Path integral description of polymers using fractional Brownian walks

The statistical properties of fractional Brownian walks are used to construct a path integral representation of the conformations of polymers with different degrees of bond correlation. We specifically derive an expression for the distribution function of the chains’ end‐to‐end distance, and evaluate it by several independent methods, including direct evaluation of the discrete limit of the path integral, decomposition into normal modes, and solution of a partial differential equation. The distribution function is found to be Gaussian in the spatial coordinates of the monomer positions, as in the random walk description of the chain, but the contour variables, which specify the location of the monomer along the chain backbone, now depend on an index h, the degree of correlation of the fractional Brownian walk. The special case of h=1/2 corresponds to the random walk. In constructing the normal mode picture of the chain, we conjecture the existence of a theorem regarding the zeros of the Bessel function.

Rectilinear Path Following in 3D Space

This paper addresses the problem of determining an optimal (shortest) path in three dimensional space for a constant speed and turn-rate constrained aerial vehicle, that would enable the vehicle to converge to a rectilinear path, starting from any arbitrary initial position and orientation. Based on 3D geometry, we propose an optimal and also a suboptimal path planning approach. Unlike the existing numerical methods which are computationally intensive, this optimal geometrical method generates an optimal solution in lesser time. The suboptimal solution approach is comparatively more efficient and gives a solution that is very close to the optimal one. Due to its simplicity and low computational requirements this approach can be implemented on an aerial vehicle with constrained turn radius to reach a straight line with a prescribed orientation as required in several applications. But, if the distance between the initial point and the straight line to be followed along the vertical axis is high, then the generated path may not be flyable for an aerial vehicle with limited range of flight path angle and we resort to a numerical method for obtaining the optimal solution. The numerical method used here for simulation is based on multiple shooting and is found to be comparatively more efficient than other methods for solving such two point boundary value problem.

Diffusion path during internal displacement reactions in multi-component oxides: Reaction between Fe and (Co,Mg)TiO3 solid solution at 1273 K

The reaction between Fe foil and a disc of ilmenite solid solution (Co-0.48 Ni-0.52) TiO3 was studied at 1273 K. At the metal/oxide interface, the displacement reaction, Fe + (Co,Mg)TiO3 = Co + (Fe,Mg)TiO3 occurs, resulting in an ilmenite solid solution containing three divalent cations. Ferrous ions diffuse into the oxide solid solution and cause the precipitation of Co-Fe alloy as discrete particles inside the oxide matrix. The morphology of the product layer was characterized by SEM. Only two phases, alloy and ilmenite, were detected in the reaction zone. This suggests that the local flux condition imposed by ilmenite stoichiometry (Co + Fe + Mg):Ti = 1:1] was satisfied during the reactive diffusion: (J(Co) + J(Fe) + J(Mg)) = J(Ti). The composition of the alloy and the oxide was determined using EPMA as a function of distance in the direction of diffusion. Although Mg does not participate in the displacement reaction, its composition in the ilmenite phase was found to be position dependent inside the reaction zone. The up-hill diffusion of inert Mg is caused by the development of chemical potential gradients as a result of displacement reaction. The evolution of composition gradients inside the reaction zone and the diffusion path in a ternary composition diagram of the system CoTiO3-FeTiO3-MgTiO3 are discussed. (C) 2010 Elsevier B.V. All rights reserved.

Synthesis of path generating flexible-link mechanisms

Flexible-link mechanisms are those linkage mechanisms (or structures) which are capable of motion by virtue of elastic deformation of one or more;links. In such mechanisms a single flexible link; can replace several rigid links and joints resulting in fewer links, fewer pin joints, reduced overall weight and reduced mechanical error. In spite of such clear advantages, contributions toward flexible-link mechanisms remain very scarce. The area of flexible-link mechanisms offers much scope for further exploration. This paper attempts to show the potential of flexible-link mechanisms in accomplishing a kinematic task like path generation. Synthesis of a four-bar mechanism with a flexible rocker for circular and straight line path generation is carried out. Displacement analysis of the structure is carried out using finite element method (FEM) and synthesis is formulated and solved as an optimization problem. Several numerical examples are presented for illustration. Based on the results obtained with these examples, the flexible-link mechanism considered shows good promise for-path generation.

Lasing in active, sub-mean-free path-sized systems with dense, random, weak scatterers

We report enhanced emission and gain narrowing in Rhodamine 590 perchlorate dye in an aqueous suspension of polystyrene microspheres. A systematic experimental study of the threshold condition for and the gain narrowing of the stimulated emission over a wide range of dye concentrations and scatterer number densities showed several interesting features, even though the transport mean free path far exceeded the system size. The conventional diffusive-reactive approximation to radiative transfer in an inhomogeneously illuminated random amplifying medium, which is valid for a transport mean-free path much smaller than the system size, is clearly inapplicable here. We propose a new probabilistic approach for the present case of dense, random, weak scatterers involving the otherwise rare and ignorable sub-mean-free-path scatterings, now made effective by the high gain in the medium, which is consistent: with experimentally observed features. (C) 1997 Optical Society of America.

Data rectification and detection of trend shifts in jet engine path measurements using median filters and fuzzy logic

Filtering methods are explored for removing noise from data while preserving sharp edges that many indicate a trend shift in gas turbine measurements. Linear filters are found to be have problems with removing noise while preserving features in the signal. The nonlinear hybrid median filter is found to accurately reproduce the root signal from noisy data. Simulated faulty data and fault-free gas path measurement data are passed through median filters and health residuals for the data set are created. The health residual is a scalar norm of the gas path measurement deltas and is used to partition the faulty engine from the healthy engine using fuzzy sets. The fuzzy detection system is developed and tested with noisy data and with filtered data. It is found from tests with simulated fault-free and faulty data that fuzzy trend shift detection based on filtered data is very accurate with no false alarms and negligible missed alarms.

Dynamic path profile aided recompilation in a JAVA just-in-time compiler

Just-in-Time (JIT) compilers for Java can be augmented by making use of runtime profile information to produce better quality code and hence achieve higher performance. In a JIT compilation environment, the profile information obtained can be readily exploited in the same run to aid recompilation and optimization of frequently executed (hot) methods. This paper discusses a low overhead path profiling scheme for dynamically profiling AT produced native code. The profile information is used in recompilation during a subsequent invocation of the hot method. During recompilation tree regions along the hot paths are enlarged and instruction scheduling at the superblock level is performed. We have used the open source LaTTe AT compiler framework for our implementation. Our results on a SPARC platform for SPEC JVM98 benchmarks indicate that (i) there is a significant reduction in the number of tree regions along the hot paths, and (ii) profile aided recompilation in LaTTe achieves performance comparable to that of adaptive LaTTe in spite of retranslation and profiling overheads.

Least path criterion (LPC) for unique indexing in a two-dimensional decagonal quasilattice

The least path criterion or least path length in the context of redundant basis vector systems is discussed and a mathematical proof is presented of the uniqueness of indices obtained by applying the least path criterion. Though the method has greater generality, this paper concentrates on the two-dimensional decagonal lattice. The order of redundancy is also discussed; this will help eventually to correlate with other redundant but desirable indexing sets.

Effect of strain path change on the evolution of texture and microstructure during rolling of copper and nickel

The effect of strain path change during rolling has been investigated for copper and nickel using X-ray diffraction and electron back scatter diffraction as well as crystal plasticity simulations. Four different strain paths namely: (i) unidirectional rolling; (ii) reverse rolling; (iii) two-step cross rolling and (iv) multi-step cross rolling were employed to decipher the effect of strain path change on the evolution of deformation texture and microstructure. The cross rolled samples showed weaker texture with a prominent Bs {1 1 0}< 1 1 2 > and P(B(ND)) {1 1 0}< 1 1 1 > component in contrast to the unidirectional and reverse rolled samples where strong S {1 2 3}< 6 3 4 > and Cu {1 1 2}< 1 1 1 > components were formed. This was more pronounced for copper samples compared to nickel. The cross rolled samples were characterized by lower anisotropy and Taylor factor as well as less variation in Lankford parameter. Viscoplastic self-consistent simulations indicated that slip activity on higher number of octahedral slip systems can explain the weaker texture as well as reduced anisotropy in the cross rolled samples. (C) 2011 Elsevier B.V. All rights reserved.