A review of the theoretical basis for bulk mass flux convective parameterization

Most parameterizations for precipitating convection in use today are bulk schemes, in which an ensemble of cumulus elements with different properties is modelled as a single, representative entraining-detraining plume. We review the underpinning mathematical model for such parameterizations, in particular by comparing it with spectral models in which elements are not combined into the representative plume. The chief merit of a bulk model is that the representative plume can be described by an equation set with the same structure as that which describes each element in a spectral model. The equivalence relies on an ansatz for detrained condensate introduced by Yanai et al. (1973) and on a simplified microphysics. There are also conceptual differences in the closure of bulk and spectral parameterizations. In particular, we show that the convective quasi-equilibrium closure of Arakawa and Schubert (1974) for spectral parameterizations cannot be carried over to a bulk parameterization in a straightforward way. Quasi-equilibrium of the cloud work function assumes a timescale separation between a slow forcing process and a rapid convective response. But, for the natural bulk analogue to the cloud-work function (the dilute CAPE), the relevant forcing is characterised by a different timescale, and so its quasi-equilibrium entails a different physical constraint. Closures of bulk parameterization that use the non-entraining parcel value of CAPE do not suffer from this timescale issue. However, the Yanai et al. (1973) ansatz must be invoked as a necessary ingredient of those closures.

Review of theoretical models of electromagnetic NDT and their applications

There is an increasing interest in modelling electromagnetic methods of NDT - particularly eddy currents. A collaboration within the International Institute of Welding led to a survey intended to explain to non mathematicians the present scope of modelling. The present review commences with this survey and then points out some of the developments and some of the outstanding problems in transferring modelling into industry.

A simple theoretical model for the intensification of tropical cyclones and polar lows

A simple theoretical model for the intensification of tropical cyclones and polar lows is developed using a minimal set of physical assumptions. These disturbances are assumed to be balanced systems intensifying through the WISHE (Wind-Induced Surface Heat Exchange) intensification mechanism, driven by surface fluxes of heat and moisture into an atmosphere which is neutral to moist convection. The equation set is linearized about a resting basic state and solved as an initial-value problem. A system is predicted to intensify with an exponential perturbation growth rate scaled by the radial gradient of an efficiency parameter which crudely represents the effects of unsaturated processes. The form of this efficiency parameter is assumed to be defined by initial conditions, dependent on the nature of a pre-existing vortex required to precondition the atmosphere to a state in which the vortex can intensify. Evaluation of the simple model using a primitive-equation, nonlinear numerical model provides support for the prediction of exponential perturbation growth. Good agreement is found between the simple and numerical models for the sensitivities of the measured growth rate to various parameters, including surface roughness, the rate of transfer of heat and moisture from the ocean surface, and the scale for the growing vortex.

Acronyms used in theoretical chemistry

An alphabetic list of acronyms used in theoretical chemistry is presented. Some explanatory references have been added to make acronyms better understandable but still more are needed. Critical comments, additional references, etc. are requested.

The molecular structure of hexamethyldigermane determined by gas-phase electron diffraction with theoretical calculations for (CH3)3M-M(CH3)3 Where M = C, Si, and Ge

Gas-phase electron diffraction (GED) data together with results from ab initio molecular orbital calculations (HF and MP2/6-311+G(d,p)) have been used to determine the structure of hexamethyldigermane ((CH3)3Ge-Ge(CH3)3). The equilibrium symmetry is D3d, but the molecule has a very low-frequency, largeamplitude, torsional mode (φCGeGeC) that lowers the thermal average symmetry. The effect of this largeamplitude mode on the interatomic distances was described by a dynamic model which consisted of a set of pseudoconformers spaced at even intervals. The amount of each pseudoconformer was obtained from the ab initio calculations (HF/6-311+G(d,p)). The results for the principal distances (ra) and angles (∠h1) obtained from the combined GED/ab initio (with estimated 1σ uncertainties) are r(Ge-Ge) ) 2.417(2) Å, r(Ge-C) ) 1.956(1) Å, r(C-H) ) 1.097(5) Å, ∠GeGeC ) 110.5(2)°, and ∠GeCH ) 108.8(6)°. Theoretical calculations were performed for the related molecules ((CH3)3Si-Si(CH3)3 and (CH3)3C-C(CH3)3).

AT(1) receptor ligands: virtual-screening-based design with TOPP descriptors, synthesis, and biological evaluation of pyrrolidine derivatives

As a continuing effort to establish the structure-activity relationships (SARs) within the series of the angiotensin II antagonists (sartans), a pharmacophoric model was built by using novel TOPP 3D descriptors. Statistical values were satisfactory (PC4: r(2)=0.96, q(2) ((5) (random) (groups))=0.84; SDEP=0.26) and encouraged the synthesis and consequent biological evaluation of a series of new pyrrolidine derivatives. SAR together with a combined 3D quantitative SAR and high-throughput virtual screening showed that the newly synthesized 1-acyl-N-(biphenyl-4-ylmethyl)pyrrolidine-2-carboxamides may represent an interesting starting point for the design of new antihypertensive agents. In particular, biological tests performed on CHO-hAT(1) cells stably expressing the human AT(1) receptor showed that the length of the acyl chain is crucial for the receptor interaction and that the valeric chain is the optimal one.

Molecular structure of 2,5-dihydropyrrole (C4NH7), obtained by gas-phase electron diffraction and theoretical calculations

The structure of 2,5-dihydropyrrole (C4NH7) has been determined by gas-phase electron diffraction (GED), augmented by the results from ab initio calculations employing third-order Moller-Plesset (MP3) level of theory and the 6-311+G(d,p) basis set. Several theoretical calculations were performed. From theoretical calculations using MP3/6-311+G(d,p) evidence was obtained for the presence of an axial (63%) (N-H bond axial to the CNC plane) and an equatorial conformer (37%) (N-H bond equatorial to the CNC plane). The five-membered ring was found to be puckered with the CNC plane inclined at 21.8 (38)° to the plane of the four carbon atoms.

Molecular structures of trimethylchlorogermane, (CH3)(3)GeCl, and trimethylbromogermane, (CH3)(3)GeBr, obtained by gas-phase electron diffraction and theoretical calculations

The structures of trimethylchlorogermane ((CH3)(3)GeCl) and trimethylbromogermane ((CH3)(3)GeBr) have been determined by gas-phase electron diffraction (GED), augmented by the results from ab initio calculations employing second-order Moller-Plesset (MP2) level of theory and the 6-311+G(d) basis set. All the electrons were included in the correlation calculation. The results from the ab initio calculations indicated that these molecules have C-3v symmetry, and models with this symmetry were used in the electron diffraction analysis. The results for the principal distances (r(g)) and angles (angle(alpha)) from the combined GED/ab initio study of trimethylchlorogermane (with estimated 2sigma uncertainties) are: r(Ge-C) = 1.950(4) Angstrom, r(Ge-Cl) = 2.173(4) Angstrom, r(C-H) = 1.090(9) Angstrom, angleCGeC = 112.7(7)degrees, angleCGeCl = 106.0(8)degrees, angleGeCH = 107.8(12)degrees. The results for the principal distances (r(g)) and angles (angle(alpha)) from the combined GED/ab initio study of trimethylbromogermane (with estimated 2sigma uncertainties) are: r(Ge-C) = 1.952(7) Angstrom, r(Ge-Br) = 2.325(4) Angstrom, r(C-H) = 1. 140(28) Angstrom, angleCGeC = 114.2(11)degrees, angleCGeBr = 104.2(13)degrees, angleGeCH 106.9(43)degrees. Local C-3v symmetry and staggered conformation were assumed for the methyl groups.

Molecular structures of benzoic acid and 2-hydroxybenzoic acid, obtained by gas-phase electron diffraction and theoretical calculations

The structures of benzoic acid (C6H5COOH) and 2-hydroxybenzoic acid (C6H4OHCOOH) have been determined in the gas phase by electron diffraction using results from quantum chemical calculations to inform restraints used on the structural parameters. Theoretical methods (HF and MP2/6-311+G(d, p)) predict two conformers for benzoic acid, one which is 25.0 kJ mol(-1) (MP2) lower in energy than the other. In the low-energy form, the carboxyl group is coplanar with the phenyl ring and the O-H group eclipses the C=O bond. Theoretical calculations (HF and MP2/6-311+ G(d, p)) carried out for 2-hydroxybenzoic acid gave evidence for seven stable conformers but one low-energy form (11.7 kJ mol-1 lower in energy (MP2)) which again has the carboxyl group coplanar with the phenyl ring, the O-H of the carboxyl group eclipsing the C=O bond and the C=O of the carboxyl group oriented toward the O-H group of the phenyl ring. The effects of internal hydrogen bonding in 2-hydroxybenzoic acid can be clearly observed by comparison of pertinent structural parameters between the two compounds. These differences for 2-hydroxybenzoic acid include a shorter exocyclic C-C bond, a lengthening of the ring C-C bond between the substituents, and a shortening of the carboxylic single C-O bond.

Molecular structures of 3-hydroxybenzoic acid and 4-hydroxybenzoic acid, obtained by gas-phase electron diffraction and theoretical calculations

The structures of 3-hydroxybenzoic acid and 4-hydroxybenzoic acid have been determined by gas-phase electron diffraction using results from quantum chemical calculations to inform the choice of restraints applied to some of the structural parameters. The results from the study presented here demonstrate that resonance hybrids are not as helpful in rationalizing the structures of 2-, 3-, and 4-hydroxybenzoic acids as are models based upon electrostatic effects.