Sharif Digital Repository

Isotropic tensor valued functions of tensor arguments play an important role in the formulation of the equations governing the behavior of solid materials in the field of continuum mechanics. When the tensor argument is non-symmetric, the complexity and the difficulty in dealing with the tensor functions are high. In this work, the issue of expressing an isotropic tensor valued tensor function of a non-symmetric tensor argument is attention by utilizing the Dunford-Taylor integral. An important subclass of the isotropic tensor functions is considered with the commutative property  

In this note, we study the behavior of independent sets of maximum probability measure in tensor graph powers. To do this, we introduce an upper bound using measure preserving homomorphisms. This work extends some previous results concerning independence ratios of tensor graph powers. © 2008 Elsevier B.V. All rights reserved  

Based on the notion of maximal correlation, we introduce a new measure of correlation between two different rankings of the same group of items. Our measure captures various types of correlation detected in previous measures of rank correlation like the Spearman correlation and the Kendall tau correlation. We show that the maximal rank correlation satisfies the data processing and tensorization properties (that make ordinary maximal correlation applicable to problems in information theory). Furthermore, MRC is shown to be intimately related to the FKG inequality. Finally, we pose the problem of the complexity of the computation of this new measure. We make partial progress by giving a simple... 

Vacuum polarization in QED in a background gravitational field induces interactions which effectively modify the classical picture of light rays as the null geodesies of spacetime. After a short introduction on the main aspects of the quantum gravitational optics, as a nontrivial example, we study this effect in the background of NUT space characterizing the spacetime of a spherical mass endowed with a gravitomagnetic monopole charge, the so called NUT factor. © 2007 IOP Publishing Ltd  

The Casimir energy for massless scalar field which satisfies periodic boundary conditions in two-dimensional domain wall background is calculated by making use of general properties of renormalized stress-tensor. The line element of domain wall is time dependent, the trace anomaly which is the nonvanishing Tμμ for a conformally invariant field after renormalization, represent the back reaction of the dynamical Casimir effect  

A family of conformational rheological models for multi-component miscible polymer blends is developed using a modified form of the Poisson bracket formulation. Two conformation tensors called c1 and c2 are introduced to show the orientation of the first and the second components of a blend, respectively. The mobility tensor and the energy function for each blend component are expressed in terms of these conformation tensors. The interaction effects are also included by energy expressions. The predictions of this family of "volume-preserving" models are illustrated for a Hookean-type energy function and several expressions of the modified mobility tensors. The results are illustrated for... 

In this paper some expressions for stresses conjugate to two-point deformation tensors are derived. These expressions are offered in both the component and basis-free forms. Although, the material time rate of a two-point deformation tensor is not an objective quantity, the stress tensor conjugate to it may be determined. The component-form expressions are obtained by using the notion of conjugacy together with the objectivity of the stress power. The component-form expressions are then extended to a unified basis-free form, using a theorem established for this purpose. The specific results are provided for all different cases of distinct and coalescent principal stretches in a... 

In many cases of constitutive modeling of continua undergoing large deformations, use of corotational rates and integrals is inevitable to avoid the effects of rigid body rotations. Making corotational rates associated with specific spin tensors is a matter of interest, which can help for a better physical interpretation of the deformation. In this paper, for a given kinematic tensor function, say G, a tensor valued function F as well as a spin tensor Ω0 is obtained in such a way that the corotational rate of F associated with the spin tensor Ω0, becomes equal to G. In other words, F is the corotational integral of G associated with the spin tensor Ω0. Here, G is decomposed additively into... 

In this paper, a unified explicit tensorial relation is sought between two stress tensors conjugate to arbitrary and general Hill strains. The approach used for deriving the tensorial relation is based on the eigenprojection method. The result is, indeed, a generalization of the relations that were derived by Farahani and Naghadabadi [1] in 2003 from a component to intrinsic form. The result is unified in the sense that it is valid for all cases of distinct and coalescent principal stretches. Also, in the case of three dimensional Euclidean inner product space, using the derived unified relation, some expressions for the conjugate stress tensors are presented. © Sharif University of... 

In Hypo-elastic constitutive models an objective rate of the Cauchy stress tensor is expressed in terms of the current state of the stress and the deformation rate tensor D in a way that the dependency on the latter is a homogeneously linear one. In this work, a type of grade-one hypo-elastic models (i.e. models with linear dependency of the hypo-elasticity tensor on the stress) is considered for isotropic materials based on the objective corotational rates of stress. A positive real parameter denoted by n is involved in the considered type. Different values can be selected for this parameter, each selection leads to a specific model within the class of grade-one hypo-elasticity. The spin of... 

A classical question of Yoneda asks when the tensor product of two injective modules is injective. A complete answer to this question was given by Enochs and Jenda in 1991. In this paper the analogue question for pure-injective modules is studied  

The stress-energy tensor of a matter shell whose history coincides with a null hypersurface in the Einstein-Cartan gravity is revisited. It is demonstrated that with a proper choice for the torsion discontinuity taken to be orthogonal to the null hypersurface and consistent with the antisymmetric property of torsion tensor, the modified expression for the asymmetric stress-energy tensor is automatically tangent to the hypersurface. The main differences with respect to a previous work are addressed. © 2019 IOP Publishing Ltd  

In this paper, a general type of Eshelby-like stress tensor is defined which is based on the right stretch tensor and is equal to the product of a general class of strain and the corresponding conjugate stress tensor. The Eshelby-like stress tensor depending on the fact that from which side the stress tensor is multiplied by, is categorized into the right-weighted and left-weighted ones. General relations for conjugate strains of Eshelby-like stress tensors are investigated using the method, based on the definition of energy conjugacy and Hill's principal axis method  

Most of numerical approaches describing the behavior of miscible displacement in porous media through the solution of advection-dispersion equation suffer from numerical dispersion. Random Walk (RW) method is a good candidate to overcome this problem especially in heterogeneous media. In addition, how treating dispersion coefficient as a tensor might affect the accuracy of RW simulation results is not well understood. Here, a RW model was developed and used for simulating miscible displacement experiments performed on heterogeneous micromodels including single fracture/flow barrier. Dispersion coefficient was treated as a tensor and a hybrid scheme was used for velocity interpolation. The... 

In this paper, the concept of energy pairs in the micropolar continuum is introduced. A brief review of the micropolar continuum theory is presented for using in the subsequent derivations. A mathematical Lagrangian strain and a wryness tensor for the micropolar continuum are introduced. Using the first law of thermodynamics and for isothermal processes, the power of deformation is obtained and the energy pairs in the Eulerian and Lagrangian descriptions are defined. Also, the micropolar stress and couple stress tensors which are energy pairs to the micropolar Lagrangian strain and wryness measures are determined. © 2006 Elsevier Ltd. All rights reserved  

In this paper, a general class of Eshelby-like or weighted stress tensors based on the right stretch tensor is defined as the product of a general type of Lagrangian stress tensor and a class of stretch measure. In addition, basis free relations for conjugate strains of Eshelby-like stress tensors are investigated, which are based on Hill's definition of energy conjugacy. The equations for strain tensors conjugate to Eshelby-like stress tensors are generally determined, but the case in which the conjugate strains are coaxial with the right stretch tensor is mostly investigated. © 2006 Elsevier Ltd. All rights reserved  

Static and parametric stability of thin symmetrically laminated composite super-elliptical plates resting on Winkler-type foundation and subjected to uniform in-plane harmonic loads, under clamped, simply supported and free boundary conditions, are investigated based on the classical laminated plate theory. The governing equations are obtained from a variational approach and then the classical Ritz method is used to reduce the problem into a set of coupled Mathieu-Hill equations. Hsu's technique is utilized to determine the dynamic instability regions of principal and combination resonance frequencies. Extensive numerical data are provided to examine the effects of plate aspect ratio,... 

Eshelby's theories on the nature of the disturbance strains due to polynomial eigenstrains inside an isotropic ellipsoidal inclusion, and the form of homogenizing eigenstrains corresponding to remote polynomial loadings in the equivalent inclusion method (EIM) are not valid for spherically anisotropic inclusions and inhomogeneities. Materials with spherically anisotropic behavior are frequently encountered in nature, for example, some graphite particles or polyethylene spherulites. Moreover, multi-inclusions/inhomogeneities/ inhomogeneous inclusions have abundant engineering and scientific applications and their exact theoretical treatment would be of great value. The present work is devoted... 

In this paper, we compare registration results obtained using different diffusion maps extracted from diffusion tensor imaging (DTI). Fractional Anisotropy (FA) and Ellipsoidal Area Ratio (EAR) are two diffusion maps (indices) that may be used for image registration. First, we use FA maps to find deformation matrix and register diffusion weighted images. Then, we use EAR maps and finally we use both of FA and EAR maps to register diffusion weighted images. The difference between FA values before deformation and after registration using the FA alone or EAR alone has a median of 0.57 and using both of them has a median of 0.29. Therefore, the results of registration using both of the FA and... 

In this paper, we introduce a novel approach based on Tucker Decomposition and quasi-periodic nature of ECG signal for fetal ECG extraction from abdominal ECG mixture. We adapt variable periodicity constraint of the ECG components to main objective function of the Tucker Decomposition and shape it to matrix form in order to simply optimize the objective function. We form a 3rd order tensor by stacking the mixed multichannel ECG and reconstructed fetal and maternal subspaces using BSS methods in order to have the benefit of further artificial observations, and apply our proposed penalized decomposition on it. The proposed method is evaluated on synthetic and real datasets using the criteria...