There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

With digital equipment becoming increasingly networked, either on wired or wireless networks, for personal and professional use alike, distributed software systems have become a crucial element in information and communications technologies. The study of these systems forms the core of the ARLES' work, which is specifically concerned with defining new system software architectures, based on the use of emerging networking technologies. In this context, we concentrate on the study of distributed systems which bring to life the vision of ubiquitous computing systems, also known as ambient intelligence.

반도체 공정 overview

The term photonic crystals appears because of the analogy between electron waves in crystals and the light waves in artificial periodic dielectric structures. During the recent years the investigation of one-, two-and three-dimensional periodic structures has attracted a widespread attention of the world optics community because of great potentiality of such structures in advanced applied optical fields. The interest in periodic structures has been stimulated by the fast development of semiconductor technology that now allows the fabrication of artificial structures, whose period is comparable with the wavelength of light in the visible and infrared ranges.

http://ieeexplore.ieee.org/iel5/6354/16969/00781867.pdf

Photonic crystals

https://msvlab.hre.ntou.edu.tw/mcs2008-dehghan.pdf

A numerical method for solution of the two-dimensional sine-Gordon equation using the radial basis functions

We present a survey of the theory of the Lyapunov Characteristic Exponents (LCEs) for dynamical systems, as well as of the numerical techniques developed for the computation of the maximal, of few and of all of them. After some historical notes on the first attempts for the numerical evaluation of LCEs, we discuss in detail the multiplicative ergodic theorem of Oseledec (102), which pro- vides the theoretical basis for the computation of the LCEs. Then, we analyze the algorithm for the computation of the maximal LCE, whose value has been exten- sively used as an indicator of chaos, and the algorithm of the so-called standard method, developed by Benettin et al. (14), for the computation of many LCEs. We also consider different discrete and continuous methods for computing the LCEs based on the QR or the singular value decomposition techniques. Although we are mainly interested in finite-dimensional conservative systems, i.e., autonomous Hamiltonian systems and symplectic maps, we also briefly refer to the evaluation of LCEs of dissipative systems and time series. The relation of two chaos detection techniques, namely the fast Lyapunov indicator (FLI) and the generalized alignment index (GALI), to the computation of the LCEs is also discussed.

https://www.springer.com/cda/content/document/cda_downloaddocument/9783642044571-c1.pdf?SGWID=0-0-45-855958-p173923511

The Lyapunov Characteristic Exponents and Their Computation

Numerical solutions of the perturbed Sine-Gordon equation in two space variables, arising from a Josephson junction are presented The method proposed arises from a two-step, one parameter method for the numerical solution of second-order ordinary differential equations Though implicit in nature, the method is applied explicitly Global extrapolation in both space and time is used to improve the accuracy The method is analysed with respect to stability criteria and numerical dispersion Numerical results are obtained for various cases involving line and ring solitons

Numerical solutions of a damped Sine-Gordon equation in two space variables

Numerical simulation of liquid sloshing phenomena in partially filled containers

Simple, mesh/grid free, explicit and implicit numerical schemes for the solution of linear advection-diffusion problems is developed and validated herein. Unlike the mesh or grid-based methods, these schemes use well distributed quasi-random points and approximate the solution using global radial basis functions. The schemes can be seen as generalized finite differences with random points instead of a regular grid system. This allows the computation of problems with complex-shaped boundaries in higher dimensions with no need for complex mesh/grid structure and with no extra implementation difficulties.

/pdf/explicit-and-implicit-meshless-methods-for-linear-advection-44dxli7g2a.pdf

Explicit and implicit meshless methods for linear advection–diffusion-type partial differential equations

A rational cubic spline based on function values

A meshless collocation method based on radial basis functions is proposed for solving the steady incompressible Navier-Stokes equations. This method has the capability of solving the governing equations using scattered nodes in the domain. We use the streamfunction formulation, and a trust-region method for solving the nonlinear problem. The no-slip boundary conditions are satisfied using a ghost node strategy. The efficiency of this method is demonstrated by solving three model problems: the driven cavity flows in square and rectangular domains and flow over a backward-facing step. The results obtained are in good agreement with benchmark solutions.

Kamal Djidjeli

Papers

Numerical solutions of a damped Sine-Gordon equation in two space variables

Numerical simulation of liquid sloshing phenomena in partially filled containers

Explicit and implicit meshless methods for linear advection–diffusion-type partial differential equations

A rational cubic spline based on function values

Radial basis function meshless method for the steady incompressible Navier-Stokes equations