Longitudinal and transverse waves in anisotropic elastic materials

Summary It is shown that a necessary and sufficient condition for a longitudinal wave to propagate in the direction n in an anisotropic elastic material is that the elastic stiffness C ₁₁ (n) is a stationary value (maximum, minimum or saddle point) at n. Explicit expressions of all n and the corresponding elastic stiffness C ₁₁ (n) for which a longitudinal wave can propagate are presented for orthotropic, tetragonal, trigonal, hexagonal and cubic materials. As to longitudinal waves in triclinic and monoclinic materials, only few explicit expressions are possible. We also present necessary and sufficient conditions for a transverse wave to propagate in the direction n. As an illustration, explicit expressions of all n, the polarization vector a and the wave speed c for which a transverse wave can propagate in cubic and hexagonal materials are given. The search for n in hexagonal materials confirms the known fact that a transverse wave can propagate in any direction. A longitudinal wave is necessarily accompanied by two transverse waves. However, a transverse wave can propagate without being accompanied by a longitudinal wave.     

Sensor Network Localization,Euclidean Distance Matrix completions,and graph realization

We study Semidefinite Programming, SDP, relaxations for Sensor Network Localization, SNL, with anchors and with noisy distance information. The main point of the paper is to view SNL as a (nearest) Euclidean Distance Matrix, EDM, completion problem that does not distinguish between the anchors and the sensors. We show that there are advantages for using the well studied EDM model. In fact, the set of anchors simply corresponds to a given fixed clique for the graph of the EDM problem.     

On the algebraic characterization of a Mueller matrix in polarization optics. II. Necessary and sufficient conditions for Jones-derived Mueller matrices

Abstract

We show that every Mueller matrix, that is a real 4 × 4 matrix M which transforms Stokes vectors into Stokes vectors, may be factored as M = L ₂ KL ₁ where L ₁ and L ₂ are orthochronous proper Lorentz matrices and K is a canonical Mueller matrix having only two different forms, namely a diagonal form for type-I Mueller matrices and a non-diagonal form (with only one non-zero off-diagonal element) for type-II Mueller matrices. Using the general forms of Mueller matrices so derived, we then obtain the necessary and sufficient conditions for a Mueller matrix M to be Jones derived. These conditions for Jones derivability, unlike the Cloude conditions which are expressed in terms of the eigenvalues of the Hermitian coherency matrix T associated with M, characterize a Jones-derived matrix M through the G eigenvalues and G eigenvectors of the real symmetric N matrix N = [Mtilde]GM associated with M. Appending the passivity conditions for a Mueller matrix onto these Jones-derivability conditions, we then arrive at an algebraic identification of the physically important class of passive Jones-derived Mueller matrices.     

Inhomogeneous deformation of crystalline skeleton of syndiotactic polypropylene under uniaxial stretching

Structure changes of syndiotactic polypropylene (sPP) under uniaxial stretching are studied with the combination of micro-tensile tester and in situ wide angle X-ray diffraction (WAXD) measurement. Lamellae stacked “vertically” and “parallel” to the stretching direction (defined as “V” and “P” part) are separated on the basis of two-dimensional WAXD patterns. For all samples with different lamellar thickness, two critical points named as b ₁ and b ₂ were found in the stress–strain curves, while b ₁ and b ₂ points are the onsets of the rotation for the lamellae of “V” part and “P” part, respectively. The corresponding true stress and true strain for b ₂ point are bigger than that of b ₁ , demonstrating that for samples with initial isotropic lamellar orientation, inhomogeneous deformation of crystalline skeleton induced by uniaxial stretching is universal. And after b ₁ point, “stress-induced melting” always occurs simultaneously with lamellar slips. Furthermore, the relationship between lamellar thickness and the true stress for b ₁ and b ₂ point was also studied, illustrating a linear correlation between ln σ and 1/l (σ is the corresponding true stress, l is the lamellar thickness), consistent with Young’s model. However, the critical true strains for these two points did not change with the varying thickness.     

Gelation theory for solutions of polymers with loci of strong interaction

This paper presents a statistical mechanical analysis of gelation in certain solutions ofA/B copolymers. Repeat unitsA, the major units, must constitute about 90 mole% or more of the copolymer, and are compatible with the solvent. Repeat unitsB, the minor units, must be totally incompatible with the solvent and represent loci of strong interaction between the macromolecular chains. If these interactions are sufficiently strong they can lead to gelation of the mixture. The following simplifications of the model afford results that can be expressed in simple, closed form: (1) TheB units are uniformly distributed along the chain backbone. (2) Polymer concentration must be greater then that for chain overlap. (3)B–B interactions lead to dimerization ofB units only. Examples include: (1) Any aqueous polymer solution where theA repeat units are hydrophilic and theB repeat units are hydrophobic;B–B interactions are thus by hydrophobic bonding. (2) Neutralized acrylic acid/acrylamide copolymers where theB are acrylamide repeat units which associate by hydrogen bonds. (3) Ionomer solutions whereB–B bonding is by dipole-dipole interaction. The results show that there is a critical copolymer concentration for gel formation, C _c . It turns out that C _c decreases withB content for low dimerization energies and increases withB content for higher dimerization energies. At intermediate dimerization energies, C _c is insensitive to theB content. The two extreme regimes of behavior are similar to contradictory predictions of previously published theories. Received: 18 September 2000 / Reviewed and accepted: 20 September 2000     

Symmetric and non-symmetric periodic orbits for the digital filter map

We exhibit instances of non-symmetric periodic orbits for the digital filter map, resolving a question posed in the literature as to whether such orbits can exist. This piecewise irrational rotation, depending on a parameter a = 2cos θ, is an isometry of [?1, 1) × [?1, 1) and reflections in the two diagonals are time-reversing symmetries for the map. Symmetric orbits are plentiful and have been much investigated. Each periodic orbit is paired with a symbolic string, from the alphabet {?, 0, +}, arising under iteration of the map because of the presence of a line of discontinuity. We prove the existence of an infinite family of non-symmetric orbits where the period N starts at 29 and increases in steps of 5; they correspond to the strings (+00)⁵(+?)² 0 ^N?19. We describe several computer algorithms to find non-symmetric periodic orbits and their symbolic strings and list non-symmetric strings both for a = 0.5, and for N ≤ 100 across the parameter range. Our evidence suggests that non-symmetric orbits, though not plentiful, are characteristic of the dynamics of the map for all parameter values.     

Optimal bandwidth selection for multivariate kernel deconvolution density estimation

Assume we have i.i.d. replications from the mismeasured random vector Y=X+ε, where X and ε are mutually independent. We consider a data-driven bandwidth, based on a cross-validation ideas, for multivariate kernel deconvolution estimator of the density of X. The proposed data-driven bandwidth selection method is shown to be asymptotically optimal. As a by-product of the proof of this result, we show that the average squared error, the integrated squared error, and the mean integrated squared error are asymptotically equivalent error measures.      

Multi-Gaussian Ultrasonic Beam Modeling for Multiple Curved Interfaces—an ABCD Matrix Approach

ABSTRACT

A multi-Gaussian beam model uses a superposition of Gaussian beams to simulate the waves radiated from an ultrasonic transducer. We show that propagation and reflection/transmission laws for Gaussian beams in fluids and elastic solids can be written in the form of A , B , C , D matrices that are analogous to the A, B, C, D scalars used in Gaussian optics. This representation leads to simple expressions for a Gaussian beam even after that beam has been transmitted or reflected at multiple curved interfaces and produces a highly modular multi-Gaussian beam model that is also computationally very efficient. Some examples of the use of this model for both planar and curved interfaces are given.     

Eigenvalues of damped structures: Vectoriteration in the original space of DOF

The equations of motion in structural dynamics as well as the corresponding eigenvalue problem are governed by 3 matrices for mass, damping and stiffness of order n which equals the number of degrees of freedom. High-performance eigenvalue-solvers are developed for only pairs A, B of matrices. Nevertheless, to benefit from these solvers, the original eigenvalue problem (λ² M+λD+K)x=0 is transformed into a linear eigenvalue representation with only two hypermatrices of double order 2n. Consequently the total numerical effort depends on this order 2n. This paper presents a vectoriteration process which actually works in the original space of order n and which needs no special actions like simultaneous iteration if complex conjugate eigenvalues λ, λˉ with identical norm have to be calculated. The theoretical foundation of this process still goes back to the pair of hypermatrices.     

Stability and electronic properties of armchair boron nitride/carbon nanotubes

In this work are studied the electronic and structural properties of armchair boron nitride/carbon nanotubes using first principles calculations. The density functional within the generalized gradient approximation (HSEh1PBE-GGA) is used. For each composition, different bonding schemes for the construction of the hybrid systems were employed. Among them, structural stability with neutral charge was determined for the following compositions: T1: B₄₀N₃₅C₇₅H₂₀, T2: B₃₅N₄₀C₇₅H₂₀, T3: B₃₇N₃₈C₇₅H₂₀, T4 : B₃₇N₃₇C₇₆H₂₀, and T7: B₃₅N₃₅C₈₀H₂₀. All these hybrid nanotubes have high polarity; the T3, T4 and T7 are semiconductors: whereas T1 and T2 are conductor in character. The formers also have magnetic behavior. These properties together with a low-chemical potential suggest applications as nano-vehicle for drug delivery. These mixed nanotubes also have potential applications in the electronic devices based on the small work function.     

Hydrothermal syntheses, structures and magnetic properties of coordination frameworks of divalent transition metals

The hydrothermal syntheses, single-crystal X-ray structures and magnetic properties of [Co(C₄O₄)(H₂O)₂] (1), [Co₃(OH)₂(C₄O₄)₂] · 3H₂O (2) and [Fe(OH)₂(C₄O₄)] (3) are described. Pale yellow cubes of 1 and brown red crystals of 2 were obtained from the reaction of Co(OH)₂ and squaric acid at 200 °C. Brown needle of 3 were obtained similarly from Fe(SO₄) · 7H₂O, squaric acid and NaOH. 1 consists of a cubic sodalite arrangement with empty cavities where the Co atoms are connected by μ₄-squarate and two trans-water molecules each, while 2 and 3 contain metal-hydroxide double-chains of edge-sharing octahedral, brucite-type for 2 and goethite for 3, connected by μ₆-squarate. 2 contains water molecules in the channels which can be removed and re-inserted repeatedly without loss of crystallinity. All three compounds possess 3D frameworks made up of coordination and hydrogen bonds. 1 behaves as a paramagnet while 2 and 3 are antiferromagnets and 2 transforms to a ferromagnet reversibly upon dehydration and rehydration. The structures of two one-dimensional polymers employing 2,5-pyridinedicarboxylate, [Co₂(H₂O)₆(2,5-pydc)₂] · 2H₂O (4) and Cu(2,5-pydc)₂ (5), are also reported.     

Process monitoring research with various estimator-based MEWMA control charts

Multivariate exponentially weighted moving average (MEWMA) control chart with five different estimators as population covariance matrix is rarely applied to monitor small fluctuations in the statistical process control. In this article, mathematical models of the five estimators (S₁, S₂, S₃, S₄, S₅) are established, with which the relevant MEWMA control charts are obtained, respectively. Thereafter, the process monitoring performance of the five control charts is simulated. And the simulation results show that the S₄ estimator-based MEWMA control chart is of the best performance both in step offset failure mode and ramp offset failure mode. Since the inline process monitoring of photovoltaic manufacturing is intended to be a problem of multivariate statistics process analysis, the feasibility and effectiveness of the proposed model are elaborated in the case study during the cell testing and sorting process control for the fabrication of multicrystalline silicon solar cells.     

Duadic Codes over F2 + uF2

Duadic codes over F ₂ + u F ₂ are introduced as abelian codes by their zeros. This is the function field analogue of duadic codes over Z ₄ introduced recently by Langevin and Solé. They produce binary self-dual codes via a suitable Gray map. Their binary images are themselves abelian, thus generalizing a result of van Lint for cyclic binary codes of even length. We classify them in modest lengths and exhibit interesting non-cyclic examples. Received: April 26, 2000; revised version: May 5, 2001     

Degradation of tobramycin in aqueous solution

Abstract

The kinetics of degradation of tobramycin (Ne-De-Ka) in aqueous solution was studied as a function of pH. Tobramycin hydrolyzes in acidic solution to yield kanosamine (Ka-OH) and nebramine (Ne-De-OH) with a pseudo first-order rate constant of 2.7 × 10^?6 s^?1 in 1 N HCl at 80°C. The activation energy for the acid catalyzed hydrolysis is 32 kcal mol^?1. In basic solution, the hydrolysis products are deoxystreptamine (De-OH), nebramine (Ne-De-OH) and deoxystreptamine-kanosaminide (HO-De-Ka). The pseudo first-order rate constant for the hydrolysis in 1 N KOH is 1 × 10^?8 s^?1 at 80°C. The activation energy for the base catalyzed hydrolysis is 15 kcal mol^?1. Tobramycin is very stable towards hydrolysis at neutral pH; however, it rapidly oxidizes giving several products including De-OH, Ne-De-OH, and HO-De-Ka. In pH 7 phosphate buffer (0.01 M), the t₉₀ value is 70 hr at 80°C.     

Two novel propylenedioxythiophene-based copolymers with donor–acceptor structures for organic solar cell materials

Two novel conjugated copolymers consisting of alternating electron-rich propylenedioxythiophene and electron-deficient 2,3-diphenyltheno[3,4-b]pyrazine or 6,7-diphenyl[1,2,5]thiadiazole units have been synthesized through palladium catalyzed Sonogashira triple-bond coupling reaction. The structures and properties of the two copolymers, P ₁ , P ₂ , were characterized by FT-IR, NMR, UV–Vis absorbance (Abs), thermal gravimetric analysis (TGA), differential scanning calorimetry (DSC), and cyclic voltammetry (CV). UV–Vis absorption spectra of the polymers show two absorption bands both in CHCl₃ solution and films. The absorption peak maxima of P ₁ , P ₂ are 600 nm, 766 nm in solution and 627 nm, 823 nm in films, respectively. Thermal gravimetric analysis demonstrates that the two polymers are stable below 300 °C. Cyclic voltammetry studies reveal that the band gaps of P ₁ , P ₂ are 1.62 eV and 1.50 eV, suggesting their potential for applications as organic solar cell materials.     

Solubility advantage of sulfanilamide and sulfacetamide in natural deep eutectic systems: experimental and theoretical investigations

Objective: The aim of this study was to explore the possibility of using natural deep eutectic solvents (NADES) as solvation media for enhancement of solubility of sulfonamides, as well as gaining some thermodynamic characteristics of the analyzed systems.

Significance: Low solubility of many active pharmaceutical ingredients is a well-recognized difficulty in pharmaceutical industry, hence the need for different strategies addressing this problem. Among such strategies, those that are environmentally and economically beneficial are of particular interest.

Methods: The solubility of sulfanilamide and sulfacetamide in 21 different NADES compositions comprising choline chloride with sugars or sugar alcohols was measured spectrophotometrically. Thermodynamic parameters describing the studied systems were determined using the COSMO-RS computational protocol.

Results: All of the considered NADES compositions gave an increase in solubility of the studied sulfonamides, with the highest solubilities obtained for the system comprising choline chloride and glycerol in unimolar proportions, which gave a solubility advantage of 83.7 and 73.8 for sulfanilamide and sulfacetamide, respectively. Theoretical studies indicated that the dissolution of both considered sulfonamides has a low endothermic character, with the lowest enthalpy values obtained for the most optimal, i.e. unimolar, proportions. The non-monotonous trend of enthalpy of dissolution was also discussed in terms of intermolecular interactions.

Conclusions: The obtained results show the feasibility of using NADES as solubility enhancers for sulfonamides and encourage for further exploration in this field.     

Continuous low-dose feeding of highly active pharmaceutical ingredients in hot-melt extrusion

Context: Manufacturing solid low-dose pharmaceutical products has always the homogeneity challenge. In continuous manufacturing, there is the additional challenge of feeding active pharmaceutical ingredient (API) dry powder at low rates. This paper presents a method for feeding API particles into a continuous extrusion process using a suspension. The challenges for feeding and the product homogeneity are both addressed.

Objective: The objective of this study is to demonstrate the feasibility of manufacturing low-dose extrudates by feeding the API particles in a diluted anti-solvent suspension.

Materials and methods: Extrudates with an Ibuprofen content of 0.021% and 0.043% (w/w) were prepared by feeding a 0.9% w/w suspension of Ibuprofen particles into a Coperion extruder.

Results and discussion: The homogeneity (RSD) of extrudates was tested during a time span of 30?min and had values between 2% and 7%.

Conclusion: Feeding particles in an anti-solvent suspension offers a simple feeding option for API and minor components which yield products of desired homogeneity. The liquid feeding approach offers a simplified process with enhanced process control possibilities.