Exact bounds for distributed graph colouring

A distributed system is a collection of networked autonomous processing units which must work in a cooperative manner. Currently, large-scale distributed systems, such as various telecommunication and computer networks, are abundant and used in a multitude of tasks. The field of distributed computing studies what can be computed efficiently in such systems. Distributed systems are usually modelled as graphs where nodes represent the processors and edges denote communication links between processors. This thesis concentrates on the computational complexity of the distributed graph colouring problem. The objective of the graph colouring problem is to assign a colour to each node in such a way that no two nodes connected by an edge share the same colour. In particular, it is often desirable to use only a small number of colours. This task is a fundamental symmetry-breaking primitive in various distributed algorithms. A graph that has been coloured in this manner using at most k different colours is said to be k-coloured. This work examines the synchronous message-passing model of distributed computation: every node runs the same algorithm, and the system operates in discrete synchronous communication rounds. During each round, a node can communicate with its neighbours and perform local computation. In this model, the time complexity of a problem is the number of synchronous communication rounds required to solve the problem. It is known that 3-colouring any k-coloured directed cycle requires at least ½(log* k - 3) communication rounds and is possible in ½(log* k + 7) communication rounds for all k ≥ 3. This work shows that for any k ≥ 3, colouring a k-coloured directed cycle with at most three colours is possible in ½(log* k + 3) rounds. In contrast, it is also shown that for some values of k, colouring a directed cycle with at most three colours requires at least ½(log* k + 1) communication rounds. Furthermore, in the case of directed rooted trees, reducing a k-colouring into a 3-colouring requires at least log* k + 1 rounds for some k and possible in log* k + 3 rounds for all k ≥ 3. The new positive and negative results are derived using computational methods, as the existence of distributed colouring algorithms corresponds to the colourability of so-called neighbourhood graphs. The colourability of these graphs is analysed using Boolean satisfiability (SAT) solvers. Finally, this thesis shows that similar methods are applicable in capturing the existence of distributed algorithms for other graph problems, such as the maximal matching problem.

Ordered Ports – a Language Concept for High-level Distributed Programming

A new language concept for high-level distributed programming is proposed. Programs are organised as a collection of concurrently executing processes. Some of these processes, referred to as liaison processes, have a monitor-like structure and contain ports which may be invoked by other processes for the purposes of synchronisation and communication. Synchronisation is achieved by conditional activation of ports and also through port control constructs which may directly specify the execution ordering of ports. These constructs implement a path-expression-like mechanism for synchronisation and are also equipped with options to provide conditional, non-deterministic and priority ordering of ports. The usefulness and expressive power of the proposed concepts are illustrated through solutions of several representative programming problems. Some implementation issues are also considered.

High-temperature dielectric response in pulsed laser deposited Bi1.5Zn1.0Nb1.5O7 thin films

Cubic pyrochlore Bi1.5Zn1.0Nb1.5O7 thin films were deposited by pulsed laser ablation on Pt(200)/SiO2/Si at 500, 550, 600, and 650 degrees C. The thin films with (222) preferred orientation were found to grow at 650 degrees C with better crystallinity which was established by the lowest full-width half maxima of similar to 0.38. The dielectric response of the thin films grown at 650 degrees C have been characterized within a temperature range of 270-650 K and a frequency window of 0.1-100 kHz. The dielectric dispersion in the thin films shows a Maxwell-Wagner type relaxation with two different kinds of response confirmed by temperature dependent Nyquist plots. The ac conduction of the films showed a varied behavior in two different frequency regions. The power law exponent values of more than 1 at high frequency are explained by a jump-relaxation-model. The possibility of grain boundary related large polaronic hopping, due to two different power law exponents and transformation of double to single response in Nyquist plots at high temperature, has been excluded. The ``attempt jump frequency'' obtained from temperature dependent tangent loss and real part of dielectric constants, has been found to lie in the range of their lattice vibronic frequencies (10(12)-10(13) Hz). The activation energy arising from a large polaronic hopping due to trapped charge at low frequency region has been calculated from the ac conduction behavior. The range of activation energies (0.26-0.59. eV) suggests that the polaronic hopping at low frequency is mostly due to oxygen vacancies. (C) 2010 American Institute of Physics. doi:10.106311.3457335]

Applications of reverse saturable absorbers in laser science

A variety of applications exist for reverse saturable absorbers (RSAs) in the area of optical pulse processing and computing. An RSA can be used as power limiter/pulse smoother and energy limiter/pulse shortner of laser pulses. A combination of RSA and saturable absorber (SA) can be used for mode locking and pulse shaping between high power laser amplifiers in oscillator amplifier chain. Also, an RSA can be used for the construction of a molecular spatial light modulator (SLM) which acts as an input/output device in optical computers. A detailed review of the theoretical studies of these processes is presented. Current efforts to find RSAs at desired wavelength for testing these theoretical predictions are also discussed.

Nanomechanical properties of silicon surfaces nanostructured by excimer laser

Excimer laser irradiation at ambient temperature has been employed to produce nanostructured silicon surfaces. Nanoindentation was used to investigate the nanomechanical properties of the deformed surfaces as a function of laser parameters, such as the angle of incidence and number of laser pulses at a fixed laser fluence of 5 J cm(-2). A single-crystal silicon 311] surface was severely damaged by laser irradiation and became nanocrystalline with an enhanced porosity. The resulting laser-treated surface consisted of nanometer-sized particles. The pore size was controlled by adjusting the angle of incidence and the number of laser pulses, and varied from nanometers to microns. The extent of nanocrystallinity was large for the surfaces irradiated at a small angle of incidence and by a high number of pulses, as confirmed by x-ray diffraction and Raman spectroscopy. The angle of incidence had a stronger effect on the structure and nanomechanical properties than the number of laser pulses.

Convergence feedback and unstable low frequency oscillations in a simple coupled ocean‐atmosphere model

The role of convergence feedback on the stability of a coupled ocean‐atmosphere system is studied using model III of Hirst (1986). It is shown that the unstable coupled mode found by Hirst is greatly modified by the convergence feedback. If the convergence feedback strength exceeds a critical value, several new unstable intraseasonal modes are also introduced. These modes have very weak dependence on the wave number. These results may explain the behaviour of some coupled models and to some extent provide a mechanism for the observed aperiodicity of the El‐Nino and Southern Oscillation (ENSO) events.

Atomic fountain of laser-cooled Yb atoms for precision measurements

We demonstrate launching of laser-cooled Yb atoms in a cold atomic fountain. Atoms in a collimated thermal beam are first cooled and captured in a magneto-optical trap (MOT) operating on the strongly allowed S-1(0) -> P-1(1) transition at 399 nm (blue line). They are then transferred to a MOT on the weakly allowed S-1(0) -> P-3(1) transition at 556 nm (green line). Cold atoms from the green MOT are launched against gravity at a velocity of around 2.5 m/s using a pair of green beams. We trap more than 107 atoms in the blue MOT and transfer up to 70% into the green MOT. The temperature for the odd isotope Yb-171 is similar to 1 mK in the blue MOT, and reduces by a factor of 40 in the green MOT.

Laser-fused refractory oxides for optical coatings

Laser sintering was carried out using a high power continuous-wave CO2 laser to prepare pellets of zirconia (ZrO2), hafnia (HfO2) and yttria (Y2O3) mixed oxides as starting materials in the deposition of optical coatings. Hardened recrystallized pellets appeared to have been formed during laser treatment. X-ray diffraction analysis revealed a monoclinic-to-tetragonal phase transformation in the binary system while the ternary system was found to have a mixture of two crystalline phases. Cross-sectional scanning electron microscopy showed two isothermal crystalline regions in the ternary system. The optical inhomogeneity was low in the films deposited from the laser-fused pellets, but the absorption at a wavelength of 351 nm increased with increasing HfO2 content. The films deposited from laser-fused pellets were analysed by electron spectroscopy for chemical analysis and found to be stoichiometric and homogeneous.

Power extraction studies in a gasdynamic laser

A generalized two‐dimensional flow‐radiation coupled model to extract power from a gasdynamic laser is proposed. The model is used for the study of power extraction from a 9.4‐μm CO2 downstream‐mixing gasdynamic laser, where a cold CO2+H2 stream is mixed with a vibrationally excited N2 stream at the nozzle exits. This model is developed by coupling radiation with the two‐dimensional, unsteady, laminar and viscous flow modeling needed for such systems. The analysis showed that the steady‐state value of 9.4‐μm intensity as high as 5×107 W/m2 can be obtained from the system studied. The role of H2 relaxant in the power extraction process has also been investigated.