Sharif Digital Repository

We consider the homogenization of a Robin boundary value problem in a locally periodic perforated domain which is also time-dependent. We aim at justifying the homogenization limit, that we derive through asymptotic expansion technique. More exactly, we obtain the so-called corrector homogenization estimate that specifies the convergence rate. The major challenge is that the media is not cylindrical and changes over time. We also show the existence and uniqueness of solutions of the microscopic problem. © 2020 American Institute of Mathematical Sciences. All rights reserved  

We use the singular sources method to detect the shape of the obstacle in a mixed boundary value problem. The basic idea of the method is based on the singular behavior of the scattered field of the incident point-sources on the boundary of the obstacle. Moreover we take advantage of the scattered field estimate by the backprojection operator. Also we give a uniqueness proof for the shape reconstruction. © 2004 Elsevier Inc. All rights reserved  

We introduce an extension of the classical neural field equation where the dynamics of the synaptic kernel satisfies the standard Hebbian type of learning (synaptic plasticity). Here, a continuous network in which changes in the weight kernel occurs in a specified time window is considered. A novelty of this model is that it admits synaptic weight decrease as well as the usual weight increase resulting from correlated activity. The resulting equation leads to a delay-type rate model for which the existence and stability of solutions such as the rest state, bumps, and traveling fronts are investigated. Some relations between the length of the time window and the bump width is derived. In... 

This work is devoted to study a class of singular perturbed elliptic systems and their singular limit to a phase segregating system. We prove existence and uniqueness and study the asymptotic behavior of limiting problem as the interaction rate tends to infinity. The limiting problem is a free boundary problem such that at each point in the domain at least one of the components is zero, which implies that all components can not coexist simultaneously. We present a novel method, which provides an explicit solution of the limiting problem for a special choice of parameters. Moreover, we present some numerical simulations of the asymptotic problem. © 2022 American Institute of Mathematical... 

This study develops the governing equations and characterizes the mechanical properties of a new orthotropic accordion morphing honeycomb structure containing periodic arrays of U-type beams reinforced with glass fibers. Castigliano’s second theorem is modified to develop the analytical equations to predict the deformation behavior of a single orthotropic ply under a combined axial, bending, and shear loadings. Accordingly, the elastic properties of the orthotropic structure including elastic stiffness, shear stiffness, and in-plane Poisson’s ratios are calculated by the developed equations. The honeycomb structure is manufactured by 3D printing, and the samples are subjected to tensile... 

Traditional mathematical models of epidemic disease had for decades conventionally considered static structure for contacts. Recently, an upsurge of theoretical inquiry has strived towards rendering the models more realistic by incorporating the temporal aspects of networks of contacts, societal and online, that are of interest in the study of epidemics (and other similar diffusion processes). However, temporal dynamics have predominantly focused on link fluctuations and nodal activities, and less attention has been paid to the growth of the underlying network. Many real networks grow: Online networks are evidently in constant growth, and societal networks can grow due to migration flux and... 

One of the most important issues in planning the "reservoir" type of hydro-power plants (HPP) is to determine the installation capacity of the HPPs and estimate its annual energy value. In this paper, a method is presented. A computer program has been developed to analyze energy calculation and estimation of the most important economic indices of an HPP using the sensitivity analysis method. Another program, developed by Matlab software, calculates the reliability indices for a number of units of an HPP with a specified load duration curve using the Monte Carlo method. Ultimately, comparing the technical, economic and reliability indices will determine the installation capacity of an HPP. By... 

The present paper describes a set of procedures for the solution of nonlinear equilibrium problems in complex multibody systems. To find the equilibrium position of the system, six different optimization algorithms are used to minimize the total potential energy (TPE) of the system and compared with respect to accuracy and efficiency. A computer program is developed to evaluate the equality constraints and objective function of a general multibody dynamic system to find the equilibrium condition. It is seen that the indirect methods have better results and converge faster. Also it is shown that the genetic algorithm (GA) results in a global optimum while the other methods converge to a local... 

A combined texture- and color-based skin detection is proposed in this paper. Nonsubsampled contourlet transform is used to represent texture of the whole image. Local neighbor contourlet coefficients of a pixel are used as feature vectors to classify each pixel. Dimensionality reduction is addressed through principal component analysis (PCA) to remedy the curse of dimensionality in the training phase. Before texture classification, the pixel is tested to determine whether it is skin-colored. Therefore, the classifier is learned to discriminate skin and non-skin texture for skin colored regions. A multi-layer perceptron is then trained using the feature vectors in the PCA reduced space. The... 

We study the regularity of solutions of the following semilinear problem(Formula presented.)where B1 is the unit ball in ℝn, 0 < q < 1 and λ± satisfy a Hölder continuity condition. Our main results concern local regularity analysis of solutions and their nodal set {u = 0}. The desired regularity is C[κ],κ−[κ] for κ = 2/(1 − q) and we divide the singular points in two classes. The first class contains the points where at least one of the derivatives of order less than κ is nonzero, the second class which is named (Formula presented.), is the set of points where all the derivatives of order less than κ exist and vanish. We prove that (Formula presented.) when κ is not an integer. Moreover,... 

We study the regularity of solutions of the following semilinear problemΔu=−λ+(x)(u+)q+λ−(x)(u−)qinB1,where B1 is the unit ball in ℝn, 0 < q < 1 and λ± satisfy a Hölder continuity condition. Our main results concern local regularity analysis of solutions and their nodal set {u = 0}. The desired regularity is C[κ],κ−[κ] for κ = 2/(1 − q) and we divide the singular points in two classes. The first class contains the points where at least one of the derivatives of order less than κ is nonzero, the second class which is named Sκ, is the set of points where all the derivatives of order less than κ exist and vanish. We prove that Sκ= ∅ when κ is not an integer. Moreover, with an example we show... 

The singular sources method is given to detect the shape of a thin infinitely cylindrical obstacle from a knowledge of the TM-polarized scattered electromagnetic field in large distance. The basic idea is based on the singular behaviour of the scattered field of the incident point source on the cross-section of the cylinder. We assume that the scatterer is a perfect conductor which is possibly coated by a material and investigate two models with different boundary conditions. Also we give a uniqueness proof for the shape reconstruction. Copyright © 2006 John Wiley & Sons, Ltd  

This report aims the study of dynamic stability of single walled carbon nanocone for some axial length conditions and declination angles of 60°, 120°and 240°. For dynamic stability analysis of Single Walled Carbon Nanocone (SWCNC), the mode shapes and frequencies of the carbon nanocone are extracted using the molecular mechanics approach. The mechanical properties of SWCNC were obtained by the Molecular Mechanics (MM) method. The obtained parameters are used for extraction of the conical shell virtual model of nanocone with the same dimensions. The equations of coupled fluid-structural dynamics of SWCNC are derived using the modal expansion for the structural displacements of the conical... 

Detection of skin pixels in arbitrary images is addressed in this paper. We have combined texture and color information to segment skin regions. First, a pixel-based boosted skin detection method is used to locate skin pixels. To further improve the detect performance, skin region texture features are employed using the nonsubsampled contourlet coefficients. For the candidate skin pixels, the set of 8×8 patches around that pixel in all subimages are selected and the feature vector of each patch is extracted. Multilayer perceptron is then utilized to learn features and classify any given input sample. The proposed algorithm has achieved true positive rate of about 82.8% and false positive... 

Let Ω = R 2 B(0 , 1) ¯ be the exterior of the closed unit ball. We prove the existence of extremal constant-sign solutions as well as sign-changing solutions of the following boundary value problem -Δu=a(x)f(u)inΩ,u=0on∂Ω=∂B(0,1),where the nonnegative coefficient a satisfies a certain integrability condition. We are looking for solutions in the space D01,2(Ω) which is the completion of Cc∞(Ω) with respect to the ‖ ∇ · ‖ 2 , Ω -norm. Unlike in the situation of R N with N≥ 3 , the behavior of solutions in the borderline case N= 2 considered here is qualitatively significantly different, such as for example, constant-sign solutions in the borderline case are not decaying to zero at infinity,... 

New methods for the Inverse and forward kinematic analysis of the novel six Degrees of Freedom (6DOF) parallel manipulator which has only two legs are presented. The actuation of the new mechanism is through two base-mounted spherical actuators. In the inverse pose kinematic, active joint variables are directly calculated with no need for the evaluation of passive joint variables. In the forward pose kinematic, closed form solution adopting a new approach is presented. It is shown that the inverse and forward pose kinematic have sixteen and four different solutions, respectively. Moreover, closed form equations for the rate kinematic analysis are proposed. Finally, two different categories... 

The effect of elastic foundation on the free vibration characteristics of embedded nanocones is investigated in this paper. The nanocone is modeled as a thin shell and the nonlocal elasticity theory is used to derive the governing equations of motion. Also the elastic medium is simulated using Winkler and Pasternak foundation models. Based on the modal analysis technique and applying the Galerkin method the governing equations are solved to obtain the natural frequencies. The drawn results emphasis the effects of geometry and small-scale parameter on the natural frequencies of nanocone. Also the effect of elastic foundation modulus on the resonance frequencies of the nanocones are studied... 

The purpose of this paper is to provide a full analysis of the null controllability problem for the one dimensional degenerate/singular parabolic equation ut - (a(x)ux)x - λ/x βu = 0, (t,x) ∈ (0, T) × (0,1), where the diffusion coefficient a(·) is degenerate at x = 0. Also the boundary conditions are considered to be Dirichlet or Neumann type related to the degeneracy rate of a(·). Under some conditions on the function a(·) and parameters β, λ, we prove global Carleman estimates. The proof is based on an improved Hardy-type inequality  

We study the null controllability properties of some degenerate/singular parabolic equations in a bounded interval of ℝ. For this reason we derive a new Carleman estimate whose proof is based on Hardy inequalities