Transverse vibrations of hybrid laminated plates

In this paper, an attempt is made to obtain the free vibration response of hybrid, laminated rectangular and skew plates. The Galerkin technique is employed to obtain an approximate solution of the governing differential equations. It is found that this technique is well suited for the study of such problems. Results are presented in a graphical form for plates with one pair of opposite edges simply supported and the other two edges clamped. The method is quite general and can be applied to any other boundary conditions.

Anisochrony of O-methylene protons of ethyl ester functions and structural factors in the connected chiral entities

(i) Incistrans pairs of cyclic 1,3-dicarboxylic acid ethyl esters thecis-foms exhibit higher O-methylene proton (HA, HB) anisochrony than thetrans-forms; (ii) anisochrony, easily observed in certain decalin-10-carboxylic ethyl esters, ‘disappears’ on one of the rings attaining the possibility of transforming into a ‘twist’ form; (iii) in certain pairs of chiralsecethyl esters and theirtert-methylated analogues anisochrony is higher in the latter, contrary to expectation, while, in certain others, the reverse is observed. Attempted explanations are based on assessments whether H A and H B are or are not in highly different magnetic environments in confomers regarded as preferred. This subsumes the possibility thatXYZC-CO2H A H B Me chiral ethyl acetates differ fromXYZC-CH A H B Me ethanes because intervention by the carboxyl group insulates the prochiral centre and allows anisotropic effects to gain somewhat in importance among mechanisms that discriminate between H A and H B so long as rotamerpopulation inequalities persist. Background information on why rotamer-population inequalities will always persist and on a heuristic that attempts to generalize the effects ofXYZ inXYZC - CU AUB V is provided. Possible effects when connectivity exists between a pair amongX, Y, Z or when specific interactions occur betweenV andX, Y orZ are considered. An interpretation in terms of ‘increasing conformational mobility’ has been suggested for the observed increase in the rate of temperature-dependence of O-methylene anisochrony down a series of chiral ethyl esters.

Crystal Structure, Ultraviolet Spectrum, and Electronic Structure of a Strongly Twisted Push-Pull Ethylene, approaching an Amidinium-Vinylogous Dithioate Zwitterion

The crystal structure of 1,3-di benzyl -2 - (4,4-dimet hyl- 2,5- bist hioxocyclo hexylidene) imidazolidine (2) shows a twist of 80.8(5)' about the inter-ring bond, which has a length of 1.482(6) A. The near orthogonality of the donor and acceptor parts of this formal push-pull ethylene makes the structure approach that of a zwitterion, as evidenced by bond lengths indicating strong electron delocalization. The acceptor part approaches a vinylogous dithioate structure, the donor part an amidinium system. The U.V. spectrum shows an n + R and a R + R transition, at 51 1 and 41 7.5 nm, respectively; according to CNDO/S calculations these are located entirely in the [S-C-C-C-SI- part. Two bands at shorter wavelength are ascribed to transitions from combinations of the lone-pair orbitals on the sulphur atoms to a n* orbital in the [N-C-N] + part; this is facilitated by the near perpendicularity of the two parts of the molecule.

Crystal and molecular structures of alkali- and alkaline-earth-metal complexes of N,N-dimethylformamide

Structures of lithium, sodium, magnesium, and calcium complexes of NJ-dimethylformamide (DMF) have been investigated by X-ray crystallography. Complexes with the formulas LiCl.DMF.1/2H20, NaC104.2DMF, CaC12.2DMF.2H20, and Mg(C104)2.6DMF crystallized in space groups P2]/c, P2/c, Pi, and Ella, respectively, with the following cell dimensions: Li complex, a = 13.022 (7) A, b = 5.978 (4) A, c = 17.028 (10) A, = 105.48 (4)O, Z = 8; Na complex, a = 9.297 (4)A, b = 10.203 (3) A, c = 13.510 (6) A, /3 = 110.08 (4)O, Z = 4; Ca complex, a = 6.293 (4) A, b = 6.944 (2) A, c = 8.853(5) A, a = 110.15 (3)O, /3 = 105.60 (6)", y = 95.34 (5)", Z = 1; Mg complex, a = 20.686 (11) A, b = 10.962 (18) A,c = 14.885 (9) A, /3 = 91.45 (5)O, Z = 4. Lithium is tetrahedrally coordinated while the other three cations are octahedrally coordinated; the observed metal-oxygen distances are within the ranges generally found in oxygen donor complexes of these metals. The lithium and sodium complexes are polymeric, with the amide and the anion forming bridging groups between neighboring cations. The carbonyl distances become longer in the complexes accompanied by a proportionate decrease in the length of the central C-N bond of the amide; the N-C bond of the dimethylamino group also shows some changes in the complexes. The cations do not deviate significantly from the lone-pair direction of the amide carbonyl and remain in the amide plane. Infrared spectra of the complexes reflect the observed changes in the amide bond distances.

Dynamics of dense sheared granular flows. Part 1. Structure and diffusion

Shear flows of inelastic spheres in three dimensions in the Volume fraction range 0.4-0.64 are analysed using event-driven simulations.Particle interactions are considered to be due to instantaneous binary collisions, and the collision model has a normal coefficient of restitution e(n) (negative of the ratio of the post- and pre-collisional relative velocities of the particles along the line joining the centres) and a tangential coefficient of restitution e(t) (negative of the ratio of post- and pre-collisional velocities perpendicular to the line Joining the centres). Here, we have considered both e(t) = +1 and e(t) = e(n) (rough particles) and e(t) =-1 (smooth particles), and the normal coefficient of restitution e(n) was varied in the range 0.6-0.98. Care was taken to avoid inelastic collapse and ensure there are no particle overlaps during the simulation. First, we studied the ordering in the system by examining the icosahedral order parameter Q(6) in three dimensions and the planar order parameter q(6) in the plane perpendicular to the gradient direction. It was found that for shear flows of sufficiently large size, the system Continues to be in the random state, with Q(6) and q(6) close to 0, even for volume fractions between phi = 0.5 and phi = 0.6; in contrast, for a system of elastic particles in the absence of shear, the system orders (crystallizes) at phi = 0.49. This indicates that the shear flow prevents ordering in a system of sufficiently large size. In a shear flow of inelastic particles, the strain rate and the temperature are related through the energy balance equation, and all time scales can be non-dimensionalized by the inverse of the strain rate. Therefore, the dynamics of the system are determined only by the volume fraction and the coefficients of restitution. The variation of the collision frequency with volume fraction and coefficient of estitution was examined. It was found, by plotting the inverse of the collision frequency as a function of volume fraction, that the collision frequency at constant strain rate diverges at a volume fraction phi(ad) (volume fraction for arrested dynamics) which is lower than the random close-packing Volume fraction 0.64 in the absence of shear. The volume fraction phi(ad) decreases as the coefficient of restitution is decreased from e(n) = 1; phi(ad) has a minimum of about 0.585 for coefficient of restitution e(n) in the range 0.6-0.8 for rough particles and is slightly larger for smooth particles. It is found that the dissipation rate and all components of the stress diverge proportional to the collision frequency in the close-packing limit. The qualitative behaviour of the increase in the stress and dissipation rate are well Captured by results derived from kinetic theory, but the quantitative agreement is lacking even if the collision frequency obtained from simulations is used to calculate the pair correlation function used In the theory.

X-ray studies on crystalline complexes involving amino acids. IV. The structure of L-arginine L-ascorbate

L-Arginine ascorbate, C6HIsN40+.C6H706, a 1"1 crystalline complex between the amino acid arginineand the vitamin ascorbic acid, crystallizes in the monoclinic space group P21 with two formula units in a cell of dimensions a = 5.060 (8), b = 9.977 (9), c = 15.330 (13) A, fl = 97.5 (2) °. The structure was solved by the symbolic addition procedure and refined to an R of 0.067 for 1501 photographically observed reflec- tions. The conformation of the arginine molecule in the structure is different from any observed so far. The present structure provides the first description of the ascorbate anion unaffected by the geometrical constraints and disturbances imposed by the requirements of metal coordination. The lactone group and the deprotonated enediol group in the anion are planar and the side chain assumes a conformation which appears to be sterically the most favourable. In the crystals, the arginine molecules and the ascorbate anions aggregate separately into alternating layers. The molecules in the arginine layer are held together by interactions involving a-amino and ~t-carboxylate groups, a situation analogous to that found in proteins. The two layers of unlike molecules are interconnected primarily through the interactions of the side-chain guanidyl group of arginine with the ascorbate ion. These involve a specific ion-pair interaction accompanied by two convergent hydrogen bonds and another pair of nearly parallel hydrogen bonds.

Studies on crystalline complexes involving amino acids. V. The structure of L-serine-L-ascorbic acid

L-Serine-L-ascorbic acid, C3HTNOa. C6HsO6, a 1:1 complex between the amino acid serine and the vitamin ascorbic acid, crystallizes in the orthorhombic space group P2~2~2~ with four formula units in a cell of dimensions a = 5.335(3), b = 8.769(2), c = 25.782 (5) A. The structure was solved by direct methods and refined by full-matrix least squares to an R of 0.036 for 951 observed reflections. Both molecules are neutral in the structure. The conformation of the serine molecule is different from that observed in the crystal structures of L-serine, DL-serine and L-serine monohydrate. The enediol group in the ascorbic acid molecule is planar, whereas significant departures from planarity are observed in the lactone group. The conformation of this molecule is similar to that observed in arginine ascorbate. The unlike molecules aggregate into separate columns in the crystal structure. The columns are held together by hydrogen bonds. Among these, a pair of hydrogen bonds between the enediol group of ascorbic acid and the carboxylate group of serine provides a possible model for a specific interaction between ascorbic acid and a carboxylate ion.

Shape-Dependent Confinement in Ultrasmall Zero-, One-, and Two-Dimensional PbS Nanostructures

Spatial dimensionality affects the degree of confinement when an electron-hole pair is squeezed from one or more dimensions approaching the bulk exciton Bohr radius (alpha(B)) limit. The etectron-hole interaction in zero-dimensional (0D) dots, one-dimensional (1D) rods/wires, and two-dimensional (2D) wells/sheets should be enhanced by the increase in confinement dimensions in the order 0D > 1D > 2D. We report the controlled synthesis of PbS nanomateriats with 0D, 1D, and 2D forms retaining at least one dimension in the strongly confined regime far below alpha(B) (similar to 10 nm for PbS) and provide evidence through varying the exciton-phonon coupling strength that the degree of confinement is systematically weakened by the loss of confinement dimension. Geometry variations show distinguishable far-field optical polarizations, which could find useful applications in polarization-sensitive devices.

Orbital diamagnetism of a charged Brownian particle undergoing a birth-death process

Considers the magnetic response of a charged Brownian particle undergoing a stochastic birth-death process. The latter simulates the electron-hole pair production and recombination in semiconductors. The authors obtain non-zero, orbital diamagnetism which can be large without violating the Van Leeuwen theorem (1921).

Structural Crystallography and Crystal Chemistry

CaH406P-.K +, M r = 206.10, is orthorhombic, space group Pbca (from systematic absences), a = 14.538(4), b = 13.364(5), c = 6.880 (6)A, U = 1383.9 A 3, D x = 2.07 Mg m -a, Z = 8, ~.(Mo Ka) = 0.7107/~, p(MO Ka) = 1.015 mm -1. The final R value is 0.042 for a total of 1397 reflections. The high energy P-O(13) and the enolic C(1)-O(13) bonds are 1.612 and 1.374 A respectively. The enolpyruvate moiety is essentially planar. The orientation of the phosphate with respect to the pyruvate group in PEP.K is distinctly different from that in the PEP-cyclohexylammonium salt, the torsion angle C (2)-C (1)-O(13)- P being -209.1 in the former and -90 ° in the latter. The K + ion binds simultaneously to both the phosphate and carboxyl ends of the same PEP molecule. The ester O(13) is also a binding site for the cation. The K + ion is coplanar with the pyruvate moiety and binds to 0(22) and O(13) almost along their lone-pair directions. The carbonyl 0(22) prefers to bind to the K + ion rather than take part in the formation of hydrogen bonds usually observed in carboxylic acid structures.

Structure and Bonding in N-Methylacetamide Complexes of Alkali and Alkaline Earth Metals

A detailed crystallographic investigation of N-methylacetamide complexes of Li, Na, K, Mg and Ca has been made in view of its importance in the coordination chemistry and biochemistry of alkali and alkaline earth metals. The metal ions bind to the amide oxygen causing an increase in the carbonyl distance and a proportionate decrease in the central C-N bond distance. The decrease in the central C-N distance is accompanied by an increase in the distance of the adjacent C-C bond and a decrease in the adjacent C-N bond distance. The metal ion generally deviates from the direction of the lone pair of the carbonyl oxygen and also from the plane of the peptide, the out-of-plane deviation varying with the ionic potential of the cation. The metal-oxygen distance in alkali and alkaline earth metal complexes of a given coordination number also varies with the ionic potential of the cation, as does the strength of binding of the cations to the amide. The amide molecules are essentially planar in these complexes, as expected from the increased bond order of the central C-N bond. The NH bonds of the amide are generally hydrogen bonded to anions. The structures of the amide complexes are compared with those of other oxygen donor complexes of alkali and alkaline earth metals. The structural study described here also provides a basis for the interpretation of results from spectroscopic and theoretical investigations of the interaction of alkali and alkaline earth metal cations with amides.

A rational synthesis of vibration isolators

The paper deals with a rational approach to the development of general design criteria for non-dissipative vibration isolation systems. The study covers straight-through springmass systems as well as branched ones with dynamic absorbers. Various design options, such as the addition of another spring-mass pair, replacement of an existing system by one with more spring-mass pairs for the same space and material requirements, provision of one or more dynamic absorbers for the desired frequency range, etc., are investigated quantitatively by means of an algebraic algorithm which enables one to write down straightaway the velocity ratio and hence transmissibility of a linear dynamical system in terms of the constituent parameters.

Decoupling in non-linear systems with two degrees of freedom

The problem of decoupling a class of non-linear two degrees of freedom systems is studied. The coupled non-linear differential equations of motion of the system are shown to be equivalent to a pair of uncoupled equations. This equivalence is established through transformation techniques involving the transformation of both the dependent and independent variables. The sufficient conditions on the form of the non-linearity, for the case wherein the transformed equations are linear, are presented. Several particular cases of interest are also illustrated.

Intersoliton forces in weak-coupling quantum field theories

We offer a procedure for evaluating the forces exerted by solitons of weak-coupling field theories on one another. We illustrate the procedure for the kink and the antikink of the two-dimensional φ4 theory. To do this, we construct analytically a static solution of the theory which can be interpreted as a kink and an antikink held a distance R apart. This leads to a definition of the potential energy U(R) for the pair, which is seen to have all the expected features. A corresponding evaluation is also done for U(R) between a soliton and an antisoliton of the sine-Gordon theory. When this U(R) is inserted into a nonrelativistic two-body problem for the pair, it yields a set of bound states and phase shifts. These are found to agree with exact results known for the sine-Gordon field theory in those regions where U(R) is expected to be significant, i.e., when R is large compared to the soliton size. We take this agreement as support that our procedure for defining U(R) yields the correct description of the dynamics of well-separated soliton pairs. An important feature of U(R) is that it seems to give strong intersoliton forces when the coupling constant is small, as distinct from the forces between the ordinary quanta of the theory. We suggest that this is a general feature of a class of theories, and emphasize the possible relevance of this feature to real strongly interacting hadrons.

Use of transverse beam polarization to probe anomalous V V H interactions at a Linear Collider

We investigate use of transverse beam polarization in probing anomalous coupling of a Higgs boson to a pair of vector bosons, at the International Linear Collider (ILC). We consider the most general form of V V H (V = W/Z) vertex consistent with Lorentz invariance and investigate its effects on the process e(+)e(-) -> f (f) over barH, f being a light fermion. Constructing observables with definite C P and naive time reversal ((T) over tilde) transformation properties, we find that transverse beam polarization helps us to improve on the sensitivity of one part of the anomalous Z Z H Coupling that is odd under C P. Even more importantly it provides the possibility of discriminating from each other, two terms in the general Z Z H vertex, both of which are even under C P and (T) over bar. Use of transversebeam polarization when combined with information from unpolarized and linearly polarized beams therefore, allows one to have completely independent probes of all the different parts of a general ZZH vertex.