Modern engineering and materials sciences are facing many challenges pertaining to optimization, efficiency, economic growth, reliability, safety, green energy, technology and other modern problems. In this new section of Symmetry, Engineering and Materials, we aim to gather expert reviews and mainstream research articles in the fields of engineering and materials science. This section will focus on mathematical models and trends in engineering and materials science, enriching the literature with new developments in these fields of research. The aim is to provide an online synthetic and multidisciplinary library which will enhance our knowledge of materials and engineering and set the stage for future researchers to find solutions to modern problems in these areas. This will require highly non-trivial mathematical modelling and, in most cases, multidisciplinary approaches. The synergy between engineering and modern materials sciences will also be highlighted in this section of the journal.

There is no better way to highlight the motivations of an editorial on Engineering Science and Materials than to quote Thomson Reuters, who stated that “Fundamental discoveries in physics dominated the first half of the 20th century, whereas discoveries in molecular biology, such as the structure of DNA, dominated the second half. The 21st century may well bring forth a new era, one of revolutionary discoveries in materials research that result in far-reaching changes for society and how we live” [1]. This perspective captures the aims and scopes of modern engineering and materials sciences: to revolutionize the way we live, and to some extent the well-being of mankind. To this end, by creating the section Engineering and Materials [2], we aim to offer a synthetic online library composed of mainstream articles and reviews in these two sciences, highlighting the elevated role of mathematical modelling, which is the cornerstone of modern science. Synergistically with the experimental approaches, the mathematical modelling will offer a deep understanding of both engineering and materials sciences. Materials science and engineering is a broad, multilayered diverse and multidisciplinary field of research, and developments in these two interrelated scientific disciplines are in continuous interaction with both human wellbeing and the so-called Grand Societal Challenges. The examples of this continuous interaction between the society and engineering and materials sciences are numerous, and range from transportation to communication and other everyday actions that are made simpler due to technological developments. Economic growth is also heavily reliant on engineering and materials sciences. One of the main aims with this new section of Symmetry is to enlarge and consolidate the knowledge in mathematical modelling in engineering and material sciences and to set the stage for future developments and perspectives that will inform future researchers in the field. The mathematical modelling in engineering and materials stretches quite far in terms of the physics involved in these sciences, and provides a synthetic continuous interaction between the ways materials are constructed and processed. Many technological advancements rely on the way materials are tailored and engineered; for example, in communications, the photonics and lasers play a prominent role; in energy, Li-ion batteries form the cornerstone of modern energy-storage devices; new superconducting materials may play a fundamental role in the future well-being of mankind. One cannot imagine the literally groundbreaking outcomes of the discovery of room temperature and pressure superconductors. In all these advancements, the fundamental importance of establishing the theory, and thus of mathematical modelling, before the experimental test is profound and invaluable. In addition the cutting-edge technologies, various societal challenges and constraints imposed in relation to modern engineering and materials. This leads to greater scrutiny of the ways that materials are formed, in a tailored way aligned with these societal constraints—for example, green technology—in order to compensate the ${\mathrm{CO}}_2$ emissions, and prevent or delay climate change. The worldwide economy will be made more efficient and sustainable by new technological developments originating from engineering and material sciences.

In a nutshell, modern engineering and material sciences present the following challenges:

In the new section, we will gather research on mathematical modelling in the following fields.

Typical examples of articles that meet the requirements to be included in this online synthetic library of mathematical modelling are papers that rely on computational methods applied in materials [3], modelling in modern materials [4], methodological approaches [5], and mathematical models in material formation [6,7,8]. A fine example of the aim of the Engineering and Materials section of Symmetry is the newly introduced field of quantum geometry and superconductors [9,10].

Multidisciplinary mathematical approaches that aim to revolutionize modelling in engineering and material sciences, along with articles which aim to promote artificial intelligence modelling toward refined material production and efficient engineering, are particularly encouraged.