**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**5

# Search results for: Green function

##### 5 Green Function and Eshelby Tensor Based on Mindlin’s 2nd Gradient Model: An Explicit Study of Spherical Inclusion Case

**Authors:**
A. Selmi,
A. Bisharat

**Abstract:**

Using Fourier transform and based on the Mindlin's 2^{nd} gradient model that involves two length scale parameters, the Green's function, the Eshelby tensor, and the Eshelby-like tensor for a spherical inclusion are derived. It is proved that the Eshelby tensor consists of two parts; the classical Eshelby tensor and a gradient part including the length scale parameters which enable the interpretation of the size effect. When the strain gradient is not taken into account, the obtained Green's function and Eshelby tensor reduce to its analogue based on the classical elasticity. The Eshelby tensor in and outside the inclusion, the volume average of the gradient part and the Eshelby-like tensor are explicitly obtained. Unlike the classical Eshelby tensor, the results show that the components of the new Eshelby tensor vary with the position and the inclusion dimensions. It is demonstrated that the contribution of the gradient part should not be neglected.

**Keywords:**
Green’s Function,
Eshelby tensor,
Eshelby-like tensor,
Mindlin’s 2nd gradient model,
spherical inclusion

##### 4 Behavior of Current in a Semiconductor Nanostructure under Influence of Embedded Quantum Dots

**Authors:**
H. Paredes Gutiérrez,
S. T. Pérez-Merchancano

**Abstract:**

Motivated by recent experimental and theoretical developments, we investigate the influence of embedded quantum dot (EQD) of different geometries (lens, ring and pyramidal) in a double barrier heterostructure (DBH). We work with a general theory of quantum transport that accounts the tight-binding model for the spin dependent resonant tunneling in a semiconductor nanostructure, and Rashba spin orbital to study the spin orbit coupling. In this context, we use the second quantization theory for Rashba effect and the standard Green functions method. We calculate the current density as a function of the voltage without and in the presence of quantum dots. In the second case, we considered the size and shape of the quantum dot, and in the two cases, we worked considering the spin polarization affected by external electric fields. We found that the EQD generates significant changes in current when we consider different morphologies of EQD, as those described above. The first thing shown is that the current decreases significantly, such as the geometry of EQD is changed, prevailing the geometrical confinement. Likewise, we see that the current density decreases when the voltage is increased, showing that the quantum system studied here is more efficient when the morphology of the quantum dot changes.

**Keywords:**
Nanostructures,
Quantum Dots,
quantum semiconductors,
spin polarization

##### 3 Effect of adding Supercritical Carbon Dioxide Extracts of Cinnamomum tamala (Bay Leaf) on Nutraceutical Property of Tofu

**Authors:**
Sudip Ghosh,
Probir Kumar Ghosh,
Paramita Bhattacharjee

**Abstract:**

Supercritical carbon dioxide extracts of *Cinnamomum tamala *(bay) leaves obtained at 55°C, 512 bar was found to have appreciable nutraceutical properties and was successfully employed as value-added ingredients in preparation of tofu. The bay leaf formulated tofu sample was evaluated for physicochemical properties (pH, texture analysis and lipid peroxidation), proximate analysis, phytochemical properties (total phenol content, antioxidant properties and total reducing sugar), microbial load and sensory profile analysis for a storage period of ten days, *vis-à-vis* an experimental control sample. These assays established the superiority of the tofu sample formulated with supercritical carbon dioxide extract of bay leaf over the control sample. Bay leaf extract formulated tofu is a new green functional food with promising nutraceutical benefits.

**Keywords:**
Cinnamomum tamala,
supercritical carbon dioxide extraction,
Physicochemical properties Phytochemical properties,
Tofu

##### 2 A New Composition Method of Admissible Support Vector Kernel Based on Reproducing Kernel

**Authors:**
Wei Zhang,
Xin Zhao,
Yi-Fan Zhu,
Xin-Jian Zhang

**Abstract:**

Kernel function, which allows the formulation of nonlinear variants of any algorithm that can be cast in terms of dot products, makes the Support Vector Machines (SVM) have been successfully applied in many fields, e.g. classification and regression. The importance of kernel has motivated many studies on its composition. It-s well-known that reproducing kernel (R.K) is a useful kernel function which possesses many properties, e.g. positive definiteness, reproducing property and composing complex R.K by simple operation. There are two popular ways to compute the R.K with explicit form. One is to construct and solve a specific differential equation with boundary value whose handicap is incapable of obtaining a unified form of R.K. The other is using a piecewise integral of the Green function associated with a differential operator L. The latter benefits the computation of a R.K with a unified explicit form and theoretical analysis, whereas there are relatively later studies and fewer practical computations. In this paper, a new algorithm for computing a R.K is presented. It can obtain the unified explicit form of R.K in general reproducing kernel Hilbert space. It avoids constructing and solving the complex differential equations manually and benefits an automatic, flexible and rigorous computation for more general RKHS. In order to validate that the R.K computed by the algorithm can be used in SVM well, some illustrative examples and a comparison between R.K and Gaussian kernel (RBF) in support vector regression are presented. The result shows that the performance of R.K is close or slightly superior to that of RBF.

**Keywords:**
Green function,
admissible support vector kernel,
reproducing kernel,
reproducing kernel Hilbert space,
support vectorregression

##### 1 Integral Operators Related to Problems of Interface Dynamics

**Authors:**
Pa Pa Lin

**Abstract:**

This research work is concerned with the eigenvalue problem for the integral operators which are obtained by linearization of a nonlocal evolution equation. The purpose of section II.A is to describe the nature of the problem and the objective of the project. The problem is related to the “stable solution" of the evolution equation which is the so-called “instanton" that describe the interface between two stable phases. The analysis of the instanton and its asymptotic behavior are described in section II.C by imposing the Green function and making use of a probability kernel. As a result , a classical Theorem which is important for an instanton is proved. Section III devoted to a study of the integral operators related to interface dynamics which concern the analysis of the Cauchy problem for the evolution equation with initial data close to different phases and different regions of space.

**Keywords:**
Evolution,
Green function,
instanton,
integral operators