Mode stability on the real axis

A generalization of the mode stability result of Whiting (1989) for the Teukolsky equation is proved for the case of real frequencies. The main result of the paper states that a separated solution of the Teukolsky equation governing massless test fields on the Kerr spacetime, which is purely outgoing at infinity, and purely ingoing at the horizon, must vanish. This has the consequence, that for real frequencies, there are linearly independent fundamental solutions of the radial Teukolsky equation which are purely ingoing at the horizon, and purely outgoing at infinity, respectively. This fact yields a representation formula for solutions of the inhomogenous Teukolsky equation.Comment: 20 pages, 4 figures. Reference added, revtex4-1 forma

No Events on Closed Causal Curves

We introduce the Causal Compatibility Conjecture for the Events, Trees, Histories (ETH) approach to Quantum Theory (QT) in the semi-classical setting. We then prove that under the assumptions of the conjecture, points on closed causal curves are physically indistinguishable in the context of the ETH approach to QT and thus the conjecture implies a compatibility of the causal structures even in presence of closed causal curves. As a consequence of this result there is no observation that could be made by an observer to tell any two points on a closed causal curve apart. We thus conclude that closed causal curves have no physical significance in the context of the ETH approach to QT. This is an indication that time travel will not be possible in a full quantum theory of gravity and thus forever remain a fantasy

Structured coprime factor model reduction based on LMIs

In this paper we discuss dynamic model reduction methods which preserve a certain structure in the underlying system. Specifically, we consider the situation where the reduction must be consistent with a partition of the system states. This is motivated, for instance, in situations where state variables are associated with the topology of a networked system, and the reduction should preserve this. We build on the observation that imposing block structure to generalized controllability and observability gramians automatically yields such state-partitioned model reduction. The difficulty lies in ensuring feasibility of the resulting Lyapunov inequalities, which is in general very restrictive. To overcome this, we consider coprime factor model reduction. We derive an LMI characterization of expansive and contractive coprime factorizations that preserve structure, and use this to build a more flexible method for structured model reduction. An example is given to illustrate the method. © 2004 Elsevier Ltd. All rights reserved

LMI relaxation to Riccati equations in structured ℋ<inf>2</inf> control

In this paper we discuss structured [image omitted] control methods for large-scale interconnected systems. Based on a relaxation of Riccati equations, we derive some linear matrix inequality (LMI) conditions for sub-optimal controllers in which information structure can be imposed. In particular, we derive controllers by solving low-dimensional LMIs, which are decentralized except for the sharing information between neighbours, as determined by the plant interconnection; also we optimize a performance bound for each of the derived controllers

Fireshape: a shape optimization toolbox for Firedrake

Shape optimization studies how to design a domain such that a shape function is minimized. Ubiquitous in industrial applications, shape optimization is often constrained to partial differential equations (PDEs). One of the main challenges in PDE-constrained shape optimization is the coupling of domain updates and PDE-solvers. Fireshape addresses this challenge by elegantly coupling the finite element library Firedrake and the Rapid Optimization Library (ROL). The main features of Fireshape are: accessibility to users with minimal shape optimization knowledge; decoupled discretization of control and state variables; full access to Firedrake's PDE-solvers; automated derivation of adjoint equations and shape derivatives; different metrics to define shape gradients; access to ROL's optimization algorithms via PyROL. Fireshape is available at https://github.com/fireshape/fireshape. Fireshape's documentation comprises several tutorials and is available at https://fireshape.readthedocs.io/en/latest/

Modified Measures as an Effective Theory for Causal Fermion Systems

We compare the structures of the theory of causal fermion systems (CFS), an approach to unify Quantum Theory with General Relativity, with those of modified measure theories (MMT), which are a set of modified gravity theories. Spacetimes with MMT can be obtained as the continuum limit of a CFS. This suggests that MMT could serve as effective descriptions of modifications to General Relativity implied by CFS. The goal is to lay the foundation for future research on exploring which MMTs are consistent with the causal action principle of CFS