Sharif Digital Repository

A finite element technique is used to mimic radial deformation of single-walled carbon nanotubes under hydrostatic pressure. The elastic deformation of nanotubes is modeled via elastic beams. Properties of the beam element are evaluated by considering characteristics of the covalent bonds between the carbon atoms in a hexagonal lattice. Applying the beam model in a three dimensional space, the elastic properties of the nanotube in the transverse direction are evaluated. The effects of diameter and wall thickness on the radial and circumferential elastic moduli of zigzag and armchair nanotubes are considered. Results are in good agreement with molecular structural mechanics data in the... 

The ground and thermal states of a quadratic Hamiltonian representing the interaction of bosonic modes or particles are always Gaussian states. We investigate the entanglement properties of these states for the case where the interactions are represented by harmonic forces acting along the edges of symmetric graphs-i.e., one-, two-, and three-dimensional rectangular lattices, mean-field clusters, and platonic solids. We determine the entanglement of formation (EOF) as a function of the interaction strength, calculate the maximum EOF in each case, and compare these values with the bounds found previously for quadratic Hamiltonians. © 2005 The American Physical Society  

We consider general multispecies models of reaction diffusion processes and obtain a set of constraints on the rates which give rise to closed systems of equations for correlation functions. Our results are valid in any dimension and on any type of lattice. We also show that under these conditions the evolution equations for two point functions at different times are also closed. As an example we introduce a class of two species models that may be useful for the description of voting processes or the spreading of epidemics. © 2002 The American Physical Society  

In this research, we will use an accelerator for MD simulations, called Atomic Approximation Method, which leads to more efficient simulations without harming the physical properties in simulations. The main idea of this method is to define a virtual material with lower number of atoms, which has the same physical properties as the original material. To demonstrate the validity of the proposed technique the modal analysis results are compared with the ones of the conventional molecular dynamics method. It is shown that this method accelerates conventional MD simulations significantly. Copyright © 2006 by ASME  

A novel approach for photonic crystals devices analysis, based on perturbation theory is reported. In this method the photonic crystal device is considered as the superposition of a parent lattice and a perturbing one. Then the solution is investigated in terms of the eigensolutions of the parent lattice. This way, one can easily obtain analytic expressions within the first order perturbation, describing the effects of different parameters on the eigensolutions of the structure. The perturbation theory employed in this work is typical of what is conventionally used in quantum mechanics literature. The proposed method is explicit, works fast, and does not involve complicated numerical... 

We have performed a numerical solution for band structure of an Abrikosov vortex lattice in type-II superconductors forming a periodic array in two dimensions for applications of incorporating the photonic crystals concept into superconducting materials with possibilities for optical electronics. The implemented numerical method is based on the extensive numerical solution of the Ginzburg-Landau equation for calculating the parameters of the two-fluid model and obtaining the band structure from the permittivity, which depends on the above parameters and the frequency. This is while the characteristics of such crystals highly vary with an externally applied static normal magnetic field,... 

We have performed a numerical solution for band structure of an Abrikosov vortex lattice in type-11 superconductors forming a periodic array in two dimensions for applications of incorporating the photonic crystals concept into superconducting materials with possibilities for optical electronics. The implemented numerical method is based on the extensive numerical solution of the Ginzburg-Landau equation for calculating the parameters of the two-fluid model and obtaining the band structure from the permittivity, which depends on the above parameters and the frequency. This is while the characteristics of such crystals highly vary with an externally applied static normal magnetic field,... 

Let p be a prime number and let n be a positive integer prime to p. By an Ihara-result, one means the existence of an injection with torsion-free cokernel, from a full lattice, in the space of p-old modular forms, into a full lattice, in the space of all modular forms of level np. In this paper, Ihara-results are proven for genus two Siegel modular forms, Siegel-Jacobi forms and Hilbert modular forms. Ihara did the genus one case of elliptic modular forms [1]. A geometric formulation is proposed for the notion of p-old Siegel modular forms of genus two, using clarifying comments by R. Schmidt [2] and, then, following suggestions in an earlier paper [3] on how to prove Ihara results. The main... 

The six-fold rotational symmetry of photonic crystal fibers has important manifestations in the radiated fields in terms of i) a focusing phenomena at a finite distance from the end-facet and ii) the formation of low-intensity satellite peaks in the asymptotic far field. For our study, we employ a surface equivalence principle which allows us to rigorously calculate radiated fields starting from fully-vectorial simulations of the near field. Our simulations show that the focusing is maximal at a characteristic distance from the end-facet. For large-mode area fibers the typical distance is of the order 10 x A with A being the pitch of the triangular air-hole lattice of the photonic crystal... 

We show that the two-dimensional (12D) Ising model is complete, in the sense that the partition function of any lattice model on any graph is equal to the partition function of the 2D Ising model with complex coupling. The latter model has all its spin-spin coupling equal to iπ4 and all parameters of the original model are contained in the local magnetic fields of the Ising model. This result has already been derived by using techniques from quantum information theory and by exploiting the universality of cluster states. Here we do not use the quantum formalism and hence make the completeness result accessible to a wide audience. Furthermore, our method has the advantage of being algorithmic... 

A simple and efficient transmission line model is proposed here to study how the transmission characteristics of photonic crystal waveguides are tailored by introduction of stubs patterned in the photonic crystal lattice. It is shown that band-pass and band-stop optical filters can be easily designed and optimized when stubs of appropriate length are brought in. Since the lengths of the designed stubs are not necessarily integer multiples of the photonic crystal lattice constant, a geometric shift in a portion of the photonic crystal structure is shown to be essential. The proposed model is verified by using a rigorous numerical method. An excellent agreement is observed between the... 

We study the zero-Temperature phase diagram of transverse field Ising model on the J 1-J 2 square lattice. In zero magnetic field, the model has a classical Néel phase for J 2/J 1 < 0.5 and an antiferromagnetic collinear phase for J 2/J 1 > 0.5. We incorporate harmonic fluctuations by using linear spin wave theory (LSWT) with single spin flip excitations above a magnetic order background and obtain the phase diagram of the model in this approximation. We find that harmonic quantum fluctuations of LSWT fail to lift the large degeneracy at J 2/J 1 = 0.5 and exhibit some inconsistent regions on the phase diagram. However, we show that anharmonic fluctuations of cluster operator approach (COA)... 

The competition and interaction of two edge cracks within the triangular lattice of an fcc material are addressed. We have also examined the effect of presence of a nanovoid in the vicinity of one of the crack-tips, on the competition of the cracks. An atomic scale finite element method (AFEM) [B. Liu, Y. Huang, H. Jiang, S. Qu, K.C. Hwang, The atomic-scale finite element method, Comput. Methods Appl. Mech. Eng. 193 (2004) 1849-1864], based on the Morse interatomic potential, is employed to explore the events in the (1 1 1) plane. Particular attention is given to the phenomenon of brittle-to-ductile transition (BDT) that occurs during crack propagation. © 2007 Elsevier B.V. All rights... 

An artificial neural network model was developed for modeling of the effects of mechanical alloying parameters including milling time, milling speed and ball to powder weight ratio on the characteristics of Al-8 vol%SiC nanocomposite powders. The crystallite size and lattice strain of the aluminum matrix were considered for modeling. This nanostructured nanocomposite powder was synthesized by utilizing planetary high energy ball mill and the required data for training were collected from the experimental results. The characteristics of the particles were determined by X-ray diffraction, scanning and transmission electron microscopy. Two types of neural network architecture, i.e. multi-layer... 

Poly(butadiene-stat-styrene)/poly(methylmetacrylate), SBR/PMMA, structural latices were synthesized by using equal moles of different kinds of surfactants: anionic, nonionic, and anionic/nonionic mixture in a two-stage emulsion polymerization. The results indicate that the application of anionic surfactants for the first stage, accompanying sodium persulfate initiator, KPS, for both stages led to core/shell and raspberry morphologies depended upon the hydrophilic lipophilic balance (HLB) of the surfactant. On the other hand, a core/shell structure was observed for structural latices which were synthesized via application of nonionic or anionic/non-ionic mixed surfactants along with... 

Single electron wavefunction of a vacancy in diamond lattice has been calculated in different symmetric configurations of the nearest neighbor (NN) atoms. We used ab initio density functional theory (DFT) and unrestricted Hartree-Fock (UHF) cluster methods. The variation of electron or spin localization on NN atoms have been investigated with respect to the lattice relaxation in the ground state of the neutral and negatively charged vacancy. Calculated variations are not symmetric with respect to the sign of the lattice relaxation. We obtain about 90% localization for electronic charge and spin density for the neutral and negatively charged vacancy, respectively. This is in good agreement... 

Supercoiled DNA, crumpled interphase chromosomes, and topologically constrained ring polymers often adopt treelike, double-folded, randomly branching configurations. Here we study an elastic lattice model for tightly double-folded ring polymers, which allows for the spontaneous creation and deletion of side branches coupled to a diffusive mass transport, which is local both in space and on the connectivity graph of the tree. We use Monte Carlo simulations to study systems falling into three different universality classes: ideal double-folded rings without excluded volume interactions, self-avoiding double-folded rings, and double-folded rings in the melt state. The observed static properties... 

The ultrathin films of pyrochlore lattice along [111] direction provide a fertile ground for exploring topological states in oxide materials, where the electron correlations are strong and magnetically ordered states are favored. As a result of strong interactions, most of states are magnetic insulators with strong Dzyaloshinskii–Moriya and anisotropic spin interactions. We considered three types of heterostructures, a bilayer of triangular-kagome (TK), and two trilayers of triangular-kagome-triangular (TKT) and kagome-triangular-kagome (KTK) thin films. The ground states are magnetically ordered with the low-energy excitations, the magnons, characterized by nontrivial topology. While for TK... 

Blends of low-density polyethylene (LDPE) and poly[ethylene-co-(vinyl acetate)] (PEVA), crosslinked by electron-beam (EB) radiation, formed separate crystalline lattices with a homogeneous amorphous phase. The crystallinity of the EB-exposed samples slightly decreased, as verified by a slight reduction in the densities and melting heats and temperatures of the samples. The results obtained from both gel content and hot set tests showed that the degree of crosslinking in the amorphous regions was dependent on the dose and blend composition. The molecular weights between the crosslinks, measured from creep data, showed that an increasing PEVA content resulted in tighter network structures,... 

Mindlin's (1965) second strain gradient theory due to its competency in capturing the effects of edges, corners, and surfaces is of particular interest. Formulation in this framework, in addition to the usual Lamé constants, requires the knowledge of sixteen additional materials constants. To date, there are no successful experimental techniques for measuring these material parameters which reflect the discrete nature of matter. The present work gives an accurate remedy for the atomistic calculations of these parameters by utilizing the first principles density functional theory (DFT) for the calculations of the atomic force constants combined with an analytical formulation. It will be shown...