Scattering theory and the discrete linear optimal control problem

This paper deals with the interpretation of the discrete-time optimal control problem as a scattering process in a discrete medium. We treat the discrete optimal linear regulator, constrained end-point and servo and tracking problems, providing a unified approach to these problems. This approach results in an easy derivation of the desired results as well as several new ones.

Vertical distribution of aerosols over the east coast of India inferred from airborne LIDAR measurements

The information on altitude distribution of aerosols in the atmosphere is essential in assessing the impact of aerosol warming on thermal structure and stability of the atmosphere.In addition, aerosol altitude distribution is needed to address complex problems such as the radiative interaction of aerosols in the presence of clouds. With this objective,an extensive, multi-institutional and multi-platform field experiment (ICARB-Integrated Campaign for Aerosols, gases and Radiation Budget) was carried out under the Geosphere Biosphere Programme of the Indian Space Research Organization (ISRO-GBP) over continental India and adjoining oceans during March to May 2006. Here, we present airborne LIDAR measurements carried out over the east Coast of the India during the ICARB field campaign. An increase in aerosol extinction (scattering + absorption) was observed from the surface upwards with a maximum around 2 to 4 km. Aerosol extinction at higher atmospheric layers (>2 km) was two to three times larger compared to that of the surface. A large fraction (75-85%) of aerosol column optical depth was contributed by aerosols located above 1 km. The aerosol layer heights (defined in this paper as the height at which the gradient in extinction coefficient changes sign) showed a gradual decrease with an increase in the offshore distance. A large fraction (60-75%) of aerosol was found located above clouds indicating enhanced aerosol absorption above clouds. Our study implies that a detailed statistical evaluation of the temporal frequency and spatial extent of elevated aerosol layers is necessary to assess their significance to the climate. This is feasible using data from space-borne lidars such as CALIPSO,which fly in formation with other satellites like MODIS AQUA and MISR, as part of the A-Train constellation.

Femtosecond carrier dynamics and saturable absorption in graphene suspensions

Nonlinear optical properties and carrier relaxation dynamics in graphene, suspended in three different solvents, are investigated using femtosecond (80 fs pulses) Z-scan and degenerate pump-probe spectroscopy at 790 nm. The results demonstrate saturable absorption property of graphene with a nonlinear absorption coefficient, beta of (similar to 2-9) x 10(-8) cm/W. Two distinct time scales associated with the relaxation of photoexcited carriers, a fast one in the range of 130-330 fs (related to carrier-carrier scattering) followed by it slower one in 3.5-4.9 ps range (associated with carrier-phonon scattering) are observed. (C) 2009 American Institute of Physics.

Electrical switching and in situ Raman scattering studies on the set-reset processes in Ge-Te-Si glass

Bulk Ge15Te83Si2 glass has been found to exhibit memory-type switching for 1 mA current with a threshold electric field of 7.3 kV/cm. The electrical set and reset processes have been achieved with triangular and rectangular pulses, respectively, of 1 mA amplitude. In situ Raman scattering studies indicate that the degree of disorder in Ge15Te83Si2 glass is reduced from off to set state. The local structure of the sample under reset condition is similar to that in the off state. The Raman results are consistent with the switching results which indicate that the Ge15Te83Si2 glass can be set and reset easily. (C) 2007 American Institute of Physics.

Raman evidence for orbiton-mediated multiphonon scattering in multiferroic TbMnO3

Temperature-dependent Raman spectra of TbMnO3 from 5 to 300 K in the spectral range of 200-1525 cm(-1) show five first-order Raman allowed modes and two high frequency modes. The intensity ratio of the high frequency Raman band to the corresponding first-order Raman mode is nearly constant and high (similar to 0.6) at all temperatures, suggesting an orbiton-phonon mixed nature of the high frequency mode. One of the first-order phonon modes shows anomalous softening below T-N (similar to 46 K), suggesting a strong spin-phonon coupling.

Quantitative photoacoustic tomography from boundary pressure measurements: noniterative recovery of optical absorption coefficient from the reconstructed absorbed energy map

We describe a noniterative method for recovering optical absorption coefficient distribution from the absorbed energy map reconstructed using simulated and noisy boundary pressure measurements. The source reconstruction problem is first solved for the absorbed energy map corresponding to single- and multiple-source illuminations from the side of the imaging plane. It is shown that the absorbed energy map and the absorption coefficient distribution, recovered from the single-source illumination with a large variation in photon flux distribution, have signal-to-noise ratios comparable to those of the reconstructed parameters from a more uniform photon density distribution corresponding to multiple-source illuminations. The absorbed energy map is input as absorption coefficient times photon flux in the time-independent diffusion equation (DE) governing photon transport to recover the photon flux in a single step. The recovered photon flux is used to compute the optical absorption coefficient distribution from the absorbed energy map. In the absence of experimental data, we obtain the boundary measurements through Monte Carlo simulations, and we attempt to address the possible limitations of the DE model in the overall reconstruction procedure.

Diffusion of Pure CH4 and Its Binary Mixture with CO2 in Faujasite NaY: A Combination of Neutron Scattering Experiments and Molecular Dynamics Simulations

The self-diffusion properties of pure CH4 and its binary mixture with CO2 within MY zeolite have been investigated by combining an experimental quasi-elastic neutron scattering (QENS) technique and classical Molecular dynamics simulations. The QENS measurements carried out at 200 K led to an unexpected self-diffusivity profile for Pure CH4 with the presence of a maximum for a loading of 32 CH4/unit cell, which was never observed before for the diffusion of apolar species in azeolite system With large windows. Molecular dynamics simulations were performed using two distinct microscopic models for representing the CH4/NaY interactions. Depending on the model, we are able to fairly reproduce either the magnitude or the profile of the self-diffusivity.Further analysis allowed LIS to provide some molecular insight into the diffusion mechanism in play. The QENS measurements report only a slight decrease of the self-diffusivity of CH4 in the presence of CO2 when the CO2 loading increases. Molecular dynamics simulations successfully capture this experimental trend and suggest a plausible microscopic diffusion mechanism in the case of this binary mixture.

Small-angle x-ray scattering study of the aggregation of gold nanoparticles during formation at the toluene-water interface

We report the results of an in situ small-angle x-ray scattering (SAXS) study of the aggregation of gold nanoparticles formed by an interfacial reaction at the toluene-water interface. The SAXS data provide a direct evidence for aggregate formation of nanoparticles having 1.3 nm gold core and an organic shell that gives a core-core separation of about 2.5 nm. Furthermore, the nanoparticles do not occupy all the cites of 13-member cluster. This occupancy decreases with reaction time and indicate reorganization of the clusters that generates planner disklike structures. A gradual increase in fractal dimension from 1.82 to 2.05 also indicate compactification of cluster aggregation with reaction time, the final exponent being close to 2 expected for disklike aggregates.

Anomalous Raman scattering from phonons and electrons of superconducting FeSe0.82

We report interesting anomalies in the temperature dependent Raman spectra of FeSe0.82 measured from 3 K to 300 K in the spectral range from 60 to 1800 cm(-1) and determine their origin using complementary first-principles density functional calculations. A phonon mode near 100 cm-1 exhibits a sharp increase by similar to 5% in the frequency below a temperature T-s (similar to 100 K) attributed to strong spin-phonon coupling and onset of short-range antiferromagnetic order. In addition, two high frequency modes are observed at 1350 cm-1 and 1600 cm-1, attributed to electronic Raman scattering from (x(2)-y(2)) to xz/yz d-orbitals of Fe. (C) 2010 Elsevier Ltd. All rights reserved.

Scattering polarization in the presence of magnetic and electric fields

The polarization of radiation by scattering on an atom embedded in combined external quadrupole electric and uniform magnetic fields is studied theoretically. Limiting cases of scattering under Zeeman effect, and Hanle effect in weak magnetic fields are discussed. The theory is general enough to handle scattering in intermediate magnetic fields (Hanle-Zeeman effect) and for arbitrary orientation of magnetic field. The quadrupolar electric field produces asymmetric line shifts, and causes interesting level-crossing phenomena either in the absence of an ambient magnetic field, or in its presence. It is shown that the quadrupolar electric field produces an additional depolarization in the Q/I profiles and rotation of the plane of polarization in the U/I profile over and above that arising from magnetic field itself. This characteristic may have a diagnostic potential to detect steady-state and time-varying electric fields that surround radiating atoms in solar atmospheric layers. (c) 2007 Elsevier Ltd. All rights reserved.

Tribology of steel/steel interaction in oil-in-water mulsion; a rationale for lubricity

Oil droplets are dispersed in water by an anionic urfactant to form an emulsion. The lubricity of this emulsion in steel/steel interaction is explored in a ball on flat nanotribometer. The droplet size and charge are measured using dynamic light scattering, while the substrate charge density is estimated using the pH titration method. These data are combined to calculate the DLVO forces for the droplets generated for a range of surfactant concentration and two oil to water volume ratios. The droplets have a clear bi-modal size distribution. The study shows that the smaller droplets which experience weak repulsion are situated (at the highest DLVO barrier) much closer to the substrate than thebigger droplets, which experience the same DLVO force, are. We suggest that the smaller droplets thus play a more important role in lubricity than what the bigger droplets do. The largest volume of such small droplets occurs in the 0.5 mM-1 mM range of surfactant concentration and 1% oil to water volume ratio, where the coefficient of friction is also observed to be the least. (C) 2010 Elsevier Inc. All rights reserved.

Levitation effect in zeolites: Quasielastic neutron scattering and molecular dynamics study of pentane isomers in zeolite NaY

We report the quasielastic neutron scattering (QENS) and molecular dynamics (MD) investigations into diffusion of pentane isomers in zeolite NaY. The molecular cross section perpendicular to the long molecular axis varies for the three isomers while the mass and the isomer-zeolite interaction remains essentially unchanged. Both QENS and MD results show that the branched isomers neopentane and isopentane have higher self-diffusivities as compared with n-pentane at 300 K in NaY zeolite. This result provides direct experimental evidence for the existence of nonmonotonic, anomalous dependence of self-diffusivity on molecular diameter known as the levitation effect. The energetic barrier at the bottleneck derived from MD simulations exists for n-pentane which lies in the linear regime while no such barrier is seen for neopentane which is located clearly in the anomalous regime.Activation energy is in the order E-a(n-pentane)>E-a(isopentane)>E-a(neopentane) consistent with the predictions of the levitation effect. In the liquid phase, it is seen thatD(n pentane)>D(isopentane)>D(neopentane) and E-a(n-pentane)< E-a(isopentane)< E-a(neopentane). Intermediate scattering function for small wavenumbers obtained from MD follows a single exponential decay for neopentane and isopentane. For n-pentane, a single exponential fit provides a poor fit especially at short times. Cage residence time is largest for n-pentane and lowest for neopentane. For neopentane, the width of the self-part of the dynamic structure factor shows a near monotonic decrease with wavenumber. For n-pentane a minimum is seen near k=0.5 A degrees(-1) suggesting a slowing down of motion around the 12-ring window, the bottleneck for diffusion. Finally, the result that the branched isomer has a higher diffusivity as compared with the linear analog is at variation from what is normally seen.

Reciprocity relation in scattering by media subjected to an external magnetic field

Krishnan's reciprocity theorem in colloid optics, ρ{variant}u=1+l/ρ{variant}h/1+1/ρ{variant}v is generalised for the case when the scattering medium is subjected to an external orienting field. It is shown theoretically that a general relation of the type IBA=I′AB results in this case, where IBA is the intensity of the component of the scattered light having its electric vector inclined at an angle B to the vertical with the incident light polarised at an angle A to the vertical, the external field direction being parallel to the incident beam. I′AB is the corresponding intensity with the magnetic field parallel of the scattered ray. Experimental verification of the above generalisation is also given.