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16. Nonlinear dynamics of the RL-diode circuit

Author

Marsh, Luke

Subjects
003.85701515355
Abstract

The nonlinear second order differential equation which describes the driven series RL-diode circuit, biased to operate only in the depletion region is given by X + γX + Xμ = α - βsin&tau, where differentiation is with respect to time τ and γ > 0, α > |β| > 0, μ > 1 and X ≥ 0. Without these restrictions and specifically with μ = 2, this differential equation has also been found to exist in a couple of other research contexts, namely in the studies of ship roll and capsize, as well as in a perturbed Korteweg-de Vries equation, where stationary wave solutions are described by a special case of the differential equation. Particular attention is paid firstly to the case μ = 2, which in contrast to Duffing’s equation (μ = 3) has received little attention, and secondly, the case μ = 1.67, which arises from measured values made on a practical diode. The main aim here has been to give a detailed analysis of some properties of the system’s solutions. A rigorous phase plane analysis establishes solution behaviour and a criterion for which solutions grow without bound, before subharmonic solutions of various orders are exhibited. By partitioning the phase plane into regions in which only certain solution behaviour occurs, a variety of invariant sets can be constructed. A numerical scheme which detects unstable periodic orbits is applied to the system, resulting in detection of a set of unstable periodic solutions. This detailed analysis goes some way towards understanding the dynamics of this system.

Published
2006

27. Resuscitating criminal courts after Covid-19: Trialling a cure worse than the disease.

Author

McConville, Mike and Marsh, Luke

Subjects
*CRIMINAL courts, *COVID-19 pandemic, *DEFENDANTS
Abstract

This article, focusing on the issue of custody time limits litigated under Covid-19 conditions, sets out how reasoned decisions to refuse to extend custody for unconvicted defendants excited the disapproval of senior judges such that fundamental changes were made to evidence, procedure and proof as well as effecting permanent manipulation of the composition of the adjudicating panels authorised to deal with such cases. This additionally raises fundamental questions about the administration and governance of the courts, the independence of the judiciary in decision-making and the basic utility of the presumption of innocence in such cases. [ABSTRACT FROM AUTHOR]

Published
2022
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34. Judicial Oversight in Criminal Justice and Procedural Legality.

Author

McConville, Mike and Marsh, Luke

Subjects
*JUDGE-made law, *RULE of law, *COURTS
Abstract

The article discusses the role of the senior judiciary in policy-making in criminal justice in England and Wales. Topics covered include the independence of the senior judiciary from the executive, its implications for the rule of law, and the restructuring of the criminal justice system including the Criminal Procedure Rules.

Published
2021
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35. The "Tommy Robinson" Case and Contempt of Court: Conflicting Interpretations of the Criminal Procedure Rules.

Author

Marsh, Luke

Subjects
CONTEMPT of court, COURT rules, CRIMINAL procedure
Abstract

This article assesses the Court of Appeal's (Criminal Division) judgment in Stephen Yaxley-Lennon1 which arose from two separate findings of contempt of court against Tommy Robinson--an individual with a chequered profile attracting widespread public interest. The criminal process underpinning the 13-month prison sentence received by Tommy Robinson stemming from his use of livestreaming to report on criminal trials was characterised by procedural defects, the Court of Appeal's handling of which reveals a questionable approach taken towards the implementation of the Criminal Procedure Rules (CrimPR). The procedural safeguards around the use of the contempt power are clearly critical; the issue becoming increasingly important in the modern age of social media. The article will argue that the Court of Appeal s most recent interpretation of the requirement of compliance with provisions of the CrimPR in contempt proceedings should be revisited in light of a fuller acknowledgment of the context in which the now largely defunct ratio of Re West (Ian Stuart) (a barrister)2 was pronounced. [ABSTRACT FROM AUTHOR]

Published
2020

36. Meeting abstracts from the 64th British Thyroid Association Annual Meeting

Author

Bartalena, Luigi, primary, Fliers, Eric, additional, Hellen, Nicola, additional, Taylor, Peter N., additional, Lacey, Arron, additional, Thayer, Daniel, additional, Yusof, Mohd Draman, additional, Tabasum, Arshiya, additional, Muller, Illaria, additional, Marsh, Luke, additional, Ludgate, Marian, additional, Rees, Alex, additional, Boelaert, Kristien, additional, Chan, Shiao, additional, Nelson, Scott, additional, Rees, Aled, additional, Lazarus, John H., additional, Dayan, Colin M., additional, Vaidya, Bijay, additional, Okosieme, Onyebuchi, additional, Poole, Vikki L., additional, Fletcher, Alice, additional, Modasia, Bhavika, additional, Sharma, Neil, additional, Thompson, Rebecca J., additional, Imruetaicharoenchoke, Waraporn, additional, Read, Martin L., additional, McCabe, Christopher J., additional, Smith, Vicki E., additional, Fong, Jim C. W., additional, Nieto, Hannah, additional, Thompson, Rebecca, additional, Watkinson, John C., additional, Turnell, Andrew S., additional, Pariani, Nadia, additional, Willis, Mark, additional, Muller, Ilaria, additional, Healy, Sarah, additional, Nasser, Taha, additional, Jones, Joanne, additional, Chatterjee, Krishna, additional, Dayan, Colin, additional, Robertson, Neil, additional, Coles, Alasdair, additional, Moran, Carla, additional, Hales, Charlotte, additional, Taylor, Peter, additional, Channon, Sue, additional, McEwan, Kirsten, additional, Gregory, John, additional, Draman, Mohd S., additional, Langley, Kate, additional, Thapar, Anita, additional, Lazarus, John, additional, Torlinska, Barbara, additional, Franklyn, Jayne, additional, Coleman, Jamie, additional, Zhang, Lei, additional, Bakhsh, Ameen, additional, Gyedu, Michael, additional, Soto-Pedre, Enrique, additional, Leese, Graham P., additional, Zhou, Kaixin, additional, Smith, Joel A., additional, Hoffman, Jon, additional, Morgan, Neil V., additional, Campbell, Christopher, additional, Wake, Naomi C., additional, Wallis, Yvonne, additional, Maher, Eamonn R., additional, Woodward, Emma R., additional, Tee, Su A., additional, Bishop, David R., additional, Al-Sharefi, Ahmed, additional, Leng, Owain, additional, James, Robert A., additional, Salota, Rashim, additional, Rodin, Andrew, additional, Johri, Nikhil, additional, Hyer, Stephen L., additional, Mcdonnell, Thomas, additional, Ooi, Cheong G., additional, Knight, Bridget A, additional, Shields, Beverley M., additional, Pearce, Elizabeth, additional, Braverman, Lewis, additional, He, Xuemei, additional, and Sturley, Rachel, additional

Published
2017
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37. Controlled Antenatal Thyroid Screening Study; Obstetric Outcomes

Author

Taylor, Peter, primary, Lacey, Arron, additional, Thayer, Daniel, additional, Draman, Mohd, additional, Tabasum, Arshiya, additional, Muller, Ilaria, additional, Marsh, Luke, additional, Poacher, Arwel, additional, Roberts, Aled, additional, Ludgate, Marian, additional, Rees, Alex, additional, Boelaert, Kristien, additional, Rees, Aled, additional, Chan, Shiao, additional, Lazarus, John, additional, Nelson, Scott, additional, Vaidya, Bijay, additional, and Okosieme, Onyebuchi, additional

Published
2016
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44. Nonlinear Dynamics of The RL-Diode Circuit

Author

Marsh, Luke.

Abstract

The nonlinear second order differential equation which describes the driven series RL-diode circuit, biased to operate only in the depletion region is given by X + γX + Xμ = α - βsin&tau, where differentiation is with respect to time τ and γ > 0, α > |β| > 0, μ > 1 and X ≥ 0. Without these restrictions and specifically with μ = 2, this differential equation has also been found to exist in a couple of other research contexts, namely in the studies of ship roll and capsize, as well as in a perturbed Korteweg-de Vries equation, where stationary wave solutions are described by a special case of the differential equation. Particular attention is paid firstly to the case μ = 2, which in contrast to Duffing’s equation (μ = 3) has received little attention, and secondly, the case μ = 1.67, which arises from measured values made on a practical diode. The main aim here has been to give a detailed analysis of some properties of the system’s solutions. A rigorous phase plane analysis establishes solution behaviour and a criterion for which solutions grow without bound, before subharmonic solutions of various orders are exhibited. By partitioning the phase plane into regions in which only certain solution behaviour occurs, a variety of invariant sets can be constructed. A numerical scheme which detects unstable periodic orbits is applied to the system, resulting in detection of a set of unstable periodic solutions. This detailed analysis goes some way towards understanding the dynamics of this system.

Published
2006

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