Optimal design of pipes in series: An explicit approximation

This paper introduces a new methodology for the optimum design of pipes in series, named Optimum Hydraulic Grade Line (OHGL). This methodology is explicit and is based on the knowledge of the series topology and the geometrical distribution of water demands on nodes, i.e. the way in which the pipe in series delivers water mass as function of the distance from the entrance. OHGL consists in the pre-determination of that hydraulic grade line which gives the minimum construction cost, in an explicit way. Once this line has been established, calculation of the pipe’s continuous diameters is direct; after a round up to commercial diameters is developed. To validate the proposed methodology, several pipes in series were designed both using GA and OHGL. Four hundred series were used in total, each with different topological characteristics and demands. Keywords: Pipe in series, optimum design, genetic algorithms, optimum hydraulic grade line

A computational approach to the Thompson group FF

Let $F$ denote the Thompson group with standard generators $A=x_0$, $B=x_1$. It is a long standing open problem whether $F$ is an amenable group. By a result of Kesten from 1959, amenability of $F$ is equivalent to $$(i)\qquad ||I+A+B||=3$$ and to $$(ii)\qquad ||A+A^{-1}+B+B^{-1}||=4,$$ where in both cases the norm of an element in the group ring $\mathbb{C} F$ is computed in $B(\ell^2(F))$ via the regular representation of $F$. By extensive numerical computations, we obtain precise lower bounds for the norms in $(i)$ and $(ii)$, as well as good estimates of the spectral distributions of $(I+A+B)^*(I+A+B)$ and of $A+A^{-1}+B+B^{-1}$ with respect to the tracial state $\tau$ on the group von Neumann Algebra $L(F)$. Our computational results suggest, that $$||I+A+B||\approx 2.95 \qquad ||A+A^{-1}+B+B^{-1}||\approx 3.87.$$ It is however hard to obtain precise upper bounds for the norms, and our methods cannot be used to prove non-amenability of $F$.Comment: appears in International Journal of Algebra and Computation (2015

Circuit Quantum Electrodynamics with a Superconducting Quantum Point Contact

We consider a superconducting quantum point contact in a circuit quantum electrodynamics setup. We study three different configurations, attainable with current technology, where a quantum point contact is coupled galvanically to a coplanar waveguide resonator. Furthermore, we demonstrate that the strong and ultrastrong coupling regimes can be achieved with realistic parameters, allowing the coherent exchange between a superconducting quantum point contact and a quantized intracavity field.Comment: 5 pages, 4 figures. Updated version, accepted for publication as a Rapid Communication in Physical Review

Parity-dependent State Engineering and Tomography in the ultrastrong coupling regime

Reaching the strong coupling regime of light-matter interaction has led to an impressive development in fundamental quantum physics and applications to quantum information processing. Latests advances in different quantum technologies, like superconducting circuits or semiconductor quantum wells, show that the ultrastrong coupling regime (USC) can also be achieved, where novel physical phenomena and potential computational benefits have been predicted. Nevertheless, the lack of effective decoupling mechanism in this regime has so far hindered control and measurement processes. Here, we propose a method based on parity symmetry conservation that allows for the generation and reconstruction of arbitrary states in the ultrastrong coupling regime of light-matter interactions. Our protocol requires minimal external resources by making use of the coupling between the USC system and an ancillary two-level quantum system.Comment: Improved version. 9 pages, 5 figure

Quantum Simulations of Relativistic Quantum Physics in Circuit QED

We present a scheme for simulating relativistic quantum physics in circuit quantum electrodynamics. By using three classical microwave drives, we show that a superconducting qubit strongly-coupled to a resonator field mode can be used to simulate the dynamics of the Dirac equation and Klein paradox in all regimes. Using the same setup we also propose the implementation of the Foldy-Wouthuysen canonical transformation, after which the time derivative of the position operator becomes a constant of the motion.Comment: 13 pages, 3 figure