Semi-similar solution of an unsteady compressible three-dimensional stagnation point boundary layer flow with massive blowing

A semi-similar solution of an unsteady laminar compressible three-dimensional stagnation point boundary layer flow with massive blowing has been obtained when the free stream velocity varies arbitrarily with time. The resulting partial differential equations governing the flow have been solved numerically using an implicit finite-difference scheme with a quasi-linearization technique in the nodal point region and an implicit finite-difference scheme with a parametric differentiation technique in the saddle point region. The results have been obtained for two particular unsteady free stream velocity distributions: (i) an accelerating stream and (ii) a fluctuating stream. Results show that the skin-friction and heat-transfer parameters respond significantly to the time dependent arbitrary free stream velocity. Velocity and enthalpy profiles approach their free stream values faster as time increases. There is a reverse flow in the y-wise velocity profile, and overshoot in the x-wise velocity and enthalpy profiles in the saddle point region, which increase as injection and wall temperature increase. Location of the dividing streamline increases as injection increases, but as the wall temperature and time increase, it decreases.

Stereochemistry of Peptides Containing 1-AminocyclopentanecarboxylicA cid ( Am5): Solution and Solid-state Conformations of Boc-Acc '-Acc'-NHMe

The conformational analysis of a protected homodipeptide of 1-aminocyclopentanecarboxylic acid (Acc5) has been carried out. 1H-nmr studies establish a -turn conformation for Boc-Acc5-Acc5-NHMe in chloroform and dimethylsulfoxide solutions involving the methylamide NH in an intramolecular hydrogen bond. Supportive evidence for the formation of an intramolecular hydrogen bond is obtained from ir studies. X-ray diffraction studies reveal a type III -turn conformation in the solid state stabilized by a 4 1 hydrogen bond between the Boc CO and methylamide NH groups. The , values for both Acc5 residues are close to those expected for an ideal 310-helical conformation ( ± 60°, ±30°).

Conformations of the amino aterminal tetrapeptide of emerimicins and antiamoebins in solution and in the solid state

The conformations of Boc-l-Phe-(AiB)3-OH (1) and Boc-l-Phe-(Aib)3-OMe (2) which correspond to the amino terminal sequence of the emerimicins and antiamoebins have been studied in solution using 270 MHz 1H n.m.r. In dimethyl sulphoxide solution both peptides show the presence of two strongly solvent shielded Aib NH groups, consistent with a consecutive β-turn conformation, involving the Aib(3) and Aib(4) NH groups in intramolecular 4 → I hydrogen bonds. This folded conformation is maintained for 2 in chloroform solution. Nuclear Overhauser effect studies provide evidence for a Type II Phe-Aib β-turn. An X-ray diffraction study of Boc-(d,l)-Phe-(Aib)3-OH establishes a single type III(III′) β-turn conformation with Aib(2)-Aib(3) as the corner residues. A single intramolecular 4 → I hydrogen bond between Phe(I) CO and Aib(4) NH groups is observed in the crystal. The solution conformation may incorporate a consecutive type II-III′ structure for the Phe(1)-Aib(2)-Aib(3) segment, with the initial type II β-turn being destabilized by intermolecular interactions in the solid state.

Structure and properties of two component hydrogels comprising lithocholic acid and organic amines

We demonstrate the aptitude of supramolecular hydrogel formation using simple bile acid such as lithocholic acid in aqueous solution in the presence of various dimeric or oligomeric amines. By variation of the choice of the amines in such mixtures the gelation properties could be modulated. However, the replacement of lithocholic acid (LCA) by cholic acid or deoxycholic acid resulted in no hydrogel formation. FT-IR studies confirm that the carboxylate and ammonium residues of the two components are involved in the salt (ion-pair) formation. This promotes further assembly of the components reinforced by a continuous hydrogen bonded network leading to gelation. Electron microscopy shows the morphology of the internal organization of gels of two component systems which also depends significantly on the amine part. Variation of the amine component from the simple 1,2-ethanediamine (EDA) to oligomeric amines in such gels of lithocholic acid changes the morphology of the assembly from long one-dimensional nanotubes to three-dimensional complex structures. Single crystal X-ray diffraction analysis with one of the amine-LCA complexes suggested the motif of fiber formation where the amines interact with the carboxylate and hydroxyl moieties through electrostatic forces and hydrogen bonding. From small angle neutron scattering study, it becomes clear that the weak gel from LCA-EDA shows scattering oscillation due to the presence of non-interacting nanotubules while for gels of LCA with oligomeric amines the individual fibers come together to form complex three-dimensional organizations of higher length scale. The rheological properties of this class of two component system provide clear evidence that the flow behavior can be modulated varying the acid-amine ratio.

Cyclic Peptide Disulfides - Solution And Solid-State Conformation Of Boc-Cys-Pro-Aib-Cys-S-S-Bridge-Nhme,A Disulfide-Bridged Peptide Helix

The solution and solid-state conformations of the peptide disulfide Boc-Cys-Pro-Aib-Cys-NHMe have been determined by NMR spectroscopy and X-ray diffraction. The Cys(4) and methylamide NH groups are solvent shielded in CDCI3 and (CD,),SO, suggesting their involvement in intramolecular hydrogen bonding. On the basis of known stereochemical preferences of Pro and Aib residues, a consecutive @-turn structure is favored in solution. X-ray diffraction analysis reveals a highly folded 310 helical conformation for the peptide, with the S-S bridge lying approximately parallel to the helix axis, linking residues 1 and 4. The backbone conformational angles are Cys(1) 4 = -121.1', $ = 65.6"; Pro(2) 4 = -58.9', 4 = -34.0'; Aib(3) 4 = -61.8', $ = -17.9'; Cys(4) 4 = -70.5', $ = -18.6'. Two intramolecular hydrogen bonds are observed between Cys(1) CO--HN Cys(4) and Pro(2) CO--HNMe. The disulfide bond has a right-handed chirality, with a dihedral angle (xss) of 82'.

Self-similar solution of unsteady compressible three-dimensional stagnation-point boundary layers

The self-similar solution of the unsteady laminar compressible boundary-layer flow with variable properties at a three-dimensional stagnation point with mass transfer has been obtained when the free-stream velocity varies inversely as a linear function of time. The resulting ordinary differential equations have been solved numerically using an implicit finite-difference scheme. The results are found to be strongly dependent on the parameter characterizing the unsteadiness in the free-stream velocity. The velocity profiles show some features not encountered in steady flows.

A new algorithm for parallel solution of linear equations

Abstract is not available.

Resonances, scattering theory, and rigged Hilbert spaces

The problem of decaying states and resonances is examined within the framework of scattering theory in a rigged Hilbert space formalism. The stationary free,''in,'' and ''out'' eigenvectors of formal scattering theory, which have a rigorous setting in rigged Hilbert space, are considered to be analytic functions of the energy eigenvalue. The value of these analytic functions at any point of regularity, real or complex, is an eigenvector with eigenvalue equal to the position of the point. The poles of the eigenvector families give origin to other eigenvectors of the Hamiltonian: the singularities of the ''out'' eigenvector family are the same as those of the continued S matrix, so that resonances are seen as eigenvectors of the Hamiltonian with eigenvalue equal to their location in the complex energy plane. Cauchy theorem then provides for expansions in terms of ''complete'' sets of eigenvectors with complex eigenvalues of the Hamiltonian. Applying such expansions to the survival amplitude of a decaying state, one finds that resonances give discrete contributions with purely exponential time behavior; the background is of course present, but explicitly separated. The resolvent of the Hamiltonian, restricted to the nuclear space appearing in the rigged Hilbert space, can be continued across the absolutely continuous spectrum; the singularities of the continuation are the same as those of the ''out'' eigenvectors. The free, ''in'' and ''out'' eigenvectors with complex eigenvalues and those corresponding to resonances can be approximated by physical vectors in the Hilbert space, as plane waves can. The need for having some further physical information in addition to the specification of the total Hamiltonian is apparent in the proposed framework. The formalism is applied to the Lee–Friedrichs model and to the scattering of a spinless particle by a local central potential. Journal of Mathematical Physics is copyrighted by The American Institute of Physics.

Behaviour of methylmethacrylate-acrylonitrile random copolymers in dilute solution

Studies on the dilute solution properties of methylmethacrylate-acrylonitrile random copolymers of three different compositions, 0.236, 0.5 and 0.74 mole fraction (m.f.) of acrylonitrile (AN) designated as MAa, MAb and MAc, respectively, have been made in good solvents and theta solvents. MAa has been studied in benzene (Bz) and ethylacetate (EAc). MAb in acetonitrile (MeCN), dimethyl sulphoxide (DMSO) and a binary solvent mixture of Bz and dimentyl formamide (DMF) in the volume ratio 6.5:1 designated as BM1 and MAc in MeCN, DMSO and Bz + DMF in the volume ratio 1.667:1 designated as BM2. The Mark-Houwink exponent ‘a’ reveals that Bz is a theta solvent for MAa at 20°C. For MAb and MAc, BM1 and BM2, respectively have ‘a’ values of 0.5 at all three temperatures studied (30°, 40° and 50°C). It is not clear whether they represent theta states or preferential adsorption plays a role complicating the behaviour in solution. The values of A2 are very low in MeCN considering that it is a very good solvent for the copolymer, ‘a’ values for MAb and MAc being 0.75 and 0.7, respectively.

Elasticity solution for a long circular sandwich cylindrical shell subjected to axisymmetric load

An elasticity solution has been obtained for a long circular sandwich cylindrical shell subjected to axisymmetric radial ring load using Love's stress function approach. Numerical results are presented for different ratios of modulus of elasticity of the layers. The results obtained from this analysis have been compared with those obtained from sandwich shell theory due to Fulton.

Derivation of the solution of certain singular integral equations

It is shown that the a;P?lication of the Poincare-Bertrand fcm~ulaw hen made in a suitable manner produces the s~lutiano f certain singular integral equations very quickly, thc method of arriving at which, otherwise, is too complicaled. Two singular integral equations are considered. One of these quaiions is with a Cauchy-tyge kcrnel arid the other is an equalion which appears in the a a w guide theory and the theory of dishcations. Adifferent approach i? alw made here to solve the singular integralquation> of the waveguide theor? ind this i ~ v o l v eth~e use of the inversion formula of the Cauchy-type singular integral equahn and dudion to a system of TIilberl problems for two unknowns which can be dwupled wry easily to obi& tbe closed form solutim of the irilegral equatlou at band. The methods of the prescnt paper avoid all the complicaled approaches of solving the singular integral equaticn of the waveguide theory knowr todate.

beta.-Turn conformation of N-acetyl-L-prolylglycyl-L-phenylalanine. Crystal structure and solution studies

Pro-Gly segments in peptides and proteins are prone to adopt the 0-turn conformation. This paper reports experimental data for the presence of this conformation in a linear tripeptide N-acetyl-L-prolylglycyl-L-phenylalanineb oth in the solid state and in solution. X-ray diffraction data on the tripeptide crystal show that it exists in the type I1 0-turn conformation. CD and proton NMR data show that this conformation persists in trifluoroethanol and methanol solutions in equilibrium with the nonhydrogen-bonded structures. Isomerization around the acetyl-prolyl bond is seen to take place in dimethyl sulfoxide solutions of the tripeptide.

Electron-electron scattering and ultrasonic attenuation in potassium

The electron-electron scattering contribution to the ultrasonic attenuation in potassium at low temperatures is evaluated using the Landau Fermi liquid theory. The scattering function is evaluated using the approximation suggested by MacDonald and Geldart. The results are compared with theoretically evaluated electron-phonon scattering contributions. The results show that the electron-electron scattering contribution is of the same order as the electron-phonon scattering contribution in the 2–5 K range. Below 2 K the electron-electron scattering predominates.

X-ray and IR characterisation of Nasicon solid solution, Na1+xZr2SixP3−xO12

X-ray and IR studies on Nasicon solid solutions, Na1+xZr2SixP3−xO12, are carried out as a function of composition x. X-ray diffraction studies show that the unit cell volume increases as x increases and exhibits a maximum at x ≈ 2. On further increase in x the unit cell volume decreases. The infrared absorption peak positions and the splitting of these absorption peaks suggest a distortion of the PO4 and SiO4 tetrahedra. But the distortion is not large enough to change the local symmetry around the phosphorus or silicon ion from Td to C3v.

Electrical transport in the perovskite solid solution LaNi1-xCoxO3

We have studied the resistivity and thermopower of the solid solution LaNi1-xCoxO3 in the temperature range 1.4K-300K. Effect of interaction and localization are seen in the low temperature transport data for x<0.55. A negative anomaly in the thermopower has been observed at low temperature for 0.1