Unitary Processes with Independent Increments and Representations of Hilbert Tensor Algebras

The aim of this article is to characterize unitary increment process by a quantum stochastic integral representation on symmetric Fock space. Under certain assumptions we have proved its unitary equivalence to a Hudson-Parthasarathy flow.

Two-temperature accretion around rotating black holes: a description of the general advective flow paradigm in the presence of various cooling processes to explain low to high luminous sources

We investigate viscous two-temperature accretion disc flows around rotating black holes. We describe the global solution of accretion flows with a sub-Keplerian angular momentum profile, by solving the underlying conservation equations including explicit cooling processes self-consistently. Bremsstrahlung, synchrotron and inverse Comptonization of soft photons are considered as possible cooling mechanisms. We focus on the set of solutions for sub-Eddington, Eddington and super-Eddington mass accretion rates around Schwarzschild and Kerr black holes with a Kerr parameter of 0.998. It is found that the flow, during its infall from the Keplerian to sub-Kepleria transition region to the black hole event horizon, passes through various phases of advection: the general advective paradigm to the radiatively inefficient phase, and vice versa. Hence, the flow governs a much lower electron temperature similar to 10(8)-10(9.5) K, in the range of accretion rate in Eddington units 0.01 less than or similar to (M) over dot less than or similar to 100, compared to the hot protons of temperature similar to 10(10.2)-10(11.8) K. Therefore, the solution may potentially explain the hard X-rays and gamma-rays emitted from active galactic nuclei (AGNs) and X-ray binaries. We then compare the solutions for two different regimes of viscosity. We conclude that a weakly viscous flow is expected to be cooling dominated, particularly at the inner region of the disc, compared to its highly viscous counterpart, which is radiatively inefficient. With all the solutions in hand, we finally reproduce the observed luminosities of the underfed AGNs and quasars (e. g. Sgr A*) to ultraluminous X-ray sources (e. g. SS433), at different combinations of input parameters, such as the mass accretion rate and the ratio of specific heats. The set of solutions also predicts appropriately the luminosity observed in highly luminous AGNs and ultraluminous quasars (e. g. PKS 0743-67).

Effects of compressibility and heat release on entrainment processes in mixing layers

Characteristics of the process of entrainment in plane mixing layers, and the changes with compressibility and heat release, were studied using temporal DNS with simultaneous fluid packet tracking. Convective Mach numbers of the simulations are 0.15, 0.7 and 1.1. The Reynolds number is quite high (between 11 000 and 37 000 based on layer width and velocity difference), and is above the mixing transition. The study agrees with recent findings in round jets: first, engulfed fluid volume and its growth rate are both very small compared with the volume of the turbulent region and its growth rate, respectively. Secondly, most often, the process occurs close to the turbulent-nonturbulent boundaries. A new finding is that both compressibility and heat release retard the entrainment process so that it takes an O(1) time for vorticity or scalar levels to grow even after growth has been initiated. This delay is manifested as the fall in mixing layer growth rates as compressibility and heat release levels increase.

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.

Dynamic simulation of activated sludge based wastewater treatment processes: Case studies with Titagarh Sewage Treatment Plant, India

STOAT has been extensively used for the dynamic simulation of an activated sludge based wastewater treatment plant in the Titagarh Sewage Treatment Plant, near Kolkata, India. Some alternative schemes were suggested. Different schemes were compared for the removal of Total Suspended Solids (TSS), b-COD, ammonia, nitrates etc. A combination of IAWQ#1 module with the Takacs module gave best results for the existing scenarios of the Titagarh Sewage Treatment Plant. The modified Bardenpho process was found most effective for reducing the mean b-COD level to as low as 31.4 mg/l, while the mean TSS level was as high as 100.98 mg/l as compared to the mean levels of TSS (92 62 mg/l) and b-COD (92.0 mg/l) in the existing plant. Scheme 2 gave a better scenario for the mean TSS level bringing it down to a mean value of 0.4 mg/l, but a higher mean value for the b-COD level at 54.89 mg/l. The Scheme Final could reduce the mean TSS level to 2.9 mg/l and the mean b-COD level to as low as 38.8 mg/l. The Final Scheme looks to be a technically viable scheme with respect to the overall effluent quality for the plant. (C) 2009 Elsevier B.V. All rights reserved.

A reinforcement learning based algorithm for finite horizon Markov decision processes

We develop a simulation based algorithm for finite horizon Markov decision processes with finite state and finite action space. Illustrative numerical experiments with the proposed algorithm are shown for problems in flow control of communication networks and capacity switching in semiconductor fabrication.

Critical age-dependent branching Markov processes and their scaling limits

This paper studies:(i)the long-time behaviour of the empirical distribution of age and normalized position of an age-dependent critical branching Markov process conditioned on non-extinction;and (ii) the super-process limit of a sequence of age-dependent critical branching Brownian motions.

Characterization of unitary processes with independent and stationary increments

This is a continuation of the earlier work (Publ. Res. Inst. Math. Sci. 45 (2009) 745-785) to characterize unitary stationary independent increment Gaussian processes. The earlier assumption of uniform continuity is replaced by weak continuity and with technical assumptions on the domain of the generator, unitary equivalence of the process to the solution of an appropriate Hudson-Parthasarathy equation is proved.

The status and use of tree biomass in a semi-arid village ecosystem

The status of the tree biomass resource was investigated in Ungra, a semi-arid village ecosystem in South India. There were 57 tree species with 12 trees capita−1 and 35 trees ha−1. Multiple benefit yielding local tree species dominated the village ecosystem, while fuel only or single end use trees accounted for a small proportion of trees. The standing tree biomass is adequate to meet the requirement of biomass fuels for cooking only for about two years. Village tree biomass is presently being depleted largely for export to urban areas. Tree regeneration is now characterized by transformation from multiple-use local tree species to a few single-use species. A large potential exists for tree biomass production along field boundaries (bunds), stream banks and roadsides. Biomass estimation equations were developed for 10 species.

Experimental analysis of thermo-physical processes in acoustically levitated heated droplets

An experimental setup using radiative heating has been used to understand the thermo-physical phenomena and chemical transformations inside acoustically levitated cerium nitrate precursor droplets. In this transformation process, through infrared thermography and high speed imaging, events such as vaporization, precipitation and chemical reaction have been recorded at high temporal resolution, leading to nanoceria formation with a porous morphology. The cerium nitrate droplet undergoes phase and shape changes throughout the vaporization process. Four distinct stages were delineated during the entire vaporization process namely pure evaporation, evaporation with precipitate formation, chemical reaction with phase change and formation of final porous precipitate. The composition was examined using scanning and transmission electron microscopy that revealed nanostructures and confirmed highly porous morphology with trapped gas pockets. Transmission electron microscopy (TEM) and high speed imaging of the final precipitate revealed the presence of trapped gases in the form of bubbles. TEM also showed the presence of nanoceria crystalline structures at 70 degrees C. The current study also looked into the effect of different heating powers on the process. At higher power, each phase is sustained for smaller duration and higher maximum temperature. In addition, the porosity of the final precipitate increased with power. A non-dimensional time scale is proposed to correlate the effect of laser intensity and vaporization rate of the solvent (water). The effect of acoustic levitation was also studied. Due to acoustic streaming, the solute selectively gets transported to the bottom portion of the droplet due to strong circulation, providing it rigidity and allows it become bowl shaped. (C) 2010 Elsevier Ltd. All rights reserved.

Indian Ocean Dipole: Processes and impacts

Equatorial Indian Ocean is warmer in the east, has a deeper thermocline and mixed layer, and supports a more convective atmosphere than in the west. During certain years, the eastern Indian Ocean becomes unusually cold, anomalous winds blow from east to west along the equator and southeastward off the coast of Sumatra, thermocline and mixed layer lift up and the atmospheric convection gets suppressed. At the same time, western Indian Ocean becomes warmer and enhances atmospheric convection. This coupled ocean-atmospheric phenomenon in which convection, winds, sea surface temperature (SST) and thermocline take part actively is known as the Indian Ocean Dipole (IOD). Propagation of baroclinic Kelvin and Rossby waves excited by anomalous winds, play an important role in the development of SST anomalies associated with the IOD. Since mean thermocline in the Indian Ocean is deep compared to the Pacific, it was believed for a long time that the Indian Ocean is passive and merely responds to the atmospheric forcing. Discovery of the IOD and studies that followed demonstrate that the Indian Ocean can sustain its own intrinsic coupled ocean-atmosphere processes. About 50% percent of the IOD events in the past 100 years have co-occurred with El Nino Southern Oscillation (ENSO) and the other half independently. Coupled models have been able to reproduce IOD events and process experiments by such models – switching ENSO on and off – support the hypothesis based on observations that IOD events develop either in the presence or absence of ENSO. There is a general consensus among different coupled models as well as analysis of data that IOD events co-occurring during the ENSO are forced by a zonal shift in the descending branch of Walker cell over to the eastern Indian Ocean. Processes that initiate the IOD in the absence of ENSO are not clear, although several studies suggest that anomalies of Hadley circulation are the most probable forcing function. Impact of the IOD is felt in the vicinity of Indian Ocean as well as in remote regions. During IOD events, biological productivity of the eastern Indian Ocean increases and this in turn leads to death of corals over a large area.Moreover, the IOD affects rainfall over the maritime continent, Indian subcontinent, Australia and eastern Africa. The maritime continent and Australia suffer from deficit rainfall whereas India and east Africa receive excess. Despite the successful hindcast of the 2006 IOD by a coupled model, forecasting IOD events and their implications to rainfall variability remains a major challenge as understanding reasons behind an increase in frequency of IOD events in recent decades.

Discrete-Time Controlled Markov Processes with Average Cost Criterion: A Survey

This work is a survey of the average cost control problem for discrete-time Markov processes. The authors have attempted to put together a comprehensive account of the considerable research on this problem over the past three decades. The exposition ranges from finite to Borel state and action spaces and includes a variety of methodologies to find and characterize optimal policies. The authors have included a brief historical perspective of the research efforts in this area and have compiled a substantial yet not exhaustive bibliography. The authors have also identified several important questions that are still open to investigation.

Impact of physical processes on the chlorophyll distribution in the Bay of Bengal

Satellite-derived chlorophyll a concentration (chl a) maps show three regions with high chl a in the Bay of Bengal. First among these is close to the coast, particularly off river mouths, with high values coinciding with the season of peak discharge; second is in the southwestern bay during the northeast monsoon, which is forced by local Ekman pumping; and the third is to the east of Sri Lanka in response to the summer monsoon winds. Chlorophyll-rich water from the mouths of rivers flows either along the coast or in an offshore direction, up to several hundred kilometers, depending on the prevailing ocean current pattern. The Irrawady River plume flows toward offshore and then turns northwestward during October–December, but it flows along the coast into the Andaman Sea for the rest of the year. From the Ganga-Brahmaputra river mouth, chl a–rich water flows directly southward into the open bay during spring but along the Indian coast during summer and winter. Along the Indian coast, the flow of chl a–rich water is determined by the East India Coastal Current (EICC). Whenever the EICC meanders off the Indian coast, it leads to an offshore outbreak of chl a–rich water from the coastal region into open ocean. The EICC as well as open ocean circulation in the bay is made up of several eddies, and these eddies show relatively higher chl a. Eddies near the coast, however, can often have higher chl a because of advection from the coastal region rather than generation within the eddy itself. The bay experiences several cyclones in a year, most of them occurring during October–November. These cyclones cause a drop in the sea surface temperature, a dip in the sea level, and a local increase in chl a. The impact of a cyclone is weaker in the northern part of the bay because of stronger stratification compared to the southern parts.