Theoretical Description of Time-Resolved Photoemission Spectroscopy: Application to Pump-Probe Experiments

The theory for time-resolved, pump-probe, photoemission spectroscopy and other pump-probe experiments is developed. The formal development is completely general, incorporating all of the nonequilibrium effects of the pump pulse and the finite time width of the probe pulse, and including possibilities for taking into account band structure and matrix element effects, surface states, and the interaction of the photoexcited electrons with the system leading to corrections to the sudden approximation. We also illustrate the effects of windowing that arise from the finite width of the probe pulse in a simple model system by assuming the quasiequilibrium approximation.

Optimum choice of wavelengths in the anomalous scattering technique with synchrotron radiation

A formula has been derived for the mean-square error in the phases of crystal reflections determined through the multiwavelength anomalous scattering method.The error is written in terms of a simple function of the positions in the complex plane of the 'centres' corresponding to the different wavelengths. For the case of three centres, the mean-square error is inversely proportional to the area of the triangle formed by them.

A global convergence criterion for discrete-time multivariable adaptive systems

The paper deals with the basic problem of adjusting a matrix gain in a discrete-time linear multivariable system. The object is to obtain a global convergence criterion, i.e. conditions under which a specified error signal asymptotically approaches zero and other signals in the system remain bounded for arbitrary initial conditions and for any bounded input to the system. It is shown that for a class of up-dating algorithms for the adjustable gain matrix, global convergence is crucially dependent on a transfer matrix G(z) which has a simple block diagram interpretation. When w(z)G(z) is strictly discrete positive real for a scalar w(z) such that w-1(z) is strictly proper with poles and zeros within the unit circle, an augmented error scheme is suggested and is proved to result in global convergence. The solution avoids feeding back a quadratic term as recommended in other schemes for single-input single-output systems.

Indentation strength of a piezoelectric ceramic: Experiments and simulations

The spherical indentation strength of a lead zirconate titanate (PZT) piezoelectric ceramic was investigated under poled and unpoled conditions and with different electrical boundary conditions (arising through the use of insulating or conducting indenters). Experimental results show that the indentation strength of the poled PZT is higher than that of the unpoled PZT. The strength of a poled PZT under a conducting indenter is higher than that under an insulating indenter. Poling direction (with respect to the direction of indentation loading) did not significantly affect the strength of material. Complementary finite element analysis (FEA) of spherical indentation of an elastic, linearly coupled piezoelectric half-space is conducted for rationalizing the experimental observations. Simulations show marked dependency of the contact stress on the boundary conditions. In particular, contact stress redistribution in the Coupled problem leads to a change in the fracture initiation, from Hertzian cracking in the unpoled material to Subsurface damage initiation in poled PZT. These observations help explain the experimental ranking of strength the PZT in different material conditions or under different boundary conditions.

Choice of the End Functional Groups in Tri(p-phenylenevinylene) Derivatives Controls Its Physical Gelation Abilities

New supramolecular organogels based on all-trans-tri(p-phenylenevinylene) (TPV) systems possessing different terminal groups, e.g., oxime, hydrazone, phenylhydrazone, and semicarbazone have been synthesized. The self-assembly properties of the compounds that gelate in specific organic solvents and the aggregation motifs of these molecules in the organogels were investigated using UV−vis, fluorescence, FT-IR, and 1H NMR spectroscopy, electron microscopy, differential scanning calorimetry (DSC), and rheology. The temperature variable UV−vis and fluorescence spectroscopy in different solvents clearly show the aggregation pattern of the self-assemblies promoted by hydrogen bonding, aromatic π-stacking, and van der Waals interactions among the individual TPV units. Gelation could be controlled by variation in the number of hydrogen-bonding donors and acceptors in the terminal functional groups of this class of gelators. Also wherever gelation is observed, the individual fibers in gels change to other types of networks in their aggregates depending on the number of hydrogen-bonding sites in the terminal functions. Comparison of the thermal stability of the gels obtained from DSC data of different gelators demonstrates higher phase transition temperature and enthalpy for the hydrazone-based gelator. Rheological studies indicate that the presence of more hydrogen-bonding donors in the periphery of the gelator molecules makes the gel more viscoelastic solidlike. However, in the presence of more numbers of hydrogen-bonding donor/acceptors at the periphery of TPVs such as with semicarbazone a precipitation as opposed to gelation was observed. Clearly, the choice of the end functional groups and the number of hydrogen-bonding groups in the TPV backbone holds the key and modulates the effective length of the chromophore, resulting in interesting optical properties.

Application of Mathematical Programming to the Plywood Design and Manufacturing Problem

Plywood manufacture includes two fundamental stages. The first is to peel or separate logs into veneer sheets of different thicknesses. The second is to assemble veneer sheets into finished plywood products. At the first stage a decision must be made as to the number of different veneer thicknesses to be peeled and what these thicknesses should be. At the second stage, choices must be made as to how these veneers will be assembled into final products to meet certain constraints while minimizing wood loss. These decisions present a fundamental management dilemma. Costs of peeling, drying, storage, handling, etc. can be reduced by decreasing the number of veneer thicknesses peeled. However, a reduced set of thickness options may make it infeasible to produce the variety of products demanded by the market or increase wood loss by requiring less efficient selection of thicknesses for assembly. In this paper the joint problem of veneer choice and plywood construction is formulated as a nonlinear integer programming problem. A relatively simple optimal solution procedure is developed that exploits special problem structure. This procedure is examined on data from a British Columbia plywood mill. Restricted to the existing set of veneer thicknesses and plywood designs used by that mill, the procedure generated a solution that reduced wood loss by 79 percent, thereby increasing net revenue by 6.86 percent. Additional experiments were performed that examined the consequences of changing the number of veneer thicknesses used. Extensions are discussed that permit the consideration of more than one wood species.

A conditionally linearized Monte Carlo filter in non-linear structural dynamics

State and parameter estimations of non-linear dynamical systems, based on incomplete and noisy measurements, are considered using Monte Carlo simulations. Given the measurements. the proposed method obtains the marginalized posterior distribution of an appropriately chosen (ideally small) subset of the state vector using a particle filter. Samples (particles) of the marginalized states are then used to construct a family of conditionally linearized system of equations and thus obtain the posterior distribution of the states using a bank of Kalman filters. Discrete process equations for the marginalized states are derived through truncated Ito-Taylor expansions. Increased analyticity and reduced dispersion of weights computed over a smaller sample space of marginalized states are the key features of the filter that help achieve smaller sample variance of the estimates. Numerical illustrations are provided for state/parameter estimations of a Duffing oscillator and a 3-DOF non-linear oscillator. Performance of the filter in parameter estimation is also assessed using measurements obtained through experiments on simple models in the laboratory. Despite an added computational cost, the results verify that the proposed filter generally produces estimates with lower sample variance over the standard sequential importance sampling (SIS) filter.

Visualization of enantiomers using natural abundant 13C-filtered single and double quantum selective refocusing experiments: Application to small chiral molecules

The routine use of proton NMR for the visualization of enantiomers, aligned in the chiral liquid crystal solvent poly-γ-benzyl-l-glutamate (PBLG), is restricted due to severe loss of resolution arising from large number of pair wise interaction of nuclear spins. In the present study, we have designed two experimental techniques for their visualization utilizing the natural abundance 13C edited selective refocusing of single quantum (CH-SERF) and double quantum (CH-DQSERF) coherences. The methods achieve chiral discrimination and aid in the simultaneous determination of homonuclear couplings between active and passive spins and heteronuclear couplings between the excited protons and the participating 13C spin. The CH-SERF also overcomes the problem of overlap of central transitions of the methyl selective refocusing (SERF) experiment resulting in better chiral discrimination. Theoretical description of the evolution of magnetization in both the sequences has been discussed using polarization operator formalism.

Design and Performance Evaluation of EXMAN: An EXtended MANchester Data Flow Computer

Data flow computers are high-speed machines in which an instruction is executed as soon as all its operands are available. This paper describes the EXtended MANchester (EXMAN) data flow computer which incorporates three major extensions to the basic Manchester machine. As extensions we provide a multiple matching units scheme, an efficient, implementation of array data structure, and a facility to concurrently execute reentrant routines. A simulator for the EXMAN computer has been coded in the discrete event simulation language, SIMULA 67, on the DEC 1090 system. Performance analysis studies have been conducted on the simulated EXMAN computer to study the effectiveness of the proposed extensions. The performance experiments have been carried out using three sample problems: matrix multiplication, Bresenham's line drawing algorithm, and the polygon scan-conversion algorithm.

Evolution of texture during equal channel angular extrusion of commercially pure aluminum: Experiments and simulations

The evolution of crystallographic texture has been comprehensively studied for commercially pure Al as a function of amount of ECAE deformation for the three major routes of ECAE processing. It has been observed that processing through different routes leads to different type of texture, in both qualitative as well as quantitative sense. The results have been analyzed on the basis of existing concepts on ECAE deformation and simulations have been carried out using the simple shear model of ECAE implemented into the Viscoplastic Self Consistent model of polycrystal plasticity. The simulations revealed that non-octahedral slip is needed to reproduce the experimental texture development.

Numerical studies on quasilinear and linear elliptic equations

We explore here the acceleration of convergence of iterative methods for the solution of a class of quasilinear and linear algebraic equations. The specific systems are the finite difference form of the Navier-Stokes equations and the energy equation for recirculating flows. The acceleration procedures considered are: the successive over relaxation scheme; several implicit methods; and a second-order procedure. A new implicit method—the alternating direction line iterative method—is proposed in this paper. The method combines the advantages of the line successive over relaxation and alternating direction implicit methods. The various methods are tested for their computational economy and accuracy on a typical recirculating flow situation. The numerical experiments show that the alternating direction line iterative method is the most economical method of solving the Navier-Stokes equations for all Reynolds numbers in the laminar regime. The usual ADI method is shown to be not so attractive for large Reynolds numbers because of the loss of diagonal dominance. This loss can however be restored by a suitable choice of the relaxation parameter, but at the cost of accuracy. The accuracy of the new procedure is comparable to that of the well-tested successive overrelaxation method and to the available results in the literature. The second-order procedure turns out to be the most efficient method for the solution of the linear energy equation.

Similarities in Different Experiments of Erosion Caused by Cavitation and Liquid Impingement

Correlations of erosion resistances of materials tested in different equipment are reported. Analysis of the authors' data from rotating disk and venturi equipment indicates that there exists a good correlation between the erosion resistances of materials tested at different intensities. The study indicates that time effects on erosion are important in correlations of this type. The erosion resistances of materials tested in two different devices exhibit good correlations indicating a quantitative similarity between different forms of erosion. The investigations also show that the prediction of erosion resistances of materials in a field device may be made with the data from a laboratory device which may not fully reproduce the flow conditions in the field. These conclusions are also checked with data reported from other laboratories.

Multi-state-choice automata model for expedient learning in random environment

A new automata model Mr,k, with a conceptually significant innovation in the form of multi-state alternatives at each instance, is proposed in this study. Computer simulations of the Mr,k, model in the context of feature selection in an unsupervised environment has demonstrated the superiority of the model over similar models without this multi-state-choice innovation.

New light on the optical equivalence theorem and a new type of discrete diagonal coherent state representation

In many instances we find it advantageous to display a quantum optical density matrix as a generalized statistical ensemble of coherent wave fields. The weight functions involved in these constructions turn out to belong to a family of distributions, not always smooth functions. In this paper we investigate this question anew and show how it is related to the problem of expanding an arbitrary state in terms of an overcomplete subfamily of the overcomplete set of coherent states. This provides a relatively transparent derivation of the optical equivalence theorem. An interesting by-product is the discovery of a new class of discrete diagonal representations.

Experiments on the fine structure of turbulence

Investigations have been carried out of some aspects of the fine-scale structure of turbulence in grid flows, in boundary layers in a zero pressure gradient and in a boundary layer in a strong favourable pressure gradient leading to relaminarization. Using a narrow-band filter with suitable mid-band frequencies, the properties of the fine-scale structure (appearing as high frequency pulses in the filtered signal) were analysed using the variable discriminator level technique employed earlier by Rao, Narasimha & Badri Narayanan (1971). It was found that, irrespective of the type of flow, the characteristic pulse frequency (say Np) defined by Rao et al. was about 0·6 times the frequency of the zero crossings. It was also found that, over the small range of Reynolds numbers tested, the ratio of the width of the fine-scale regions to the Kolmogorov scale increased linearly with Reynolds number in grid turbulence as well as in flat-plate boundarylayer flow. Nearly lognormal distributions were exhibited by this ratio as well as by the interval between successive zero crossings. The values of Np and of the zero-crossing rate were found to be nearly constant across the boundary layer, except towards its outer edge and very near the wall. In the zero-pressure-gradient boundary-layer flow, very near the wall the high frequency pulses were found to occur mostly when the longitudinal velocity fluctuation u was positive (i.e. above the mean), whereas in the outer part of the boundary layer the pulses more often occurred when u was negative. During acceleration this correlation between the fine-scale motion and the sign of u was less marked.