Squeezed states, photon-number distributions, and U(l) invariance

We study the photon-number distribution in squeezed states of a single-mode radiation field. A U(l)-invariant squeezing criterion is compared and contrasted with a more restrictive criterion, with the help of suggestive geometric representations. The U(l) invariance of the photon-number distribution in a squeezed coherent state, with arbitrary complex squeeze and displacement parameters, is explicitly demonstrated. The behavior of the photon-number distribution for a representative value of the displacement and various values of the squeeze parameter is numerically investigated. A new kind of giant oscillation riding as an envelope over more rapid oscillations in this distribution is demonstrated.

Studies on a stove for powdery biomass

The sawdust stove, classically known for several decades, is considered here in a scientific study. The poor ignition characteristics and smoky start up are related to improper geometric dimensions. Based on a parametric study, the startup procedure and the dimensions of the stove were modified to achieve a smooth start up. Also, the range of acceptable fuels was enlarged to include tiny unprocessed dry twigs, weeds and wood sticks o the extent of about 50%, with the rest being sawdust-like material. The efficiency of the stove was measured to be 30–40%, depending on the relative size and shape of the vessel and the power level of the stove. A simple procedure for designing this class of stove for various power levels, as well as burning times, is presented. A new concept of multiport design is also discussed.

The scratch hardness and friction of a soft rigid-plastic solid

The paper describes an experimental and analytical study of the normal and scratch hardnesses of a model soft rigid-plastic solid. The material known as ‘Plasticine’, a mixture of dry particles and a mineral oil, has been deformed with a range of rigid conical indentors with included angles of between 30° and 170°. The sliding velocity dependence of the computed scratch hardness and friction has been examined in the velocity range 0.19 mm/s to 7.3 m/s. Data are also described for the time dependence of the normal hardness and also the estimated rate dependence of the intrinsic flow stress. The latter values were estimated from data obtained during the upsetting of right cylinders. Three major conclusions are drawn from these data and the associated analysis. (1) A first-order account of the scratching force may be provided by adopting a model which sums the computed plastic deformation and interfacial sliding contributions to the total sliding work. This is tantamount to the adoption of the two-term non-interacting model of friction. (2) For this system during sliding, at high sliding velocities at least, the interface shear stress which defines the boundary condition is not directly related to the bulk shear stress. The interface rheological characteristics indicate an appreciable dependence on the imposed strain or strain rate. In particular, the relative contributions of the slip and stick boundary conditions appear to be a function of the imposed sliding velocity. (3) The computed normal and scratch hardness values are not simply interrelated primarily because of the evolving boundary conditions which appear to exist in the scratching experiments.

AB-initio study of alpha-silyl and beta-silyl substituent effects on vinyl radicals

The geometries of alpha- and beta-silyl substituted vinyl radicals and of alpha,beta-disilylvinyl radical have been optimised with the STO-3G and the STO-3G* basis sets. The relative stabilities of various conformers have been determined at the UMP2/6-31G* level. The stabilisation of vinyl radicals through alpha-silyl substitution is larger than that due to corresponding alkyl groups. The presence of an alpha-silyl group also leads to a tendency towards linearisation of the vinyl radical centre and a corresponding reduction in the inversion barrier. In marked contrast, the beta-silyl effect is negligible. The geometric, conformational and energetic consequences are insignificant. Overall, the silyl substituent effect at vinyl radicals is very different from that computed earlier for the vinyl cations, but qualitatively similar to that found in carbanions.

E. C. G. Sudarshan and Symmetry in Classical Dynamics, Optics and Quantum Mechanics

We review work initiated and inspired by Sudarshan in relativistic dynamics, beam optics, partial coherence theory, Wigner distribution methods, multimode quantum optical squeezing, and geometric phases. The 1963 No Interaction Theorem using Dirac's instant form and particle World Line Conditions is recalled. Later attempts to overcome this result exploiting constrained Hamiltonian theory, reformulation of the World Line Conditions and extending Dirac's formalism, are reviewed. Dirac's front form leads to a formulation of Fourier Optics for the Maxwell field, determining the actions of First Order Systems (corresponding to matrices of Sp(2,R) and Sp(4,R)) on polarization in a consistent manner. These groups also help characterize properties and propagation of partially coherent Gaussian Schell Model beams, leading to invariant quality parameters and the new Twist phase. The higher dimensional groups Sp(2n,R) appear in the theory of Wigner distributions and in quantum optics. Elegant criteria for a Gaussian phase space function to be a Wigner distribution, expressions for multimode uncertainty principles and squeezing are described. In geometric phase theory we highlight the use of invariance properties that lead to a kinematical formulation and the important role of Bargmann invariants. Special features of these phases arising from unitary Lie group representations, and a new formulation based on the idea of Null Phase Curves, are presented.

An actor-critic algorithm with function approximation for discounted cost constrained Markov decision processes

We develop in this article the first actor-critic reinforcement learning algorithm with function approximation for a problem of control under multiple inequality constraints. We consider the infinite horizon discounted cost framework in which both the objective and the constraint functions are suitable expected policy-dependent discounted sums of certain sample path functions. We apply the Lagrange multiplier method to handle the inequality constraints. Our algorithm makes use of multi-timescale stochastic approximation and incorporates a temporal difference (TD) critic and an actor that makes a gradient search in the space of policy parameters using efficient simultaneous perturbation stochastic approximation (SPSA) gradient estimates. We prove the asymptotic almost sure convergence of our algorithm to a locally optimal policy. (C) 2010 Elsevier B.V. All rights reserved.

Double Aromaticity in the 3,5-Dehydrophenyl Cation and in Cyclo[6]carbon

The presence of two (4n+2)-electron conjugated systems in perpendicular planes results in considerable aromatic stabilization. Despite having two fewer hydrogens, the 6 pi e-2 sigma e 3,5-dehydrophenyl cation (C6H3+, 1) is 32.7 (CCSD(T)/6-31G**) and 35.2 kcal/mol (RMP4sdtq/6-3iG*//RMP2(fu)/6-31G*) more stable than the phenyl cation (evaluated by an isodesmic reaction involving benzene and m-dehydrobenzene (4)). Cation 1, the global C6H3+ minimum, is 11.7,24.2, 11.8, and 30.4 kcal/mol lower in energy than the 2,6- (11) and 3,4-dehydrophenyl (12) cations as well as the open-chain isomers 13 and 14 (RMP4sdtq/6-31G*//RMP2(fu)/6-31G* + ZPE(RMP2(fu)/6-31G*)). The stability of 1 is increased hyperconjugatively by 2,4,6-trisilyl substitution. The double aromaticity of 1 is indicated by the computed magnetic susceptibility exaltations (IGLO/II//RMP2(fu)/6-31G*) of -5.2, -6.8, -15, and -23.2 relative to 11, 12, 13, and 14, respectively. Thus, 1 fulfills the geometric, energetic, and magnetic criteria of aromaticity. The double aromaticity of the D-6h cyclo[6]carbon is apparent from the same criteria

Variations in the copper(I)-copper(I) distances in multinuclear clusters with identical coordination geometries. Short metal-metal contacts induced by oligomerization

Factors contributing to the variations in the Cu(I)-Cu(I) distances in two clusters with identical ligand and coordination geometries have been analyzed. While the hexamer, 4, exhibits metal-metal distances in the range 2.81-3.25 Angstrom, shorter contacts are found in the corresponding tetramer, 3 (2.60-2.77 Angstrom). EHT calculations reveal relatively little attractive interactions in the corresponding Cu-4(4+) and Cu-6(6+) cores. Introduction of the ligands lowers the reduced overlap populations between the metals further. MNDO calculations with model electrophiles have been carried out to determine the bite angle requirements of the ligands. These are satisfactorily met in the structures of both 3 and 4. The key geometric feature distinguishing 3 and 4 is the Cu-S-Cu angle involving the bridging S- unit. In 4, the corresponding angles are about 90 degrees, while the values in 3 are smaller (70-73 degrees). Wider angles are computed to be energetically favored and are characterized by an open three-center bond and a long Cu-Cu distance. The bridging angles are suggested to be primarily constrained by the mode of oligomerization. Implications of these results for the stability and reactivity of these clusters and for short metal-metal distances in d(10) systems in general are discussed.

Factors contributing to phantom bonds in inorganic molecules: Interpretations and predictions

The validity of various qualitative proposals for interpreting and predicting the existence of short contacts between formally non-bonded atoms, as in cyclodisiloxane and related inorganic ring systems, is critically evaluated. The models range from simple considerations of geometric constraints, lone pair repulsions and pi-complex formation to proposals such as the unsupported pi-bond model and the sigma-bridged-pi bond concept. It is pointed out that a unified description based on a combination of closed and open 3-centre 2-electron bonds is possible. The role of hybridisation is emphasized in the short phantom bond computed in an earlier model system. These insights are used to predict structures with exceptionally short Si..Si and B..B phantom bonds. The proposals are confirmed by ab initio calculations.

Flow Instabilities and fracture in Ti-6Al-4V deformed in compression at 298 K to 673 K

Uniaxial compression tests were conducted on Ti-6Al-4V specimens in the strain-rate range df 0.001 to 1 s(-1) and temperature range of 298 to 673 K. The stress-strain curves exhibited a peak flow stress followed by flow softening. Up to 523 K, the specimens cracked catastrophically after the flow softening started. Adiabatic shear banding was observed in this regime. The fracture surface exhibited both mode I and II fracture features. The state of stress existing in a compression test specimen when bulging occurs is responsible for this fracture. The instabilities observed in the present tests are classified as ''geometric'' in nature and are state-of-stress dependant, unlike the ''intrinsic'' instabilities, which are dependant on the dynamic constitutive behavior of the material.

Moments estimation in Radon space

In this paper, we show a method of obtaining general and orthogonal moments, specifically Legendre and Zernicke moments, from the Radon Transform data of a two-dimensional function. The regular or geometric moments are first evaluated directly from the projection data and the orthogonal moments are derived from these regular moments.

Effect of substitution of Y on the structural, magnetic, and thermal properties of hexagonal DyMnO3 single crystals

We investigate the structural, magnetic, and specific heat behavior of the hexagonal manganite Dy0.5Y0.5MnO3 in order to understand the effect of dilution of Dy magnetism with nonmagnetic yttrium. In this compound, the triangular Mn lattice orders antiferromagnetic at T-N(Mn) approximate to 68 K observed experimentally in the derivative of magnetic susceptibility as well as in specific heat. In addition, a low-temperature peak at T-N(Dy) similar to 3 K is observed in specific heat which is attributed to rare earth order. The T-N(Mn) increases by 9 K compared to that of hexagonal (h) DyMnO3 while T-N(Dy) is unchanged. A change in slope of thermal evolution of lattice parameters is observed to occur at temperature close to T-N(Mn). This hints at strong magnetoelastic coupling in this geometric multiferroic. In magnetization measurements, steplike features are observed when the magnetic field is applied along the c axis which shift to higher fields with temperature and vanish completely above 40 K. The presence of different magnetic phases at low temperature and strong magnetoelastic effects can lead to such field-induced transitions which resemble metamagnetic transitions. This indicates the possibility of strong field-induced effects in dielectric properties of this material, which is unexplored to date.

Using Correlated Parameters for Improved Ranking of Protein-Protein Docking Decoys

A successful protein-protein docking study culminates in identification of decoys at top ranks with near-native quaternary structures. However, this task remains enigmatic because no generalized scoring functions exist that effectively infer decoys according to the similarity to near-native quaternary structures. Difficulties arise because of the highly irregular nature of the protein surface and the significant variation of the nonbonding and solvation energies based on the chemical composition of the protein-protein interface. In this work, we describe a novel method combining an interface-size filter, a regression model for geometric compatibility (based on two correlated surface and packing parameters), and normalized interaction energy (calculated from correlated nonbonded and solvation energies), to effectively rank decoys from a set of 10,000 decoys. Tests on 30 unbound binary protein-protein complexes show that in 16 cases we can identify at least one decoy in top three ranks having <= 10 angstrom backbone root mean square deviation from true binding geometry. Comparisons with other state-of-art methods confirm the improved ranking power of our method without the use of any experiment-guided restraints, evolutionary information, statistical propensities, or modified interaction energy equations. Tests on 118 less-difficult bound binary protein-protein complexes with <= 35% sequence redundancy at the interface showed that in 77% cases, at least 1 in 10,000 decoys were identified with <= 5 angstrom backbone root mean square deviation from true geometry at first rank. The work will promote the use of new concepts where correlations among parameters provide more robust scoring models. It will facilitate studies involving molecular interactions, including modeling of large macromolecular assemblies and protein structure prediction. (C) 2010 Wiley Periodicals, Inc. J Comput Chem 32: 787-796, 2011.

Selectivities in the formation of pyridines and pyrimidines by ammonia-induced cyclocondensations of vinamidiniums

Arylvinamidines (2-, 3- or 4-aryl-4-(N,N-dimethyl)amino-1-azabuta-1,3-dienes), generated from 1,1,5,5-tetramethyl-2- or -3-phenyl-1,5-diazapentadienium salts, cyclocondense orientation-specifically under two regioselections forming 1-4' + 4-3' and 1-2' + 4-1' bonds on exposure to ammonia. The initial cyclates aromatise eliminatively to give mixtures of diarylpyridines and arylpyrimidines. The 2-arylvinamidines do not participate as 2-centre reactants and their 4-aryl isomers not as 4-centre reactants in the cyclocondensations which appear to be stepwise and not concerted. Reasons for the selective participation appear to be that the required eliminations from the initial cyclates are disfavoured in the first case and that a geometric factor prevents cyclate-formation in the second.

Constrained optimization of heat exchangers

Optimizing a shell and tube heat exchanger for a given duty is an important and relatively difficult task. There is a need for a simple, general and reliable method for realizing this task. The authors present here one such method for optimizing single phase shell-and-tube heat exchangers with given geometric and thermohydraulic constraints. They discuss the problem in detail. Then they introduce a basic algorithm for optimizing the exchanger. This algorithm is based on data from an earlier study of a large collection of feasible designs generated for different process specifications. The algorithm ensures a near-optimal design satisfying the given heat duty and geometric constraints. The authors also provide several sub-algorithms to satisfy imposed velocity limitations. They illustrate how useful these sub-algorithms are with several examples where the exchanger weight is minimized.