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Our main result is that every n-dimensional polytope can be
described by at most 2n ? 1 polynomial inequalities and, moreover, these
polynomials can explicitly be constructed. For an n-dimensional pointed
polyhedral cone we prove the bound 2n ? 2 and for arbitrary polyhedra we
get a constructible representation by 2n polynomial inequalities.
Traveling wave equations are used to model the dynamics of multisection semiconductor lasers. To perform a bifurcation analysis of this system of 1-D partial differential equations its low dimensional approximations are constructed and considered. Along this paper this analysis is used for the extensive study of the pulsations in a three section distributed feedback laser. Namely, stability of pulsations, different bifurcation scenaria, tunability of the pulsation frequency and its locking by the frequency of electrical modulation are considered. All these pulsation qualities are highly important when applying lasers in optical communication systems.
We present an integer linear programming model for the design of multi-layer telecommunication
networks which are based on connection-oriented routing protocols. The formulation integrates hardware,
capacity, routing, and grooming decisions in any number of network layers. Practical hardware
restrictions and cost can accurately be taken into account.
We present a new iterative procedure for solving the multiple stopping
problem in discrete time and discuss the stability of the algorithm.
The algorithm produces monotonically increasing approximations of the
Snell envelope, which coincide with the Snell envelope after finitely many
steps. Contrary to backward dynamic programming, the algorithm allows
to calculate approximative solutions with only a few nestings of conditional
expectations and is, therefore, tailor-made for a plain Monte-Carlo
implementation.
We consider a sequence of curved rods which consist of isotropic material and which are clamped on the lower base or on both bases. We study the asymptotic behaviour of the stress tensor and displacement under the assumptions of linearized elasticity when the cross-sectional diameter of the rods tends to zero and the body force is given in the particular form. The analysis covers the case of a non-smooth limit line of centroids. We show how the body force and the choice of the approximating curved rods can affect the strong convergence and the limit form of the stress tensor for the curved rods clamped on both bases.
We prove the existence, uniqueness, regularity and smooth dependence
of the weak solution on the initial data for a certain class of semilinear first order
dissipative hyperbolic systems with spacially discontinuous coefficients. Such
kind of hyperbolic problems have succesfully been used to describe the dynamics
of distributed feedback multisection semiconductor lasers in recent years. We
show that in a suitable function space of continuous functions the weak solutions
generate a smooth semiflow.
The Modified Nodal Analysis leads to differential algebraic equations
with properly stated leading terms. In this article a special structure of the DAEs
modelling electrical circuits is exploited in order to derive a new decoupling for
nonlinear index-2 DAEs. This decoupling procedure leads to a solvability result and
is also used to study general linear methods, a class of numerical schemes that covers
both Runge-Kutta and linear multistep methods. Convergence for index-2 DAEs is
proved.
We simulate and analyse a 1D-PDE model describing the dynamics of multisection semiconductor lasers. We demonstrate how a semi-analytical computation of the spectrum and the corresponding eigenfunction expansion of the computed solutions provides a useful information allowing to achieve a better understanding of the laser dynamics. Basic algorithms implemented into a corresponding software tool are described.
An in-depth theoretical as well as experimental analysis of the nonlinear dynamics in semiconductor lasers
with active optical feedback is presented. Use of a monolithically integrated multisection device of submillimeter
total length provides access to the short-cavity regime. By introducing an amplifier section as a special
feature, phase and strength of the feedback can be separately tuned. In this way, the number of modes involved
in the laser action can be adjusted. We predict and observe specific dynamical scenarios. Bifurcations mediate
various transitions in the device output, from single-mode steadystate to self-pulsation and between different
kinds of self-pulsations, reaching eventually chaotic behavior in the multimode limit.
Im Zentrum der Arbeiten soll die Chaos- und Kohärenzkontrolle von Halbleiterlasern mit gegenseitiger optischer Kopplung stehen. Diese Fragestellung ist von erheblicher praktischer Relevanz, da Rauschen und chaotisches Verhalten generelle Probleme in der optischen Hochgeschwindigkeitskommunikation sind. Die Kontrolle von optischen Systemen mit komplexer Selbstorganisation stellt aber auch aus grundsätzlicher Sicht Neuland dar. Hierfür geeignete Konzepte sind bisher weder überzeugend theoretisch beschrieben noch experimentell umgesetzt.