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.     

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.     

The effect of ‘crystallinity’ and structural disorder on the electrochemical performance of substituted nickel hydroxide electrodes

β_bc-Nickel hydroxide exhibit non-uniform broadening reflections in their PXRD pattern due to the presence of structural disorder. β_bc-Nickel hydroxide electrodes with smaller crystallite size and structural disorder reversibly exchanges 0.9e/Ni. Co/Zn/Ca/Cd-substituted β_bc-nickel hydroxide samples also display non-uniform broadening of reflections in their powder X-ray diffraction patterns with smaller crystallite size and exchanges 0.7–0.8e/Ni. Hydrothermal treatment of β_bc-nickel hydroxide slurry at 170 °C results in an ordering of reflections in their powder X-ray diffraction pattern with an increased crystallite size. Crystalline β-nickel hydroxide electrode reversibly exchanges 0.3–0.4e/Ni. Hydrothermal-treated Co/Zn/Ca/Cd-substituted β_bc-nickel hydroxide slurries at 170 °C display sharp reflections with similar crystallite size and electrochemical activities as that of crystalline β-nickel hydroxide. This clearly demonstrates that partial substitution of Co/Zn/Ca/Cd in the nickel hydroxide matrix does not show any dramatic improvement in their electrochemical activity at 25–30 °C. Structural disordered material with smaller crystallite size delivers electrochemical activity close to theoretical capacity.     

Structural Characterization of Composite Particles of Two Commonly Used Herbicides

A spray drying technique was applied to prepare composite microparticles of a water-insoluble herbicide, atrazine(AT) and a water-soluble herbicide 2,4-dichloro phenoxy acetic acid (2,4-D) for the purpose of improving the water solubility of AT. A homogenous mixture of an ethanol solution of AT and an aqueous 2,4-D solution at different ratios were spray dried using a laboratory scale spray drier. Quantitative elemental analysis suggested that the AT/2,4-D ratio in each composite microparticle was nearly the same as the desired formulation ratio. The resulting samples were characterized by powder x-ray diffractometry (XRD), differential scanning calorimetry (DSC), Fourier transform infra red (FT-IR) and scanning electron microscopy (SEM). It was found that the crystallinity of AT and 2,4-D were maintained in the composite particles. Moreover, the release of AT from dissolved composite microparticles was markedly improved because of an increase in the effective surface area following rapid dissolution of 2, 4 D. Hence, this study shows that it is possible to prepare AT-2,4-D composite microparticles using a laboratory scale spray drier and that this can improve the ability of AT to dissolve in water.     

Prediction of cyclohexane-water distribution coefficient for SAMPL5 drug-like compounds with the QMPFF3 and ARROW polarizable force fields

We present the performance of blind predictions of water—cyclohexane distribution coefficients for 53 drug-like compounds in the SAMPL5 challenge by three methods currently in use within our group. Two of them utilize QMPFF3 and ARROW, polarizable force-fields of varying complexity, and the third uses the General Amber Force-Field (GAFF). The polarizable FF’s are implemented in an in-house MD package, Arbalest. We find that when we had time to parametrize the functional groups with care (batch 0), the polarizable force-fields outperformed the non-polarizable one. Conversely, on the full set of 53 compounds, GAFF performed better than both QMPFF3 and ARROW. We also describe the torsion-restrain method we used to improve sampling of molecular conformational space and thus the overall accuracy of prediction. The SAMPL5 challenge highlighted several drawbacks of our force-fields, such as our significant systematic over-estimation of hydrophobic interactions, specifically for alkanes and aromatic rings.