Local texture and microstructure in cube-oriented nickel single crystal deformed by equal channel angular extrusion

Local texture and microstructure was investigated to study the deformation mechanisms during equal channel angular extrusion of a high purity nickel single crystal of initial cube orientation. A detailed texture and microstructure analysis by various diffraction techniques revealed the complexity of the deformation patterns in different locations of the billet. A modeling approach, taking into account slip system activity, was used to interpret the development of this heterogeneous deformation.

Global, Local and Vector-Valued Tb Theorems on Non-Homogeneous Metric Spaces

Various Tb theorems play a key role in the modern harmonic analysis. They provide characterizations for the boundedness of Calderón-Zygmund type singular integral operators. The general philosophy is that to conclude the boundedness of an operator T on some function space, one needs only to test it on some suitable function b. The main object of this dissertation is to prove very general Tb theorems. The dissertation consists of four research articles and an introductory part. The framework is general with respect to the domain (a metric space), the measure (an upper doubling measure) and the range (a UMD Banach space). Moreover, the used testing conditions are weak. In the first article a (global) Tb theorem on non-homogeneous metric spaces is proved. One of the main technical components is the construction of a randomization procedure for the metric dyadic cubes. The difficulty lies in the fact that metric spaces do not, in general, have a translation group. Also, the measures considered are more general than in the existing literature. This generality is genuinely important for some applications, including the result of Volberg and Wick concerning the characterization of measures for which the analytic Besov-Sobolev space embeds continuously into the space of square integrable functions. In the second article a vector-valued extension of the main result of the first article is considered. This theorem is a new contribution to the vector-valued literature, since previously such general domains and measures were not allowed. The third article deals with local Tb theorems both in the homogeneous and non-homogeneous situations. A modified version of the general non-homogeneous proof technique of Nazarov, Treil and Volberg is extended to cover the case of upper doubling measures. This technique is also used in the homogeneous setting to prove local Tb theorems with weak testing conditions introduced by Auscher, Hofmann, Muscalu, Tao and Thiele. This gives a completely new and direct proof of such results utilizing the full force of non-homogeneous analysis. The final article has to do with sharp weighted theory for maximal truncations of Calderón-Zygmund operators. This includes a reduction to certain Sawyer-type testing conditions, which are in the spirit of Tb theorems and thus of the dissertation. The article extends the sharp bounds previously known only for untruncated operators, and also proves sharp weak type results, which are new even for untruncated operators. New techniques are introduced to overcome the difficulties introduced by the non-linearity of maximal truncations.

A note on "effects of couple stresses on the blood flow through an artery with mild stenosis"

Some errors have been observed in the analytical expression for the resistance to flow (lambda R), and in the computation of shear stress distribution (tau R) in the analysis of Prawal Sinha and Chandan Singh (1). These errors have been rectified in the present analysis. Also, better values have been suggested for the couple stress parameter alpha for getting better results for lambda R and tau R.

Local variability and base sequence effects in DNA crystal structures.

The importance and usefulness of local doublet parameters in understanding sequence dependent effects has been described for A- and B-DNA oligonucleotide crystal structures. Each of the two sets of local parameters described by us in the NUPARM algorithm, namely the local doublet parameters, calculated with reference to the mean z-axis, and the local helical parameters, calculated with reference to the local helix axis, is sufficient to describe the oligonucleotide structures, with the local helical parameters giving a slightly magnified picture of the variations in the structures. The values of local doublet parameters calculated by NUPARM algorithm are similar to those calculated by NEWHELIX90 program, only if the oligonucleotide fragment is not too distorted. The mean values obtained using all the available data for B-DNA crystals are not significantly different from those obtained when a limited data set is used, consisting only of structures with a data resolution of better than 2.4 A and without any bound drug molecule. Thus the variation observed in the oligonucleotide crystals appears to be independent of the quality of their crystallinity. No strong correlation is seen between any pair of local doublet parameters but the local helical parameters are interrelated by geometric relationships. An interesting feature that emerges from this analysis is that the local rise along the z-axis is highly correlated with the difference in the buckle values of the two basepairs in the doublet, as suggested earlier for the dodecamer structures (Bansal and Bhattacharyya, in Structure & Methods: DNA & RNA, Vol. 3 (Eds., R.H. Sarma and M.H. Sarma), pp. 139-153 (1990)). In fact the local rise values become almost constant for both A- and B-forms, if a correction is applied for the buckling of the basepairs. In B-DNA the AA, AT, TA and GA basepair sequences generally have a smaller local rise (3.25 A) compared to the other sequences (3.4 A) and this seems to be an intrinsic feature of basepair stacking interaction and not related to any other local doublet parameter. The roll angles in B-DNA oligonucleotides have small values (less than +/- 8 degrees), while mean local twist varies from 24 degrees to 45 degrees. The CA/TG doublet sequences show two types of preferred geometries, one with positive roll, small positive slide and reduced twist and another with negative roll, large positive slide and increased twist.(ABSTRACT TRUNCATED AT 400 WORDS)

Conformation of substituted polyacetylenes in solution : relationship between electronic properties and local order

A study of the chain conformation in solutions of polyphenylacetylene and poly(2-octyne) has been performed. The two polymers differ in many ways : polyphenylacetylene gives a red solution while poly(2-octyne) is transparent and, a marked difference on the chain rigidity is observed : the statistical length are 45 Å and 135 Å respectively. From the study of these two systems, one deduces that curvature fluctuations play a minor role on the π electrons localization, and that the torsion between monomer units is the pertinent parameter to understand the chain conformation and the π electrons localization.

Dynamic growth of tensile cracks by ductile and brittle fracture mechanisms in a viscoplastic material

In this paper, a finite element analysis of steady-state dynamic crack growth under Mode I, plane strain, small-scale yielding conditions is performed in a rate dependent plastic material characterized by the over-stress model. The main objective of the paper is to obtain theoretically the dependence of dynamic fracture toughness on crack speed. Crack propagation due to a ductile (micro-void) mechanism or a brittle (cleavage) mechanism, as well as transition from one mode to another are considered. The conversion from ductile to brittle has been observed experimentally but has received very little attention using analytical methods. Local fracture criteria based on strains and stresses are used to describe ductile and brittle fracture mechanisms. The results obtained in this paper are in general agreement with micro-structural observations of mode conversion during fracture initiation. Finally, the particular roles played by material rate sensitivity and inertia are examined in some detail.

Finite element estimation of elastic interlaminar stresses in laminates

Low interlaminar strength and the consequent possibility of interlaminar failures in composite laminates demand an examination of interlaminar stresses and/or strains to ensure their satisfactory performance. As a first approximation, these stresses can be obtained from thickness-wise integration of ply equilibrium equations using in-plane stresses from the classical laminated plate theory. Implementation of this approach in the finite element form requires evaluation of third and fourth order derivatives of the displacement functions in an element. Hence, a high precision element developed by Jayachandrabose and Kirkhope (1985) is used here and the required derivatives are obtained in two ways. (i) from direct differentiation of element shape functions; and (ii) by adapting a finite difference technique applied to the nodal strains and curvatures obtained from the finite element analysis. Numerical results obtained for a three-layered symmetric and a two-layered asymmetric laminate show that the second scheme is quite effective compared to the first scheme particularly for the case of asymmetric laminates.

Identification of Local Conformational Similarity in Structurally Variable Regions of Homologous Proteins Using Protein Blocks

Structure comparison tools can be used to align related protein structures to identify structurally conserved and variable regions and to infer functional and evolutionary relationships. While the conserved regions often superimpose well, the variable regions appear non superimposable. Differences in homologous protein structures are thought to be due to evolutionary plasticity to accommodate diverged sequences during evolution. One of the kinds of differences between 3-D structures of homologous proteins is rigid body displacement. A glaring example is not well superimposed equivalent regions of homologous proteins corresponding to a-helical conformation with different spatial orientations. In a rigid body superimposition, these regions would appear variable although they may contain local similarity. Also, due to high spatial deviation in the variable region, one-to-one correspondence at the residue level cannot be determined accurately. Another kind of difference is conformational variability and the most common example is topologically equivalent loops of two homologues but with different conformations. In the current study, we present a refined view of the ``structurally variable'' regions which may contain local similarity obscured in global alignment of homologous protein structures. As structural alphabet is able to describe local structures of proteins precisely through Protein Blocks approach, conformational similarity has been identified in a substantial number of `variable' regions in a large data set of protein structural alignments; optimal residue-residue equivalences could be achieved on the basis of Protein Blocks which led to improved local alignments. Also, through an example, we have demonstrated how the additional information on local backbone structures through protein blocks can aid in comparative modeling of a loop region. In addition, understanding on sequence-structure relationships can be enhanced through our approach. This has been illustrated through examples where the equivalent regions in homologous protein structures share sequence similarity to varied extent but do not preserve local structure.

Anomalous X-ray scattering study of local structures in the superionic conducting class (CuI)(0.3)(Cu2O)(0.35)(MoO3)(0.35)

The anomalous X-ray scattering (AXS) method using Cu and Mo K absorption edges has been employed for obtaining the local structural information of superionic conducting glass having the composition (CuI)(0.3)(Cu2O)(0.35)(MoO3)(0.35). The possible atomic arrangements in near-neighbor region of this glass were estimated by coupling the results with the least-squares analysis so as to reproduce two differential intensity profiles for Cu and Mo as well as the ordinary scattering profile. The coordination number of oxygen around Mo is found to be 6.1 at the distance of 0.187 nm. This implies that the MoO6 octahedral unit is a more probable structural entity in the glass rather than MoO4 tetrahedra which has been proposed based on infrared spectroscopy. The pre-peak shoulder observed at about 10 nm(-1) may be attributed to density fluctuation originating from the MoO6 octahedral units connected with the corner sharing linkage, in which the correlation length is about 0.8 nm. The value of the coordination number of I- around Cu+ is estimated as 4.3 at 0.261 nm, suggesting an arrangement similar to that in molten CuI.

Local polynomial convexity of the union of two totally-real surfaces at their intersection

We consider the following question: Let S (1) and S (2) be two smooth, totally-real surfaces in C-2 that contain the origin. If the union of their tangent planes is locally polynomially convex at the origin, then is S-1 boolean OR S-2 locally polynomially convex at the origin? If T (0) S (1) a (c) T (0) S (2) = {0}, then it is a folk result that the answer is yes. We discuss an obstruction to the presumed proof, and provide a different approach. When dim(R)(T0S1 boolean AND T0S2) = 1, we present a geometric condition under which no consistent answer to the above question exists. We then discuss conditions under which we can expect local polynomial convexity.

Sensitivity Enhancement in Solid-State Separated Local Field NMR Experiments by the Use of Adiabatic Cross-Polarization

Measurement of dipolar couplings using separated local field (SLF) NMR experiment is a powerful tool for structural and dynamics studies of oriented molecules such as liquid crystals and membrane proteins in aligned lipid bilayers. Enhancing the sensitivity of such SLF techniques is of significant importance in present-day solid-state NMR methodology. The present study considers the use of adiabatic cross-polarization for this purpose, which is applied for the first time to one of the well-known SLF techniques, namely, polarization inversion spin exchange at the magic angle (PISEMA). The experiments have been carried out on a single crystal of a model peptide, and a dramatic enhancement in signal-to-noise up to 90% has been demonstrated.