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Modelling and predicting coastal zone depth profile evolution: a survey 海岸带深度剖面演化模拟与预测综述
Q2 Mathematics Pub Date : 2023-01-01 DOI: 10.2478/caim-2023-0003
Denis Baramiya, Mikhail Lavrentiev, Renato Spigler
Abstract We survey results concerning the problem of identifying depth profiles at coastal zone, which evolve in time due to natural as well as anthropic activities. This issue is relevant to control the modifications of the environment occurring near sea coastlines, but also in river's estuaries and harbors. One of the main goals is to predict the time evolution of the depth profile in the long-term (i.e., over years or decades, say), and to do this on the basis of real observed and measured data , available in several databases. Most mathematical models are formulated in terms of partial differential equations of the diffusive type, in one or two space dimensions. Consequently, from the mathematical standpoint, the aforementioned identification problem takes on the form of an inverse problem for some given parabolic equation associated with suitable initial and boundary conditions.
摘要本文调查了受自然和人为活动影响而随时间变化的海岸带深度剖面识别问题。这个问题不仅关系到控制发生在海岸线附近的环境变化,而且关系到河流的河口和港口。主要目标之一是预测深度剖面的长期(例如,几年或几十年)的时间演变,并在几个数据库中可用的实际观测和测量数据的基础上进行预测。大多数数学模型是用扩散型偏微分方程在一个或两个空间维度上表述的。因此,从数学的角度来看,上述识别问题对某些给定的具有适当初始条件和边界条件的抛物方程具有反问题的形式。
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引用次数: 0
Macroscopic traffic flow modelling: from kinematic waves to autonomous vehicles 宏观交通流建模:从运动波到自动驾驶汽车
IF 1.3 Q2 Mathematics Pub Date : 2023-01-01 DOI: 10.2478/caim-2023-0001
P. Goatin
Abstract This survey offers a unified up-to-date presentation of macroscopic models of traffic flow, pointing out their main characteristics and possible drawbacks. The presentation is completed by several pictures illustrating the models’ features. Some open problems and future research directions are also given to inspire the reader.
摘要本文对交通流宏观模型进行了统一的介绍,指出了这些模型的主要特点和可能存在的缺陷。演示由几张说明模型特征的图片完成。并提出了一些有待解决的问题和今后的研究方向,以期对读者有所启发。
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引用次数: 0
A general review on the NLS equation with point-concentrated nonlinearity 具有点集中非线性的NLS方程综述
Q2 Mathematics Pub Date : 2023-01-01 DOI: 10.2478/caim-2023-0004
Lorenzo Tentarelli
Abstract The paper presents a complete (to the best of the author’s knowledge) overview on the existing literature concerning the NLS equation with point-concentrated nonlinearity. Precisely, it mainly covers the following topics: definition of the model, weak and strong local well-posedness, global well-posedness, classification and stability (orbital and asymptotic) of the standing waves, blow-up analysis and derivation from the standard NLS equation with shrinking potentials. Also some related problem is mentioned.
摘要:本文对具有点集中非线性的NLS方程的现有文献进行了全面(据作者所知)的综述。具体来说,主要包括模型的定义、弱和强局部适定性、全局适定性、驻波的分类和稳定性(轨道和渐近)、爆破分析和具有收缩势的标准NLS方程的推导。并提出了一些相关问题。
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引用次数: 0
Global Existence of Weak Solutions for Compresssible Navier—Stokes—Fourier Equations with the Truncated Virial Pressure Law 具有截断维里压力律的可压缩Navier-Stokes-Fourier方程弱解的整体存在性
IF 1.3 Q2 Mathematics Pub Date : 2023-01-01 DOI: 10.2478/caim-2023-0002
D. Bresch, P. Jabin, Fei Wang
Abstract This paper concerns the existence of global weak solutions á la Leray for compressible Navier–Stokes–Fourier systems with periodic boundary conditions and the truncated virial pressure law which is assumed to be thermodynamically unstable. More precisely, the main novelty is that the pressure law is not assumed to be monotone with respect to the density. This provides the first global weak solutions result for the compressible Navier-Stokes-Fourier system with such kind of pressure law which is strongly used as a generalization of the perfect gas law. The paper is based on a new construction of approximate solutions through an iterative scheme and fixed point procedure which could be very helpful to design efficient numerical schemes. Note that our method involves the recent paper by the authors published in Nonlinearity (2021) for the compactness of the density when the temperature is given.
摘要本文讨论了具有周期边界条件的可压缩Navier–Stokes–Fourier系统的全局弱解ála Leray的存在性,以及假设热力学不稳定的截断维里压力定律。更确切地说,主要的新颖性在于,压力定律不被假设为相对于密度是单调的。这为具有这种压力定律的可压缩Navier-Stokes傅立叶系统提供了第一个全局弱解结果,这种压力定律被强烈用作完美气体定律的推广。本文基于通过迭代格式和不动点程序构造近似解的新方法,这对设计有效的数值格式非常有帮助。请注意,我们的方法涉及作者最近发表在《非线性》(2021)上的关于给定温度时密度紧致性的论文。
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引用次数: 0
Polynomial mapped bases: theory and applications 多项式映射基:理论与应用
IF 1.3 Q2 Mathematics Pub Date : 2022-01-01 DOI: 10.48550/arXiv.2204.01555
S. Marchi, G. Elefante, E. Francomano, F. Marchetti
Abstract In this paper, we collect the basic theory and the most important applications of a novel technique that has shown to be suitable for scattered data interpolation, quadrature, bio-imaging reconstruction. The method relies on polynomial mapped bases allowing, for instance, to incorporate data or function discontinuities in a suitable mapping function. The new technique substantially mitigates the Runge’s and Gibbs effects.
摘要在本文中,我们收集了一种新技术的基本理论和最重要的应用,该技术已被证明适用于散射数据插值、正交、生物成像重建。该方法依赖于多项式映射基,例如,允许将数据或函数不连续性合并到合适的映射函数中。新技术大大减轻了龙格效应和吉布斯效应。
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引用次数: 1
Machine learning assisted droplet trajectories extraction in dense emulsions 机器学习辅助稠密乳液液滴轨迹提取
IF 1.3 Q2 Mathematics Pub Date : 2022-01-01 DOI: 10.2478/caim-2022-0006
M. Durve, A. Tiribocchi, A. Montessori, M. Lauricella, S. Succi
Abstract This work analyzes trajectories obtained by YOLO and DeepSORT algorithms of dense emulsion systems simulated via lattice Boltzmann methods. The results indicate that the individual droplet’s moving direction is influenced more by the droplets immediately behind it than the droplets in front of it. The analysis also provide hints on constraints of a dynamical model of droplets for the dense emulsion in narrow channels.
摘要本文分析了YOLO和DeepSORT算法通过格子Boltzmann方法模拟的致密乳液系统的轨迹。结果表明,单个液滴的移动方向受其正后方液滴的影响大于前方液滴的作用。该分析还为窄通道中致密乳液液滴动力学模型的约束提供了线索。
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引用次数: 0
Virtual Element Methods for three-dimensional Hellinger-Reissner elastostatic problems 三维Hellinger-Reissner弹性静力问题的虚元法
IF 1.3 Q2 Mathematics Pub Date : 2022-01-01 DOI: 10.2478/caim-2022-0005
C. Lovadina, Michele Visinoni
Abstract This note aims at illustrating the application of the Virtual Element Method to elasticity problems in mixed form, following the Hellinger-Reissner variational principle. In order to highlight the potential and the flexibility of our approach, we focus on a three-dimensional low-order Virtual Element scheme, but similar considerations apply to two-dimensional and higher-order methods.
摘要本文旨在说明虚拟单元法在混合形式弹性问题中的应用,遵循Hellinger-Reissner变分原理。为了突出我们方法的潜力和灵活性,我们关注三维低阶虚拟单元方案,但类似的考虑也适用于二维和高阶方法。
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引用次数: 0
Deep learning based non-intrusive load monitoring with low resolution data from smart meters 基于深度学习的非侵入式负荷监测与来自智能电表的低分辨率数据
IF 1.3 Q2 Mathematics Pub Date : 2022-01-01 DOI: 10.2478/caim-2022-0004
Marco Manca, L. Massidda
Abstract A detailed knowledge of the energy consumption and activation status of the electrical appliances in a house is beneficial for both the user and the energy supplier, improving energy awareness and allowing the implementation of consumption management policies through demand response techniques. Monitoring the consumption of individual appliances is certainly expensive and difficult to implement technically on a large scale, so non-intrusive monitoring techniques have been developed that allow the consumption of appliances to be derived from the sole measurement of the aggregate consumption of a house. However, these methodologies often require additional hardware to be installed in the domestic system to measure total energy consumption with high temporal resolution. In this work we use a deep learning method to disaggregate the low frequency energy signal generated directly by the new generation smart meters deployed in Italy, without the need of additional specific hardware. The performances obtained on two reference datasets are promising and demonstrate the applicability of the proposed approach.
详细了解家庭中电器的能耗和激活状态对用户和能源供应商都是有益的,可以提高能源意识,并通过需求响应技术实施消费管理政策。监测单个电器的消费当然是昂贵的,而且很难在技术上大规模地实施,因此已经开发了非侵入式监测技术,使电器的消费能够从对房屋总消费的唯一测量中得出。然而,这些方法通常需要在家庭系统中安装额外的硬件,以高时间分辨率测量总能耗。在这项工作中,我们使用深度学习方法来分解在意大利部署的新一代智能电表直接产生的低频能量信号,而不需要额外的特定硬件。在两个参考数据集上获得了良好的性能,证明了该方法的适用性。
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引用次数: 1
Deep learning-assisted analysis of automobiles handling performances 汽车操纵性能的深度学习辅助分析
IF 1.3 Q2 Mathematics Pub Date : 2022-01-01 DOI: 10.2478/caim-2022-0007
D. Sapienza, D. Paganelli, M. Prato, M. Bertogna, Matteo Spallanzani
Abstract The luxury car market has demanding product development standards aimed at providing state-of-the-art features in the automotive domain. Handling performance is amongst the most important properties that must be assessed when developing a new car model. In this work, we analyse the problem of predicting subjective evaluations of automobiles handling performances from objective records of driving sessions. A record is a multi-dimensional time series describing the temporal evolution of the mechanical state of an automobile. A categorical variable quantifies the evaluations of handling properties. We describe an original deep learning system, featuring a denoising autoencoder and hierarchical attention mechanisms, that we designed to solve this task. Attention mechanisms intrinsically compute probability distributions over their inputs’ components. Combining this feature with the saliency maps technique, our system can compute heatmaps that provide a visual aid to identify the physical events conditioning its predictions.
摘要豪华汽车市场要求制定产品开发标准,旨在为汽车领域提供最先进的功能。操控性能是开发新车型时必须评估的最重要特性之一。在这项工作中,我们分析了从驾驶过程的客观记录中预测汽车操纵性能的主观评价的问题。记录是描述汽车机械状态时间演变的多维时间序列。分类变量量化处理属性的评估。我们描述了一个原始的深度学习系统,该系统具有去噪自动编码器和分层注意力机制,我们设计用于解决这一任务。注意力机制本质上计算其输入分量的概率分布。将这一特征与显著性图技术相结合,我们的系统可以计算热图,为识别影响其预测的物理事件提供视觉帮助。
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引用次数: 0
High order Finite Difference/Discontinuous Galerkin schemes for the incompressible Navier-Stokes equations with implicit viscosity 含隐粘性不可压缩Navier-Stokes方程的高阶有限差分/不连续Galerkin格式
IF 1.3 Q2 Mathematics Pub Date : 2022-01-01 DOI: 10.2478/caim-2022-0003
W. Boscheri, M. Tavelli, Nicola Paoluzzi
Abstract In this work we propose a novel numerical method for the solution of the incompressible Navier-Stokes equations on Cartesian meshes in 3D. The semi-discrete scheme is based on an explicit discretization of the nonlinear convective flux tensor and an implicit treatment of the pressure gradient and viscous terms. In this way, the momentum equation is formally substituted into the divergence-free constraint, thus obtaining an elliptic equation on the pressure which eventually maintains at the discrete level the involution on the divergence of the velocity field imposed by the governing equations. This makes our method belonging to the class of so-called structure-preserving schemes. High order of accuracy in space is achieved using an efficient CWENO reconstruction operator that is exploited to devise a conservative finite difference scheme for the convective terms. Implicit central finite differences are used to remove the numerical dissipation in the pressure gradient discretization. To avoid the severe time step limitation induced by the viscous eigenvalues related to the parabolic terms in the governing equations, we propose to devise an implicit local discontinuous Galerkin (DG) solver. The resulting viscous sub-system is symmetric and positive definite, therefore it can be efficiently solved at the aid of a matrix-free conjugate gradient method. High order in time is granted by a semi-implicit IMEX time stepping technique. Convergence rates up to third order of accuracy in space and time are proven, and a suite of academic benchmarks is shown in order to demonstrate the robustness and the validity of the novel schemes, especially in the context of high viscosity coefficients.
摘要在这项工作中,我们提出了一种在三维笛卡尔网格上求解不可压缩Navier-Stokes方程的新的数值方法。半离散格式基于非线性对流通量张量的显式离散化和压力梯度和粘性项的隐式处理。通过这种方式,动量方程被形式化地代入无散度约束,从而获得关于压力的椭圆方程,该方程最终将控制方程施加的速度场的散度的对合保持在离散水平。这使得我们的方法属于所谓的结构保持方案的一类。使用有效的CWENO重建算子实现了空间中的高精度,该算子用于设计对流项的保守有限差分格式。在压力梯度离散化中,采用隐式中心有限差分来消除数值耗散。为了避免控制方程中与抛物项相关的粘性特征值引起的严重的时间步长限制,我们提出了一种隐式局部不连续Galerkin(DG)求解器。由此得到的粘性子系统是对称的和正定的,因此它可以在无矩阵共轭梯度法的帮助下有效地求解。时间上的高阶是通过半隐式IMEX时间步进技术授予的。证明了在空间和时间上高达三阶精度的收敛速度,并展示了一套学术基准,以证明新方案的稳健性和有效性,特别是在高粘性系数的情况下。
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引用次数: 4
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Communications in Applied and Industrial Mathematics
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