How does gravity save or kill Q-balls?

We explore stability of gravitating Q-balls with potential $V_4(\phi)={m^2\over2}\phi^2-\lambda\phi^4+\frac{\phi^6}{M^2}$ via catastrophe theory, as an extension of our previous work on Q-balls with potential $V_3(\phi)={m^2\over2}\phi^2-\mu\phi^3+\lambda\phi^4$. In flat spacetime Q-balls with $V_4$ in the thick-wall limit are unstable and there is a minimum charge $Q_{{\rm min}}$, where Q-balls with $Q<Q_{{\rm min}}$ are nonexistent. If we take self-gravity into account, on the other hand, there exist stable Q-balls with arbitrarily small charge, no matter how weak gravity is. That is, gravity saves Q-balls with small charge. We also show how stability of Q-balls changes as gravity becomes strong.Comment: 10 pages, 10 figure

Unified pictures of Q-balls and Q-tubes

While Q-balls have been investigated intensively for many years, another type of nontopological solutions, Q-tubes, have not been understood very well. In this paper we make a comparative study of Q-balls and Q-tubes. First, we investigate their equilibrium solutions for four types of potentials. We find, for example, that in some models the charge-energy relation is similar between Q-balls and Q-tubes while in other models the relation is quite different between them. To understand what determines the charge-energy relation, which is a key of stability of the equilibrium solutions, we establish an analytical method to obtain the two limit values of the energy and the charge. Our prescription indicates how the existent domain of solutions and their stability depends on their shape as well as potentials, which would also be useful for a future study of Q-objects in higher-dimensional spacetime.Comment: 11 pages, 14 figure

Fuzzy geometry

The concept of fuzzy space is due independently to Poincaré and Zeeman. (Poincaré used the term "physical continuum", Zeeman the term "tolerance space". I have reluctantly introduced a third expression since my attempts to generate a vocabulary from either of these have all proved impossibly unwieldy.) Both were led to it by the nature of our perception of space, and both adapted to it tools current in topology. Unfortunately, neither examined the application of these tools in complete detail, and as a result the argument from analogy was somewhat over-extended by both. The resemblances to topology are strong; the differences are sometimes glaring and sometimes subtle. In the latter case the difficulties produced by a topologically-conditioned intuition can be severe obstacles to progress. (Certainly, having been reared mathematically as a topologist I have found it necessary to distrust any conclusion whose proof is not painfully precise. ) For this reason many of the proofs in this paper are set out in somewhat more detail than would be natural in a more established field. For this reason also I have here not only set out the positive results I have so far obtained in the subject but, for the benefit of topologists, elaborated on the failures of analogy with topology where a more succinct exposition would have ignored them as dead ends (e.g., in Chap. I, §2)

Overheating in Scotland : lessons from 26 monitored low energy homes

There is growing awareness in the UK that overheating is a significant problem and one that is likely to intensify with climate change, increasing urbanisation, an ageing population and the move towards ?low energy? buildings. Recent research suggested that while overheating may be an issue in the South of England, particularly in urban areas, it was not likely to be an issue for Scotland and the North of the UK in the medium term. This notion is reflected in the lack of awareness of the issue in Scotland. Monitoring of 26 new-build low energy and Passivhaus homes across Scotland over a two year period indicates overheating is prevalent in living areas and in particular in bedrooms where it is acknowledged that respite from high temperatures is important. This paper describes the quantitative and qualitative results, assesses relevant factors, comments on predictive tools used and seeks a robust series of measures to avoid overheating in future low energy homes in Scotland

Mode Bifurcation and Fold Points of Complex Dispersion Curves for the Metamaterial Goubau Line

In this paper the complex dispersion curves of the four lowest-order transverse magnetic modes of a dielectric Goubau line ($\epsilon>0, \mu>0$) are compared with those of a dispersive metamaterial Goubau line. The vastly different dispersion curve structure for the metamaterial Goubau line is characterized by unusual features such as mode bifurcation, complex fold points, both proper and improper complex modes, and merging of complex and real modes

An Application of Caustics to Ultrasonic Defect Location

In this paper we describe a use of ultrasonic caustics to detect and locate defects in immersed rods and pipes.</p