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.

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.

Two-point correlation function of an exclusion process with hole-dependent rates

We consider an exclusion process on a ring in which a particle hops to an empty neighboring site with a rate that depends on the number of vacancies n in front of it. In the steady state, using the well-known mapping of this model to the zero-range process, we write down an exact formula for the partition function and the particle-particle correlation function in the canonical ensemble. In the thermodynamic limit, we find a simple analytical expression for the generating function of the correlation function. This result is applied to the hop rate u(n) = 1 + (b/n) for which a phase transition between high-density laminar phase and low-density jammed phase occurs for b > 2. For these rates, we find that at the critical density, the correlation function decays algebraically with a continuously varying exponent b - 2. We also calculate the two-point correlation function above the critical density and find that the correlation length diverges with a critical exponent nu = 1/(b - 2) for b < 3 and 1 for b > 3. These results are compared with those obtained using an exact series expansion for finite systems.

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.

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.

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.

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.

Full current statistics for a disordered open exclusion process

We consider the nonabelian sandpile model defined on directed trees by Ayyer et al. (2015 Commun. Math. Phys. 335 1065). and restrict it to the special case of a one-dimensional lattice of n sites which has open boundaries and disordered hopping rates. We focus on the joint distribution of the integrated currents across each bond simultaneously, and calculate its cumulant generating function exactly. Surprisingly, the process conditioned on seeing specified currents across each bond turns out to be a renormalised version of the same process. We also remark on a duality property of the large deviation function. Lastly, all eigenvalues and both Perron eigenvectors of the tilted generator are determined.

Electron transfer amongst flavo- and hemo-proteins: diffusible species effect the relay processes, not protein-protein binding

Hitherto, electron transfer (ET) between redox proteins has been deemed to occur via donor-acceptor binding, and diffusible reactive species are considered as deleterious side-products in such systems. Herein, ET from cytochrome P450 reductase (CPR, an animal membrane flavoprotein) and horseradish peroxidase (HRP, a plant hemoprotein) to cytochrome c (Cyt c, a soluble animal hemoprotein) was probed under diverse conditions, using standard assays. ET in the CPR-Cyt c system was critically inhibited by cyanide and sub-equivalent levels of polar one-electron cyclers like copper ions, vitamin C/Trolox and superoxide dismutase. In the presence of lipids, inhibition was also afforded by amphipathic molecules vitamin E, palmitoyl-vitamin C and the membrane hemoprotein, cytochrome b(5). Such nonspecific inhibition (by diverse agents in both aqueous and lipid phases) indicated that electron transfer/relay was effected by small diffusible agents, whose lifetimes are shortened by the diverse radical scavengers. When CPR was retained in a dialysis membrane and Cyt c presented outside in free solution, ET was still observed. Further, HRP (taken at nM levels) catalyzed oxidation of a phenolic substrate was significantly inhibited upon the incorporation of sub-nM levels of Cyt c. The findings imply that CPR-Cyt c or HRP-Cyt c binding is not crucial for ET. Further, fundamental quantitative arguments (based on diffusion/collision) challenge the erstwhile protein-protein binding-assisted ET hypothesis. It is proven beyond reasonable doubt that mobile and diffusible electron carriers (ions and radicals) serve as ``redox-relay agents'' in the biological ET models/setup studied.

Characteristic Dimensionless Numbers in Multi-Scale and Rate-Dependent Processes

For this sake, the macroscopic equations of mechanics and the kinetic equations of the microstructural transformations should form a unified set that be solved simultaneously. As a case study of coupling length and time scales, the trans-scale formulation

Effects of heat-treatment processes on the electroless Ni-B coating and its natural aging mechanism

A Ni-B coating was prepared with EN using potassium borohydride reducing agent. The as-plated micro-structure of the coating was confirmed from XRD to be a mixture of amorphous and supersaturated solid solution. Three kinds of phase transformation were observed from the DSC curve. Different from the previous works, the formation of Ni4B3 and Ni2B was found during some transformation processes. The key factors which influence the variation of micro-hardness and micro-structure in deposits are the formation, the size and amount of Ni3B, Ni4B3 and Ni2B. Aging of the deposits treated under some heat treatment conditions occurred at room temperature. Changes of the micro-hardness indicated aging phenomena evidently. the natural aging phenomena are concerned with various kinds of decomposition of borides, especially with Ni4B3 phase. The extent of natural aging depends on the formation and the quantity of Ni(4)B3 and Ni2B.