The existence of travelling waves of the discrete Nagumo equation

This thesis considers solutions to the discrete Nagumo equation u˙ n = d(un−1 − 2un + un+1) + f(un), n ∈ Z. For sufficiently large d, the solutions are of the form un(t) = U(n + ct) with c > 0. This thesis contains the proof of existence of traveling wave solutions of the discrete Nagumo equations and originates from...

Portable Parameter Analyser for Organs-on-Chip: Power Budget Analyses

Problems in drug development and personalised disease treatments are the main impulse for the development of OoCs. At the Electronic Components, Technology and Materials (ECTM) group at TU Delft an OoC sensor has been developed and the design is now at a stage where a system can be developed to take the sensor out of the initial research...

A review of optimal cloning of pure quantum states

In this project, quantum cloning machines are analyzed that take in N quantum systems in the same unknown pure state and output M quantum systems with M > N, such that the output best resembles the ideal, but impossible output of an M-fold tensor product of the pure input state. The proof of Keyl and Werner is reviewed in which a unique...

Properties of the Racahpolynomials with regard to the Lie algebrarepresentation of sl(2;C)

The Racah polynomial Rn(λ(x)) is a polynomial of degree n and is variable in λ(x). In this thesis two properties of this polynomial will be studied. One is the orthogonal property of the Racah polynomial. And the other is that the Racah polynomial can also be described as a polynomial of degree x and variable over λ(n). The Racah polynomials...

De verschillende aspecten van Riemanns ?-functie

In dit verslag wordt de analytische uitbreiding van de ?-functie besproken, samen met nog drie andere alternatieve schrijfwijzen. Er worden een aantal eigenschappen van de ?-functie en haar nulpunten afgeleid, waaronder een formule van het aantal nulpunten N(T) met imaginair deel tussen 0 en T. Daarna wordt numeriek aangetoond dat de pair...

Low-Cost Smith-Waterman Acceleration

Due to advancing technology, genetic sequencing has become cheaper over the years. This has caused the demand for computational power to grow even faster than Moore's law. To remedy this problem, we analyzed low-cost hardware solutions to parallelize the computational part of the genetic sequencing. We proposed a novel method for calculating the...