A matheuristic approach for an integrated lot-sizing and scheduling problem with a period-based learning effect arxiv.org/abs/2412.16222

A Sophisticated Analytical Methodology for Refining the Smagorinsky Model in Turbulent Flows arxiv.org/abs/2412.16230

A Sophisticated Analytical Methodology for Refining the Smagorinsky Model in Turbulent Flows

In this work, we present three important theorems related to the corrected Smagorinsky model for turbulence in time-dependent domains. The first theorem establishes an improved regularity criterion for the solution of the corrected Smagorinsky model in Sobolev spaces $H^s(Ω(t))$ with smooth and evolving boundaries. The result provides a bound on the Sobolev norm of the solution, ensuring that the solution remains regular over time. The second theorem quantifies the approximation error between the corrected Smagorinsky model and the true Navier-Stokes solution. Taking advantage of high-order Sobolev spaces and energy methods, we derive an explicit error estimate for the velocity fields, showing the relationship between the error and the external force term. The third theorem focuses on the asymptotic convergence of the corrected Smagorinsky model to the solution of the Navier-Stokes equations as time progresses. We provide an upper bound for the error in the $L^2(Ω)$ norm, demonstrating that the error decreases as time increases, especially as the external force term vanishes. This result highlights the long-term convergence of the corrected model to the true solution, with explicit dependences on the initial conditions, viscosity, and external forces.

arXiv.org

Battery swapping station location for electric vehicles: a simulation optimization approach arxiv.org/abs/2412.15233

Battery swapping station location for electric vehicles: a simulation optimization approach

Electric vehicles face significant energy supply challenges due to long charging times and congestion at charging stations. Battery swapping stations (BSSs) offer a faster alternative for energy replenishment, but their deployment costs are considerably higher than those of charging stations. As a result, selecting optimal locations for BSSs is crucial to improve their accessibility and utilization. Most existing studies model the BSS location problem using deterministic and static approaches, often overlooking the impact of stochastic and dynamic factors on solution quality. This paper addresses the facility location problem for BSSs within a city network, considering stochastic battery swapping demand. The objective is to optimize the placement of a given set of BSSs to minimize demand loss. To achieve this, we first develop a mathematical programming model for the problem. Then, we propose a simulation optimization method based on a large neighborhood search framework to handle large-scale instances. To reduce the computational cost of simulations, Bayesian optimization is employed to solve the single-station allocation subproblem during the repair process. Numerical experiments demonstrate the efficiency of the proposed approach and highlight the importance of incorporating dynamic factors in decision-making.

arXiv.org

Asymptotic efficiency of inferential models and a possibilistic Bernstein--von Mises theorem arxiv.org/abs/2412.15243

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