2063 research outputs found
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On tool wear optimized motion planning for 5-axis CNC machining of free-form surfaces using toroidal cutting tools
No full textWe propose a computational framework for motion planning for 5-axis CNC machining of free-form surfaces. Given a reference surface, a set of contact paths on it, and a shape of a toroidal cutting tool as input, the proposed algorithm designs the tool motions that are by construction locally and globally collision-free, and offers a trade-off between approximation quality and tool wear using an optimization-based framework. The proposed algorithm first quickly constructs 2D time-tilt configuration spaces along each contact path, detecting regions that are collision-free. The configuration spaces are then merged into a single time-tilt configuration space to find a global tilt function to control the overall motion of the tool. An initial collision-free tilt function in B-spline form is first estimated and then optimized to minimize the machining error while distributing the tool wear as uniformly as possible along the entire cutting edge of the tool while staying in the collision-free region. Our algorithm is validated on both synthetic free-form surfaces and industrial benchmarks, showing that one can considerably reduce the tool wear without degrading the machining accuracy.AURRERA (Elkartek KK-2024/00024)
PID2023-146640NB-I00 (MICIU/AEI/10.13039/501100011033)
CEX2021-001142-S
RYC-2017-22649 funded by MICIU/AEI/10.13039/501100011033 and EI ESF "ESF Investing in your future"
project R&D of Technologies for Advanced Digitization in the Pilsen Metropolitan Area (DigiTech) No.: CZ.02.01.01/00/23\_021/0008436 co-financed by the European Union
Effective Velocity and -based Well-Posedness for Incompressible Fluids with Odd Viscosity
No full textThe present paper is concerned with the well-posedness theory for non-homogeneous incompressible fluids exhibiting
odd (non-dissipative) viscosity effects. Differently from previous works, we consider here the full odd viscosity
tensor. Similarly to the work of Bresch and Desjardins in compressible fluid mechanics, we identify the presence
of an effective velocity in the system, linking the velocity field of the fluid and the gradient of a suitable function
of the density. By use of this effective velocity, we propose a new formulation of the original system of equations,
thus highlighting a strong similarity with the equations of the ideal magnetohydrodynamics. By taking advantage
of the new formulation of the equations, we establish a local in time well-posedness theory in Besov spaces based
on L
∞ and prove a lower bound for the lifespan of the solutions implying “asymptotically global” existence: in the
regime of small initial density variations, ρ0 − 1 = O(ε) for small ε > 0, the corresponding solution is defined up
to some time Tε > 0 satisfying the property Tε −→ +∞ when ε → 0
+
An Adaptive Sampling Algorithm for Level-set Approximation
No full textWe propose a new numerical scheme for approximating level-sets of Lipschitz multivariate functions which is robust to stochastic noise.
The algorithm's main feature is an adaptive grid-based stochastic approximation strategy which automatically refines the approximation over regions close to the level set.
This strategy combines a local function approximation method with a noise reduction scheme and produces -accurate approximations with an expected cost complexity reduction of compared to a non-adaptive scheme, where is the convergence rate of the function approximation method and we assume that the noise can be controlled in .
We provide numerical experiments in support of our theoretical findings. These include 2- and 3-dimensional functions with a complex level set structure, as well as a failure region estimation problem described by a hyperelasticity partial differential equation with random field coefficients.PID2023-146668OA-I00
RYC2022-036312-
Enhanced Stability of Cobalt-Free Spinel LiMn1.5Ni0.5O4 with V Doping for High-Voltage Li-Ion Batteries in Organic and Ionic Liquid Electrolytes
No full textHigh-voltage spinel cathode material LiMn1.5Ni0.5O4 (LMNO) has attracted great interest due to its large theoretical capacity, energy density and cobalt-free chemistry. However, high voltage cycling leads to accelerated decomposition of organic electrolytes (OEs) and to capacity fading in TFSI-based ionic liquid (IL) electrolytes. To address these challenges, LMNO nanorod particles were synthesized based on α-MnOOH nanorod templates, facilitating the co-precipitation of lithium and nickel cations. Several vanadium dopant contents were subsequently explored (LiMn1.5-xNi0.5VxO4, where x = 0.01, 0.03, and 0.05), resulting in spinel structures with enhanced structural and electrochemical stability in both OEs and ILs. Morphological and compositional analyses highlighted the reduction of Mn4 + to Mn3+ to sustain electroneutrality within the lattice, as well as the coexistence of two cubic spinel phases (disordered Fd3̅m and ordered P4332) in contributing to superior electrochemical performance and stability. Moreover, the rod-like particle morphology displayed a high-rate capability comparable to that of the well-known octahedral morphology. Density Functional Theory (DFT) calculations confirmed that increasing V-content promotes the formation of the Fd3̅m spinel phase, while incorporation of V in ordered P4332 is not energetically favourable. In addition, machine learning-based molecular dynamics (MD) simulations showed that increasing V-content tends to decrease Li-ion diffusion barriers, increasing the intrinsic ionic mobility in the cathode. Remarkably, LiMn1.49Ni0.5V0.01O4 demonstrated excellent capacity retention when cycled in an OE (75.11 % in LMNO vs 84.33 % in V-doped LMNO) and in IL electrolyte (30.79 % in LMNO vs 79.33 % for V-doped LMNO), positioning it as a promising and safer candidate high-voltage cathode.MICIU/AEI/10.13039/ 501100011033 and by ERDF A way for Europe under Grant PID2022–136585NB-C22;
ELKARTEK Programme under Grants KK-2024/00062, KK-2023/00017;
Ministry of Science and Innovation through “PLAN COMPLEMENTARIO MATERIALESZADOS 2022–2025 “, PROYECTO Nº:1101288;
Juan de la Cierva postdoctoral grant JDC2022–049793-I funded by MICIU/AEI/10.13039/501100011033 and by European Union NextGenerationEU/PRTR;
BCAM-IKUR grant, funded by the Basque Government by the IKUR Strategy and by the European Union NextGenerationEU/PRTR;
Diputaci´on Foral de Bizkaia through MODEL2RESIST (6/12/TT/2024/00003);
Spanish research agency through RYC2022–036500-I;
i2BASQUE academic network;
Barcelona Supercomputing Center (RES, QHS-2025–1–0027);
DIPC Computer Center;
IZO-SGI SGIker of UPV/EHU
Nondimensionalisations of the Langevin equation and small- parameter limits
No full textInspired by the success of dimensional analysis in continuum mechanics and nondimensional numbers such as Peclet, Schmidt, Lewis, and
Prandtl, we introduce the study of the Brownian motion nondimensional parameter M¼ conservativeforce=nonconservativeforce. In
particular, we nondimensionalise the Langevin equation for a Brownian particle of mass m moving in a fluid of viscosity c with diffusivity
coefficient r under the action of a conservative force in the form of a harmonic oscillator of constant k. We identify all the possible
time-scales T, and the associated length-scales L, on the basis of the nondimensional parameter M¼ m k c 2. Through this nondimension-
alisation we study the small-parameter limits with respect to Ma and we identify five different regimes due to a, in opposition to the three
identified by the standard analysis on the basis of the time-scales:T1 ¼ m=c, T2 ¼ffiffiffiffiffiffiffiffiffi
p , and T3 ¼ c=k. Because of the ratio-type definition
m=k
of M the leading force is established by the sign of a. For very short time-scales ða > 0Þ, the particle is trapped at its initial condition. For
short times ða ¼ 0Þ, the particle has the same dynamics of a free Brownian particle. That is, the action of the conservative force is negligible.
For intermediate time ð1 < a < 0Þ, the particle diffuses as a Wiener process, that is as a free Brownian particle at large elapsed times. The
over-damped timescale ða ¼ 1Þ is a critical timescale where the dynamics are given by the Smoluchowski–Kramers approximation. For
long times ða < 1Þ, the particle is trapped at the bottom of the potential well
A random free-boundary diffusive logistic model: Analysis, computing and simulation
No full textA free boundary diffusive logistic model finds application in many different fields from biological invasion to wildfire
propagation. However, many of these processes show a random nature and contain uncertainties in the parameters. In
this paper we extend the diffusive logistic model with unknown moving front to the random scenario by assuming that
the involved parameters have a finite degree of randomness. The resulting mathematical model becomes a random
free boundary partial differential problem and it is addressed numerically combining the finite difference method with
two approaches for the treatment of the moving front. Firstly, we propose a front-fixing transformation, reshaping the
original random free boundary domain into a fixed deterministic one. A second approach is using the front-tracking
method to capture the evolution of the moving front adapted to the random framework. Statistical moments of the
approximating solution stochastic process and the stochastic moving boundary solution are calculated by the Monte
Carlo technique. Qualitative numerical analysis establishes the stability and positivity conditions. Numerical exam-
ples are provided to compare both approaches, study the spreading-vanishing dichotomy, prove qualitative properties
of the schemes and show the numerical convergence
Statistical dynamics of wildfire burned area from cellular-automata simulators
No full textThe dynamics and statistics of synthetic and historical mid-sized Mediterranean forest fires that occurred in Catalonia (Spain) and Liguria (Italy) regions are investigated using a wildfire simulator PROPAGATOR based on a cellular-automaton scheme. On one hand, the mean, variance, and kurtosis of the synthetic burned area exhibits a non-linear growth during fire spread exacerbated by higher wind speeds and steeper terrain slopes, whereas its skewness decreases. On the other hand, the mean and variance of the burned area for the simulated historical wildfires increase nonlinearly over time, Albenga fire in Liguria region being the one exhibiting the minimum stochasticity. The skewness and kurtosis of all the real cases exhibit an irregular pattern. Z-score and interquartile range standardization methods are applied to find the most suitable parametric model for the statistical distribution of the burned area. Analytic formulae for the shape parameters (α, β) are derived by using a customized method of moments. Both standardization approaches indicate that a four-parameter Beta density function provides the best fit both for the ideal synthetic case under various wind intensities and terrain slopes’ angles, and for all the historical fires studied in Southern Europe. This suggests that this statistical model can serve as a good candidate for a prior distribution in a Bayesian approach. The dynamics of the synthetic forest fire’s shape parameters exhibit the same tendency regardless of meteorological and topographic conditions: α increases during fire-growth while β becomes constant after a crossover time tx (β = βeq). In the short-time regime, i.e., t tx , the distribution becomes left-skewed (α > β ), and large-size wildfires lead the process. The real-world cases are characterized by more nuanced dynamics in the long-time regime (t > tx), where the Beta distribution’s parameters are affected by the complex interplay between the inherent stochastic nature of fire dynamics and the firefighters’ actions, land cover, meteorological, and orographic conditions.BERC 2022–2025; Severo Ochoa.CEX2021-001142-S;
RETURN "Multi risk science for resilient communities under a changing climate" - Partenariato Esteso PE00000005 - M.I.U.R Ministry of Education and Merit, CUP code: "CUP_B57G22001180002- PROGETTO RETURN PNRR
A phenotype-structured mathematical model for the influence of hypoxia on oncolytic virotherapy
No full textronment, which reduce the ability of the virus to infect cancer cells. In this work, we focus on the influence of hypoxia on this therapy and develop a novel continuous mathematical model that considers both the spatial and epigenetic heterogeneity of the tumour. We investigate how oxygen gradients within tumours affect the spatial distribution and replication of both the tumour and oncolytic viruses, focusing on regions of severe hypoxia versus normoxic areas. Additionally, we analyse the evolutionary dynamics of tumour cells under hypoxic conditions and their influence on susceptibility to viral infection. Our findings show that the reduced metabolic activity of hypoxic cells may significantly impact the virotherapy effectiveness; the knowledge of the tumour’s oxygenation could, therefore, suggest the most suitable type of virus to optimise the outcome. The combination of numerical
simulations and theoretical results for the model equilibrium values allows us to elucidate the complex interplay between viruses, tumour evolution and oxygen dynamics, ultimately contributing to developing more effective and personalised cancer treatments
The initial-to-final-state inverse problem with time-independent potentials
No full textThe initial-to-final-state inverse problem consists in determining a quantum Hamiltonian assuming the knowledge of the state of the system at some fixed time, for every initial state. This problem was formulated by Caro and Ruiz and motivated by the data-driven prediction problem in quantum mechanics. Caro and Ruiz analysed the question of uniqueness for Hamiltonians of the form −Δ+V with an electric potential V=V(t,x) that depends on the time and space variables. In this context, they proved that uniqueness holds in dimension n≥2 whenever the potentials are bounded and have super-exponential decay at infinity. Although their result does not seem to be optimal, one would expect at least some degree of exponential decay to be necessary for the potentials. However, in this paper, we show that by restricting the analysis to Hamiltonians with time-independent electric potentials, namely V=V(x), uniqueness can be established for bounded integrable potentials exhibiting only super-linear decay at infinity, in any dimension n≥2. This surprising improvement is possible because, unlike Caro and Ruiz's approach, our argument avoids the use of complex geometrical optics (CGO). Instead, we rely on the construction of stationary states at different energies -- this is possible because the potential does not depend on time. These states will have an explicit leading term, given by a Herglotz wave, plus a correction term that will vanish as the energy grows. Besides the significant relaxation of decay assumptions on the potential, the avoidance of CGO solutions is important in its own right, since such solutions are not readily available in more complicated geometric settings
-ESTIMATES FOR SINGULAR INTEGRAL OPERATORS ALONG CODIMENSION ONE SUBSPACES
No full textIn this paper we study maximal directional singular integral operators in R given
by a Hörmander–Mihlin multiplier on an (−1)-dimensional subspace and acting trivially in
the perpendicular direction. The subspace is allowed to depend measurably on the first −1
variables of R. Assuming the subspace to be non degenerate in the sense that it is away from
a cone around and the function to be frequency supported in a cone away from R−1
,
we prove -bounds for these operators for > 3/2. If we assume, additionally, that is
supported in a single frequency band, we are able to extend the boundedness range to > 1.
The non-degeneracy assumption cannot in general be removed, even in the band-limited case