Quantisation of second class systems in the Batalin-Tyutin formalism

We review the Batalin-Tyutin approach of quantising second class systems which consists in enlarging the phase space to convert such systems into first class. The quantisation of first class systems, it may be mentioned, is already well founded. We show how the usual analysis of Batalin-Tyutin may be generalised, particularly if one is dealing with nonabelian theories. In order to gain a deeper insight into the formalism we have considered two specific examples of second class theories-- the massive Maxwell theory (Proca model) and its nonabelian extension. The first class constraints and the involutive Hamiltonian are explicitly constructed. The connection of our Hamiltonian approach with the usual Lagrangian formalism is elucidated. For the Proca model we reveal the importance of a boundary term which plays a significant role in establishing an exact identification of the extra fields in the Batalin-Tyutin approach with the St\"uckelberg scalar. Some comments are also made concerning the corresponding identification in the nonabelian example.Comment: 26 pages, Latex file, e-mail [email protected] SINP-TNP/94-

Some Aspects of Modelling of the High Temperature Mechanical Behaviour of Nickel Base Superalloys

On the basis of a new physical model based approach a computer package named CRISPEN has been developed jointly by the Cambridge University and the National Physical Laboratory, Teddington. This system allows creep strain prediction engineering alloys subject to various stress and temperature histories using a set of the coupled diff-erential equations . The first describes the strain rate in terms of stress temperature and two internal state variables: an internal stress and a damage parameter. The other two describe the rate of evolution of the internal stress and the damage. A major unresolved problem is the detailed form of the equations describing the evolution of the internal state variables. Different classes of mat- erial may require an altogether different set of equat-ions. However using the simplest possible approach CRISPEN does predict fairly well the creep behaviour of the class of material exhibiting either linear of exponential strain softening such as the superalloys. A detailed analysis of the creep data of a range of superalloys reveals that oiler certain conditions both of these mechanism may occur in parallel

Creep life prediction of single crystal superalloys

There has been a limited attempt to map the creep performance of superalloy single crystals for all possible orientations as it requires a very large number of experi-ments, some of which may run for several years. Convent-ional life prediction techniques would indeed require a large data-base for a reliable estimation of the creep life of a single crystal. Moreover single crystals with a tensile axis having a low symmetry orientation would und-ergo a time dependent rotation well. Therefore life predi-ction in this case is no doubt more complex and it needs an entirely different approach. Creep in single crystals is known to take place through viscous glides on several slip systems such as (111) , [0011 and (111) (112> in the case of Ni based superalloys. The paper rev-iews he such information has recently led to the devel-opment of a generalised model of creep deformation in cubic single crystals. Using this approach it is possible tonume-rically simulate the creep test on a crystal of arbitrary orientation based-on the material constants estimated from a limited database on and crystals. Although this approach has been used to explain the creep behaviour of SRR99 a Ni base superalloy it is applicable to any cubic crystal. Such an analysis not only helps to identify the operative slip systems but also predicts both strain-time plots and crystal rotations that are consistent with the experimental observations

Identification of Novelty in R&D

: Most inventions originate from novel and simple ideas. These ideas which are raw to begin-with are nurtured and nourished by R&D organization before they are tried on a large scale. However, all such ideas may not lead to commercially successful products. Hence there is a need to correctly identify the novelty of an idea before it is commercialized. The paper analyzes some problems associated with the identification of novelty and suggests important criteria that help in transforming novelty to commercial success. Keywords : Novelty identification

Welding of Non-Ferrous Metals

The paper deals with various methods of welding both by gas and electric welding processes, although it deals chiefly with the oxy-acetylene process

Remaining life assessment of engineering components

A structure or a component is expected to perform specific functions for a minimum specified duration of time. If it ceases to do so, it is said to have failed. The consequence of service failure can be tragic and expensive. There are innumerable cases of engineering disasters resulting in loss of life and property. Therefore, utmost care and attention are required to be given to critical structures / components to ensure that such incidents do not take place. Life assessment exercise performed at regular intervals is a means to ensure absence of such tragic service failure. It gives us an estimate of remaining life of the component, which is essential to plan future course of action so that it could be used till the very end of its real life. Recent development of powerful non-destructive techniques and availability of modem computational facility at affordable cost has made this a routine exercise for many critical applications. This paper describes the basic principles behind remaining life assessment of engineering components and also presents some of our experiences

Physical Metallurgy of Steel - Basic Principles

Steel is primarily an alloy of carbon in iron although most commercial grades contain other alloying elements as well. It is well known that if pure iron is slowly cooled from its liquid state to room temperature it undergoes isothermal transformations at 15340C from liquid to 8 phase, and, at 13900C from 8 to y phase, and at 9100C from y to a phase (Fig.1). These phases have different crystal structures; 8 and a phases are BCC whereas y is FCC. Addition of carbon to iron signi-ficantly alters the above transformation characteristics. While in liquid state iron can dissolve considerable amount of carbon, its solubility in solid state is significantly less. This is determined by the spacing of iron atoms in the crystal lattice. FCC structure although more closely packed has larger inters-titial spacing than BCC lattice and therefore can accomm-odate relatively larger amount of carbon. For example maxi-mum solubility of carbon in a or 8 (also called ferrite) is 0.08 whereas that in y (also called austenite) it is 2.06. Carbon in excess of this limit is usually present in steel as a carbide called cementite which is a stable non equilibrium compound represented as Fe3C. Thus steel at a given temperature and pressure may therefore contain more than one phases. Equilibrium diagram provides a graphic representation of the distribution of various phases as function temperature and overall composition. If properly interpreted this also provides compositions of respective phases and their relative amount.Fig. 2 represents such a diagram for Fe-Fe3C system. This contains three horizontal lines representing three invariant transformations viz. peritectic, eutectic and cutectoid; signifying coexistence of three phases of specific composition in equilibrium at a fixed temperature. Peritectic: L (0.55) + 8 (0.08) = 7 (0.18) 14930C Eutectic: L (4.30) = y (2.06) + Fe3C(6.67) 11470C Eutectoid: y (0.80) = a (0.02) + Fe3C(6.67) 7230C Amongst these the one which takes place completely in the solid state viz. eutectoid transformation is of consi-derable importance to the heat treaters. This is because solid state diffusion is relatively slow, and hence it can be completely inhibited by quenching the steel rapidly from a temperature above 7230C giving an entirely differ-ent transformation product not indicated in the phase diagram. Development of structures ranging from equilib-rium- non equilibrium constituents (or phase) in steel products forms the very basis of heat treatment techn-ology. This lecture presents an over view of the basic principles of the evolution of various microstructures in steel and describes how it could be controlled to achieve a wide range of mechanical/physical properties the steel is known for

Acoustical Impedance of Fog

The acoustical impedance of Porous bodies has been related to their porosity, and flow resistance, and it is possible to evaluate it when their physical properties are known. In the present note the acoustical impedance of air containing water particles in suspension has been calculated in a straight forward manner directly from the hydrodynamical laws. The resulting formula is practically similar to that for solids