arXiv subjects

Nicolas Schaeffer

Publications and source records attributed to Nicolas Schaeffer.

4 recordsLinked to original sources

arXiv2026

Comprehensive parameter and electrochemical dataset for a 1 Ah graphite/LNMO battery cell for physical modelling as a blueprint for data reporting in battery research

While current technology has enabled their widespread use, further improvements are needed for stationary, portable, and mobile applications, for example by the development of novel cathode materials. Digitalization of battery development, combining both experimental and modelling efforts is extremely valuable in this development. This is addressed in the present paper, where the authors present a comprehensive dataset for a graphite/LNMO 1 Ah pouch cell, including material, design, and electrochemical data. The dataset, validated through the BattMo modelling framework, supports physical modelling and aims to benefit the battery modelling community by offering a comprehensive resource for future studies. Both the dataset and the accompanying software for numerical validation is openly available and processed in such a way that it can serve as blueprint for reporting of comparable research data.

cond-mat.mtrl-sci↗

arXiv2022

Multilinear smoothing and local well-posedness of a stochastic quadratic nonlinear Schr{ö}dinger equation

In this article, we study a $d$-dimensional stochastic quadratic nonlinear Schrödinger equation (SNLS), driven by a fractional derivative (of order $-α<0$) of a space-time white noise: $$\left\{ \begin{array}{l}i\partial_t u-Δu= ρ^2 |u|^2 + \langle \nabla \rangle^{-α}\dot{W} \, , \quad t\in [0,T] \, , \, x\in \mathbb{R}^d \, ,\\ u_0 = ϕ\, ,\end{array}\right.$$ where $ρ:\mathbb{R}^d \rightarrow \mathbb{R}$ is a smooth compactly-supported function. When $α< \frac{d}{2}$, the stochastic convolution is a function of time with values in a negative-order Sobolev space and the model has to be interpreted in the Wick sense by means of a time-dependent renormalization. When $1\leq d \leq 3$, combining both the classical Strichartz estimates and a deterministic local smoothing, we establish the local well-posedness of (SNLS) for a small range of $α$, in the spirit of \cite{Schaeffer1}. Then, we revisit our arguments and establish multilinear smoothing on the second order stochastic term. This allows us to improve our local well-posedness result for some $α$. We point out that this is the first result concerning a Schrödinger equation on $\mathbb{R}^d$ driven by such an irregular noise and whose local well-posedness results from both a stochastic multilinear smoothing and a deterministic local one combined with Strichartz inequalities.

math.AP↗

arXiv2021

Study of a fractional stochastic heat equation

In this article, we study a $d$-dimensional stochastic nonlinear heat equation (SNLH) with a quadratic nonlinearity, forced by a fractional space-time white noise: \begin{equation*} \left\{\begin{array}{l} \partial_t u-Δu= ρ^2 u^2 + \dot B \, , \quad t\in [0,T] \, , \, x\in \mathbb{R}^d \, ,\\ u_0=ϕ\, . \end{array} \right. \end{equation*} Two types of regimes are exhibited, depending on the ranges of the Hurst index $H=(H_0,...,H_d)$ $\in (0,1)^{d+1}$. In particular, we show that the local well-posedness of (SNLH) resulting from the Da Prato-Debussche trick, is easily obtained when $2 H_0+\sum_{i=1}^{d}H_i >d$. On the contrary, (SNLH) is much more difficult to handle when $2H_0+\sum_{i=1}^{d}H_i \leq d$. In this case, the model has to be interpreted in the Wick sense, thanks to a time-dependent renormalization. Helped with the regularising effect of the heat semigroup, we establish local well-posedness results for (SNLH) for all dimension $d\geq1.$

math.AP↗

arXiv2020

A nonlinear Schr{ö}dinger equation with fractional noise

We study a stochastic Schr{ö}dinger equation with a quadratic nonlinearity and a space-time fractional perturbation, in space dimension less than 3. When the Hurst index is large enough, we prove local well-posedness of the problem using classical arguments. However, for a small Hurst index, even the interpretation of the equation needs some care. In this case, a renormalization procedure must come into the picture, leading to a Wick-type interpretation of the model. Our fixed-point argument then involves some specific regularization properties of the Schr{ö}dinger group, which allows us to cope with the strong irregularity of the solution.

math.AP↗