Consistent implementation of real fluid EOS in pseudopotential lattice Boltzmann models

Pseudopotential lattice Boltzmann models have emerged as successful methods to simulate liquid-vapor coexistence systems. However, the equation of state (EOS) of such systems, which is found to be thermodynamically consistent, is unique and lacks the potential to cover a broad range of physical fluids. In this study, we employ multiple pseudopotentials and extend the consistent EOS to enhance the capability of pseudopotential models in reproducing a wider range of thermodynamic states. The new system has the format which preserves the consistency between the lattice pressure tensor and the free energy density. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Spectral analysis for the Gauss problem on continued fractions

We present a new derivation of the formula appearing in Babenko (1978) and Mayer and Roepstorff (1987) that gives the probability distribution of τ⁻ⁿ${\tau }^{-n}$ in terms of the eigenvalues of a symmetric operator. Here τ$\tau$ is the well-known Gauss-map.     

Singular solutions for second-order non-divergence type elliptic inequalities in punctured balls

We study the existence and non-existence of positive singular solutions of second-order non-divergence type elliptic inequalities of the form $\sum\limits_{i,j = 1}^N {a_{ij} (x)\frac{{\partial ^2 u}} {{\partial x_i \partial x_j }}} + \sum\limits_{i = 1}^N {b_i (x)\frac{{\partial u}} {{\partial x_i }} \geqslant K(x)u^p ,} - \infty < p - \infty , $ with measurable coefficients in a punctured ball B _R \{0} of ? ^N , N ≥ 1. We prove the existence of a critical value p* which separates the existence region from the non-existence region. We show that in the critical case p = p*, the existence of a singular solution depends on the rate at which the coefficients (a _{i j} ) and (b _i ) stabilize at zero, and we provide some optimal conditions in this setting.     

Expeditious synthesis of TADDOL-derived phosphoramidite and phosphonite ligands

A simple and reliable protocol for the synthesis of TADDOL-derived monodentate ligands is reported. The reaction of the requisite TADDOL with PCl₃ is immediately followed by the treatment of the crude intermediate with both nitrogen and carbon nucleophiles. Several previously unknown or difficult-to-make phosphoramidite and phosphonite ligands L1–L3 and L4–L9 were accessed using this novel procedure.     

Ground state solutions for the singular Lane-Emden-Fowler equation with sublinear convection term

We are concerned with singular elliptic equations of the form −Δu=p(x)(g(u)+f(u)+a|∇u|) in RN (N?3), where p is a positive weight and 0<a<1. Under the hypothesis that f is a nondecreasing function with sublinear growth and g is decreasing and unbounded around the origin, we establish the existence of a ground state solution vanishing at infinity. Our arguments rely essentially on the maximum principle.     

Nuclear resonance vibrational spectroscopy reveals the FeS cluster composition and active site vibrational properties of an O2-tolerant NAD+-reducing [NiFe] hydrogenase

Hydrogenases are complex metalloenzymes that catalyze the reversible splitting of molecular hydrogen into protons and electrons essentially without overpotential. The NAD⁺-reducing soluble hydrogenase (SH) from Ralstonia eutropha is capable of H₂ conversion even in the presence of usually toxic dioxygen. The molecular details of the underlying reactions are largely unknown, mainly because of limited knowledge of the structure and function of the various metal cofactors present in the enzyme. Here, all iron-containing cofactors of the SH were investigated by ⁵⁷Fe specific nuclear resonance vibrational spectroscopy (NRVS). Our data provide experimental evidence for one [2Fe2S] center and four [4Fe4S] clusters, which is consistent with the amino acid sequence composition. Only the [2Fe2S] cluster and one of the four [4Fe4S] clusters were reduced upon incubation of the SH with NADH. This finding explains the discrepancy between the large number of FeS clusters and the small amount of FeS cluster-related signals as detected by electron paramagnetic resonance spectroscopic analysis of several NAD⁺-reducing hydrogenases. For the first time, Fe–CO and Fe–CN modes derived from the [NiFe] active site could be distinguished by NRVS through selective ¹³C labeling of the CO ligand. This strategy also revealed the molecular coordinates that dominate the individual Fe–CO modes. The present approach explores the complex vibrational signature of the Fe–S clusters and the hydrogenase active site, thereby showing that NRVS represents a powerful tool for the elucidation of complex biocatalysts containing multiple cofactors.     

Metal oxidation states in biological water splitting

A central question in biological water splitting concerns the oxidation states of the manganese ions that comprise the oxygen-evolving complex of photosystem II. Understanding the nature and order of oxidation events that occur during the catalytic cycle of five S_i states (i = 0–4) is of fundamental importance both for the natural system and for artificial water oxidation catalysts. Despite the widespread adoption of the so-called “high-valent scheme”—where, for example, the Mn oxidation states in the S₂ state are assigned as III, IV, IV, IV—the competing “low-valent scheme” that differs by a total of two metal unpaired electrons (i.e. III, III, III, IV in the S₂ state) is favored by several recent studies for the biological catalyst. The question of the correct oxidation state assignment is addressed here by a detailed computational comparison of the two schemes using a common structural platform and theoretical approach. Models based on crystallographic constraints were constructed for all conceivable oxidation state assignments in the four (semi)stable S states of the oxygen evolving complex, sampling various protonation levels and patterns to ensure comprehensive coverage. The models are evaluated with respect to their geometric, energetic, electronic, and spectroscopic properties against available experimental EXAFS, XFEL-XRD, EPR, ENDOR and Mn K pre-edge XANES data. New 2.5 K ⁵⁵Mn ENDOR data of the S₂ state are also reported. Our results conclusively show that the entire S state phenomenology can only be accommodated within the high-valent scheme by adopting a single motif and protonation pattern that progresses smoothly from S₀ (III, III, III, IV) to S₃ (IV, IV, IV, IV), satisfying all experimental constraints and reproducing all observables. By contrast, it was impossible to construct a consistent cycle based on the low-valent scheme for all S states. Instead, the low-valent models developed here may provide new insight into the over-reduced S states and the states involved in the assembly of the catalytically active water oxidizing cluster.     

Resolvent estimates and smoothing for homogeneous partial differential operators on graded Lie groups

By using commutator methods, we show uniform resolvent estimates and obtain globally smooth operators for self-adjoint injective homogeneous operators H on graded groups, including Rockland operators, sublaplacians, and many others. Left or right invariance is not required. Typically the globally smooth operator has the form T = V|H|^1∕2, where V only depends on the homogeneous structure of the group through Sobolev spaces, the homogeneous dimension and the minimal and maximal dilation weights. For stratified groups improvements are obtained, by using a Hardy-type inequality. Some of the results involve refined estimates in terms of real interpolation spaces and are valid in an abstract setting. Even for the commutative group ?^N some new classes of partial differential operators are treated.