Search results for "singular"

Understanding the microscopic processes that govern the charge-induced deformation of carbon nanotubes

2009

While carbon nanotubes have technological potential as actuators, the underlying actuation mechanisms remain poorly understood. We calculate charge-induced stresses and strains for electrochemical actuation of carbon nanotubes with different chiralities and defects, using density-functional theory and various tight-binding models. For a given deformation mode the concept of bonding and antibonding orbitals can be redefined depending on the sign of a differential band-structure stress. We use this theoretical framework to analyze orbital contributions to the actuation. These show charge asymmetric behavior which is due to next-nearest-neighbor hopping while Coulombic contributions account fo…

Modelling of Pe C alloys solidification using the artificial heat source method

1997

Abstract In the paper the numerical solutions concerning the cast iron and also the carbon steel solidification are presented. In order to take into account the non-linearities appearing in differential equations describing the boundary-initial problem considered — a certain algorithm called the artificial heat source method has been used. The examples illustrating the possibilities of proposed method applications have been solved by means of the boundary element method, but the others numerical methods can be also utilized.

Magneto-Electro-Elastic Bimorph Analysis by the Boundary Element Method

2008

The influence of the magnetic configuration on the behavior of magneto-electro-elastic bimorph beams is analyzed by using a boundary element approach. The problem is formulated by using the generalized displacements and generalized tractions. The boundary integral equation formulation is obtained by extending the reciprocity theorem to magneto-electro-elastic problems; it is numerically implemented by using the boundary element method multidomain technique to address problems involving nonhomogeneous configurations. Results under different magnetic configurations are compared highlighting the characteristic features of magnetopiezoelectric behavior particularly focusing on the link between …

Series expansion for the effective conductivity of a periodic dilute composite with thermal resistance at the two-phase interface

2019

We study the asymptotic behavior of the effective thermal conductivity of a periodic two-phase dilute composite obtained by introducing into an infinite homogeneous matrix a periodic set of inclusions of a different material, each of them of size proportional to a positive parameter ?. We assume that the normal component of the heat flux is continuous at the two-phase interface, while we impose that the temperature field displays a jump proportional to the normal heat flux. For ? small, we prove that the effective conductivity can be represented as a convergent power series in ? and we determine the coefficients in terms of the solutions of explicit systems of integral equations.

Size effects on the plastic collapse limit load of thin foils in bending and thin wires in torsion

2011

Abstract Following a previous paper by the author [Strain gradient plasticity, strengthening effects and plastic limit analysis, Int. J. Solids Struct. 47 (2010) 100–112], a nonconventional plastic limit analysis for a particular class of micron scale structures as, typically, thin foils in bending and thin wires in torsion, is here addressed. An idealized rigid-perfectly plastic material is considered, which is featured by a strengthening potential degree-one homogeneous function of the effective plastic strain and its spatial gradient. The nonlocal (gradient) nature of the material resides in the inherent strengthening law, whereby the yield strength is related to the effective plastic st…

Singular value decomposition approach to the yttrium occurrence in mineral maps of rare earth element ores using laser-induced breakdown spectroscopy

2017

Laser-induced breakdown spectroscopy (LIBS) has been used in analysis of rare earth element (REE) ores from the geological formation of Norra Kärr Alkaline Complex in southern Sweden. Yttrium has been detected in eudialyte (Na15 Ca6(Fe,Mn)3 Zr3Si(Si25O73)(O,OH,H2O)3 (OH,Cl)2) and catapleiite (Ca/Na2ZrSi3O9·2H2O). Singular value decomposition (SVD) has been employed in classification of the minerals in the rock samples and maps representing the mineralogy in the sampled area have been constructed. Based on the SVD classification the percentage of the yttrium-bearing ore minerals can be calculated even in fine-grained rock samples. peerReviewed

A Variational Approach to Boundary Element Methods

1988

Numerical study of blow-up and dispersive shocks in solutions to generalized Korteweg–de Vries equations

2015

Abstract We present a detailed numerical study of solutions to general Korteweg–de Vries equations with critical and supercritical nonlinearity, both in the context of dispersive shocks and blow-up. We study the stability of solitons and show that they are unstable against being radiated away and blow-up. In the L 2 critical case, the blow-up mechanism by Martel, Merle and Raphael can be numerically identified. In the limit of small dispersion, it is shown that a dispersive shock always appears before an eventual blow-up. In the latter case, always the first soliton to appear will blow up. It is shown that the same type of blow-up as for the perturbations of the soliton can be observed whic…

Nonlocal Third Order Boundary Value Problems with Solutions that Change Sign

2014

We investigate the existence and the number of solutions for a third order boundary value problem with nonlocal boundary conditions in connection with the oscillatory behavior of solutions. The combination of the shooting method and scaling method is used in the proofs of our main results. Examples are included to illustrate the results.

Numerical model of macro-segregation during directional crystallization process

1998

Abstract In the paper the mathematical model of macro-segregation proceeding during the directional crystallization process is presented. The boundary-initial problem considered is discussed. Next the numerical approximation constructed on the basis of the boundary element method supplemented by a procedure called the artificial heat source method is described. The boundary condition on the solidification front resulting from the alloy component balance is introduced, while in finally the practical aspects of computations concerning the course of the process are discussed.