A roe-average algorithm for a granular-gas model with non-conservative terms

A Roe-average algorithm has been derived for a granular-gas model, proposed by Goldshtein and Shapiro [Goldshtein, Shapiro, Mechanics of collisional motion of granular materials: Part 1. General hydrodynamic equations, J. Fluid Mech. 282 (1995) 75–114], which contains non-conservative terms in the Euler-like hyperbolic governing equations apart from sink terms, which arise from inelastic collision of granules and are present only in the energy equation. The non-conservative terms introduce non-isentropic effects in acoustic-wave propagation within granular media and they also contribute to the Rankine–Hugoniot relations across a discontinuity. A Roe-average algorithm, based on the same granular-gas model, was derived in the literature [V. Kamenetsky, A. Goldshtein, M. Shapiro, D. Degani, Evolution of a shock wave in a granular gas, Phys. Fluids, 12 (2000) 3036–3049] which then required the implementation of a shock-fitting technique at a discontinuity. In the present work, Roe-averaged variables have been obtained from the Rankine–Hugoniot jump relations and the non-conservative terms have been incorporated in the numerical flux formula consistent with upwind principles associated with the granular speed of sound. Results for unsteady one-dimensional granular flows, colliding with a wall, demonstrate the capability of the proposed algorithm to capture strong shocks in addition to flow features not found in molecular gases, such as a fluidized region downstream of the shock and a compacted solid-block region adjacent to the wall.     

Structural Synthon Approach to the Study of Stacking Faults in the Layered Double Hydroxides of Lithium and Aluminum

A single layer of the Li‐Al layered double hydroxide (LDH) can be considered to be a structural synthon that can be stacked in a number of ways to give rise to the polytypes of the Li‐Al LDH family. The topotactic imbibition of lithium into gibbsite and bayerite precursors gives rise to crystalline 2H and 1M₁ polytypes respectively. In contrast the sample formed through a gel to crystallite route is found to be a 1M₁ polytype with stacking disorders whose local symmetry corresponds to the 1M₂ polytype. On heating, a solid‐solid 1M₁→1H polytype transformation is observed.     

Tail bounds for occupancy and the satisfiability threshold conjecture

The classical occupancy problem is concerned with studying the number of empty bins resulting from a random allocation of m balls to n bins. We provide a series of tail bounds on the distribution of the number of empty bins. These tail bounds should find application in randomized algorithms and probabilistic analysis. Our motivating application is the following well-known conjecture on threshold phenomenon for the satisfiability problem. Consider random 3-SAT formulas with cn clauses over n variables, where each clause is chosen uniformly and independently from the space of all clauses of size 3. It has been conjectured that there is a sharp threshold for satisfiability at c* ≈? 4.2. We provide a strong upper bound on the value of c*, showing that for c > 4.758 a random 3-SAT formula is unsatisfiable with high probability. This result is based on a structural property, possibly of independent interest, whose proof needs several applications of the occupancy tail bounds.     

The superconformal anomaly in the 1 + 1 dimensional Wess-Zumino model

The superconformal trace anomaly is worked out to one-loop order in perturbation theory for the 1+1 dimensional Wess-Zumino model.     

Effect of non-stoichiometry on the charge storage capacity of NiO conversion anodes in Li-ion batteries

Conversion anodes comprising non-stoichiometric black NiO suffer severe capacity fading in Li-ion batteries despite having a high Li⁺ ion diffusion coefficient. We attribute this capacity fading to (i) its small crystallite size (~?8 nm) and (ii) high charge transfer resistance (R_ct ~?60–180 Ω cm²). Small crystallites enhance grain boundaries which promote Li⁺ ion diffusion without efficient material utilization. In contrast, the stoichiometric green NiO anodes deliver a stable capacity of 280 mAh g^?1 over 50 charge-discharge cycles. The comparatively higher capacity of green NiO can be explained from its (i) large crystallite size (~?104 nm) and (ii) negligible R_ct values.     

Synthesis,characterization and catalytic activity of Rh (PPh3)2 (en)Cl complex

Ethylenediamine bis(triphenylphosphine) monochlororhodium has been prepared by the interaction of Wilkinson's catalyst and ethylenediamine in benzene. The complex has been isolated and characterized by conventional and spectroscopic methods. The catalytic activity of the complex was investigated for the hydrogenation of 1-octene as a model reaction at a hydrogen pressure of 1 atmosphere (101 kPa) using methanol as a solvent. The influence of various factors such as catalyst, substrate concentrations and temperature have been studied. The hydrido complex has been identified as an intermediate product by IR and NMR studies. The experimental data are in accordance with a rate expression of the form: .     

Role of hydrogen in catalytic dehydrogenation: Film diffusion controlled deactivation

The function of hydrogen used as carrier gas in catalytic dehydrogenation is to increase the selectivity and stability of catalysts. It slows down catalyst deactivation by either inhibiting deposition of potential coke precursors or facilitating their desorption by rehydrogenation. This function, in gas-solid catalytic dehydrogenation appears to be interphase mass transfer controlled by increased hydrogen linear flow velocities decreasing the extent of deactivation. Besides, deactivation appears to progress through two regimes, an initial short term followed by a long term deactivation.