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Advances in Continuous and Discrete Models

Theory and Modern Applications

Advances in Continuous and Discrete Models Cover Image

Featured Article: Kinetic theory without pain: an unpublished paper by Jean Ginibre

Featured here is a previously unpublished manuscript written by the late Jean Ginibre on Kinetic Theory from the mid 1960's. The manuscript has been scanned and published here as it survives in its original French.  Yves Pomeau, emeritus research director at the CNRS and corresponding member of the French Academy of sciences, has graciously provided a generous English summary of the manuscript as well as a concise contextualization of the content for when it was written. 

Featured Collection: New Mathematical Trends in the Study of Materials Behavior

This collection provides an up-to-date view of the broad research field of nonlinear PDEs and material science with an attention to modeling, analysis and computation of fluid and solid dynamics, elasticity, complex materials and environmental phenomena. The emergence of scale structures driven by nonlinearities constitutes a major challenge to understanding continuum physics deeply founded in the PDEs framework.

Giuseppe Mario Coclite, Professore Ordinario di Analisi Matematica at Politecnico di Bari in Italy, and Francesco Maddalena, Associate Professor of Mathematical Analysis at Politecnico di Bari in Italy, were our esteemed guest editors for this collection. 

Call for Papers: Expanded scope for Advances in Continuous and Discrete Models

Advances in Continuous and Discrete Models: Theory and Modern Applications now accepts a broader range of high-quality original research and survey articles covering algorithmic and analytical developments in numerical analysis, differential equations, control, optimization, data driven modelling and scientific computing. We are also considering submissions connecting mathematical research to applications such as signal and image processing, mathematical biology and bioengineering, material science, and computer vision.

Aims and scope

Computational and applied mathematics along with data science play a vital role in contemporary society by driving innovation. This success can be attributed to revolutionary theoretical and algorithmic developments in machine learning, data driven modeling, differential equations, numerical analysis, scientific computing, control, optimization, and computing resources together with new tools to deal with uncertainty and randomness.

This journal encourages new research in these broad areas. In addition to research on algorithmic and analytical developments, the journal also encourages papers related to (but not limited to) broad applications in Signal and Image Processing, Computer Vision, Materials Science, Mathematical Biology and Bioengineering. As a result, the journal will be an excellent connecting bridge between mathematical research and real world applications. 

The journal accepts high-quality articles containing original research results and survey articles of exceptional merit.  Below are short descriptions of the scope of the Areas within the journal: 


Data Science: 

Computer Science, Mathematics, and Statistics are the infrastructure and baseline of the development of data science, with crucial topics including optimization, operational research, scientific computing, and so on. In data science section of this journal, we are interested in submissions that can advance cutting-edge research in computational, mathematical, and statistical methods and models in data science, and solve important theoretical, numerical, and practical questions remain unsolved or even completely open, in data science.


Numerical Analysis and Scientific Computing: 


Numerical methods for ODEs/PDEs, Inverse problems, Optimisation and Control, Model reductions, Uncertainty quantification, computational science and engineering, computational mechanics

Partial Differential Equations and Mathematical Physics: 

The Partial Differential Equations and Mathematical Physics section accepts papers on all aspects of ordinary, partial differential equations and mathematical physics. The section also covers all applications concerning partial differential equations.



The Control section welcomes contributions on the Control theory considered in a broad sense, comprising areas of Controllability, Optimal control, Control engineering, Inverse problems, etc. The papers must provide novel theoretical and/or application approaches to non-isolated research topics whose relevance has to be justified with clear links to established methods and theories.


Stochastic Modeling, Analysis and Uncertainty Quantification: 

This section accepts research papers on financial markets and population system related stochastic models, analysis of models, including stability and optimal control. 


Mathematical Biology and Bioengineering: 

We welcome innovative simple mathematical modeling efforts inspired by biological phenomena, including but not limited to ecology and epidemiology. We also welcome the analysis of mathematical properties of existing models with biological implications through new technologies.

Computer Vision: 

The Computer Vision section accepts papers on optimization techniques related to machine learning, computer vision and intelligent control systems. Relevant topics include image processing, target tracking, intelligent systems for the aged care and remote sensing.  


Materials Science: 

The Materials Science section accepts papers on mathematical approaches to describe the behaviour of materials, e.g., in  engineering or life science applications. Relevant topics include physics of solids and soft materials, coupled problems, and material modelling.


Meet the Editors-in-Chief

Harbir Antil is Founder and Director at the Center for Mathematics and Artificial Intelligence as well as a Professor in the Department of Mathematical Sciences at George Mason University in Virginia, USA. His research interests include calculus of variations, inverse problems, numerical analysis, scientific computing and software development, and dimensional reduction. 
Recent Publications

Xue-Cheng Tai is a professor at the Hong Kong Center for Cerebro-cardiovascular Health Engineering (COCHE). His research interests include numerical PDEs, optimization techniques, inverse problems, and image processing. 
Recent Publications

Enrique Zuazua is Chair for Dynamics, Control and Numerics in the Department of Data Science at Friedric-Alexander Universität in Germany. his fields of expertise include PDEs, Control Theory, and Numerical Analysis. 
Recent Publications

Click here to view the new editorial board for Advances in Continuous and Discrete Models: Theory and Applications. 


Articles Collections

Thematic series
New Mathematical Trends in the Study of Materials Behavior
Advances in Continuous and Discrete Models
Edited by Giuseppe Coclite (Polytechnic University of Bari, Italy) and Francesco Maddalena (Polytechnic University of Bari, Italy)
Collection: Closed

Thematic Series
Nonlinear Waves, Kinetic Theory, and Related Topics: A Tribute to the Memory of Jean Ginibre
Edited by: Tran Minh Binh (Texas A&M, USA)
Collection: Ongoing

View all collections

Annual Journal Metrics

  • 2022 Citation Impact
    4.1 - 2-year Impact Factor
    2.9 - 5-year Impact Factor
    1.702 - SNIP (Source Normalized Impact per Paper)
    0.672 - SJR (SCImago Journal Rank)

    2022 Speed
    15 days submission to first editorial decision for all manuscripts (Median)
    235 days submission to accept (Median)

    2022 Usage 
    9 Altmetric mentions 

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