Path-integral derivation of the superconformal anomaly for the N=1 supersymmetric Yang-Mills theory

Fujikawa's method of evaluating the supercurrent and the superconformal current anomalies, using the heat-kernel regularization scheme, is extended to theories with gauge invariance, in particular, to the off-shell N=1 supersymmetric Yang-Mills (SSYM) theory. The Jacobians of supersymmetry and superconformal transformations are finite. Although the gauge-fixing term is not supersymmetric and the regularization scheme is not manifestly supersymmetric, we find that the regularized Jacobians are gauge invariant and finite and they can be expressed in such a way that there is no one-loop supercurrent anomaly for the N=1 SSYM theory. The superconformal anomaly is nonzero and the anomaly agrees with a similar result obtained using other methods.

Path-integral derivation of the superconformal anomaly for the Wess-Zumino model

Fujikawa's method of evaluating the anomalies is extended to the on-shell supersymmetric (SUSY) theories. The supercurrent and the superconformal current anomalies are evaluated for the Wess-Zumino model using the background-field formulation and heat-kernel regularization. We find that the regularized Jacobians for SUSY and superconformal transformations are finite. The results can be expressed in a form such that there is no supercurrent anomaly but a finite nonzero superconformal anomaly, in agreement with similar results obtained using other methods.

Derivation and consistency of the partial functions of the ternary system involving interaction coefficients

The logarithm of activity coefficients of the components of the ternary system is derived based on the Maclaurin infinite series, which is expressed in terms of the integral property of the system and subjected to appropriate boundary conditions. The derivation of the functions involves extensive summation of various infinite series pertaining to the first-order interaction coefficients that have been shown completely to remove any truncational error. Since the conventional equations involving interaction coefficients are internally inconsistent, a consistent form of the partial functions is developed in the article using the technique just described. The thermodynamic consistency of the functions based on the Maxwell and the Gibbs-Duhem relations has been established. The derived values of the logarithmic activity coefficients of the components have been found to be in agreement with the thermodynamic data of the Fe-Cr-Ni system at 1873 K and have been found to be independent of the compositional paths.

Minimal set of generators for the derivation module of certain monomial curves

Let K be a field of characteristic zero and let m(0),..., m(e-1) be a sequence of positive integers. Let C be an algebroid monomial curve in the affine e-space A(K)(e) defined parametrically by X-0 = T-m0,..., Xe-1 = Tme-1 and let A be the coordinate ring of C. In this paper, we assume that some e - 1 terms of m(0),..., m(e-1) form an arithmetic sequence and construct a minimal set of generators for the derivation module Der(K)(A) of A and write an explicit formula for mu (Der(K)(A)).

On the characterisation of syntactic foam core sandwich composites for compressive properties

Sandwich structures, especially those with honeycomb and grid structures as the core material, are very commonly employed in aircraft structures. There is an increasing use of closed-pore rigid syntactic foams as core materials in sandwich constructions because they possess a number of favourable properties. The syntactic foams, owing to their structure and formation, behave differently under compression compared to other traditionally used core materials. In the present study, therefore, syntactic foam core sandwich constructions are evaluated for their behaviour under compression in both edgewise and flatwise orientations. Further, the work characterises the relative performance of two sets of sandwich materials, one containing glass-epoxy and the other, glass/carbon hybrid-epoxy skins. As non-standard geometry test specimens were involved, only a comparative evaluation was contemplated in this approach. The experiments indicate that the nature of the reinforcement fabric in the skin has a bearing on the test results in edgewise orientation. Thus, the tendency towards initiation of vertical crack in the central plane of the core material, which is a typical fracture event in this kind of material, was found to occur after a delay for the specimens containing the glass fabric in the skin. Attempts are made to establish the correlation between observations made on the test specimen visually during the course of testing and the post-compression microscopic examinations of the fracture features.

Compressive fracture features of syntactic foams-microscopic examination

Syntactic foams made by mechanical mixing of polymeric binder and hollow spherical particles are used as core materials in sandwich structured materials. Low density of such materials makes them suitable for weight sensitive applications. The present study correlates various postcompression microscopic observations in syntactic foams to the localized events leading the material to fracture. Depending upon local stress conditions the fracture features of syntactic foam are identified for various modes of fracture such as compressive, shear and tensile. Microscopic observations were also taken at sandwich structures containing syntactic foam as core materials and also at reinforced syntactic foam containing glass fibers. These observations provide conclusive evidences for the fracture features generated under different failure modes. All the microscopic observations were taken using scanning electron microscope in secondary electron mode. (C) 2002 Kluwer Academic Publishers.

Effect of absorption in aqueous and hygrothermal media on the compressive properties of glass fiber reinforced syntactic foam

Absorption due to immersion in aqueous media consisting of either saline or seawater or due to exposure to water vapor conditions and the attendant effect on the compressive properties of syntactic foam reinforced with E-glass fibers in the form of chopped strands were studied. Whereas the compressive strength decreased in samples exposed to water vapor, the saline or seawater immersed samples showed increase when compared to the dry sample. The decrease in strength in the vapor-exposed case is ascribed to higher absorption of water and to debonding and damaged features for interfaces. The enhancement of strength values for the samples immersed in saltish media is traced to the larger size of the chloride ion and resultant changes in the stress state around the fiber-bearing regions. Recourse to an analysis of scanning electron microscopic pictures of the compression-failed samples is taken to explain the observed trends.

Studies on compressive failure features in syntactic foam material

Syntactic foam made by mechanical mixing of glass hollow spheres in epoxy resin matrix is characterized for compressive properties in the present study. Volume fraction of hollow spheres in the syntactic foam under investigation is kept at 67.8%. Effect of specimen aspect ratio on failure behavior and stress-strain curve of the material is highlighted. Considerable differences are noted in the macroscopic fracture features of the specimen and the stress-strain curve with the variation in specimen aspect ratio, although compressive yield strength values were within a narrow range. Post compression test scanning electron microscopic observations coupled with the macroscopic observations taken during the test helped in explaining the deviation in specimen behavior and in gathering support for the proposed arguments.

A derivation of thermodynamic quantities of liquid alloys from their structure factors

A method of deriving the thermodynamic properties of mixing in liquid alloys Delta G, Delta S and Delta H, from low-Q scattering data has been presented. As an example, the method has been demonstrated with liquid Na-Ga alloys for which both thermodynamic and diffraction data have recently been obtained by the authors.

A non-syntactic approach for text sentiment classification with stopwords

The present approach uses stopwords and the gaps that oc- cur between successive stopwords –formed by contentwords– as features for sentiment classification.

Compressive and Flexural Properties of Functionally Graded Fly Ash Cenosphere-Epoxy Resin Syntactic Foams

The present study focuses on developing functionally graded syntactic foams (FGSFs) based on a layered co-curing technique. The FGSFs were characterized for compressive and flexural properties and compared with plain syntactic foams. The results showed that the specific compressive modulus was 3-67% higher in FGSFs compared to plain syntactic foams. FGSF exhibited 5-34% and 34-87% higher specific modulus and strength, respectively in flexural mode. The microscopic examinations of comparative responses of the filler and matrix to deformation suggest that the failure is dominated by the matrix. The gradient in the composition of syntactic foams helps in effectively distributing the stress throughout the microstructure and results in improved mechanical performance of syntactic foams. From the microscopy studies, it is evident that, the failure mechanism in the FGSF under flexural loading is governed by a crack that initiated on the tensile side of the specimen and propagated through the thickness to cause complete fracture. The microscopic observations further clearly demonstrate the existence of seamless interfaces between the layers and a clear difference in the cenosphere concentration across the interface, affirming the gradation in the prepared samples. The results show that appropriate compositions of FGSFs can be selected to develop materials with improved mechanical performance. POLYM. COMPOS., 36:685-693, 2015. (c) 2014 Society of Plastics Engineers

Dry sliding wear of epoxy/cenosphere syntactic foams

Dry sliding wear behavior of epoxy matrix syntactic foams filled with 20, 40 and 60 wt% fly ash cenosphere is reported based on response surface methodology. Empirical models are constructed and validated based on analysis of variance. Results show that syntactic foams have higher wear resistance than the matrix resin. Among the parameters studied, the applied normal load (F) had a prominent effect on wear rate, specific wear rate (w(s)) and coefficient of friction (mu). With increasing F, the wear rate increased, whereas ws and mu decreased. With increase in filler content, the wear rate and w(s) decreased, while the mu increased. With increase in sliding velocity as well as sliding distance, the wear rate and ws show decreasing trends. Microscopy revealed broken cenospheres forming debris and extensive deformation marks on the wear surface. (C) 2015 Elsevier Ltd. All rights reserved.

Relationship between entropy and diffusion: A statistical mechanical derivation of Rosenfeld expression for a rugged energy landscape

Diffusion-a measure of dynamics, and entropy-a measure of disorder in the system are found to be intimately correlated in many systems, and the correlation is often strongly non-linear. We explore the origin of this complex dependence by studying diffusion of a point Brownian particle on a model potential energy surface characterized by ruggedness. If we assume that the ruggedness has a Gaussian distribution, then for this model, one can obtain the excess entropy exactly for any dimension. By using the expression for the mean first passage time, we present a statistical mechanical derivation of the well-known and well-tested scaling relation proposed by Rosenfeld between diffusion and excess entropy. In anticipation that Rosenfeld diffusion-entropy scaling (RDES) relation may continue to be valid in higher dimensions (where the mean first passage time approach is not available), we carry out an effective medium approximation (EMA) based analysis of the effective transition rate and hence of the effective diffusion coefficient. We show that the EMA expression can be used to derive the RDES scaling relation for any dimension higher than unity. However, RDES is shown to break down in the presence of spatial correlation among the energy landscape values. (C) 2015 AIP Publishing LLC.

Derivation Of A Nonlinear Reynolds Stress Model Using Renormalization Group Analysis And Two-Scale Expansion Technique

Adopting Yoshizawa's two-scale expansion technique, the fluctuating field is expanded around the isotropic field. The renormalization group method is applied for calculating the covariance of the fluctuating field at the lower order expansion. A nonlinear Reynolds stress model is derived and the turbulent constants inside are evaluated analytically. Compared with the two-scale direct interaction approximation analysis for turbulent shear flows proposed by Yoshizawa, the calculation is much more simple. The analytical model presented here is close to the Speziale model, which is widely applied in the numerical simulations for the complex turbulent flows.