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颤动时空中的微粒光：普朗克辐射定律与温度极限的几何基础
No full textDie Quantisierung der Strahlungsenergie, die erstmals von Max Planck eingeführt wurde, um die ultraviolette Katastrophe zu lösen, markiert den historischen Ursprung der Quantentheorie. Plancks Postulat blieb jedoch lange eine phänomenologische Annahme ohne Herleitung aus ersten Prinzipien. In dieser Arbeit leiten wir sowohl Plancks Postulat als auch das Strahlungsgesetz von Planck aus den geometrischen Grundlagen der Theorie der zitternden Raumzeit (TSRT) ab. In diesem Rahmen ist die Raumzeit nicht glatt, sondern weist begrenzte mikroskopische Fluktuationen auf, die durch die Forderung eingeschränkt sind, dass die Eigenzeit real und zukunftsgerichtet bleibt. Photonen werden nicht als Welle-Teilchen-Dualitäten modelliert, sondern als korpuskulare Anregungen, die sich entlang gestörter Nullgeodäten fortbewegen, wobei diese Störungen durch das geometrische Zittern verursacht sind. Die Quantisierung der Energie ergibt sich als direkte Folge von Kohärenzbedingungen in der Geodätenabweichung – ohne Rückgriff auf Operatorformalismen, Wellenüberlagerung oder probabilistische Postulate. Eine statistische Behandlung dieser Geodätenkonfigurationen führt zum Planck-Spektrum, selbst bei absolutem Nullpunkt, wo ein Restzittern fortbesteht. Darüber hinaus leiten wir konsistente, geometrisch definierte Größen für Entropie und Temperatur ab und zeigen, dass die TSRT nicht nur bekannte thermodynamische Grenzwerte reproduziert, sondern auch eine maximale Temperatur vorhersagt, die mit dem Zusammenbruch der kausalen Geodätenstruktur verbunden ist. Trotz der strikt korpuskularen Natur der Photonen in der TSRT reproduziert die Theorie exakt den relativistischen Dopplereffekt und zeigt, dass spektrale und thermodynamische Observablen kovariant zwischen Inertialsystemen transformieren. Damit bietet die TSRT eine deterministische und überprüfbare Grundlage für die Schwarzkörperstrahlung und die Thermodynamik des Lichts, vollständig verankert in der kausalen Geometrie der Raumzeit. Schließlich leiten wir eine lokale, durch die Raumzeitkrümmung unterdrückte Entropieformel aus zitternden Geodäten her, die im stark gekrümmten Fall in das Flächengesetz von Bekenstein–Hawking übergeht und so eine geometrisch fundierte Grundlage für die gravitative Thermodynamik ohne Quantenfeldtheorie bietet.The quantization of radiation energy, first introduced by Max Planck to resolve the ultraviolet catastrophe, marked the historical origin of quantum theory. However, Planck's postulate has long remained a phenomenological insertion without a first-principles derivation. In this work, we derive both Planck’s postulate and Planck’s radiation law from the geometric foundations of Trembling Spacetime Relativity Theory (TSRT). Here, spacetime is not smooth but exhibits bounded microscopic fluctuations, constrained by the requirement that proper time remains real and forward-directed. Photons are modeled not as wave–particle dual entities but as corpuscular excitations traveling along null geodesics perturbed by this geometric trembling. The quantization of energy emerges as a direct consequence of coherence conditions in geodesic deviation, without invoking operator formalism, wave superposition, or probabilistic postulates. A statistical treatment of these geodesic configurations leads to the Planck spectrum, even at zero temperature, where residual trembling persists. Furthermore, we derive consistent, geometric definitions of entropy and temperature in this framework, showing that TSRT not only reproduces known thermodynamic limits but also predicts a maximal temperature associated with the breakdown of causal geodesic structure. Despite the strict corpuscular nature of photons in TSRT, the theory exactly reproduces the relativistic Doppler shift, demonstrating that spectral and thermodynamic observables transform covariantly across inertial frames. This offers a deterministic and falsifiable foundation for black body radiation and the thermodynamics of light, grounded entirely in the causal geometry of spacetime. We further derive a local, curvature-suppressed entropy formula from trembling geodesics, which reduces to the Bekenstein–Hawking area law in strongly curved regions, providing a first-principles geometric foundation for gravitational thermodynamics without invoking quantum field theory.La cuantización de la energía del campo de radiación, introducida por primera vez por Max Planck para resolver la catástrofe ultravioleta, marcó el origen histórico de la teoría cuántica. Sin embargo, el postulado de Planck ha permanecido durante mucho tiempo como una inserción fenomenológica sin una derivación a partir de primeros principios. En este trabajo, derivamos tanto el postulado de Planck como la ley de radiación de Planck a partir de los fundamentos geométricos de la Teoría de la Relatividad del Espaciotiempo Tembloroso (TSRT). En este marco, el espaciotiempo no es suave, sino que presenta fluctuaciones microscópicas acotadas, restringidas por la exigencia de que el tiempo propio sea real y dirigido hacia el futuro. Los fotones no se modelan como entidades con dualidad onda-partícula, sino como excitaciones corpusculares que viajan a lo largo de geodésicas nulas perturbadas por este temblor geométrico. La cuantización de la energía emerge como una consecuencia directa de condiciones de coherencia en la desviación geodésica, sin invocar el formalismo de operadores, la superposición de ondas ni postulados probabilísticos. Un tratamiento estadístico de estas configuraciones geodésicas conduce al espectro de Planck, incluso a temperatura cero, donde persiste un temblor residual. Además, derivamos definiciones coherentes y geométricas de entropía y temperatura dentro de este marco, mostrando que la TSRT no solo reproduce los límites termodinámicos conocidos, sino que también predice una temperatura máxima asociada con la ruptura de la estructura causal de las geodésicas. A pesar de la naturaleza estrictamente corpuscular de los fotones en TSRT, la teoría reproduce exactamente el efecto Doppler relativista, demostrando que los observables espectrales y termodinámicos se transforman covariantemente entre marcos inerciales. Esto ofrece una base determinista y falsable para la radiación del cuerpo negro y la termodinámica de la luz, completamente fundamentada en la geometría causal del espaciotiempo. Finalmente, derivamos una fórmula local de entropía, suprimida por la curvatura, a partir de las geodésicas temblorosas, que se reduce a la ley de área de Bekenstein–Hawking en regiones fuertemente curvadas, proporcionando así una base geométrica de primeros principios para la termodinámica gravitacional sin recurrir a la teoría cuántica de campos.La quantification de l’énergie du rayonnement, introduite pour la première fois par Max Planck afin de résoudre la catastrophe ultraviolette, marque l’origine historique de la théorie quantique. Pourtant, le postulat de Planck est longtemps resté une hypothèse phénoménologique, sans dérivation fondée sur des premiers principes. Dans ce travail, nous dérivons à la fois le postulat de Planck et la loi du rayonnement de Planck à partir des fondements géométriques de la théorie de la relativité de l’espace-temps frémissant (TSRT). Dans ce cadre, l’espace-temps n’est pas lisse, mais présente des fluctuations microscopiques bornées, contraintes par l’exigence que le temps propre reste réel et orienté vers le futur. Les photons ne sont pas modélisés comme des entités à double nature onde–particule, mais comme des excitations corpusculaires se propageant le long de géodésiques nulles perturbées par ce frémissement géométrique. La quantification de l’énergie émerge alors comme une conséquence directe des conditions de cohérence dans la déviation géodésique, sans recours à un formalisme opérateur, à la superposition ondulatoire, ni à des postulats probabilistes. Un traitement statistique de ces configurations géodésiques conduit au spectre de Planck, y compris à température nulle, où subsiste un frémissement résiduel. Nous dérivons en outre des définitions cohérentes et géométriques de l’entropie et de la température dans ce cadre, montrant que la TSRT reproduit non seulement les limites thermodynamiques connues, mais prédit aussi une température maximale associée à la rupture de la structure causale des géodésiques. Bien que les photons soient strictement corpusculaires en TSRT, la théorie reproduit exactement le décalage Doppler relativiste, démontrant que les observables spectrales et thermodynamiques se transforment de manière covariante entre référentiels inertiels. Cela fournit une base déterministe et falsifiable pour le rayonnement du corps noir et la thermodynamique de la lumière, ancrée entièrement dans la géométrie causale de l’espace-temps. Nous dérivons enfin une formule locale de l’entropie, atténuée par la courbure, à partir des géodésiques frémissantes, laquelle se réduit à la loi de surface de Bekenstein–Hawking dans les régions fortement courbées, offrant ainsi une fondation géométrique de la thermodynamique gravitationnelle sans recours à la théorie quantique des champs.辐射能量的量子化最早由马克斯·普朗克提出，以解决紫外灾难的问题，这一突破标志着量子理论的历史起点。然而，普朗克的量子假设长期以来仅作为一种现象学的插入，缺乏从第一性原理出发的推导。在本研究中，我们从颤动时空相对论理论（TSRT）的几何基础出发，推导出普朗克假设及其辐射定律。在该理论框架中，时空并非光滑连续，而是存在受限的微观涨落，这些涨落受到“固有时间必须保持实数且向前演化”的因果性要求所约束。光子并不被视为具有波粒二象性的实体，而是作为沿着受几何颤动扰动的零测地线传播的微粒激发。能量量子化直接源于测地线偏差中的相干性条件，无需引入算符形式、波动叠加或概率性公设。通过对这些测地线配置的统计分析，我们在零温度下仍可导出普朗克谱律，因为此时仍存在残余颤动。此外，我们在该框架中建立了与几何结构一致的熵和温度定义，展示了 TSRT 不仅能重现已知的热力学极限，还预测了一个与因果测地结构崩溃相关的最大温度。尽管在 TSRT 中光子严格表现为微粒，理论仍准确重现了相对论性多普勒效应，说明光谱与热力学可观测量在惯性系之间的变换具有协变性。因此，TSRT 为黑体辐射与光的热力学提供了一个基于时空因果几何、具备确定性与可检验性的理论基础。最后，我们从颤动测地线出发导出一条局域的、受曲率抑制的熵公式，该公式在强曲率区域自然趋于贝肯斯坦–霍金面积定律，从而在无需依赖量子场论的情况下，为引力热力学建立了几何上的第一性原理基础
Haptic Shape Discrimination in Virtual Environments Using Force Direction
No full textInternational audienceShape discrimination of objects relies on sensory and contextual cues. While existing studies explored cues for shape discrimination, an underexplored question remains what the minimal haptic cue (one kind of the sensory cues) is sufficient for such discrimination with contextual cues in virtual environments (VE). This study examined whether the changes of force direction – as a haptic cue – could serve this sufficiency. The results of the study confirmed the sufficiency for the discrimination under certain conditions. This confirmation implied a potential of applying force direction to simplify the design of haptic cues for VE applications
On the strain energy decomposition in phase field brittle fracture: established models and novel cleavage plane-based techniques
No full textInternational audienceThis work offers a detailed examination of the phase field approach for modeling brittle fracture, emphasizing its theoretical foundations, mathematical descriptions, and computational strategies. Central to our discussion is an in-depth analysis of strain energy decomposition methods integral to phase field models. We introduce an innovative technique using a cleavage plane based degradation that has shown promising results under various loading scenarios. We meticulously evaluate each method's inherent limitations and challenges to highlight their respective advantages and drawbacks across different loading scenarios. This review aims not only to catalog existing knowledge but also to pave the way for future research directions in the application of phase field approach to fracture analysis.Ce travail propose une analyse approfondie de l’approche par champ de phase pour la modélisation de la rupture fragile, en mettant l’accent sur ses fondements théoriques, ses formulations mathématiques et ses stratégies de mise en œuvre numérique. Au cœur de notre étude se trouve une investigation détaillée des méthodes de décomposition de l’énergie de déformation, essentielles aux modèles à champ de phase. Nous présentons une technique innovante fondée sur une dégradation orientée selon un plan de clivage, ayant démontré des résultats prometteurs sous divers scénarios de chargement. Chaque méthode est examinée avec rigueur afin d’en évaluer les limites intrinsèques et les défis spécifiques, dans le but de faire ressortir leurs avantages et inconvénients respectifs selon les cas de sollicitation. Cette revue vise non seulement à dresser un état des lieux des connaissances actuelles, mais également à ouvrir de nouvelles perspectives de recherche sur l’application du champ de phase à l’analyse de la rupture
Le Wabi-Sabi dans le dessin en réalité virtuelle : vers un changement de posture du créateur numérique
No full textInternational audienceTraditional design promotes abundant, inexpensive, and disposable ways to create that are not compatible with sustainability. The authors explore alternatives to this paradigm by comparing a virtual reality sketch method with a new approach inspired by the traditional Japanese concept Wabi-Sabi. An experiment limited users’ amount of virtual paint and removed users’ ability to erase, and while participants’ creative approaches and processes changed, they were satisfied with the results. Combining Wabi-Sabi with digital technologies provides a concrete opportunity to “go forward” by incorporating sustainable considerations in practice and in the development of tools for digital artists and creators
Minimization of the circulating currents of an interleaved converter for particle accelerator using inversion-based control
No full textInternational audienceAn interleaved DC/DC converter is used to supply a magnet for particle accelerator. A very high accuracy of 50 parts per million is required to control the particle beam. Any disturbance can reduce this accuracy. An inversion-based control is derived from the Energetic Macroscopic Representation of this power converter. This control is composed of several control loops and compensations. The control leads to the right accuracy despite some ripple due to current measurement
Hip-lumbar mobility loss affects quality of life in patients undergoing both lumbar fusion and total hip arthroplasty
No full textInternational audienceAimsOverall sagittal flexion is restricted in patients who have undergone both lumbar fusion and total hip arthroplasty (THA). However, it is not evident to what extent this movement is restricted in these patients and how this influences quality of life (QoL). The purpose of this study was to determine the extent to which hip-lumbar mobility is decreased in these patients, and how this affects their QoL score.MethodsPatients who underwent primary THA at our hospital between January 2010 and March 2021 were considered (n = 976). Among them, 44 patients who underwent lumbar fusion were included as cases, and 44 THA patients without lumbar disease matched by age, sex, and BMI as Control T. Among those who underwent lumbar fusion, 44 patients without hip abnormalities matched by age, sex, and BMI to the cases were considered as Control F. Outcome and spinopelvic parameters were measured radiologically in extension and flexed-seated positions. Hip, lumbar, and hip-lumbar mobility were calculated as parameter changes between positions.ResultsThere were 20 male and 112 female patients in the case and control groups, with a mean age of 77 years (5 to 94) and a mean BMI of 24 kg/m2 (15 to 34). QoL score and hip-lumbar mobility were reduced in cases compared to Control T and F, and were further reduced as the number of fused levels increased. Hip-lumbar mobility was associated with reduction in activity-related QoL, mostly for those activities requiring sagittal flexion.ConclusionThis study confirmed that hip-lumbar mobility is a factor that influences activity, most of all those requiring overall sagittal flexion. Clinicians should focus on hip-lumbar mobility and counteract disability by suggesting appropriate assistive devices
L’intelligence géospatiale appliquée à la surveillance des espaces maritimes du bassin Pacifique
No full textInternational audienc
Mechanical characterization and constitutive law of porcine urethral tissues: a hyperelastic fiber model based on a physical approach
No full textInternational audienceLower urinary tract symptoms (LUTS), particularly urinary incontinence (UI), represent a significant global health challenge, affecting millions of patients worldwide. The artificial urinary sphincter (AUS) remains one of the most effective intervention for severe UI, with its design relying on a detailed understanding of the urethral biomechanics. Given the ethical and logistical constraints of using human tissue, porcine urethras, which share anatomical and mechanical similarities with human urethras, are widely employed in preclinical studies. This study investigates the uniaxial mechanical characterization of porcine urethral tissue under controlled conditions. Fresh porcine urethral samples were subjected to uniaxial tensile testing along both the longitudinal and circumferential directions to characterize their anisotropic mechanical properties. Experimental results were compared with existing datasets to validate findings. Additionally, conventional hyperelastic models were assessed to fit experimental results, and a novel anisotropic constitutive model with physical parameters was developed. This fiber model, which incorporates fiber modulus, volume, and orientation, uses a single set of parameters to predict behavior in both directions. It demonstrated improved accuracy, reaching the performance of the Gasser-Ogden-Holzapfel (GOH) model, with root mean square errors (RMSEs) of 9.24% and 12.98% in the circumferential and longitudinal directions, respectively. In contrast, the Yeoh and Ogden models were unable to fit both directions using a single set of parameters, yielding RMSEs values exceeding 30%. With its enhanced physical relevance, the fiber model having a more physical meaning holds promise for applications in the biomechanical analysis of fiber-composed soft tissues
Residual stress control in large format polylactic acid additive manufacturing via fast thermomechanical simulation and in-operando imaging techniques
No full textInternational audiencePolymer-based Large Format Additive Manufacturing (LFAM) is an extrusion-based technology utilizing a robotic arm-mounted nozzle to deposit large-diameter polymer beads from heated polymer pellets. However, technical challenges arise due to slower cooling rates and heat accumulation, significant deformation that should be accounted for updating the nozzle path, as well as the development of residual stresses from thermo-chemical shrinkage leading to debonding. To overcome these challenges, the study proposes to combine recent and fast thermal and mechanical approaches. This computationally efficient digital twin of the process is validated experimentally on a thin-wall structure using polylactic acid as a feedstock material. To do so, anisotropic material properties are characterized, and in-operando temperature and displacement field measurements are performed using an infrared thermal camera and backward Digital Image Correlation techniques. Numerical results are in satisfying agreement with experimental data. The validated digital twin is then utilized to characterize the effect of process parameters on the number of layers above the glass transition temperature, the formation of residual stresses and the position offset between the top surface of the structure and the nozzle. This paper presents a fast numerical tool to better design fabrication conditions and improve the quality and fabricability of LFAM-produced parts