Threshold of Singularity Formation in the Semilinear Wave Equation

Solutions of the semilinear wave equation are found numerically in three spatial dimensions with no assumed symmetry using distributed adaptive mesh refinement. The threshold of singularity formation is studied for the two cases in which the exponent of the nonlinear term is either $p=5$ or $p=7$. Near the threshold of singularity formation, numerical solutions suggest an approach to self-similarity for the $p=7$ case and an approach to a scale evolving static solution for $p=5$.Comment: 6 pages, 7 figure

Using a prisoner advisory group to develop diversity research in a maximum-security prison

This paper addresses groupwork processes with a group of prisoners advising a research project in a maximum-security prison in England. The research project (Appreciative Inquiry into the Diversity Strategy of HMP Wakefield. RES-000-22-3441) was funded by the Economic and Social Research Council (ESRC) and lasted 9 months. The research explored the experiences of prisoners in diverse minority groupings and the strategies of the prison to accommodate the complex needs of these groups. The Prisoner Advisory Group (PAG) was made up of representatives from Black and Minority Ethnic (BME) prisoners; older prisoners (over 60s); Disabled prisoners (with physical disabilities, learning difficulties; and mental health problems); Gay, Bi-sexual and Transgender prisoners; and prisoners affiliated to Faith groups. It met regularly during the research. The paper considers the forming norming and performing aspects of establishing an effective participant voice in a prison-based project. It considers the contribution of the PAG to developing a research strategy that engaged prisoners in the research. It reflects on the nature of ‘participative research’ in general and whether such research is possible within a high-security prison environment

Properties of global monopoles with an event horizon

We investigate the properties of global monopoles with an event horizon. We find that there is an unstable circular orbit even if a particle does not have an angular momentum when the core mass is negative. We also obtain the asymptotic form of solutions when the event horizon is much larger than the core radius of the monopole, and discuss if they could be a model of galactic halos.Comment: 5 pages, 7 figure

Analysis of the feasibility of an experiment to measure carbon monoxide in the atmosphere

The feasibility of measuring atmospheric carbon monoxide from a remote platform using the correlation interferometry technique was considered. It has been determined that CO data can be obtained with an accuracy of 10 percent using this technique on the first overtone band of CO at 2.3 mu. That band has been found to be much more suitable than the stronger fundamental band at 4.6 mu. Calculations for both wavelengths are presented which illustrate the effects of atmospheric temperature profiles, inversion layers, ground temperature and emissivity, CO profile, reflectivity, and atmospheric pressure. The applicable radiative transfer theory on which these calculations are based is described together with the principles of the technique

Black Hole Critical Phenomena Without Black Holes

Studying the threshold of black hole formation via numerical evolution has led to the discovery of fascinating nonlinear phenomena. Power-law mass scaling, aspects of universality, and self-similarity have now been found for a large variety of models. However, questions remain. Here I briefly review critical phenomena, discuss some recent results, and describe a model which demonstrates similar phenomena without gravity.Comment: 13 pages, 6 figures; Submission for the proceedings of ICGC 2000 in the journal Preman

Stability and Observability of Magnetic Primordial Black Hole-Neutron Star Collisions

The collision of a primordial black hole with a neutron star results in the black hole eventually consuming the entire neutron star. However, if the black hole is magnetically charged, and therefore stable against decay by Hawking radiation, the consequences can be quite different. Upon colliding with a neutron star, a magnetic black hole very rapidly comes to a stop. For large enough magnetic charge, we show that this collision can be detected as a sudden change in the rotation period of the neutron star, a glitch or anti-glitch.We argue that the magnetic primordial black hole, which then settles to the core of the neutron star, does not necessarily devour the entire neutron star; the system can instead reach a long-lived, quasi-stable equilibrium. Because the black hole is microscopic compared to the neutron star, most stellar properties remain unchanged compared to before the collision. However, the neutron star will heat up and its surface magnetic field could potentially change, both effects potentially observable.Comment: 16 pages, 5 figure

Continuous wavelet transform ridge extraction for spectral interferometry imaging

The combination of wavelength multiplexing and spectral interferometry allows for the encoding of multidimensional information and its transmission over a mono-dimensional channel; for example, measurements of a surface's topography acquired through a monomode fiber in a small endoscope. The local depth of the imaged object is encoded in the local spatial frequency of the signal measured at the output of the fiber-decoder system. We propose a procedure to retrieve the depth-map by determining the signal's instantaneous frequency. First, we compute its continuous, complex-valued, wavelet transform (CWT). The frequency signature at every position is contained in the resulting scalogram. We then extract the ridge of maximal response by use of a dynamic programming algorithm thus directly recovering the object's topography. We present results that validate this procedure based on both simulated and experimental data

Induced scalarization in boson stars and scalar gravitational radiation

The dynamical evolution of boson stars in scalar-tensor theories of gravity is considered in the physical (Jordan) frame. We focus on the study of spontaneous and induced scalarization, for which we take as initial data configurations on the well-known S-branch of a single boson star in general relativity. We show that during the scalarization process a strong emission of scalar radiation occurs. The new stable configurations (S-branch) of a single boson star within a particular scalar-tensor theory are also presented.Comment: 18 pages, 11 figures. Minor changes to match the published versio

Voronoi diagrams on piecewise flat surfaces and an application to biological growth

This paper introduces the notion of Voronoi diagrams and Delaunay triangulations generated by the vertices of a piecewise flat, triangulated surface. Based on properties of such structures, a generalized flip algorithm to construct the Delaunay triangulation and Voronoi diagram is presented. An application to biological membrane growth modeling is then given. A Voronoi partition of the membrane into cells is maintained during the growth process, which is driven by the creation of new cells and by restitutive forces of the elastic membrane