This Special Issue of Mathematics and Computers in Simulation collects a selection of peer-reviewed original articles on research topics developed in connection with IMACS2023, the IMACS World Congress, held in Rome (Italy) at the Faculty of Engineering, Sapienza University of Rome on September 11 - 15, 2023, that we organized, in the role of Local Scientific Committee, together with Rosa Maria Spitaleri, Congress Chair.

In this editorial the historical premises of the world Congress IMACS2023 are delineated in order to appreciate the development of IMACS as a scientific association keeping up with the ultimate scientific aspirations of society in the fields of Applied Mathematics and Scientific Computing. The World Congress, IMACS2023, the last considered step, celebrates successfully such a prestigious story.

Literature confirms the crucial influence on glacier and rock glacier flow of non-viscous deformations together with temperature impact. This observation suggests numerical glaciologists ought to reconsider the established mathematical modeling based on the representation of ice as a power-law viscous fluid and the Glen's law. Along this line, we propose the numerical solution of a two-dimensional rock-glacier flow model, based on a constitutive law of second grade of complexity two, as just published for a one-dimensional set-up by two of the authors. With the representation of the composition of the rocky ice as a mixture of ice and rock and sand grains, and the inclusion of the local impact of pressure and of thermal effects, this model has allowed the reproduction of borehole measurement data from alpine glacier internal sliding motion via a similarity solution of the flow governing equations. Here, the adopted numerical procedure uses a second order finite difference scheme and imposes the incompressibility constrain up to computer accuracy via the pressure method, that we have extended from Newtonian computational fluid dynamics. This method solves the governing equations for the flow in primitive variables with the advantage that no pre-/post-processing is required; in addition, it avoids splitted solution of the Poisson equation for pressure which might be source of undesired numerical mass unbalancing. The results of a numerical test on the Murtel-Corvatsch alpine glacier flow, reporting satisfactory matching with published on-field observations, are presented.

Modeling the evolution of the melt front under gravity in the presence of a horizontal thermal gradient is a challenging issue, hitherto tackled exclusively with the concepts and tools of computational continuum thermomechanics, too phenomenologically driven to have satisfactory predictive capabilities. Here, we show that this complex phenomenon is amenable to treatment by the methods and tools of Non-Equilibrium Molecular Dynamics (NEMD). To do so, we addressed all the difficulties caused by the necessity of applying suitable boundary conditions and minimizing surface effects so that the bulk behavior of the system in non-equilibrium conditions can be detected. Sufficient adiabatic separation of the time scales permits us to use macroscopically relatively short-but microscopically long enough-time averages to get the macroscopic bulk behavior of the system accurately. To get an adequate signal-to-noise ratio, we had to use an unphysically large value of the gravity. However, we know from NEMD simulations in transport studies that the phenomena produced are stable over many orders of magnitude. In conclusion, our work proves that molecular simulation can be a good tool to study this family of non-equilibrium phenomena, although further work is needed to achieve quantitative predictive capabilities.

Nel cuore della scuola primaria, luogo privilegiato per la costruzione delle conoscenze di base e per lo sviluppo delle prime competenze trasversali, si colloca il progetto STI2MA, acronimo di Scienza, Tecnica, Ingegno, Italiano, Matematica e Arte. Si tratta di una proposta strutturata di rinnovamento della didattica della matematica in chiave interdisciplinare e sostenibile, nel solco delle Indicazioni Nazionali e dei più recenti orientamenti internazionali in materia di educazione alla cittadinanza globale. L’autrice mette a punto un curricolo integrato che muove dall’idea, tanto Montessoriana quanto di epistemologia scientifica contemporanea, secondo cui la matematica non è solo una disciplina ma un linguaggio per pensare, per interpretare il mondo, per agire con consapevolezza, per riflettere e per scoprire tutte le dimensioni del proprio universo culturale. L’autrice mette a punto un curricolo integrato che muove dall’idea, tanto Montessoriana quanto di epistemologia scientifica contemporanea, secondo cui la matematica non è solo una disciplina ma un linguaggio per pensare, per interpretare il mondo, per agire con consapevolezza, per riflettere e per scoprire tutte le dimensioni del proprio universo culturale.

We present a mathematical model describing the evolution of sea ice and meltwater during summer. The system is described by two coupled partial differential equations for the ice thickness h(x,t) and pond depth w(x,t) fields. The model is similar, in principle, to the one put forward by Luthije et al. (2006), but it features i) a modified melting term, ii) a non-uniform seepage rate of meltwater through the porous ice medium and a minimal coupling with the atmosphere via a surface wind shear term, ?s (Scagliarini et al. 2020). We test, in particular, the sensitivity of the model to variations of parameters controlling fluid- dynamic processes at the pond level, namely the variation of turbulent heat flux with pond depth and the lateral melting of ice enclosing a pond. We observe that different heat flux scalings determine different rates of total surface ablations, while the system is relatively robust in terms of probability distributions of pond surface areas. Finally, we study pond morphology in terms of fractal dimensions, showing that the role of lateral melting is minor, whereas there is evidence of an impact from the initial sea ice topography.

This booklet contains all the abstracts of the results which are going to be presented at the IMACS World Congress taking place in Rome at theEngineering Faculty of University 'La Sapienza', September 11-15, 2023.This is the 21st one in a series of World Conferences whose complete list goes back to 1955 and covered the whole continents. The subsequent World Conferences, usually, take place every three years. Unfortunately, due to the COVID pandemics, IMACS2023, initially scheduled in 2020, had to be postponed also in order to follow the spirit of the IMACS World Conference which prescribes to gather scientists in presence from all over the world. So, in the present occasion, the whole participants are expected to convene in Rome for exchanging their works, ideas and experiences.This Book of Abstracts, reflecting the Congress structure, is organized in sections: Keynote Lectures, General Session, Mini-symposia, Special Sessions and Posters. According to the IMACS philosophy, different aspects of applied mathematics are represented with a special interest towards the numerical methods and solutions.

During melting under gravity in the presence of a horizontal thermal gradient, buoyancy-driven convection in the liquid phase affects significantly the evolution of the liquid-solid interface. Due to the obvious engineering interest in understanding and controlling melting processes, fluid dynamicists and applied mathematicians have spent many efforts to model and simulate them numerically. Their endeavors concentrated in the twenty-five years period between the publication of the paper by Brent, Voller & Reid (1988) and that by Mansutti & Bucchignani (2011). The former--and most of the following ones--adopted a phase-field model (where the interface is blurred into a smooth transition zone), while the latter was based on a Stefan-like model with sharp interface. With suitably chosen values of many ad-hoc material and numerical parameters, all of the above simulations were able to attain some agreement with their common benchmark, the melt fronts obtained experimentally by Gau & Viskanta (1986) on a sample of gallium enclosed in a parallelepipedal box with one vertical wall heated. This left unresolved several fine issues, such as whether the elastic response of the solid phase plays a role in determining the shape of the liquid-solid interface.Here, for the first time, we tackle this problem at the atomistic level with a molec- ular dynamics approach. The advantage we gain is that a unique microscopic model describes all of the aggregation states of the molecules, and in particular the solid- liquid interface, without any further assumptions. The price we have to pay is that the hydrodynamical quantities of interest, computed out of the microscopic state using the Irwing & Kirkwood (1950) prescriptions, need to be obtained under gravitational acceleration and thermal gradients much larger than those in real experiments.

Recent literature confirms the crucial influence of non-viscous deformations together with temperature impact on glacier and rock glacier flow numerical simulation. Along this line, supported by the successful test on a one-dimensional set-up developed by two of the author, we propose the numerical solution of a two-dimensional rock-glacier flow model based on an ice constitutive law of second grade differential type . The procedure adopted uses a 2nd order finite difference scheme and imposes the incompressibility constrain up to computer precision via the pressure method, ex- tended from newtonian computational fluid dynamics. The governing equations are solved in primitive variables with the advantage to avoid pre-/post-processing; splitted solution of the derived Poisson equation for pressure, source of undesired numerical mass unbalancing, is avoided as well. Numerical results will be shown.The financial support of Piano Nazionale Ricerca Antartide (project PNRA16-0012) is acknowledged.

In this study, we computationally corroborate the flow of rock glaciers against borehole measurements, within the context of a model previously developed (2020). The model is, here, tested against the simulation of the sliding motion of the Murtel-Corvatsch alpine glacier, which is characterized in detail in the literature with internal structure description and borehole deformations measurement. The capability of the model to take into account the composition of the rock glacier, as a mixture of ice and rock and sand grains with the local impact of pressure and heat transfer, results in the accurate detection of the internal sliding. With careful calibration of the model parameters, the computed numerical solution of the model reports a relative error of 1.8% and of 0.3% in the reproduction of the measured shear zone velocity and of the ratio of measured shear zone deformation over top surface deformation, respectively. Furthermore a deeper understanding of the role of the model parameters involved in the simulation of such a process is also gained and we discuss the same in detail.

Up-to-date computational glaciology is very often basing its investigations about glacier flow on the intensive use of the large amount of data, gathered in (alpine or polar) on-field campaigns, and on the "brute force" adaptation of the Glen's law via phenomenological multi-parametrical functional factors and/or addenda. Although, reasonable to fully satisfactory numerical results have been being obtained with this approach adopted by the most popular open-source computational glaciology codes, a modelling effort is worth in order to include the normal stress gradient effects which are not covered by such a power law model and are indeed physically significant in the case of moraine ice and rock glaciers. In this trend Kannan, Mansutti and Rajagopal have proposed (2021) a mathematical numerical model which has been successfully challenged on the reproduction of borehole deformation measurements of the Murtel-Corvatsch rock glacier on the Grisons Alps, Switzerland. This case, and possibly other numerical results at the present time in progress, will be discussed.

This Special Issue collects peer-reviewed original articles dealing with further developments of research results presented at MASCOT2018, the 15th IMACS/ISGG International Workshop. This one is the last edition in time of the MASCOT series of meetings, yearly organized since 2001 under the auspices of the Istituto per le Applicazioni del Calcolo (IAC) of the Consiglio Nazionale delle Ricerche (CNR), the principal organizer and co-sponsor. For a straightforward browsing of the Issue Contents all the articles are shortly introduced according to the following thematic Sections: Mathematical modeling in thermodynamics, Numerical methods for approximation, Numerical solution of partial differential equations, Data and signal processing, Subdivision schemes. Main advancements are delineated.

This Special Issue collects peer-reviewed original articles dealing with further developments of research results presented at MASCOT2018, the 15th IMACS/ISGG International Workshop. This one is the last edition in time of the MASCOT series of meetings, yearly organized since 2001 under the auspices of the Istituto per le Applicazioni del Calcolo (IAC) of the Consiglio Nazionale delle Ricerche (CNR), the principal organizer and co-sponsor.

This book presents important recent applied mathematics research on environmental problems and impacts due to climate change. Although there are inherent difficulties in addressing phenomena that are part of such a complex system, exploration of the subject using mathematical modelling is especially suited to tackling poorly understood issues in the field. It is in this spirit that the book was conceived.It is an outcome of the International INDAM Workshop "Mathematical Approach to Climate Change Impacts - MAC2I", held in Rome in March 2017. The workshop comprised four sessions, on Ecosystems, Hydrology, Glaciology, and Monitoring. The book includes peer-reviewed contributions on research issues discussed during each of these sessions or generated by collaborations among the specialists involved. Accurate parameter determination techniques are explained and innovative mathematical modelling approaches, presented. The book also provides useful material and mathematical problem-solving tools for doctoral programs dealing with the complexities of climate change.

This paper stems from the interest in the numerical study of the evolu- tion of Boulder Clay Glacier in Antarctica, whose morphological characteristics have required the revision of the basis for most of the recent mathematical models for glacier dynamics. Bearing in mind the need to minimize the complexity of the mathematical model, we have selected the constitutive equation of rock glacier ice recently presented by two of the authors. Here, this model is extended in order to include temperature effects. In addition to the effects of climate change, it is also necessary to take into consideration the non-negligible level of melting due to tem- perature changes induced by normal stresses arising from the interactions of ice and the rock fragments that are within the rock glacier. In fact, local phase transition that occurs leading to the release of water implies significant modifications of ice viscosity, the main intrinsic factor driving the flow. In this paper we derive the model that describes the flow of rock glaciers that takes into consideration the effects of temperature and the normal stresses generated by the ice and rock fragments interactions.

This book presents important recent applied mathematics research on environmental problems and impacts due to climate change. Although there are inherent difficulties in addressing phenomena that are part of such a complex system, exploration of the subject using mathematical modelling is especially suited to tackling poorly understood issues in the field. It is in this spirit that the book was conceived. It is an outcome of the International INDAM Workshop "Mathematical Approach to Climate Change Impacts - MAC2I", held in Rome in March 2017. The workshop comprised four sessions, on Ecosystems, Hydrology, Glaciology, and Monitoring. The book includes peer-reviewed contributions on research issues discussed during each of these sessions or generated by collaborations among the specialists involved. Accurate parameter determination techniques are explained and innovative mathematical modelling approaches, presented. The book also provides useful material and mathematical problem-solving tools for doctoral programs dealing with the complexities of climate change.

This work concerns the rock glacier flow model introduced, in its basic form, by Kannan and Rajagopal in [1] and extended with inclusion of temperature effects by Kannan, Rajagopal, Mansutti and Urbini in [2]. This one is based on the general conservation laws (momentum, mass and energy) and takes into account the effect of shear rate, pressure and rocks and sand grains volume fraction onto viscosity, also by implementing the effects of local pressure melting point variation. Here we present the results of a sensitivity analysis of the parameters developed by shooting the location of the internal sliding occurence, induced by the presence of rocks and sand grains trapped within the interstices of the glacier, and the value of the shear velocity. The case of the Murtel-Corvatsch glacier in Switzerland is considered for the availability of the detailed description based on measured data published by Arenson, Hoelzle and Springman in [3]. The numerical results obtained improve those ones presented in [1] and show clearly the contribution of each numerical and functional parameter of the model. They also exhibit a very good agreement with observations which makes this modelling approach very promising for general application. [1] Kannan, K., Rajagopal, K.R.: A model for the flow of rock glaciers. Int. J. Non-lin. Mech., 48, pp. 59– 64 (2013) [2] Kannan, K., Mansutti, D., Rajagopal, K.R. and Urbini, S.: Mathematical modeling of rock glacier flow with temperature effects, in Mathematical Approach to Climate Change and its Impacts (P. Cannarsa, D. Mansutti and A. Provenzale, eds.), pp. 137-148, Springer-INDAM series, vol.38 (2020) [3] Arenson, L., Hoeltzle, M. and Springman, S.: Borehole Deformation Measurements and Internal Structure of Some Rock Glaciers in Switzerland. Permafrost and Periglacial Processes, 13, pp. 117-135 (2002).

We present a mathematical model describing the evolution ofsea ice andmeltwater during summer. The system is described by two coupled partial differential equations for the ice thickness h and pond depth w fields. We test the sensitivity of the model to variations of parameters controlling fluid-dynamic processes at the pond level, namely the variation of turbulent heat flux with pond depth and the lateral melting of ice enclosing a pond. We observe that different heat flux scalings determine different rates of total surface ablations, while the system is relatively robust in terms of probability distributions of pond surface areas. Finally, we study pond morphology in terms of fractal dimensions, showing that the role of lateral melting is minor, whereas there is evidence of an impact from the initial sea ice topography.

In this talk I shall present different mathematical models aimed to describe evolving thermo-mechanics of ice in different topo-morphological and climatic conditions. Up-to-date computational glaciology address to the intensive use of the large amount of data, gathered in (alpine or polar) on-field campaigns, and to the 'brute force' adaptation of the mathematical modelling of glacier evolution based on Glen's law via phenomenological multi-parametrical functional factors and/or addenda. Although, reasonable to fully satisfactory numerical results have been being obtained with this approach adopted by the most popular open-source computational glaciology codes, with the aim to improve the comprehension of the physical mechanisms and processes, I shall discuss extensions of such models by explicit inclusion of natural phase transition occurrence (inherent and/or at a boundary interface) and by expansion of Glen's constitutive equation in order to take into account the effects of the presence of sand and rock fragments in glacier interstices. Several problems will be discussed: the description of the thermo-mechanical evolution of the icy crust of Europa, Juppiter's satellite; the check of the compatibility of the existence of a subglacial lake at Svalbard archipelago; the reproduction of the borehole measurements at the Murtel-Corvatsch glacier, Grisons Alps, Switzerland. Thus extraterrestrial, polar and alpine environments, respectively, will be considered.