We investigate an alternative approach to the dark matter problem by employing a non-commutative geometry (NCG) framework, wherein spacetime coordinates exhibit intrinsic quantum uncertainty. In this model, the classical point-mass source is replaced by a smeared energy density characterized by a minimal length scale β . This leads to a modified Schwarzschild-like solution with an effective mass profile that yields flat galactic rotation curves—mimicking the effects commonly attributed to dark matter. We derive the corresponding gravitational potential and evaluate the velocity profile analytically and numerically. A detailed comparison with the standard ΛCDM model is performed using observational data from the spiral galaxy NGC 3198. The results demonstrate that the NCG model can successfully reproduce the flat rotation curve without invoking exotic matter components. This suggests that quantum corrections to spacetime geometry may provide a viable explanation for dark matter phenomenology, motivating further investigation into geometric extensions of gravity. The present work should be interpreted as an effective non-commutative geometry-inspired model, in which non-commutative effects are incorporated through a smeared matter distribution while Einstein’s field equations remain unchanged.
Nous considérons l’évolution collisionnelle vers l’équilibre du gaz de phonons spatialement homogène et isotrope d’un superfluide tridimensionnel à branche d’excitation acoustique concave, à une température T non nulle mais arbitrairement basse. Les collisions à trois phonons 1 ϕ ↔ 2 ϕ sont interdites par la conservation de l’énergie-impulsion. Les collisions à quatre phonons 2 ϕ → 2 ϕ de Landau et Khalatnikov ne conduisent, au bout d’un temps ∝ T –7 , qu’à un équilibre thermique partiel, une loi de Bose de potentiel chimique non nul pour les phonons, car elles en conservent le nombre total. La relaxation vers l’équilibre thermochimique complet est donc assurée par les collisions beaucoup plus lentes à cinq phonons 2 ϕ ↔ 3 ϕ de Khalatnikov, en un temps ∝ T –9 . Au moyen d’équations cinétiques sur les nombres d’occupation des modes de phonons et après calcul explicite par l’hydrodynamique quantique de l’amplitude de collision 2 ϕ → 3 ϕ à basse température, nous déterminons l’évolution correspondante de la fugacité z ϕ du gaz de phonons depuis le régime non dégénéré z ϕ = 0 + jusqu’à l’équilibre complet z ϕ = 1 – . En utilisant la conservation de l’énergie totale, nous trouvons que la fugacité varie avec une loi de puissance non entière ∝ t 4/5 aux temps courts et une loi exponentielle aux temps longs ; la vitesse de variation de l’entropie, toujours positive, est asymptotiquement proportionnelle au carré de la vitesse de variation de la fugacité, (d/d t ) S ϕ ∝ [(d/d t ) z ϕ ] 2 , comme l’avait prédit Landau pour une transformation adiabatique arbitrairement lente. Nos résultats portent à son terme l’étude commencée par Khalatnikov en 1950 et pourraient être vérifiés expérimentalement dans un gaz d’atomes froids fermioniques de spin 1/2 dans le secteur du raccordement CBE-BCS où la branche acoustique est de départ concave, ou dans l’hélium 4 liquide superfluide à suffisamment haute pression.
In this foreword, we pay a personal tribute to Renaud Parentani, who suddenly passed away in 2020. We express our desire to gather in his memory a series of scientific articles in the field of analogous gravity, which was so dear to his heart. We also bring together a collection of personal memories of Renaud from his closest friends and collaborators: Serge Massar, Florent Michel, Stefano Finazzi, Jeff Steinhauer, and Uwe Fischer.
This study investigates the photocatalytic and dielectric properties of green-synthesized silver-doped zinc oxide nanoparticles (Ag:ZnONPs). FTIR analysis confirmed the presence of functional groups derived from the plant extract, which played a key role in the capping, and stabilization of the nanoparticles. SEM observations revealed rod-like and quasi-spherical nanostructures, while EDX analysis verified the successful incorporation of Ag into the ZnO matrix. XRD results confirmed the hexagonal wurtzite structure of synthesized sample, with an average crystallite size of approximately 20 nm. Photoluminescence studies showed near-band-edge emission with suppressed defect-related recombination, indicating improved charge carrier separation due to Ag doping. The Ag:ZnONPs demonstrated excellent visible-light photocatalytic performance, achieving nearly 99% degradation of crystal violet within 24 h and methyl orange within 72 h. Dielectric investigations revealed reduced impedance, and enhanced AC conductivity at room temperature, reflecting improved charge transport. The results highlight the multifunctional potential of green-synthesized Ag:ZnONPs for environmental remediation and advanced electronic applications.
In the context of the energy transition and the growing demand for electrochemical energy storage, the development of efficient and sustainable battery materials is a major scientific and technological challenge. Chalcogenide-based materials, including sulfides, selenides, and tellurides, have attracted increasing attention due to their versatile structural and electronic properties. This article provides a concise overview of the role of chalcogenides in battery technologies, from their historical contribution to the emergence of lithium-ion batteries to their current applications as intercalation and conversion electrodes, nanostructured negative electrodes, solid electrolytes, and lithium-rich positive electrodes in solid-state batteries. Particular emphasis is placed on the relationships between composition, structure, electrochemical mechanisms, and performance. Finally, the potential of chalcogenide materials for post-lithium battery technologies, such as sodium-, potassium-, and magnesium-ion systems, is discussed, highlighting remaining challenges and future research perspectives.
