In this article, the anti-plane deformation of an orthotropic sector with multiple defects is studied analytically. The solution of a Volterra-type screw dislocation problem in a sector is first obtained by means of a finite Fourier cosine transform. The closed form solution is then derived for displacement and stress fields over the sector domain. Next, the distributed dislocation method is em...

We show that Lagrangian and Legendre varieties associated with matrix singularities and singularities of composite functions are stable in a sense which is a natural modification of Givental’s notion of stability of Lagrangian projections. The study of singular Lagrangian and Legendre varieties was initiated about twenty five years ago by Arnold when he was investigating singularities in the va...

Abstract. The paper gives the systematic analysis of singularities of transition The paper gives the systematic analysis of singularities of transition processes in general dynamical systems. Dynamical systems depending on parameter are studied. A system of relaxation times is constructed. Each relaxation time depends on three variables: initial conditions, parameters k of the system and accura...

Nonlinear vector fields have two important types of singularities: the fixed points in phase space and the time singularities in the complex plane. The first singularities are locally analyzed via normal form theory whereas the second ones are studied by the Painlevé analysis. In this paper, normal form theory is used to describe the solutions around their complex-time singularities. To do so, ...

Sudden singularities occur in FRW spacetimes when the scale factor remains finite and different from zero while some of its derivatives diverge. After proper rescaling, the scale factor close to such a singularity at t = 0 takes the form a(t) = 1 + c|t| (where c and η are parameters and η ≥ 0). We investigate analytically and numerically the geodesics of free and gravitationally bound particles...

1.1. Moduli of stable varieties: the case of surfaces. In the paper [KSB88], Kollár and Shepherd-Barron introduced stable surfaces as a generalization of stable curves. This class is natural from the point of view of the minimal model program, which shows that any one-parameter family of surfaces of general type admits a unique stable limit. Indeed, the stable reduction process of Deligne and M...

The singularities of manipulators with offset wrists are difficult to enumerate. This article presents a numerical study to illuminate singularity problems when using an offset wrist with an articulated regional arm. Ironically, the regional manipulator singularity problem is worsened when using a singularity-free offset wrist. No wrist singularities exist (they are forced by design to lie outs...

Dielectrophoresis (DEP) is broadly used in microfluidic systems for the cell therapies or medical diagnostics [1] because of its capability to handle and sort biological cells [2,3]. In this paper, a new method to trap cells on-chip with high density arraying capabilities is proposed. The principle is based on the use of metallic singularities arrayed within the flowing channel of the biochip. ...

The mathematical envelopes to families of both rigid and non-rigid moving shapes play a fundamental role in a variety of problems from very diverse application domains, from engineering design and manufacturing to computer graphics and computer assisted surgery. Geometric singularities in these envelopes are known to induce malfunctions or unintended system behavior, and the corresponding theor...