Can black holes have Euclidean cores?

The search for regular black hole solutions in classical gravity leads us to consider a core of Euclidean signature in the interior of a black hole. Solutions of Lorentzian and Euclidean general relativity match in such a way that energy densities and pressures of an isotropic perfect fluid form are everywhere finite and continuous. Although the weak energy condition cannot be satisfied for these solutions in general relativity, it can be when higher derivative terms are added. A numerical study shows how the transition becomes smoother in theories with more derivatives. As an alternative to the Euclidean core, we also discuss a closely related time dependent orbifold construction with a smooth space-like boundary inside the horizon.Comment: 14 pages with figures, version to appear in PR

Molecular dynamics simulations for the prediction of the dielectric spectra of alcohols, glycols, and monoethanolamine

The response of molecular systems to electromagnetic radiation in the microwave region (0.3–300 GHz) has been principally studied experimentally, using broadband dielectric spectroscopy. However, relaxation times corresponding to reorganisation of molecular dipoles due to their interaction with electromagnetic radiation at microwave frequencies are within the scope of modern molecular simulations. In this work, fluctuations of the total dipole moment of a molecular system, obtained through molecular dynamics simulations, are used to determine the dielectric spectra of water, a series of alcohols and glycols, and monoethanolamine. Although the force fields employed in this study have principally been developed to describe thermodynamic properties, most them give fairly good predictions of this dynamical property for these systems. However, the inaccuracy of some models and the long simulation times required for the accurate estimation of the static dielectric constant can sometimes be problematic. We show that the use of the experimental value for the static dielectric constant in the calculations, instead of the one predicted by the different models, yields satisfactory results for the dielectric spectra, and hence the heat absorbed from microwaves, avoiding the need for extraordinarily long simulations or re-calibration of molecular models

Freezing properties of alkenyl succinic anhydrides derived from linear isomerised olefins

Alkenyl succinic anhydrides are important specialty chemicals that are used in the paper, oilfield and fuel additives industries. In this paper we investigate the link between the physical properties of alkenyl succinic anhydrides and the identities of their linear alkyl olefin precursors. We describe a straightforward GC analysis of olefin isomer distributions and show that these correlate well with the freezing temperatures of the subsequent alkenyl succinic anhydride products. This allows the identification of olefin isomer profiles that are required to give the desired physical properties in the alkenyl succinic anhydrides; it also provides a method to predict the freezing temperatures of alkenyl succinic anhydrides synthesised from a particular supply of olefin

A Random Matrix Model of Adiabatic Quantum Computing

We present an analysis of the quantum adiabatic algorithm for solving hard instances of 3-SAT (an NP-complete problem) in terms of Random Matrix Theory (RMT). We determine the global regularity of the spectral fluctuations of the instantaneous Hamiltonians encountered during the interpolation between the starting Hamiltonians and the ones whose ground states encode the solutions to the computational problems of interest. At each interpolation point, we quantify the degree of regularity of the average spectral distribution via its Brody parameter, a measure that distinguishes regular (i.e., Poissonian) from chaotic (i.e., Wigner-type) distributions of normalized nearest-neighbor spacings. We find that for hard problem instances, i.e., those having a critical ratio of clauses to variables, the spectral fluctuations typically become irregular across a contiguous region of the interpolation parameter, while the spectrum is regular for easy instances. Within the hard region, RMT may be applied to obtain a mathematical model of the probability of avoided level crossings and concomitant failure rate of the adiabatic algorithm due to non-adiabatic Landau-Zener type transitions. Our model predicts that if the interpolation is performed at a uniform rate, the average failure rate of the quantum adiabatic algorithm, when averaged over hard problem instances, scales exponentially with increasing problem size.Comment: 9 pages, 7 figure

Dark Matter and Dark Energy

I briefly review our current understanding of dark matter and dark energy. The first part of this paper focusses on issues pertaining to dark matter including observational evidence for its existence, current constraints and the `abundance of substructure' and `cuspy core' issues which arise in CDM. I also briefly describe MOND. The second part of this review focusses on dark energy. In this part I discuss the significance of the cosmological constant problem which leads to a predicted value of the cosmological constant which is almost $10^{123}$ times larger than the observed value \la/8\pi G \simeq 10^{-47}GeV$^4$. Setting \la to this small value ensures that the acceleration of the universe is a fairly recent phenomenon giving rise to the `cosmic coincidence' conundrum according to which we live during a special epoch when the density in matter and \la are almost equal. Anthropic arguments are briefly discussed but more emphasis is placed upon dynamical dark energy models in which the equation of state is time dependent. These include Quintessence, Braneworld models, Chaplygin gas and Phantom energy. Model independent methods to determine the cosmic equation of state and the Statefinder diagnostic are also discussed. The Statefinder has the attractive property \atridot/a H^3 = 1 for LCDM, which is helpful for differentiating between LCDM and rival dark energy models. The review ends with a brief discussion of the fate of the universe in dark energy models.Comment: 40 pages, 11 figures, Lectures presented at the Second Aegean Summer School on the Early Universe, Syros, Greece, September 2003, New References added Final version to appear in the Proceeding

Quantum diffusion of microcavity solitons

Coherently pumped (Kerr) solitons in an ideal optical microcavity are expected to undergo random quantum motion that determines fundamental performance limits in applications of the soliton microcombs. Here this random walk and its impact on Kerr soliton timing jitter are studied experimentally. The quantum limit is discerned by measuring the relative position of counter-propagating solitons. Their relative motion features weak interactions and also presents common-mode suppression of technical noise, which typically hides the quantum fluctuations. This is in contrast to co-propagating solitons, which are found to have relative timing jitter well below the quantum limit of a single soliton on account of strong correlation of their mutual motion. Good agreement is found between theory and experiment. The results establish the fundamental limits to timing jitter in soliton microcombs and provide new insights on multisoliton physics

Constraints on alternative models to dark energy

The recent observations of type Ia supernovae strongly support that the universe is accelerating now and decelerated in the recent past. This may be the evidence of the breakdown of the standard Friemann equation. We consider a general modified Friedmann equation. Three different models are analyzed in detail. The current supernovae data and the Wilkinson microwave anisotropy probe data are used to constrain these models. A detailed analysis of the transition from the deceleration phase to the acceleration phase is also performed.Comment: 10 pages, 1 figure, revtex

Non-Abelian Monopole and Dyon Solutions in a Modified Einstein-Yang-Mills-Higgs System

We have studied a modified Yang-Mills-Higgs system coupled to Einstein gravity. The modification of the Einstein-Hilbert action involves a direct coupling of the Higgs field to the scalar curvature. In this modified system we are able to write a Bogomol'nyi type condition in curved space and demonstrate that the positive static energy functional is bounded from below. We then investigate non-Abelian sperically symmetric static solutions in a similar fashion to the `t Hooft-Polyakov monopole. After reviewing previously studied monopole solutions of this type, we extend the formalism to included electric charge and we present dyon solutions.Comment: 18 pages LaTeX, 7 eps-figure

Objective assessment of limb tissue elasticity : development of a manual indentation procedure

Rehabilitation Engineering CentreVersion of RecordPublishe

Constraining Modified Gravity and Growth with Weak Lensing

The idea that we live in a Universe undergoing a period of acceleration is a strongly held notion in cosmology. As this can, potentially, be explained with a modification to General Relativity we look at current cosmological data with the purpose of testing aspects of gravity. Firstly we constrain a phenomenological model (mDGP) motivated by a possible extra dimension. This is characterised by $\alpha$ which interpolates between (LCDM) and (the Dvali Gabadadze Porrati (DGP) model). In addition, we analyse general signatures of modified gravity given by the growth parameter $\gamma$ and power spectrum parameter $\Sigma$. We utilise Weak Lensing data (CFHTLS-wide) in combination with Baryon Acoustic Oscillations (BAOs) and Supernovae data. We show that current weak lensing data is not yet capable of constraining either model in isolation. However we demonstrate that this probe is highly beneficial, for in combination with BAOs and Supernovae we obtain $\alpha < 0.58$ and $\alpha < 0.91$ at $1\sigma$ and $2\sigma$, respectively. Without the lensing data no constraint is possible. Both analyses disfavour the flat DGP braneworld model ($\alpha = 1$) at over $2\sigma$. We highlight these are insensitive to potential systematics in the lensing data. For the growth signature $\gamma$ we show that, in combination, these probes do not yet have sufficient constraining power. Finally, we look beyond these present capabilities and demonstrate that Euclid, a future weak lensing survey, will deeply probe the nature of gravity. A $1\sigma$ error of 0.104 is found for $\alpha$ ($l_{max} = 500$) whereas for the general modified signatures we forecast $1\sigma$ errors of 0.045 for $\gamma$ and 0.25 for $\Sigma_{0}$ ($l_{max} = 500$), which is further tightened to 0.038 for $\gamma$ and 0.069 for $\Sigma_{0}$ ($l_{max} = 10000$).Comment: 15 pages, 9 figure