Weak Coulomb blockade effect in quantum dots

We develop the general nonequilibrium theory of transport through a quantum dot, including Coulomb blockade effects via a 1/N expansion, where N is the number of scattering channels. At lowest order we recover the Landauer formula for the current plus a self-consistent equation for the dot potential. We obtain the leading corrections and compare with earlier approaches. Finally, we show that to leading and to next leading order in 1/N there is no interaction correction to the weak localization, in contrast to previous theories, but consistent with experiments by Huibers et al. [Phys. Rev. Lett. 81, 1917 (1998)], where N=4.     

The Impact of Compaction and Sand Migration on Permeability and Non-Darcy Coefficient from Pore-Scale Simulations

Transport in Porous Media - Compaction and sand migration are important problems in loosely consolidated and unconsolidated high-rate gas reservoirs, and proppants in the hydraulic fractures. Their...     

Composition of particles emitted at largep T and medium angles inpp,dd, andαα collisions at the CERN intersecting storage rings

The relative yields of kaons and protons compared with the yield of pions at highp _T and polar angles θ away from 90° (in the range from 10° to 45°) are presented forpp, dd, and αα interactions at a centre-of-mass energy \(\sqrt {s_{NN} } = 31\) GeV per nucleon-nucleon collision. The measured particle ratios depend on the atomic mass numberA of the beam particles and on θ. TheA dependence of the ratios becomes stronger for largerp _T and is more pronounced at smaller polar angles.     

The <Emphasis Type="Italic">k</Emphasis>-domatic number of a graph

Let k be a positive integer, and let G be a simple graph with vertex set V (G). A k-dominating set of the graph G is a subset D of V (G) such that every vertex of V (G)-D is adjacent to at least k vertices in D. A k-domatic partition of G is a partition of V (G) into k-dominating sets. The maximum number of dominating sets in a k-domatic partition of G is called the k-domatic number d _k (G). In this paper, we present upper and lower bounds for the k-domatic number, and we establish Nordhaus-Gaddum-type results. Some of our results extend those for the classical domatic number d(G) = d ₁(G).      

Fe valence state at the surface of the Fe0.5Cu0.5Cr2S4 spinel

Here we present X‐ray absorption measurements of a vacuum cleaved Fe_0.5Cu_0.5Cr₂S₄ single crystal. Measurements at different positions on the cleaved sample surface clearly reveal a difference between the valence state of the Fe ions in the sur‐ face layers and the valency of the Fe ions present in the bulk. These results confirm the findings of recent measurements outlined previously. (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Aldehyde‐Assisted Ruthenium(II)‐Catalyzed CH Oxygenations

Versatile ruthenium(II) complexes allow for site‐selective C? H oxygenations with weakly‐coordinating aldehydes. The challenging C? H functionalizations proceed with high chemoselectivity by rate‐determining C? H metalation. The new method features an ample substrate scope, which sets the stage for the step‐economical preparation of various bioactive heterocycles.     

Relative quantification of long chain branching in essentially linear polyethylenes

The aim of this work is to describe a method whereby low levels of long chain branching, LCB, can be quantified on a relative basis for whole, unfractionated, and essentially linear ethylene/α-olefin copolymers. The method is based on a well established, relatively fast and robust experiment, namely the measurement of the linear viscoelastic properties by a single, isothermal, small amplitude oscillatory shear experiment. The analysis of the data is predicated on the use of the so-called van Gurp-Palmen plots (the phase angle, δ (=tan⁻¹(G″/G′)), plotted against the absolute value of the dynamic complex modulus, |G∗| = (G′²+G″²)^1/2). From this plot, the value of δ at |G∗| = 10 kPa is recorded, and it is demonstrated that the amount of LCB inversely correlates with such value of the phase angle, δ. Depending on the desired frequency range, the experiment duration varies between 15 and 60 min rendering this technique well suited for high throughput parallel testing. Its applicability is critically examined with a wide variety of commercial ethylene/α-olefin copolymers. Moreover, we have improved on the long chain branching index (LCBI) proposed by Shroff and Mavridis [Shroff RN, Mavridis H. Long-chain-branching index for essentially linear polyethylenes. Macromolecules 1999;32:8454-64] by basing it on data of truly linear polyethylenes (hydrogenated anionically synthesized polybutadienes) instead of apparently linear commercial polyethylenes.     

Molybdenum and tungsten structural differences are dependent on ndz(2)/(n + 1)s mixing: comparisons of (silox)3MX/R (M = Mo, W; silox = (t)Bu3SiO)

Treatment of trans-(Et 2O) 2MoCl 4 with 2 or 3 equiv of Na(silox) (i.e., NaOSi (t) Bu 3) afforded (silox) 3MoCl 2 ( 1-Mo) or (silox) 3MoCl ( 2-Mo). Purification of 2-Mo was accomplished via addition of PMe 3 to precipitate (silox) 3ClMoPMe 3 ( 2-MoPMe 3), followed by thermolysis to remove phosphine. Use of MoCl 3(THF) 3 with various amounts of Na(silox) produced (silox) 2ClMoMoCl(silox) 2 ( 3-Mo). Alkylation of 2-Mo with MeMgBr or EtMgBr afforded (silox) 3MoR (R = Me, 2-MoMe; Et, 2-MoEt). 2-MoEt was also synthesized from C 2H 4 and (silox) 3MoH, which was prepared from 2-Mo and NaBEt 3H. Thermolysis of WCl 6 with HOSi ( t )Bu 3 afforded (silox) 2WCl 4 ( 4-W), and sequential treatment of 4-W with Na/Hg and Na(silox) provided (silox) 3WCl 2 ( 1-W, tbp, X-ray), which was alternatively prepared from trans-(Et 2S) 2WCl 4 and 3 equiv of Tl(silox). Na/Hg reduction of 1-W generated (silox) 3WCl ( 2-W). Alkylation of 2-W with MeMgBr produced (silox) 3WMe ( 2-WMe), which dehydrogenated to (silox) 3WCH ( 6-W) with Delta H (double dagger) = 14.9(9) kcal/mol and Delta S (double dagger) = -26(2) eu. Magnetism and structural studies revealed that 2-Mo and 2-MoEt have triplet ground states (GS) and distorted trigonal monopyramid (tmp) and tmp structures, respectively. In contrast, 2-W and 2-WMe possess squashed-T d (distorted square planar) structures, and the former has a singlet GS. Quantum mechanics/molecular mechanics studies of the S = 0 and S = 1 states for full models of 2-Mo, 2-MoEt, 2-W, and 2-WMe corroborate the experimental findings and are consistent with the greater nd z (2) /( n + 1)s mixing in the third-row transition-metal species being the dominant feature in determining the structural disparity between molybdenum and tungsten.