Approximation of Spatio-Temporal Random Processes Using Tensor Decomposition

A new representation of spatio-temporal random processes is proposed in this work. In practical applications, such processes are used to model velocity fields, temperature distributions, response of vibrating systems, to name a few. Finding an efficient representation for any random process leads to encapsulation of information which makes it more convenient for a practical implementations, for instance, in a computational mechanics problem. For a single-parameter process such as spatial or temporal process, the eigenvalue decomposition of the covariance matrix leads to the well-known Karhunen-Loeve (KL) decomposition. However, for multiparameter processes such as a spatio-temporal process, the covariance function itself can be defined in multiple ways. Here the process is assumed to be measured at a finite set of spatial locations and a finite number of time instants. Then the spatial covariance matrix at different time instants are considered to define the covariance of the process. This set of square, symmetric, positive semi-definite matrices is then represented as a third-order tensor. A suitable decomposition of this tensor can identify the dominant components of the process, and these components are then used to define a closed-form representation of the process. The procedure is analogous to the KL decomposition for a single-parameter process, however, the decompositions and interpretations vary significantly. The tensor decompositions are successfully applied on (i) a heat conduction problem, (ii) a vibration problem, and (iii) a covariance function taken from the literature that was fitted to model a measured wind velocity data. It is observed that the proposed representation provides an efficient approximation to some processes. Furthermore, a comparison with KL decomposition showed that the proposed method is computationally cheaper than the KL, both in terms of computer memory and execution time.

Sensitivity of simulated climate to latitudinal distribution of solar insolation reduction in solar radiation management

Solar radiation management (SRM) geoengineering has been proposed as a potential option to counteract climate change. We perform a set of idealized geoengineering simulations using Community Atmosphere Model version 3.1 developed at the National Center for Atmospheric Research to investigate the global hydrological implications of varying the latitudinal distribution of solar insolation reduction in SRM methods. To reduce the solar insolation we have prescribed sulfate aerosols in the stratosphere. The radiative forcing in the geoengineering simulations is the net forcing from a doubling of CO2 and the prescribed stratospheric aerosols. We find that for a fixed total mass of sulfate aerosols (12.6 Mt of SO4), relative to a uniform distribution which nearly offsets changes in global mean temperature from a doubling of CO2, global mean radiative forcing is larger when aerosol concentration is maximum at the poles leading to a warmer global mean climate and consequently an intensified hydrological cycle. Opposite changes are simulated when aerosol concentration is maximized in the tropics. We obtain a range of 1 K in global mean temperature and 3% in precipitation changes by varying the distribution pattern in our simulations: this range is about 50% of the climate change from a doubling of CO2. Hence, our study demonstrates that a range of global mean climate states, determined by the global mean radiative forcing, are possible for a fixed total amount of aerosols but with differing latitudinal distribution. However, it is important to note that this is an idealized study and thus not all important realistic climate processes are modeled.

Implications of multiple scattering on the assessment of black carbon aerosol radiative forcing

The effects of radiative coupling between scattering and absorbing aerosols, in an external mixture, on the aerosol radiative forcing (ARF) due to black carbon (BC), its sensitivity to the composite aerosol loading and composition, and surface reflectance are investigated using radiative transfer model simulations. The ARF due to BC is found to depend significantly on the optical properties of the `neighboring' (non-BC) aerosol species. The scattering due to these species significantly increases the top of the atmospheric warming due to black carbon aerosols, and significant changes in the radiative forcing efficiency of BC. This is especially significant over dark surfaces (such as oceans), despite the ARF due to BC being higher over snow and land-surfaces. The spatial heterogeneity of this effect (coupling or multiple scattering by neighboring aerosol species) imposes large uncertainty in the estimation ARF due to BC aerosols, especially over the oceans. (C) 2014 Elsevier Ltd. All rights reserved.

Breakup processes of pressure swirl spray in gaseous cross-flow

Injection of liquid fuel in cross flowing air has been a strategy for future aircraft engines in order to control the emissions. In this context, breakup of a pressure swirl spray in gaseous cross-flow is investigated experimentally. The atomizer discharges a conical swirling sheet of liquid that interacts with cross-flowing air. This complex interaction and the resulting spray structures at various flow conditions are studied through flow visualization using still as well as high speed photography. Experiments are performed over a wide range of aerodynamic Weber number (2-300) and liquid-to-air momentum flux ratio (5-150). Various breakup regimes exhibiting different breakup processes are mapped on a parameter space based on flow conditions. This map shows significant variations from breakup regime map for a plain liquid jet in cross-flow. It is observed that the breakup of leeward side of the sheet is dominated by bag breakup and the windward side of the sheet undergoes breakup through surface waves. Similarities and differences between bag breakup present in plain liquid jet in cross-flow and swirl spray in cross-flow are explained. Multimodal drop size distribution from bag breakup, frequency of bag breakup, wavelength of surface waves and trajectory of spray in cross-flow are measured by analyzing the spray images and parametric study of their variations is also presented. (C) 2014 Elsevier Ltd. All rights reserved.

Sources of major ions and processes affecting the geochemical and isotopic signatures of subsurface waters along a tropical river, Southwestern India

Systematic monitoring of subsurface hydrogeochemistry has been carried out for a period of one year in a humid tropical region along the Nethravati-Gurupur River. The major ion and stable isotope (delta O-18 and delta H-2) compositions are used to understand the hydrogeochemistry of groundwater and its interaction with surface water. In the study, it is observed that intense weathering of source rocks is the major source of chemical elements to the surface and subsurface waters. In addition, agricultural activities and atmospheric contributions also control the major ion chemistry of water in the study area. There is a clear seasonality in the groundwater chemistry, which is related to the recharge and discharge of the hydrological system. On a temporal scale, there is a decrease in major cation concentrations during the monsoon which is a result of dilution of sources from the weathering of rock minerals, and an increase in anion concentrations which is contributed by the atmosphere, accompanied by an increase in water level during the monsoon. The stable isotope composition indicates that groundwater in the basin is of meteoric origin and recharged directly from the local precipitation during the monsoonal season. Soon after the monsoon, groundwater and surface water mix in the subsurface region. The groundwater feeds the surface water during the lean river flow season.

Investigation on two magnon scattering processes in pulsed laser deposited epitaxial nickel zinc ferrite thin film

Ferromagnetic resonance (FMR) measurements are employed to evaluate the presence of the two magnon scattering contribution in the magnetic relaxation processes of the epitaxial nickel zinc ferrite thin films deposited using pulsed laser deposition (PLD) on the (0 0 1) MgAl2O4 substrate. Furthermore, the reciprocal space mapping reveals the presence of microstructural defects which acts as an origin for the two magnon scattering process in this thin film. The relevance of this scattering process is further discussed for understanding the higher FMR linewidth in the in-plane configuration compared to the out-of-plane configuration. FMR measurements also reveal the presence of competing uniaxial and cubic anisotropy in the studied films.

Comparative evaluation of inversion approaches of the radiative transfer model for estimation of crop biophysical parameters

The inversion of canopy reflectance models is widely used for the retrieval of vegetation properties from remote sensing. This study evaluates the retrieval of soybean biophysical variables of leaf area index, leaf chlorophyll content, canopy chlorophyll content, and equivalent leaf water thickness from proximal reflectance data integrated broadbands corresponding to moderate resolution imaging spectroradiometer, thematic mapper, and linear imaging self scanning sensors through inversion of the canopy radiative transfer model, PROSAIL. Three different inversion approaches namely the look-up table, genetic algorithm, and artificial neural network were used and performances were evaluated. Application of the genetic algorithm for crop parameter retrieval is a new attempt among the variety of optimization problems in remote sensing which have been successfully demonstrated in the present study. Its performance was as good as that of the look-up table approach and the artificial neural network was a poor performer. The general order of estimation accuracy for para-meters irrespective of inversion approaches was leaf area index > canopy chlorophyll content > leaf chlorophyll content > equivalent leaf water thickness. Performance of inversion was comparable for broadband reflectances of all three sensors in the optical region with insignificant differences in estimation accuracy among them.

Risk-Sensitive Ergodic Control of Continuous Time Markov Processes With Denumerable State Space

In this article, we study risk-sensitive control problem with controlled continuous time Markov chain state dynamics. Using multiplicative dynamic programming principle along with the atomic structure of the state dynamics, we prove the existence and a characterization of optimal risk-sensitive control under geometric ergodicity of the state dynamics along with a smallness condition on the running cost.

Exciton-phonon scattering and nonradiative relaxation of excited carriers in hydrothermally synthesized CdTe quantum dots

Naturally formed CdTe/CdS core/shell quantum dot (QD) structures in the presence of surface stabilizing agents have been synthesized by a hydrothermal method. Size and temperature dependent photoluminescence (PL) spectra have been investigated to understand the exciton-phonon interaction, and radiative and nonradiative relaxation of carriers in these QDs. The PL of these aqueous CdTe QDs (3.0-4.8 nm) has been studied in the temperature range 15-300 K. The strength of the exciton-LO-phonon coupling, as reflected in the Huang-Rhys parameter `S' is found to increase from 1.13 to 1.51 with the QD size varying from 4.8 to 3.0 nm. The PL linewidth (FWHM) increases with increase in temperature and is found to have a maximum in the case of QDs of 3.0 nm in size, where the exciton-acoustic phonon coupling coefficient is enhanced to 51 mu eV K-1, compared to the bulk value of 0.72 mu eV K-1. To understand the nonradiative processes, which affect the relaxation of carriers, the integrated PL intensity is observed as a function of temperature. The integrated PL intensity remains constant until 50 K for relatively large QDs (3.9-4.8 nm) beyond which a thermally activated process takes over. Below 150 K, a small activation energy, 45-19 meV, is found to be responsible for the quenching of the PL. Above 150 K, the thermal escape from the dot assisted by scattering with multiple longitudinal optical (LO) phonons is the main mechanism for the fast quenching of the PL. Besides this high temperature quenching, interestingly for relatively smaller size QDs (3.4-3.0 nm), the PL intensity enhances as the temperature increases up to 90-130 K, which is attributed to the emission of carriers from interface/trap states having an activation energy in the range of 6-13 meV.

The electronic, chemical and electrocatalytic processes and intermediates on iron oxide surfaces during photoelectrochemical water splitting

We re-assess experimental soft X-ray absorption spectra of the oxygen K-shell which we recorded operando from iron oxide during photoelectrochemical water splitting in KOH electrolyte. In particular, we refer to recently reported transitional electron hole states which originate within the charge carrier depletion layer of the iron oxide and on the iron oxide surface. For the latter we find that an intermediate oxy-peroxo species is formed on the iron oxide with increasing bias potential, which disappears upon further polarization of the electrode, concomitantly with the evolution and disappearance of the aforementioned surface state. The oxygen spectra contain also the spectroscopic signatures of the electrolyte water, the position of which changes with increasing bias potential towards lower X-ray energies, revealing the breaking and formation of hydrogen bonds in the water during the experiment. Combined with potential dependent impedance spectroscopy data we are able to sketch the molecular structure of chemical intermediates and their charge carrier dynamics. (C) 2015 Elsevier B.V. All rights reserved.

Use of Sr isotopes as a tool to decipher the soil weathering processes in a tropical river catchment, southwestern India

River water composition (major ion and Sr-87/Sr-86 ratio) was monitored on a monthly basis over a period of three years from a mountainous river (Nethravati River) of southwestern India. The total dissolved solid (TDS) concentration is relatively low (46 mg L-1) with silica being the dominant contributor. The basin is characterised by lower dissolved Sr concentration (avg. 150 nmol L-1), with radiogenic Sr-87/Sr-86 isotopic ratios (avg. 0.72041 at outlet). The composition of Sr and Sr-87/Sr-86 and their correlation with silicate derived cations in the river basin reveal that their dominant source is from the radiogenic silicate rock minerals. Their composition in the stream is controlled by a combination of physical and chemical weathering occurring in the basin. The molar ratio of SiO2/Ca and Sr-87/Sr-86 isotopic ratio show strong seasonal variation in the river water, i.e., low SiO2/Ca ratio with radiogenic isotopes during non-monsoon and higher SiO2/Ca with less radiogenic isotopes during monsoon season. Whereas, the seasonal variation of Rb/Sr ratio in the stream water is not significant suggesting that change in the mineral phase being involved in the weathering reaction could be unlikely for the observed molar SiO2/Ca and Sr-87/Sr-86 isotope variation in river water. Therefore, the shift in the stream water chemical composition could be attributed to contribution of ground water which is in contact with the bedrock (weathering front) during non-monsoon and weathering of secondary soil minerals in the regolith layer during monsoon. The secondary soil mineral weathering leads to limited silicate cation and enhanced silica fluxes in the Nethravati river basin. (C) 2015 Elsevier Ltd. All rights reserved.

Determinantal point processes in the plane from products of random matrices

We show that the density of eigenvalues for three classes of random matrix ensembles is determinantal. First we derive the density of eigenvalues of product of k independent n x n matrices with i.i.d. complex Gaussian entries with a few of matrices being inverted. In second example we calculate the same for (compatible) product of rectangular matrices with i.i.d. Gaussian entries and in last example we calculate for product of independent truncated unitary random matrices. We derive exact expressions for limiting expected empirical spectral distributions of above mentioned ensembles.

Comparison of Convective and Radiative Heating Modes on the Thermophysical Changes of a Cerium Nitrate Droplet

In this paper, we try to establish the equivalence or similarity in the thermal and physiochemical changes in precursor droplets (cerium nitrate) in convective and radiative fields. The radiative field is created through careful heating of the droplet using a monochromatic light source (CO2 laser). The equivalence is also established for different modes of convection like droplet injected into a high-speed flow and droplet experiencing a convective flow due to acoustic streaming (levitated) only. The thermophysical changes are studied in an aqueous cerium nitrate droplet, and the dissociation of cerium nitrate to ceria is modeled using modified Kramers' reaction rate formulation. It is observed that vaporization, species accumulation, and chemical characteristics obtained in a convectively heated droplet are retained in a radiatively heated droplet by careful adjustment of the laser intensity. The timescales and ceria yield match reasonably well for both the cases. It is also noted that similar conclusions are drawn in both levitated droplet and a nonlevitated droplet.

Case studies on the formation of chalcogenide self-assembled monolayers on surfaces and dissociative processes

This report examines the assembly of chalcogenide organic molecules on various surfaces, focusing on cases when chemisorption is accompanied by carbon-chalcogen atom-bond scission. In the case of alkane and benzyl chalcogenides, this induces formation of a chalcogenized interface layer. This process can occur during the initial stages of adsorption and then, after passivation of the surface, molecular adsorption can proceed. The characteristics of the chalcogenized interface layer can be significantly different from the metal layer and can affect various properties such as electron conduction. For chalcogenophenes, the carbon-chalcogen atombond breaking can lead to opening of the ring and adsorption of an alkene chalcogenide. Such a disruption of the pi-electron system affects charge transport along the chains. Awareness about these effects is of importance from the point of view of molecular electronics. We discuss some recent studies based on X-ray photoelectron spectroscopy that shed light on these aspects for a series of such organic molecules.