Magnetohydrodynamic regime of the born-infeld electromagnetism

The Born-Infeld (BI) model is a nonlinear correction of Maxwell's equations. By adding the energy and Poynting vector as additional variables, it can be augmented as a 10$\times$10 system of hyperbolic conservation laws, called the augmented BI (ABI) equations. The author found that, through a quadratic change of the time variable, the ABI system gives a simple energy dissipation model that combines Darcy's law and magnetohydrodynamics (MHD). Using the concept of "relative entropy" (or "modulated energy"), borrowed from the theory of hyperbolic systems of conservation laws, we introduce a notion of generalized solutions, that we call dissipative solutions. For given initial conditions, the set of generalized solutions is not empty, convex, and compact. Smooth solutions to the dissipative system are always unique in this setting

Hyperbolicity of the time-like extremal surfaces in minkowski spaces

In this paper, it is established, in the case of graphs, that time-like extremal surfaces of dimension $1+n$ in the Minkowski space of dimension $1+n+m$ can be described by a symmetric hyperbolic system of PDEs with the very simple structure (reminiscent of the inviscid Burgers equation)$$\partial\_t W + \sum\_{j=1}^n A\_j(W)\partial\_{x\_j} W =0,\;\;\;W:\;(t,x)\in\mathbb{R}^{1+n}\rightarrow W(t,x)\in\mathbb{R}^{n+m+\binom{m+n}{n}},$$where each $A\_j(W)$ is just a $\big(n+m+\binom{m+n}{n}\big)\times\big(n+m+\binom{m+n}{n}\big)$ symmetric matrix dependinglinearly on $W$

AutoOptLib: Tailoring Metaheuristic Optimizers via Automated Algorithm Design

Metaheuristics are prominent gradient-free optimizers for solving hard problems that do not meet the rigorous mathematical assumptions of analytical solvers. The canonical manual optimizer design could be laborious, untraceable and error-prone, let alone human experts are not always available. This arises increasing interest and demand in automating the optimizer design process. In response, this paper proposes AutoOptLib, the first platform for accessible automated design of metaheuristic optimizers. AutoOptLib leverages computing resources to conceive, build up, and verify the design choices of the optimizers. It requires much less labor resources and expertise than manual design, democratizing satisfactory metaheuristic optimizers to a much broader range of researchers and practitioners. Furthermore, by fully exploring the design choices with computing resources, AutoOptLib has the potential to surpass human experience, subsequently gaining enhanced performance compared with human problem-solving. To realize the automated design, AutoOptLib provides 1) a rich library of metaheuristic components for continuous, discrete, and permutation problems; 2) a flexible algorithm representation for evolving diverse algorithm structures; 3) different design objectives and techniques for different optimization scenarios; and 4) a graphic user interface for accessibility and practicability. AutoOptLib is fully written in Matlab/Octave; its source code and documentation are available at https://github.com/qz89/AutoOpt and https://AutoOpt.readthedocs.io/, respectively

Ultrahigh-Frequency Surface Acoustic Wave Sensors with Giant Mass-Loading Effects on Electrodes

Surface acoustic wave (SAW) devices are widely used for physical, chemical, and biological sensing applications, and their sensing mechanisms are generally based on frequency changes due to mass-loading effects at the acoustic wave propagation area between two interdigitated transducers (IDTs). In this paper, a new sensing mechanism has been proposed based on a significantly enhanced mass-loading effect generated directly on Au IDT electrodes, which enables significantly enhanced sensitivity, compared with that of conventional SAW devices. The fabricated ultrahigh-frequency SAW devices show a significant mass-loading effect on the electrodes. When the Au-electrode thickness increased from 12 to 25 nm, the Rayleigh mode resonant frequency decreased from 7.77 to 5.93 GHz, while that of the higher longitudinal leaky SAW decreased from 11.87 to 9.83 GHz. The corresponding mass sensitivity of 7309 MHz·mm2·μg–1 (Rayleigh mode) is ∼8.9 × 1011 times larger than that of a conventional quartz crystal balance (with a frequency of 5 MHz) and ∼1000 times higher than that of conventional SAW devices (with a frequency of 978 MHz). Trinitrotoluene concentration as low as 4.4 × 10–9 M (mol·L–1) can be detected using the fabricated SAW sensor, proving its giant mass-loading effect and ultrahigh sensitivity

30 GHz surface acoustic wave transducers with extremely high mass sensitivity

A nano-patterning process is reported in this work, which can achieve surface acoustic wave (SAW) devices with an extremely high frequency and a super-high mass sensitivity. An integrated lift-off process with ion beam milling is used to minimize the short-circuiting problem and improve the quality of nanoscale interdigital transducers (IDTs). A specifically designed proximity-effect-correction algorithm is applied to mitigate the proximity effect occurring in the electron-beam lithography process. The IDTs with a period of 160 nm and a finger width of 35 nm are achieved, enabling a frequency of ∼30 GHz on lithium niobate based SAW devices. Both centrosymmetric type and axisymmetric type IDT structures are fabricated, and the results show that the centrosymmetric type tends to excite lower-order Rayleigh waves and the axisymmetric type tends to excite higher-order wave modes. A mass sensitivity of ∼388.2 MHz × mm2/μg is demonstrated, which is ∼109 times larger than that of a conventional quartz crystal balance and ∼50 times higher than a conventional SAW device with a wavelength of 4 μm

Space advanced technology demonstration satellite

The Space Advanced Technology demonstration satellite (SATech-01), a mission for low-cost space science and new technology experiments, organized by Chinese Academy of Sciences (CAS), was successfully launched into a Sun-synchronous orbit at an altitude of similar to 500 km on July 27, 2022, from the Jiuquan Satellite Launch Centre. Serving as an experimental platform for space science exploration and the demonstration of advanced common technologies in orbit, SATech-01 is equipped with 16 experimental payloads, including the solar upper transition region imager (SUTRI), the lobster eye imager for astronomy (LEIA), the high energy burst searcher (HEBS), and a High Precision Magnetic Field Measurement System based on a CPT Magnetometer (CPT). It also incorporates an imager with freeform optics, an integrated thermal imaging sensor, and a multi-functional integrated imager, etc. This paper provides an overview of SATech-01, including a technical description of the satellite and its scientific payloads, along with their on-orbit performance

Transport optimal et diffusions de courants

Our work concerns about the study of partial differential equations at the hinge of the continuum physics and differential geometry. The starting point is the model of non-linear electromagnetism introduced by Max Born and Leopold Infeld in 1934 as a substitute for the traditional linear Maxwell's equations. These equations are remarkable for their links with differential geometry (extremal surfaces in the Minkowski space) and have regained interest in the 90s in high-energy physics (strings and D-branches).The thesis is composed of four chapters.The theory of nonlinear degenerate parabolic systems of PDEs is not very developed because they can not apply the usual comparison principles (maximum principle), despite their omnipresence in many applications (physics, mechanics, digital imaging, geometry, etc.). In the first chapter, we show how such systems can sometimes be derived, asymptotically, from non-dissipative systems (typically non-linear hyperbolic systems), by simple non-linear change of the time variable degenerate at the origin (where the initial data are set). The advantage of this point of view is that it is possible to transfer some hyperbolic techniques to parabolic equations, which seems at first sight surprising, since parabolic equations have the reputation of being easier to treat (which is not true , in reality, in the case of degenerate systems). The chapter deals with the curve-shortening flow as a prototype, which is the simplest exemple of the mean curvature flows in co-dimension higher than 1. It is shown how this model can be derived from the two-dimensional extremal surface in the Minkowski space (corresponding to the classical relativistic strings), which can be reduced to a hyperbolic system. We obtain, almost automatically, the parabolic version of the relative entropy method and weak-strong uniqueness, which, in fact, is much simpler to establish and understand in the hyperbolic framework.In the second chapter, the same method applies to the Born-Infeld system itself, which makes it possible to obtain, in the limit, a model (not listed to our knowledge) of Magnetohydrodynamics (MHD) where we have non-linear diffusions in the magnetic induction equation and the Darcy's law for the velocity field. It is remarkable that a system of such distant appearance of the basic principles of physics can be so directly derived from a model of physics as fundamental and geometrical as that of Born-Infeld.In the third chapter, a link is established between the parabolic systems and the concept of gradient flow of differential forms with suitable transport metrics. In the case of volume forms, this concept has had an extraordinary success in the field of optimal transport theory, especially after the founding work of Felix Otto and his collaborators. This concept is really only on its beginnings: in this chapter, we study a variant of the curve-shortening flow studied in the first chapter, which has the advantage of being integrable (in a certain sense) and lead to more precise results.Finally, in the fourth chapter, we return to the domain of hyperbolic EDPs considering, in the particular case of graphs, the extremal surfaces of the Minkowski space of any dimension and co-dimension. We can show that the equations can be reformulated in the form of a symmetric first-order enlarged system (which automatically ensures the well-posedness of the equations) of a remarkably simple structure (very similar to the Burgers equation) with quadratic nonlinearities, whose calculation is not obvious.Les travaux portent sur l'étude d'équations aux dérivées partielles à la charnière de la physique de la mécanique des milieux continus et de la géométrie différentielle, le point de départ étant le modèle d'électromagnétisme non-linéaire introduit par Max Born et Leopold Infeld en 1934 comme substitut aux traditionnelles équations linéaires de Maxwell. Ces équations sont remarquables par leurs liens avec la géométrie différentielle (surfaces extrémales dans l'espace de Minkowski) et ont connu un regain d'intérêt dans les années 90 en physique des hautes énergies (cordes et D-branes).Le travail se décompose en quatre chapitres.La théorie des systèmes paraboliques dégénérés d'EDP non-linéaires est fort peu développée, faute de pouvoir appliquer les principes de comparaison habituels (principe du maximum), malgré leur omniprésence dans de nombreuses applications (physique, mécanique, imagerie numérique, géométrie...). Dans le premier chapitre, on montre comment de tels systèmes peuvent être parfois dérivés, asymptotiquement, à partir de systèmes non-dissipatifs (typiquement des systèmes hyperboliques non-linéaires), par simple changement de variable en temps non-linéaire dégénéré à l'origine (où sont fixées les données initiales). L'avantage de ce point de vue est de pouvoir transférer certaines techniques hyperboliques vers les équations paraboliques, ce qui semble à première vue surprenant, puisque les équations paraboliques ont la réputation d'être plus facile à traiter (ce qui n'est pas vrai, en réalité, dans le cas de systèmes dégénérés). Le chapitre traite, comme prototype, du curve-shortening flow", qui est le plus simple des mouvements par courbure moyenne en co-dimension supérieure à un. Il est montré comment ce modèle peut être dérivé de la théorie des surfaces de dimension deux d'aire extrémale dans l'espace de Minkowski (correspondant aux cordes relativistes classiques) qui peut se ramener à un système hyperbolique. On obtient, presque automatiquement, l'équivalent parabolique des principes d'entropie relative et d'unicité fort-faible qu'il est, en fait, bien plus simple d'établir et de comprendre dans le cadre hyperbolique.Dans le second chapitre, la même méthode s'applique au système de Born-Infeld proprement dit, ce qui permet d'obtenir, à la limite, un modèle (non répertorié à notre connaissance) de Magnétohydrodynamique (MHD), où on retrouve à la fois une diffusivité non-linéaire dans l'équation d'induction magnétique et une loi de Darcy pour le champ de vitesse. Il est remarquable qu'un système d'apparence aussi lointaine des principes de base de la physique puisse être si directement déduit d'un modèle de physique aussi fondamental et géométrique que celui de Born-Infeld.Dans le troisième chapitre, un lien est établi entre des systèmes paraboliques et le concept de flot gradient de formes différentielles pour des métriques de transport. Dans le cas des formes volumes, ce concept a eu un succès extraordinaire dans le cadre de la théorie du transport optimal, en particulier après le travail fondateur de Felix Otto et de ses collaborateurs. Ce concept n'en est vraiment qu'à ses débuts: dans ce chapitre, on étudie une variante du «curve-shortening flow» étudié dans le premier chapitre, qui présente l'avantage d'être intégrable (en un certain sens) et de conduire à des résultats plus précis.Enfin, dans le quatrième chapitre, on retourne au domaine des EDP hyperboliques en considérant, dans le cas particulier des graphes, les surfaces extrémales de l'espace de Minkowski, de dimension et co-dimension quelconques. On parvient à montrer que les équations peuvent se reformuler sous forme d'un système élargi symétrique du premier ordre (ce qui assure automatiquement le caractère bien posé des équations) d'une structure remarquablement simple (très similaire à l'équation de Burgers) avec non linéarités quadratiques, dont le calcul n'a rien d'évident

An integrable example of gradient flows based on optimal transport of differential forms

Optimal transport theory has been a powerful tool for the analysis of parabolic equationsviewed as gradient flows of volume forms according to suitable transportation metrics.In this paper, we present an example of gradient flows for closed (d-1)-forms in theEuclidean space R^d. In spite of its apparent complexity, the resulting verydegenerate parabolic system is fully integrable and can be viewed as the Eulerianversion of the heat equation for curves in the Euclidean space.We analyze this system in terms of ``relative entropy" and ``dissipative solutions"and provide global existence and weak-strong uniqueness results

From conservative to dissipative systemsthrough quadratic change of time, with application to the curve-shortening flow

We provide several examples of dissipative systems that can be obtained from conservative ones through a simple, quadratic,change of time. A typical example is the curve-shortening flow in R^d, which is a particular case ofmean-curvature flow with co-dimension higher than one (except in the case d=2).Through such a change of time, this flow can be formally derived from the conservative model of vibrating strings obtainedfrom the Nambu-Goto action. Using the concept of ``relative entropy" (or ``modulated energy"), borrowed from the theoryof hyperbolic systems of conservation laws, we introduce a notion of generalized solutions,that we call dissipative solutions, for the curve-shortening flow. For given initial conditions, the set of generalized solutionsis convex, compact, if not empty. Smooth solutions to the curve-shortening flow are always unique in this setting