arXiv subjects

Steven Rose

Publications and source records attributed to Steven Rose.

9 recordsLinked to original sources

arXiv2026

Notes on Beltrami's Essay

Eugenio Beltrami published his seminal 'Essay on the Interpretation of Non-Euclidean Geometry' in 1868, where he showed that geodesics on a surface of constant negative curvature can be mapped as straight lines on a Euclidean disc. More importantly he showed that figures on the disc would satisfy the identities of hyperbolic geometry characteristic of a surface of negative curvature. However Beltrami did not always give a full explanation of the equations which he used. These notes are an attempt to provide a derivation of some of his principal results, including his formula for hyperbolic distance on the disc, his proof that the sum of the (hyperbolic) angles of a triangle on the disc is less than two right angles and his equations for circles, equidistants and horocycles.

math.HO↗

arXiv2023

Notes on Bolyai's 'Appendix'

This paper aims to provide an explanatory edition of Bolyai's 'Appendix Demonstrating the Absolute Science of Space', first published in 1832. In this treatise Bolyai began by extending neutral (or 'absolute') geometry by deriving a number of theorems which are independent of Euclid's parallel postulate. Then, while retaining Euclid first four postulates, he explored the consequences of replacing the parallel postulate with a different assumption, that through a given point not on a given straight line, more than than one straight line can be drawn which does not intersect the given line. On this basis Bolyai developed a non-Euclidean geometry nowadays called hyperbolic geometry. The English translation of Bolyai's text is reprinted in the paper, with explanatory notes provided at the end of each section. Some of the theorems are discussed in detail, with a particular focus on those in which Bolyai derived the trigonometric identities of the hyperbolic plane and on his astonishing quadrature of the circle. Bolyai's terse style of exposition can be quite challenging, so I have tried to fill in some of the mathematical details which he chose to omit, either through lack of space or simply because he thought them to obvious too include.

math.HO↗

arXiv2022

Investigating radiatively driven, magnetised plasmas with a university scale pulsed-power generator

We present first results from a novel experimental platform which is able to access physics relevant to topics including indirect-drive magnetised ICF; laser energy deposition; various topics in atomic physics; and laboratory astrophysics (for example the penetration of B-fields into HED plasmas). This platform uses the X-Rays from a wire array Z-Pinch to irradiate a silicon target, producing an outflow of ablated plasma. The ablated plasma expands into ambient, dynamically significant B-fields (~5 T) which are supported by the current flowing through the Z-Pinch. The outflows have a well-defined (quasi-1D) morphology, enabling the study of fundamental processes typically only available in more complex, integrated schemes. Experiments were fielded on the MAGPIE pulsed-power generator (1.4 MA, 240 ns rise time). On this machine a wire array Z-Pinch produces an X-Ray pulse carrying a total energy of ~15 kJ over ~30 ns. This equates to an average brightness temperature of around 10 eV on-target.

physics.plasm-ph↗

arXiv2021

The data-driven future of high energy density physics

The study of plasma physics under conditions of extreme temperatures, densities and electromagnetic field strengths is significant for our understanding of astrophysics, nuclear fusion and fundamental physics. These extreme physical systems are strongly non-linear and very difficult to understand theoretically or optimize experimentally. Here, we argue that machine learning models and data-driven methods are in the process of reshaping our exploration of these extreme systems that have hitherto proven far too non-linear for human researchers. From a fundamental perspective, our understanding can be helped by the way in which machine learning models can rapidly discover complex interactions in large data sets. From a practical point of view, the newest generation of extreme physics facilities can perform experiments multiple times a second (as opposed to ~daily), moving away from human-based control towards automatic control based on real-time interpretation of diagnostic data and updates of the physics model. To make the most of these emerging opportunities, we advance proposals for the community in terms of research design, training, best practices, and support for synthetic diagnostics and data analysis.

physics.plasm-ph↗

arXiv2019

Using Sparse Gaussian Processes for Predicting Robust Inertial Confinement Fusion Implosion Yields

Here we present the application of an advanced Sparse Gaussian Process based machine learning algorithm to the challenge of predicting the yields of inertial confinement fusion (ICF) experiments. The algorithm is used to investigate the parameter space of an extremely robust ICF design for the National Ignition Facility, the `Simplest Design'; deuterium-tritium gas in a plastic ablator with a Gaussian, Planckian drive. In particular we show that i) GPz has the potential to decompose uncertainty on predictions into uncertainty from lack of data and shot-to-shot variation, ii) permits the incorporation of science-goal specific cost-sensitive learning e.g. focussing on the high-yield parts of parameter space and iii) is very fast and effective in high dimensions.

physics.plasm-ph↗

arXiv2018

Observing Thermal Schwinger Pair Production

We study the possibility of observing Schwinger pair production enhanced by a thermal bath of photons. We consider the full range of temperatures and electric field intensities from pure Schwinger production to pure thermal production, and identify the most promising and interesting regimes. In particular, we identify temperatures of $\sim 20~\mathrm{keV}/k_B$ and field intensities of $\sim 10^{23}~\mathrm{Wcm}^{-2}$ where pair production would be observable. In this case, the thermal enhancement over the Schwinger rate is exponentially large and due to effects which are not visible at any finite order in the loop expansion. Pair production in this regime can thus be described as more nonperturbative than the usual Schwinger process, which appears at one loop. Unfortunately, such high temperatures appear to be out of reach of foreseeable technologies, though nonthermal photon distributions with comparable energy densities are possible. We suggest the possibility that similar nonperturbative enhancements may extend out of equilibrium and propose an experimental scheme to test this.

hep-ph↗

arXiv2017

A Novel Approach For Event-By-Event Early Gluon Fields

We report on efforts to construct an event generator that calculates the classical gluon field generated at early times in high energy nuclear collisions. Existing approaches utilize numerical solutions of the Yang-Mills equations after the collision. In contrast we employ the analytically known recursion relation in the forward light cone. The few lowest orders are expected to lead to reliable results for times of up to the inverse saturation scale, tau_0 ~ 1/Q_s. In these proceedings we sketch some calculational details, and show some preliminary results.

nucl-th↗

arXiv2017

Multistage Monte-Carlo simulation of jet modification in a static medium

The modification of hard jets in an extended static medium held at a fixed temperature is studied using three different Monte-Carlo event generators (LBT, MATTER, MARTINI). Each event generator contains a different set of assumptions regarding the energy and virtuality of the partons within a jet versus the energy scale of the medium, and hence, applies to a different epoch in the space-time history of the jet evolution. For the first time, modeling is developed where a jet may sequentially transition from one generator to the next, on a parton-by-parton level, providing a detailed simulation of the space-time evolution of medium modified jets over a much broader dynamic range than has been attempted previously in a single calculation. Comparisons are carried out for different observables sensitive to jet quenching, including the parton fragmentation function and the azimuthal distribution of jet energy around the jet axis. The effect of varying the boundary between different generators is studied and a theoretically motivated criterion for the location of this boundary is proposed. The importance of such an approach with coupled generators to the modeling of jet quenching is discussed.

nucl-th↗

arXiv2016

Event-By-Event Initial Conditions for Heavy Ion Collisions

The early time dynamics of heavy ion collisions can be described by classical fields in an approximation of Quantum ChromoDynamics (QCD) called Color Glass Condensate (CGC). Monte-Carlo sampling of the color charge for the incoming nuclei are used to calculate their classical gluon fields. Following the recent work by Chen et al. we calculate the energy momentum tensor of those fields at early times in the collision event-by-event. This can then be used for subsequent hydrodynamic evolution of the single events.

nucl-th↗