neutrino energy of E_{\nu} = 3 x 10^53 erg. Our sample contains HD 110281, a retrograde orbiting low-{\alpha} halo star, showing a similar F evolution as globular clusters. This supports the theory that such halo stars are possibly accreted from dwarf galaxy progenitors of globular clusters in the halo.Comment: 8 pages, 8 figures, 2 tables, published in The Astrophysical Journa

Quantum Entanglement as a Diagnostic of Phase Transitions in Disordered Fractional Quantum Hall Liquids

We investigate the disorder-driven phase transition from a fractional quantum Hall state to an Anderson insulator using quantum entanglement methods. We find that the transition is signaled by a sharp increase in the sensitivity of a suitably averaged entanglement entropy with respect to disorder -- the magnitude of its disorder derivative appears to diverge in the thermodynamic limit. We also study the level statistics of the entanglement spectrum as a function of disorder. However, unlike the dramatic phase-transition signal in the entanglement entropy derivative, we find a gradual reduction of level repulsion only deep in the Anderson insulating phase.Comment: 8 pages, 8 figures, including the supplemental material, published in PRL as an Editors' Suggestio