A Bilinear Constitutive Model for Isotropic Bimodulus Materials

Proper formulation of stress-strain relations, particularly in tension-compression situations for isotropic biomodulus materials, is an unresolved problem. Ambartsumyan's model [8] and Jones' weighted compliance matrix model [9] do not satisfy the principle of coordinate invariance. Shapiro's first stress invariant model [10] is too simple a model to describe the behavior of real materials. In fact, Rigbi [13] has raised a question about the compatibility of bimodularity with isotropy in a solid. Medri [2] has opined that linear principal strain-principal stress relations are fictitious, and warned that the bilinear approximation of uniaxial stress-strain behavior leads to ill-working bimodulus material model under combined loading. In the present work, a general bilinear constitutive model has been presented and described in biaxial principal stress plane with zonewise linear principal strain-principal stress relations. Elastic coefficients in the model are characterized based on the signs of (i) principal stresses, (ii) principal strains, and (iii) on the value of strain energy component ratio ER greater than or less than unity. The last criterion is used in tension-compression and compression-tension situations to account for different shear moduli in pure shear stress and pure shear strain states as well as unequal cross compliances.

Nano-indentation studies on polymer matrix composites reinforced by few-layer graphene

The mechanical properties of polyvinyl alcohol (PVA) and poly(methyl methacrylate) (PMMA)-matrix composites reinforced by functionalized few-layer graphene (FG) have been evaluated using the nano-indentation technique. A significant increase in both the elastic modulus and hardness is observed with the addition of 0.6 wt% of graphene. The crystallinity of PVA also increases with the addition of FG. This and the good mechanical interaction between the polymer and the FG, which provides better load transfer between the matrix and the fiber, are suggested to be responsible for the observed improvement in mechanical properties of the polymers.

Inverse Sensitivity Analysis of Singular Solutions of FRF matrix in Structural System Identification

The problem of structural damage detection based on measured frequency response functions of the structure in its damaged and undamaged states is considered. A novel procedure that is based on inverse sensitivity of the singular solutions of the system FRF matrix is proposed. The treatment of possibly ill-conditioned set of equations via regularization scheme and questions on spatial incompleteness of measurements are considered. The application of the method in dealing with systems with repeated natural frequencies and (or) packets of closely spaced modes is demonstrated. The relationship between the proposed method and the methods based on inverse sensitivity of eigensolutions and frequency response functions is noted. The numerical examples on a 5-degree of freedom system, a one span free-free beam and a spatially periodic multi-span beam demonstrate the efficacy of the proposed method and its superior performance vis-a-vis methods based on inverse eigensensitivity.

On the probability that the determinant of an nxn matrix over a finite field vanishe

An expression is derived for the probability that the determinant of an n x n matrix over a finite field vanishes; from this it is deduced that for a fixed field this probability tends to 1 as n tends to.

Fast matrix transposition computer implementation

Eklundh's (1972) algorithm to transpose a large matrix stored on an external device such as a disc has been programmed and tested. A simple description of computer implementation is given in this note.

Don't-cares in the concurrency matrix for bit steering

The concurrency matrix aids the detection of bit steerability of microcommand sets in a microprogram. In the present work, the concept of don't-cares is introduced into the concurrency matrix to identify the bit steerable microcommand sets.

Fast Public Key Cryptosystem Based On Matrix Rings

A public key cryptosystem is proposed, which is based on the assumption that finding the square root of an element in a large finite ring is computationally infeasible in the absence of a knowledge of the ring structure. The encryption and decryption operations are very fast, and the data expansion is 1:2.

Algebraic design techniques for reliable stabilization

In this paper we study two problems in feedback stabilization. The first is the simultaneous stabilization problem, which can be stated as follows. Given plantsG_{0}, G_{1},..., G_{l}, does there exist a single compensatorCthat stabilizes all of them? The second is that of stabilization by a stable compensator, or more generally, a "least unstable" compensator. Given a plantG, we would like to know whether or not there exists a stable compensatorCthat stabilizesG; if not, what is the smallest number of right half-place poles (counted according to their McMillan degree) that any stabilizing compensator must have? We show that the two problems are equivalent in the following sense. The problem of simultaneously stabilizingl + 1plants can be reduced to the problem of simultaneously stabilizinglplants using a stable compensator, which in turn can be stated as the following purely algebraic problem. Given2lmatricesA_{1}, ..., A_{l}, B_{1}, ..., B_{l}, whereA_{i}, B_{i}are right-coprime for alli, does there exist a matrixMsuch thatA_{i} + MB_{i}, is unimodular for alli?Conversely, the problem of simultaneously stabilizinglplants using a stable compensator can be formulated as one of simultaneously stabilizingl + 1plants. The problem of determining whether or not there exists anMsuch thatA + BMis unimodular, given a right-coprime pair (A, B), turns out to be a special case of a question concerning a matrix division algorithm in a proper Euclidean domain. We give an answer to this question, and we believe this result might be of some independent interest. We show that, given twon times mplantsG_{0} and G_{1}we can generically stabilize them simultaneously provided eithernormis greater than one. In contrast, simultaneous stabilizability, of two single-input-single-output plants, g0and g1, is not generic.

Direct estimation of an element of order matrix from H-1 NMR spectra of strongly dipolar coupled spins

NMR spectra of molecules oriented in thermotropic liquid crystalline media provide information on the molecular structure and order. The spins are generally strongly dipolar coupled and the spectral analyse require the tedious and time consuming numerical iterative calculations. The present study demonstrates the application of multiple quantum spin state selective detection of single quantum transitions for mimicking the homonuclear decoupling and the direct estimation of an element of ordering matrix. This information is utilized to estimate the nearly accurate starting dipolar couplings for iterative calculations. The studies on the spectra of strongly dipolar coupled five and six interacting spin systems are reported.

Low temperature electrical transport properties of carbon matrix containing iron nanoparticles

We present a comparative study of the low temperature electrical transport properties of the carbon matrix containing iron nanoparticles and the films. The conductivity of the nanoparticles located just below the metal-insulator transition exhibits metallic behavior with a logarithmic temperature dependence over a large temperature interval. The zero-field conductivity and the negative magnetoresistance, showing a characteristic upturn at liquid helium temperature, are consistently explained by incorporating the Kondo relation and the two dimensional electron-electron interaction. The films, in contrast, exhibit a crossover of the conductivity from power-law dependence at high temperatures to an activated hopping law dependence in the low temperature region. The transition is attributed to changes in the energy dependence of the density of states near the Fermi level. The observed magnetoresistance is discussed in terms of quantum interference effect on a three-dimensional variable range hopping mechanism.

Foldable compatibility matrix for the folding of programmable logic arrays

This paper describes a switching theoretic algorithm for the folding of programmable logic arrays (PLA). The algorithm is valid for both column and row folding, although it has been presented considering only the simple column folding. The pairwise compatibility relations among all the pairs of the columns of the PLA are mapped into a square matrix, called the compatibility matrix of the PLA. A foldable compatibility matrix (FCM), a new concept introduced by the author, is then derived from the compatibility matrix. A new theorem called the folding theorem is then proved. The theorem states that the existence of an m by 2m FCM is both necessary and sufficient to fold 2m columns of the n column PLA (2m ≤ n). Once an FCM is obtained, the ordered pairs of foldable columns and the re-ordering of the rows are readily determined.

Extraordinary synergy in the mechanical properties of polymer matrix composites reinforced with 2 nanocarbons

One of the applications of nanomaterials is as reinforcements in composites, wherein small additions of nanomaterials lead to large enhancements in mechanical properties. There have been extensive studies in the literature on composites where a polymer matrix is reinforced by a single nanomaterial such as carbon nanotubes. In this article, we examine the significant synergistic effects observed when 2 different types of nanocarbons are incorporated in a polymer matrix. Thus, binary combinations of nanodiamond, few-layer graphene, and single-walled nanotubes have been used to reinforce polyvinyl alcohol. The mechanical properties of the resulting composites, evaluated by the nanoindentation technique, show extraordinary synergy, improving the stiffness and hardness by as much as 400% compared to those obtained with single nanocarbon reinforcements. These results suggest a way of designing advanced materials with extraordinary mechanical properties by incorporating small amounts of 2 nanomaterials such as graphene plus nanodiamond or nanodiamond plus carbon nanotube.

Coherent potential approximation, averaged T-matrix approximation and Lloyd's model

It is shown how the single-site coherent potential approximation and the averaged T-matrix approximation become exact in the calculation of the averaged single-particle Green function of the electron in the Anderson model when the site energy is distributed randomly with lorentzian distribution. Using these approximations, Lloyd's exact result is reproduced.

Study of linear and nonlinear optical properties of dendrimers using density matrix renormalization group method

We have used the density matrix renormalization group (DMRG) method to study the linear and nonlinear optical responses of first generation nitrogen based dendrimers with donor acceptor groups. We have employed Pariser–Parr–Pople Hamiltonian to model the interacting pi electrons in these systems. Within the DMRG method we have used an innovative scheme to target excited states with large transition dipole to the ground state. This method reproduces exact optical gaps and polarization in systems where exact diagonalization of the Hamiltonian is possible. We have used a correction vector method which tacitly takes into account the contribution of all excited states, to obtain the ground state polarizibility, first hyperpolarizibility, and two photon absorption cross sections. We find that the lowest optical excitations as well as the lowest excited triplet states are localized. It is interesting to note that the first hyperpolarizibility saturates more rapidly with system size compared to linear polarizibility unlike that of linear polyenes.

Role of Capping Ligands on the Nanoparticles in the Modulation of Properties of a Hybrid Matrix of Nanoparticles in a 2D Film and in a Supramolecular Organogel

We incorporate various gold nanoparticles (AuNPs) capped with different ligands in two-dimensional films and three-dimensional aggregates derived from N-stearoyl-L-alanine and N-lauroyl-L-alanine, respectively. The assemblies of N-stearoyl-L-alanine afforded stable films at the air-water interface. More compact assemblies were formed upon incorporation of AuNPs in the air-water interface of N-stearoyl-L-alanine. We then examined the effects of incorporation of various AuNPs functionalized with different capping ligands in three-dimensional assemblies of N-lauroyl-L-alanine, a compound that formed a gel in hydrocarbons. The profound influence of nanoparticle incorporation into physical gels was evident from evaluation of various microscopic and bulk properties. The interaction of AuNPs with the gelator assembly was found to depend critically on the capping ligands protecting the Au surface of the gold nanoparticles. Transmission electron microscopy (TEM) showed a long-range directional assembly of certain AuNPs along the gel fibers. Scanning electron microscopy (SEM) images of the freeze-dried gels and nanocomposites indicate that the morphological transformation in the composite microstructures depends significantly on the capping agent of the nanoparticles. Differential scanning calorimetry (DSC) showed that gel formation from sol occurred at a lower temperature upon incorporation of AuNPs having capping ligands that were able to align and noncovalently interact with the gel fibers. Rheological studies indicate that the gel-nanoparticle composites exhibit significantly greater viscoelasticity compared to the native gel alone when the capping ligands are able to interact through interdigitation into the gelator assembly. Thus, it was possible to define a clear relationship between the materials and the molecular-level properties by means of manipulation of the information inscribed on the NP surface.