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.
{"title":"Modelling and predicting coastal zone depth profile evolution: a survey","authors":"Denis Baramiya, Mikhail Lavrentiev, Renato Spigler","doi":"10.2478/caim-2023-0003","DOIUrl":"https://doi.org/10.2478/caim-2023-0003","url":null,"abstract":"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.","PeriodicalId":37903,"journal":{"name":"Communications in Applied and Industrial Mathematics","volume":"162 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135497982","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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.
{"title":"Macroscopic traffic flow modelling: from kinematic waves to autonomous vehicles","authors":"P. Goatin","doi":"10.2478/caim-2023-0001","DOIUrl":"https://doi.org/10.2478/caim-2023-0001","url":null,"abstract":"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.","PeriodicalId":37903,"journal":{"name":"Communications in Applied and Industrial Mathematics","volume":"14 1","pages":"1 - 16"},"PeriodicalIF":1.3,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47805225","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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.
{"title":"A general review on the NLS equation with point-concentrated nonlinearity","authors":"Lorenzo Tentarelli","doi":"10.2478/caim-2023-0004","DOIUrl":"https://doi.org/10.2478/caim-2023-0004","url":null,"abstract":"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.","PeriodicalId":37903,"journal":{"name":"Communications in Applied and Industrial Mathematics","volume":"106 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136304337","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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.
{"title":"Global Existence of Weak Solutions for Compresssible Navier—Stokes—Fourier Equations with the Truncated Virial Pressure Law","authors":"D. Bresch, P. Jabin, Fei Wang","doi":"10.2478/caim-2023-0002","DOIUrl":"https://doi.org/10.2478/caim-2023-0002","url":null,"abstract":"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.","PeriodicalId":37903,"journal":{"name":"Communications in Applied and Industrial Mathematics","volume":"14 1","pages":"17 - 49"},"PeriodicalIF":1.3,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43215148","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-01-01DOI: 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.
{"title":"Polynomial mapped bases: theory and applications","authors":"S. Marchi, G. Elefante, E. Francomano, F. Marchetti","doi":"10.48550/arXiv.2204.01555","DOIUrl":"https://doi.org/10.48550/arXiv.2204.01555","url":null,"abstract":"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.","PeriodicalId":37903,"journal":{"name":"Communications in Applied and Industrial Mathematics","volume":"13 1","pages":"1 - 9"},"PeriodicalIF":1.3,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42968145","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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.
{"title":"Machine learning assisted droplet trajectories extraction in dense emulsions","authors":"M. Durve, A. Tiribocchi, A. Montessori, M. Lauricella, S. Succi","doi":"10.2478/caim-2022-0006","DOIUrl":"https://doi.org/10.2478/caim-2022-0006","url":null,"abstract":"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.","PeriodicalId":37903,"journal":{"name":"Communications in Applied and Industrial Mathematics","volume":"13 1","pages":"70 - 77"},"PeriodicalIF":1.3,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45919262","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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.
{"title":"Deep learning based non-intrusive load monitoring with low resolution data from smart meters","authors":"Marco Manca, L. Massidda","doi":"10.2478/caim-2022-0004","DOIUrl":"https://doi.org/10.2478/caim-2022-0004","url":null,"abstract":"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.","PeriodicalId":37903,"journal":{"name":"Communications in Applied and Industrial Mathematics","volume":"13 1","pages":"39 - 56"},"PeriodicalIF":1.3,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44443079","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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.
{"title":"Virtual Element Methods for three-dimensional Hellinger-Reissner elastostatic problems","authors":"C. Lovadina, Michele Visinoni","doi":"10.2478/caim-2022-0005","DOIUrl":"https://doi.org/10.2478/caim-2022-0005","url":null,"abstract":"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.","PeriodicalId":37903,"journal":{"name":"Communications in Applied and Industrial Mathematics","volume":"13 1","pages":"57 - 69"},"PeriodicalIF":1.3,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44935015","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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.
{"title":"Deep learning-assisted analysis of automobiles handling performances","authors":"D. Sapienza, D. Paganelli, M. Prato, M. Bertogna, Matteo Spallanzani","doi":"10.2478/caim-2022-0007","DOIUrl":"https://doi.org/10.2478/caim-2022-0007","url":null,"abstract":"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.","PeriodicalId":37903,"journal":{"name":"Communications in Applied and Industrial Mathematics","volume":"13 1","pages":"78 - 95"},"PeriodicalIF":1.3,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47776659","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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.
{"title":"High order Finite Difference/Discontinuous Galerkin schemes for the incompressible Navier-Stokes equations with implicit viscosity","authors":"W. Boscheri, M. Tavelli, Nicola Paoluzzi","doi":"10.2478/caim-2022-0003","DOIUrl":"https://doi.org/10.2478/caim-2022-0003","url":null,"abstract":"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.","PeriodicalId":37903,"journal":{"name":"Communications in Applied and Industrial Mathematics","volume":"13 1","pages":"21 - 38"},"PeriodicalIF":1.3,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47868919","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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