We develop a method of constructing structure-preserving integrators for Hamiltonian systems in Jacobi manifolds. Hamiltonian mechanics, rooted in symplectic and Poisson geometry, has long provided a foundation for modeling conservative systems in classical physics. Jacobi manifolds, generalizing both contact and Poisson manifolds, extend this theory and are suitable for incorporating time-dependent, dissipative and thermodynamic phenomena. Building on recent advances in geometric integrators - specifically Poisson Hamiltonian Integrators (PHI), which preserve key features of Poisson systems - we propose a construction of Jacobi Hamiltonian Integrators. Our approach explores the correspondence between Jacobi and homogeneous Poisson manifolds, with the aim of extending the PHI techniques while ensuring preservation of the homogeneity structure. This work develops the theoretical tools required for this generalization and outlines a numerical integration technique compatible with Jacobi dynamics. By focusing on the homogeneous Poisson perspective instead of direct contact realizations, we establish a clear pathway for constructing structure-preserving integrators for time-dependent and dissipative systems that are embedded in the Jacobi framework.
Crater wear is one of the dominant failure mechanisms limiting the performance of ceramic cutting tools during high-speed dry machining. In this study, the effect of vanadium incorporation into TiAlSiN coatings on the evolution of crater wear during dry turning of 42CrMo4 steel was investigated. TiAlSiN, TiAlSiV4N and TiAlSiV11N coatings were deposited on Al2O3/SiC whisker-reinforced ceramic inserts by reactive DC magnetron sputtering and evaluated under different cutting speeds and feed rates. Crater wear was characterized using three-dimensional optical profilometry, while infrared thermography, Raman spectroscopy and energydispersive X-ray spectroscopy were used to investigate the thermal and tribochemical response of the rakeface contact. TiAlSiV11N exhibited the best overall machining performance, reducing the principal craterwear parameters by approximately 30-50% compared with the uncoated tool while lowering the measured cutting temperature by approximately 8-12%. Cutting-length-dependent measurements further showed a slower progression of crater volume for the V-containing coatings. Raman spectroscopy confirmed the formation of V2O5 together with Fe2O3, Cr2O3, TiO2, Al2O3 and SiO2. Fe and O concentrations showed a strong dependence on cutting temperature, with comparable values at similar temperatures irrespective of coating composition, indicating that thermal loading is the dominant factor governing material transfer and oxidation. The superior performance of TiAlSiV11N is therefore attributed to the combined influence of improved coating adhesion, modified mechanical and oxidation behaviour, reduced thermal loading and V-induced tribochemical reactions. These results provide experimental support for a coupled thermo-tribochemical interpretation of wear suppression in TiAlSiVxN-coated ceramic tools.
In this paper, we provide an upper bound for the number of one-element commutation classes of a permutation, that is, the number of reduced words in which no commutation can be applied. Using this upper bound, we prove a conjecture that relates the number of reduced words with the number of commutation classes of a permutation.
In 1998, Lütolf and Margot claimed, in a sidenote, that the projective plane of order 3 3 , also called the ternary plane, or PG(2,3 P G ( 2 , 3 ), cannot be the core of any minimally non-ideal clutter. In this paper, we show that, if \operatorname{\cal C} C is a minimally non-ideal clutter whose core is the PG(2,3) P G ( 2 , 3 ) then \operatorname{\cal C} C must be the blocker of the PG(2,3) P G ( 2 , 3 ) . Since no projective plane of order n \geq 3 n ≥ 3 is minimally non-ideal, the nonexistence of \operatorname{\cal C} C is a consequence of the fact that a clutter is minimally non-ideal if and only its blocker is minimally non-ideal.
Noble gas detectors that rely on electroluminescence (EL) are widely used in radiation detection and rare-event searches because they provide large signal amplification with low intrinsic fluctuations. The introduction of electronegative additives, such as SF6, modifies charge transport, opening the possibility of exploiting low diffusion through negative ion drift, but may suppress scintillation. In this work, EL production in Xe-SF6 mixtures was studied as a function of reduced electric field and SF6 concentration, using a GEM to induce electron detachment. Two complementary configurations were used to separate the contribution from light produced within the GEM holes and in the region after the GEM. Measurements show that, once the detachment threshold is reached, both charge and light signals increase with the electric field in the GEM region, with EL appearing before charge multiplication. In the scintillation region, after the GEM, a light signal can be observed that increases with the applied scintillation field, but remains much weaker than the one produced in the GEM region. In both regions, the effective EL yield is strongly reduced with respect to pure xenon and decreases as the SF6 fraction increases. For higher SF6 concentrations, the yield is approximately linear within the explored electric field range, whereas for lower concentrations it departs from linearity at higher fields. The onset of EL production was obtained and compared with the previously reported charge multiplication threshold and with a detachment cross-section prediction. Both thresholds shift to higher reduced electric fields as the SF6 concentration increases and remain, within uncertainties, consistent with the prediction. These results demonstrate that EL is still possible in Xe-SF6 mixtures, but is strongly quenched by the electronegative additive, highlighting the complex interplay of the microscopic processes in the detector.
