We analyze, both analytically and numerically, the effectiveness
of cloaking an infinite cylinder from observations by electromagnetic
waves in three dimensions. We show that, as truncated approximations
of the ideal permittivity and permeability tensors tend towards
the singular ideal cloaking fields, so that the anisotropy ratio tends to
infinity, the D and B fields blow up near the cloaking surface. Since
the metamaterials used to implement cloaking are based on effective
medium theory, the resulting large variation in D and B will pose a
challenge to the suitability of the field averaged characterization of "
and 碌. We also consider cloaking with and without the SHS (softand-
hard surface) lining, shown in [6] to be theoretically necessary
for cloaking in the cylindrical geometry. We demonstrate numerically
that cloaking is significantly improved by the SHS lining, with both
the far field of the scattered wave significantly reduced and the blow
up of D and B prevented.
GNU Octave is a high-level language, primarily intended for numerical
computations. It provides a convenient command line interface for
solving linear and nonlinear problems numerically.
This tutorial was prepared for our freshman engineering students using the student version of MATLAB, because symbolic computations are covered in almost no introductory textbook. We are pleased to make it available to the international community, and would appreciate suggestions for its improvement. MATLAB’s symbolic engine permits the user to do things easily that are difficult or impossible to do numerically
Regardless of the branch of science or engineering, theoreticians have always
been enamored with the notion of expressing their results in the form of
closed-form expressions. Quite often, the elegance of the closed-form solution
is overshadowed by the complexity of its form and the difficulty in evaluating
it numerically. In such instances, one becomes motivated to search instead for
a solution that is simple in form and simple to evaluate.
Regardless of the branch of science or engineering, theoreticians have always been
enamored with the notion of expressing their results in the form of closed-form
expressions. Quite often the elegance of the closed-form solution is overshadowed
by the complexity of its form and the difficulty in evaluating it numerically. In
such instances, one becomes motivated to search instead for a solution that is
simple in form and likewise simple to evaluate.
The basic topic of this book is solving problems from system and control theory using
convex optimization. We show that a wide variety of problems arising in system
and control theory can be reduced to a handful of standard convex and quasiconvex
optimization problems that involve matrix inequalities. For a few special cases there
are “analytic solutions” to these problems, but our main point is that they can be
solved numerically in all cases. These standard problems can be solved in polynomial-
time (by, e.g., the ellipsoid algorithm of Shor, Nemirovskii, and Yudin), and so are
tractable, at least in a theoretical sense. Recently developed interior-point methods
for these standard problems have been found to be extremely efficient in practice.
Therefore, we consider the original problems from system and control theory as solved.
