Asymptotic behaviour and boundedness of linear systems with time varying coefficients

Motivated by developments in spacecraft dynamics, the asymptotic behaviour and boundedness of solution of a special class of time varying systems in which each term appears as the sum of a constant and a time varying part, are analysed in this paper. It is not possible to apply standard textbook results to such systems, which are originally in second order. Some of the existing results are reformulated. Four theorems which explore the relations between the asymptotic behaviour/boundedness of the constant coefficient system, obtained by equating the time varying terms to zero, to the corresponding behaviour of the time varying system, are developed. The results show the behaviour of the two systems to be intimately related, provided the solutions of the constant coefficient system approach zero are bounded for large values of time, and the time varying terms are suitably restrained. Two problems are tackled using these theorems.

Behaviour of Bi-adhesive Joints

The use of relatively low modulus adhesive at the ends of overlap in a bi-adhesive bondline of a bonded joint can reduce the stress concentration significantly and, therefore, potentially lead to higher strength of the joint. This study presents the two-dimensional and three-dimensional nonlinear (geometric and material) finite element analyses of adhesively bonded single lap joints having modulus-graded bondline under monotonic loading conditions. The adhesives were modelled as an elasto-plastic multi-linear material, while the substrates were regarded as both linear elastic and bi-linear elasto-plastic material. The computational simulations have been performed to investigate the bondline behaviour by studying the stress and strain distributions both at the mid-plane as well as at the interface of the bondline. It has been observed that the static strength is higher for joints with bi-adhesive bondlines compared to those with single adhesives in bondline. Higher joint strength has also been observed for optimum bi-adhesive bondline ratio through parametric studies. Effects of load level, and bondline thickness on stress distribution in the bi-adhesive bondline have also been studied. 3D analysis results reveal the existence of complex multi-axial stress/strain state at the ends of the overlap in the bondline which cannot be observed in 2D plane strain analysis. About 1/3rd of the width of the joint from the free edge in the width direction has 3D stress state, especially in the compliant adhesive of the bondline. Magnitudes of longitudinal and lateral stress/strain components are comparable to peel stress/strain components. It has also been analytically shown that the in-plane global stiffness of the joint remains unaffected by modulus gradation of the bondline adhesive. (C) Koninklijke Brill NV, Leiden, 2010.

Influence of propellant choice on MPD arcjet cathode surface current density distribution

The radial current density on an MPD arcjet cathode surface is theoretically investigated for five propellants. It is found that excessive current concentration at the upstream end of the cathode occurs in the case of hydrogen. This undesirable effect is traced to the higher electrical conductivity of hydrogen plasma.

Tool wear monitoring using ant behaviour

In this paper we show the applicability of Ant Colony Optimisation (ACO) techniques for pattern classification problem that arises in tool wear monitoring. In an earlier study, artificial neural networks and genetic programming have been successfully applied to tool wear monitoring problem. ACO is a recent addition to evolutionary computation technique that has gained attention for its ability to extract the underlying data relationships and express them in form of simple rules. Rules are extracted for data classification using training set of data points. These rules are then applied to set of data in the testing/validation set to obtain the classification accuracy. A major attraction in ACO based classification is the possibility of obtaining an expert system like rules that can be directly applied subsequently by the user in his/her application. The classification accuracy obtained in ACO based approach is as good as obtained in other biologically inspired techniques.

Behaviour of autonomous mobile agents using linear cyclic pursuit laws

In this paper, the behaviour of a group of autonomous mobile agents under cyclic pursuit is studied. Cyclic pursuit is a simple distributed control law, in which the agent i pursues agent i + 1 modulo n.. The equations of motion are linear, with no kinematic constraints on motion. Behaviourally, the agents are identical, but may have different controller gains. We generalize existing results in the literature and show that by selecting these gains, the behavior of the agents can be controlled. They can be made to converge at a point or be directed to move in a straight line. The invariance of the point of convergence with the sequence of pursuit is also shown.

Studies on the ageing behaviour of Polyvinylchloride/ammonium perchlorate composite solid propellant

The effects of ageing on the properties of a complete polyvinyl chloride — dibutyl phthalate — ammonium perchlorate solid propellant have been studied by measurements of burning rates, thermal decomposition rates (by thermogravimetry and DTA) and calorimetric values. Ageing leads to loss of HCl by dehydrochlorination and a corresponding increase in heat of combustion.

Asynchronous behaviour in some three-atom linear concerted radical-exchange reactions

A few simple three-atom thermoneutral radical exchange reactions (i.e. A + BC --> AB + C) are examined by ab initio SCF methods. Emphasis is laid on the detailed analysis of density matrices rather than on energetics. Results reveal that the sum of the bond orders of the breaking and forming bonds is not conserved to unity, due to development of free valence on the migrating atom 'B' in the transition state. Bond orders, free valence and spin densities on the atoms are calculated. The present analysis shows that the bond-cleavage process is always more advanced than the bond-formation process in the transition state. Further analysis shows a development of the negative spin density on the migrating atom 'B' in the transition state. The depletion of the alpha-spin density on the radical site "A" in the reactant during the reaction lags behind the growth of the alpha-spin density on the terminal atom "C" of the reactant bond, 'B-C' in the transition state. But all these processes are completed simultaneously at the end of the reaction. Hence, the reactions are asynchronous but kinetically concerted in most cases.

Electrical and Dielectric Behaviour at the Critical Point of Binary Liquids: Acetonitrile + Cyclohexane

The electrical capacitance and resistance of the binary liquid mixture cyclohexane + acetonitrile are measured in the one phase and two phase regions at spot frequencies between 5 kHz and 100 kHz. This sample has a very low gravity affected (∼0.6 mK) region. In one phase region the capacitance data show a sharp, ∼0.7% increase above background within 0.5 degrees of Tc whereas the resistance has a smooth increase of ∼1.5% above background in a (T−Tc) range of 4 degrees. Two phase values of capacitance and resistance from the coexisting phases are used to determine the critical parameters Tc (critical temperature), Rc (resistance at Tc) and Cc (capacitance at Tc). A precise knowledge of these parameters reduces the uncertainty on the critical exponent 0 for C and R. The one phase capacitance data fit to an (1 - α) exponent in a limited temperature range of 0.2 degrees. Resistance data strongly support an (1 - α) exponent over the entire 5 degree range.

Development of Nonsocial Behaviour in the Asiatic Elephant

The elephant calf, a defended follower is completely dependent on adults till the age of 3 months. It begins to explore and attempts to feed at 3 to 6 months, and then becomes partially independent with some feeding on its own. The characteristics of behavior in adults are examined and the development of this pattern in the calf is traced by analyis of duration, transition and clustering of the behavioural elements. Essential activities like suckling, locomotion and lying down for rest appear soon after birth whereas elements of feeding, grooming and play appear only at a later stage. The calf takes the initiative in suckling and its termination, drinking directly by mouth till the age of 6 months. The first element of feeding appears at about a week in attempts to pick up and hold objects in the trunk. Co-ordination of limb, trunk and mouth movement is achieved by about 1 month. The calf is strong enough to pull out plants by 6 months when independent feeding begins. In about a year feeding, drinking and dusting patterns are well developed.

A general thermodynamic framework for understanding the behaviour of absorption chillers

In this article, a general definition of the process average temperature has been developed, and the impact of the various dissipative mechanisms on 1/COP of the chiller evaluated. The present component-by-component black box analysis removes the assumptions regarding the generator outlet temperature(s) and the component effective thermal conductances. Mass transfer resistance is also incorporated into the absorber analysis to arrive at a more realistic upper limit to the cooling capacity. Finally, the theoretical foundation for the absorption chiller T-s diagram is derived. This diagrammatic approach only requires the inlet and outlet conditions of the chiller components and can be employed as a practical tool for system analysis and comparison. (C) 2000 Elsevier Science Ltd and IIR. All rights reserved.

Adsorption behaviour of an oxidised starch onto haematite in the presence of calcium

The adsorption behaviour of an oxidised starch AP as well as that of calcium onto haematite have been studied both individually and together. While the adsorption density of starch AP onto haematite is enhanced in the presence of calcium, the adsorption of calcium onto haematite is not promoted by starch AP. Flocculation tests on haematite ore fines in the presence of starch AP and calcium chloride reveal that the sequence in which calcium and starch are added governs the settling rates and turbidity values. Zeta potential, viscosity and conductivity measurements, and calcium ion binding studies with starch AP indicate calcium-starch interactions. Possible mechanisms involved in such interactions with respect to haematite flocculation have been discussed.

Creep Behaviour of AE42 Magnesium Alloy and Its Composites Using Impression Creep Technique

The creep behaviour of a creep-resistant AE42 magnesium alloy has been examined in the temperature range of 150 to 240 degrees C at the stress levels ranging from 40 to 120 MPa using impression creep technique. A normal creep behaviour, i.e., strain rate decreasing with strain and then reaching a steady state, is observed at all the temperatures and stresses employed The stress exponent varies from 5.1 to 5.7 and the apparent activation energy varies from 130 to 140 kJ/mol, which suggests the high temperature climb of dislocation controlled by lattice self-diffusion being the dominant creep mechanism in the stress and temperature range employed The creep behaviour of the AE42 alloy has also been compared with its composites reinforced with Saffil short fibres and SiC particles in four combinations. All the composites exhibited a lower creep rate than the monolithic AE42 alloy tested at the same temperature and stress levels and the decrease in creep rate was greater in the longitudinal direction than in the transverse direction, as expected. All the hybrid composites, i.e., the composites reinforced with a combination of Saffil short fibres and SiC particles, exhibited creep rates comparable to the composite reinforced with 20% Saffil short fibres alone at all the temperature and stress levels employed, which is beneficial from the commercial point of view.

HNbWO6 and HTaWO6: Novel layered oxides related to the rutile structure. Synthesis and investigation of ion-exchange and intercalation behaviour

New protonated layered oxides, HMWO6·1.5H2O (M=Nb or Ta), have been synthesized by topotactic exchange of lithium in trirutile LiMWO6 with protons by treatment with dilute HNO3. The tetragonal cell constants are a=4.71 (2) and c=25.70 (8)Å for HNbWO6·1.5H2O and a=4.70 (2) and c=25.75 (9) Å for HTaWO6·1.5H2O. Partially hydrated compounds, HMWO6·0.5H2O and anhydrous compounds, HMWO6 retain the layered structure. The structure of these oxides consists of MWO6 sheets built up of M/W-oxygen octahedra with rutile type corner- and edge-sharing. Interlayer protons in HMWO6 are exchanged with Li+, Na+, K+ and Tl+. HMWO6 exhibit Brønsted acidity intercalating n-alkylamines and pyridine.

Dielectric behaviour and ferroelectricity in alums

Introduction The alum family of double salts with the general formula M1+M3+(RO4)2.12H2O where M1+ is a monovalent ion (M1+ = K, Rb, Cs, Tl, NH4, CH3NH3, NH3OH3 NH3NH2, etc.) and M3+ is a trivalent metal such as Al, Fe, Cr, V, In, Ga, etc. and R is S or Se, form an isomorphous series and their general features indicate a common cubic space group Pa3. Lipson1 showed subsequently that there exist three different structure types agr, β and γ and the structure of a particular alum is dependent on the radius of the monovalent atom. The agr structure is typical of medium sized ions, the β of the larger ones and the γ of the small Na atom.2 Ferroelectricity has been reported only in alums containing NH4, CH3NH3, NH3NH3 and NH3OH. Their hindered rotations as well as the influence of sulphate group disorder on the dielectric behaviour of alums is still not clear.3 No study of the temperature dependence of the low frequency dielectric constant of some of the alums, particularly those of Cs, Rb and Tl, have been made so The present investigation was undertaken to correlate their dielectric behaviour with their composition and structural differences. Under the same experimental conditions, methyl ammonium and ammonium alums also were studied and compared with the known data.