Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences最新文献

We are extending acoustic gas thermometry (AGT) to temperatures up to 809 K with low uncertainties to measure the difference between the thermodynamic temperature T and the temperature T90 on the International Temperature Scale of 1990 (ITS-90). A cylindrical resonator was machined from a Ni-Cr-Fe alloy and acoustic and microwave waveguides welded to the cavity's endplates transmitted sound and microwaves to and from the cavity. A long-stemmed standard platinum resistance thermometer (LSPRT) measured T90 at the cavity wall. Pure argon gas flows continuously through the cavity to minimize the effects of desorption from the cavity walls. The resonator was hung in a pressure vessel surrounded by a radiation shield, a heat pipe and a furnace. We measured the acoustic resonant frequencies in argon in the range 580 to 809 K with relative standard uncertainty (3-5)×10-6. We applied a second-order boundary-layer correction to these frequencies. Each microwave resonance frequency was measured with a relative standard uncertainty of 3×10-7. The inconsistency between four independent microwave modes was 2.2×10-6 at 809 K, which contributed an uncertainty of 3.6 mK to the determination of T. The inconsistencies were not temperature dependent, which showed the structural stability of the resonator from room temperature to 809 K. This article is part of the Theo Murphy meeting issue 'The redefined kelvin: progress and prospects'.

In 2019, the basic unit of thermodynamic temperature, the kelvin, was redefined by fixing the value of the Boltzmann constant, opening new avenues for implementing and disseminating the kelvin with lower uncertainty, especially at temperatures below 25 K. In response, the Mise en Pratique for the definition of the kelvin (MeP-K) (2019) has recommended several primary thermometry methods, including acoustic gas thermometry (AGT), dielectric-constant gas thermometry (DCGT), refractive index gas thermometry (RIGT) and Johnson noise thermometry (JNT), as viable alternatives for realizing and disseminating the kelvin. Since the International System of Units (SI) revolution, significant progress on implementing the new kelvin has been made below 25 K. This progress indicates that primary thermometry, particularly its relative variants, can offer promising practical options for realizing and disseminating thermodynamic temperature directly linking to the new kelvin below 25 K with lower uncertainty. This is very important for metrological applications of science and industry, which require precise and accurate temperature calibrations. This article is part of the Theo Murphy meeting issue 'The redefined kelvin: progress and prospects'.

Semiconductors are extremely useful for temperature sensing owing to the strong temperature dependence of their optical and electronic properties. Silicon, the most widely used semiconductor, underpins modern electronics and is increasingly important in integrated photonics, offering a cost-effective platform for optical sensors. Silicon-based ring resonator (RR) temperature sensors operate via the temperature-dependent change in silicon's refractive index (dn/dT), which affects the optical modes in the ring. However, silicon has two main limitations: its indirect band gap makes it a poor light emitter, necessitating external light sources, and its thermal properties are fixed. In contrast, compound semiconductors, such as indium phosphide (InP), gallium arsenide (GaAs), gallium nitride (GaN) and indium arsenide (InAs), have direct band gaps, making them efficient light emitters as commonly used in light-emitting diodes and lasers. Their thermal properties can also be tailored through alloying. These features make them ideal for 'active resonator' temperature sensors with integrated light sources, allowing customization for various temperature ranges. This paper focuses on InP-based alloys, highlighting their fundamental properties and potential for integration into active quantum well-based heterostructures. These can be fabricated into micro-ring and other resonator designs. Integrating light sources within the sensor enhances both simplicity and functionality, paving the way for versatile temperature sensors suited to a wide range of applications. This article is part of the Theo Murphy meeting issue 'The redefined kelvin: progress and prospects'.

Doppler-broadening thermometry (DBT) can be used as a calibration-free primary thermometer suitable for practical applications, e.g. reliably measuring temperatures over long periods of time in environments where sensor retrieval for recalibration is impractical. We report on our proof-of-concept investigations into DBT with alkali-metal-vapour cells, with a particular focus on both absorption and frequency accuracy during scans. We reach sub-kelvin temperature accuracy, and experimental absorption-fit residuals below 0.05%, in a simple set-up. The outlook for portable, practical devices is bright, with clear prospects for future improvement. This article is part of the Theo Murphy meeting issue 'The redefined kelvin: progress and prospects'.

Many new techniques for ensuring traceable temperature measurements at the point of use are being developed and some are approaching maturity. The aim of this study is to examine the formalism associated with traceability to the SI kelvin for these practical techniques, as well as to identify areas of research which should be a priority. First, the status quo of thermodynamic temperature realization and dissemination is summarized. Then the state of the art of two main types of thermometry which can potentially provide in situ traceability is discussed. These are self-validating thermometers which make use of the phase change of materials, and practical primary thermometers, examples of which are given in order of decreasing commercial readiness: relative primary radiometry, acoustic gas thermometry (AGT), Johnson noise thermometry (JNT) and Doppler broadening thermometry (DBT). It is shown that relative primary thermometry is, in general, much more likely to become a day-to-day practical reality than absolute primary thermometry, and that this has a significant bearing on what the formalism might look like regarding metrological traceability and demonstrations of equivalence. This article is part of the Theo Murphy meeting issue 'The redefined kelvin: progress and prospects'.

The 2019 redefinition of the kelvin and its accompanying Mise en pratique (MeP-K) herald a bold new future for the thermometry community. The MeP-K offers a blueprint for putting the kelvin into practice, and the proliferation of the new realization options it enables will lead to both benefits and practical inconsistencies for thermometer users. Users have been accustomed to a straightforward International Temperature Scale of 1990 T90 measurement chain with traceability and trust assured by national metrology institutes (NMIs). In contrast, the emerging world of coexisting T and T90 thermometers, with some offering in situ temperature traceability unconnected to NMIs, will challenge this straightforward measurement chain. Here, we discuss practical solutions to the practical inconsistencies users will encounter. These solutions focus on the triad of trust in metrology-traceability, equivalence and competence-to allow thermometry end users to broadly benefit from new technologies while maintaining trust in measurements and minimizing net disruption. This article is part of the Theo Murphy meeting issue 'The redefined kelvin: progress and prospects'.

The interplay between physics and mathematics with history deals with the role played by the relationship between physical and mathematical objects within a scientific theory. Taking into account the rigour of proof in mathematics and of the measurability/reproducibility of experiments in physics, a question arises: how can we read the interplay between physics and mathematics as a historical category of inquiry in order to analyse the development of a physical-mathematical theory, e.g., with respect to a physical theory, or with respect to a purely mathematical one (inspired by physical phenomena)? The role played by the interplay between physical and mathematical objects in a scientific theory is also specified by definitions, suppositions, theorems, diagrams, calculus, etc. Therefore, taking into account our interest in inquiring physics-mathematics relationships with the history of science, in this paper, we first propose a methodological account in order to show how the relationships between physics and mathematics with history work, and second, we use it in order to analyse Newton's three-body problem within his physical and mathematical backgrounds. But, how does the Geneva Edition description of this differ from how this was described by Newton? In detail, we analyse the case study of Proposition LXVI as presented and discussed in Newton's Principia Geneva Edition (Newton ([1726] [1739-1742] 1822, Book I), which, with its 22 corollaries, is the longest proposition of Newton's masterpiece. It deals with the three-body problem (a physical-mathematical interplay, also a relationship). Therefore, our historical-scientific analysis concerns the explanation of the Principia Geneva Edition's notes added by the three editors to Newton's treatment of the three-body problem as novel, as a separate step after Newton's treatment (and before Poincaré's statement). This article is part of the theme issue 'Newton, Principia, Newton Geneva Edition (17th-19th) and modern Newtonian mechanics: heritage, past & present'.

Generally speaking, isochronous timing events (and the related consequent problem of isochronism) describes a sequential set of events that may be defined isochronous if the events (and/or the interplay between two or more events) follow recurrently within certain given time-periodical parameters. In other words, it is a property of a physical system where a sequence is at equal time intervals; it also applies to variations in other measurable quantities within the same physical system. Our scientific-historical research is dedicated to the propositions Newton devoted to the problem of isochronism property (at that time) in his Principia and to the notes added by the editors of the Geneva edition (hereafter GE) to such propositions. Isochronism was a problem that had interested scientists at least since Galileo's studies in the late 16th and early 17th century. Huygens gave the definitive solution, discovering the cycloid to be the isochronous curve. However, Newton improved the theory of isochronism in a fundamental way: he inserted such a theory within the picture of his rational mechanics, considered the normal cycloid as a limit case of hypocycloids and epicycloids and specified the nature of force for the tautochrone to be a cycloid. On this last topic, the editors of the GE added an interesting note to Newton's text, thus reaching results that were only implicit in his masterpiece; we analyse one such note-it concerns advanced research in physics and mathematics. Nonetheless, the editors, as usual, added a numerous series of notes to Newton's theory of isochronism, most of which are dedicated to the explanation of Newton's text, although some of them regard, as the one mentioned above, advanced research and others, the history of physics. We offer a broad picture of these notes. They will be useful for the reader to understand the tone of the editors' intervention. Taking into account our numerous publications on Newton and Newton's GE topics, for the historical context of GE and other physical-mathematical analyses on the subject, we refer the reader to consult our list of publications at the end of this article. This article is part of the theme issue 'Newton, Principia, Newton Geneva Edition (17th-19th) and modern Newtonian mechanics: heritage, past & present'.

In this essay-based on previous research and publication by two of us (since 2012)-we propose an introduction of Newton's Philosophiae Naturalis Principia Mathematica Geneva Edition ([1739-1742] 1822) for the current Philosophical Transactions of the Royal Society-A Special Issue, Newton, Principia, Newton Geneva Edition (17th-19th) and Modern Newtonian Mechanics: Heritage, Past-&-Present. This special issue is linked to the International two-day Symposium that, in September 2023, we organized at the University of Oxford, UK, to celebrate 200 years since its publication (1822-2022), and that featured our most significant recent findings. The programme included an examination of the importance of the Geneva Edition (GE) of Newton's Principia. A key aspect of the discussions focused on the historical-scientific characteristics of this edition, including the history of physics and mathematics, as well as its typographical and epistemological attributes. Furthermore, the dissemination of Newtonianism throughout Europe during the eighteenth and nineteenth centuries has been explored. In this essay, we aim to refer to the main features of the GE and to the development of our research on this subject. This article is part of the theme issue 'Newton, Principia, Newton Geneva Edition (17th-19th) and modern Newtonian mechanics: heritage, past & present'.

This article examines the intellectual contexts in France that facilitated the reception between 1670 and 1790 of Newton's work in optics and celestial mechanics-it deals with his early optical work, and the content of the Principia, along with the various adaptations and interpretations of this work in France and Switzerland. This article is part of the theme issue 'Newton, Principia, Newton Geneva Edition (17th-19th) and modern Newtonian mechanics: heritage, past & present'.