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The global shift toward renewable energy has accelerated during the past decade, driven by the pursuit of a sustainable and cleaner future. Technological progress has significantly increased the efficiency of renewable energy systems, enhancing their competitive position of these renewable systems relative to traditional fossil fuels. However, the inherent variability and unpredictability of renewable sources, such as solar and wind, present considerable challenges to maintaining the stability and efficiency of power grids. This paper proposes a multiscale spatio-temporal model (MSTM) to improve power line loss predictions, optimize power dispatch, reduce energy waste, and enhance grid stability and efficiency. MSTM leverages multi-level and multiscale modeling of grid topology and designs a deep learning model to extract and fuse spatio-temporal features. Comparative studies demonstrate that MSTM outperforms existing methods regarding inline loss prediction accuracy. Furthermore, through visualization techniques, we investigate and discuss the impact of temporal and topological characteristics on line loss prediction outcomes, providing a deeper insight into the factors influencing line loss in power networks. These findings underscore the potential of advanced spatio-temporal analysis to enhance renewable energy integration.

A multiscale approach is used to simulate the translocation of DNA through a nanopore. Within this scheme, the interactions of the molecule with the surrounding fluid (solvent) are explicitly taken into account. By generating polymers of various initial configurations and lengths we map the probability distibutions of the passage times of the DNA through the nanopore. A scaling law behavior for the most probable of these times with respect to length is derived, and shown to exhibit an exponent that is in a good agreement with the experimental findings. The essential features of the DNA dynamics as it passes through the pore are explored.

Computational modeling plays an important role in biology and medicine to assess the effects of hemodynamic alterations in the onset and development of vascular pathologies. Synthetic analytic indices are of primary importance for a reliable and effective a priori identification of the risk. In this scenario, we propose a multiscale fluid-structure interaction (FSI) modeling approach of hemodynamic flows, extending the recently introduced three-band decomposition (TBD) analysis for moving domains. A quantitative comparison is performed with respect to the most common hemodynamic risk indicators in a systematic manner. We demonstrate the reliability of the TBD methodology also for deformable domains by assuming a hyperelastic formulation of the arterial wall and a Newtonian approximation of the blood flow. Numerical simulations are performed for physiologic and pathologic axially symmetric geometry models with particular attention to abdominal aortic aneurysms (AAAs). Risk assessment, limitations and perspectives are finally discussed.

Studying temperature effects on defect behaviors during thermal annealing is significant for understanding the performance degradation and recovery of semiconductor devices under irradiation. We systematically studied temperature effects on annealing crucial deep-level defects in neutron-irradiated silicon, by developing a multiscale modeling approach. The temperature-dependent concentrations and electron occupation ratios of crucial defects of divacancies (V₂) and tri-vacancies (V₃) were given for dynamic and post-irradiation annealing. Besides the common direct dissociation, we found a new approach to eliminating V₂ and V₃ by their recombination with interstitials dissociated from interstitial-relative defects at relatively low temperatures. To effectively eliminate V₂ and V₃ by post-irradiation annealing, we further determined the activation energies of 1.98eV and 1.71eV for V₂ and V₃, respectively. We also found that, within the operation temperature range of devices, the higher the temperature, the better the radiation resistance. It is thus recommended that the optimal temperature of post-irradiation annealing for device performance recovery is near 600K.

We review the use of phase field methods in solidification modeling, describing their fundamental connection to the physics of phase transformations. The inherent challenges associated with simulating phase field models across multiple length and time scales are discussed, as well as how these challenges have been addressed in recent years. Specifically, we discuss new asymptotic analysis methods that enable phase field equations to emulate the sharp interface limit even in the case of quite diffuse phase-field interfaces, an aspect that greatly reduces computation times. We then review recent dynamic adaptive mesh refinement algorithms that have enabled a dramatic increase in the scale of microstructures that can be simulated using phase-field models, at significantly reduced simulation times. Combined with new methods of asymptotic analysis, the adaptive mesh approach provides a truly multi-scale capability for simulating solidification microstructures from nanometers up to centimeters. Finally, we present recent results on 2D and 3D dendritic growth and dendritic spacing selection, which have been made using phase-field models solved with adaptive mesh refinement.

The final solidification structures of Vacuum Arc Remelting (VAR) ingots depend on the temperature distribution and fluid motion within the molten pool. In this paper, a three-dimensional multi-physics macroscale model for VAR is developed, based on the modular CFD software PHYSICA. This model is used to provide estimates of process parameters and to study complex physical phenomena, such as liquid metal flow with turbulence, heat transfer, solidification, and magnetohydrodynamics in the VAR process. The macromodel is coupled to a microscale solidification model. The micromodel combines stochastic nucleation and a modified decentred square/octahedron method to describe dendritic growth with a finite difference computation of solute diffusion. The resulting multiscale model allows prediction of the formation of microstructures in the solidifying mushy zone. This gives a better understanding of the whole VAR process from operational conditions to final ingot microstructures, as well as an essential first step in defect prediction.

When a load is applied to a dense granular material, the stress is largely transmitted by relatively rigid, heavily stressed chains of particles forming a sparse network of larger contact forces. Force chains act as the key determinant of mechanical properties such as stability, elasticity and flowability. To understand the structure and evolution of force chains, related physical processes and three corresponding characteristic time scales are analyzed in this study. We also propose three dimensionless numbers for the measurement of the relative importance of force chains. To solely study the effect of particle surface friction on force chains, uniaxial compression tests of 11,000 equal-sized particles in 2D were numerically simulated using the discrete element method. By proposing three conditions to define a force chain, the chain length distribution is found in the form of a power law. The exponent of 1.744 is independent of the surface friction. Although these results were obtained from partially crystallized jammed packings, they provide new insight into the physical processes and the structure of force chains, and thus will be helpful in the interpretation of force chains in other dense granular systems.

We deduce a model for glioma invasion that accounts for the dynamics of brain tissue being actively degraded by tumor cells via excessive acidity production, but also according to the local orientation of tissue fibers. Our approach has a multiscale character: we start with a microscopic description of single cell dynamics including biochemical and/or biophysical effects of the tumor microenvironment, translated on the one hand into cell stress and corresponding forces and on the other hand into receptor binding dynamics. These lead on the mesoscopic level to kinetic equations involving transport terms with respect to all considered kinetic variables and eventually, by appropriate upscaling, to a macroscopic reaction–diffusion equation for glioma density with multiple taxis, coupled to (integro-)differential equations characterizing the evolution of acidity and macro- and mesoscopic tissue. Our approach also allows for a switch between fast and slower moving regimes, according to the local tissue anisotropy. We perform numerical simulations to assess the importance of each tactic term and investigate the influence of two models for tissue dynamics on the tumor shape. We also suggest how the model can be used to perform a numerical necrosis-based tumor grading or support radiotherapy planning by dose painting. Finally, we discuss alternative ways of including cell level environmental influences in such a multiscale modeling approach, ultimately leading in the macroscopic limit to (multiple) taxis.

A Markov chain individual-based model for virus diffusion is investigated. Both the virus growth within an individual and the complexity of the contagion within a population are taken into account. A careful work of parameter choice is performed. The model captures very well the statistical variability of quantities like the incubation period, the serial interval and the time series of infected people in Tuscany towns.

This paper shows how a new theory of epidemics can be developed for viral pandemics in a globally interconnected world. The study of the in-host dynamics and, in parallel, the spatial diffusion of epidemics defines the goal of our work, which looks ahead to new mathematical tools to model epidemics beyond the traditional approach of population dynamics. The approach takes into account the evolutionary nature of the virus, which can generate pseudo-Darwinian mutations and selection, while learning the presence of the virus and activating adaptive immunity. The study of immune competition plays a key role in both the in-host dynamics and the contagion dynamics.

An accurate evaluation of the dynamic responses on critical components of orthotropic bridge decks is of significance for identifying structural damage and predicting the fatigue life of long-span cable-stayed bridges. However, the traditional finite element (FE) methods are computationally cost-prohibitive for this application. In response, a new multiscale time-varying analysis method based on the dynamic balance equations and FE strategies is proposed and derived theoretically in this paper. Unlike most existing methods, the dynamic responses of this refined model is easily solved through repeated iterations, using the dynamic responses of a large-scale model as the boundary conditions. To validate the effectiveness of the method, a simply supported steel plate beam was used in a field test that demonstrated good correlation between the analytical dynamic responses and the experimental ones. To further validate this method, a case study involving a whole segment model of the Pingtan Bridge orthotropic bridge deck was established and the complex junction area between the plate and longitudinal ribs was modeled using two refinement processes. For comparison, a sufficiently refined model was also developed using ANSYS software based on the traditional FE methods. This study attempted to provide a new high-efficiency analysis framework for accurate analysis of local vibration problems. Under relatively small and easily manageable calculation conditions at each cross-scale processing level, the proposed method meets not only the requirements of global design for actual engineering applications, but also supports further in depth analysis.

The wind-induced fatigue damage is an important reason for the structural deterioration of transmission tower-line systems. The study of the fatigue damage of transmission towers is a basic requirement to ensure their normal service. To simulate the fatigue damage evolution occurring in the joints of the tower, a verified hybrid multiscale finite element (FE) model is first developed by concurrent modeling and substructuring techniques. Second, a fatigue damage model based on continuum damage mechanics is calibrated by conducting a fatigue crack initiation experiment and integrated into the FE material model by subroutines technique. Third, an improved Bayesian updated probability density evolution method (BUPDEM) with higher efficiency is proposed based on the Kriging method. Finally, based on the multiscale FE model and the damaged material model, the strategies for stochastic analysis of fatigue damage of transmission tower-line systems are proposed together with a numerical example for illustration. The results of the example show a good accuracy of the proposed BUPDEM.

The surging interest in porous lightweight structures has been witnessed in recent years to pursue material innovations in broad engineering disciplines for sustainable developments and multifunctional proposes. Functionally graded (FG) porous composites represent a novel way to adjust mechanical characteristics by controlling the porosity distributions. However, the further advance in this field is challenged by the scale gap between mesoscopic and macroscopic aspects of porous structural analysis, i.e. how the local cellular morphologies impact the overall behaviors. The purpose of this paper is to bridge this gap by conducting a theoretical investigation on the performance of inclined self-weight sandwich beams with FG porous cores, where Young’s modulus is obtained with representative volume elements (RVEs) in a multiscale modeling study and depends on the cellular morphologies: average cell size and cell wall thickness. The material properties of closed-cell steel foams are adopted in a two-step assessment on target beams, including a static calculation to examine their bending deformations under gravitational loading which are then imported into a forced vibration analysis considering constant and harmonic moving forces. Timoshenko beam theory is used to establish the displacement field, while Ritz and Newmark methods are employed to solve the governing equations in terms of bending, free vibration, and forced vibration. The inclined beams are assumed to rest on a Pasternak foundation, and the corresponding structural responses can be determined based on the specific cell size and cell wall thickness, of which the effects are quantitatively revealed: the stiffness degradation induced from cellular morphologies increases the dynamic deflections, while the corresponding self-weight static deformations are reduced and the fundamental natural frequencies are raised. The influence from geometrical, boundary, and foundation conditions is also discussed to provide a comprehensive overview. This will be valuable for engineers to develop devisable foam-based load-carrying components with enhanced properties.

Dual phase (DP) steels were modeled using 2D and 3D representative volume elements (RVE). Both the 2D and 3D models were generated using the Monte-Carlo-Potts method to represent the realistic microstructural details. In the 2D model, a balance between computational efficiency and required accuracy in truly representing heterogeneous microstructure was achieved. In the 3D model, a stochastic template was used to generate a model with high spatial fidelity. The 2D model proved to be efficient for characterization of the mechanical properties of a DP steel where the effect of phase distribution, morphology and strain partitioning was studied. In contrast, the current 3D modeling technique was inefficient and impractical due to significant time cost. It is shown that the newly proposed 2D model generation technique is versatile and sufficiently accurate to capture mechanical properties of steels with heterogeneous microstructure.

In this paper, we introduce a mesh-free computational model for the simulation of high-speed impact phenomena. Within the framework of particle dynamics simulations we model a macroscopic solid ceramic tile as a network of overlapping discrete particles of microscopic size. Using potentials of the Lennard–Jones type, we integrate the classical Newtonian equations of motion and perform uni-axial, quasi-static load simulations to customize our three model parameters to the typical tensile strength, Young’s modulus and the compressive strength of a ceramic. Subsequently we perform shock load simulations in a standard experimental setup, the edge-on impact (EOI) configuration. Our obtained results concerning crack initiation and propagation through the material agree well with corresponding high-speed EOI experiments with Aluminum Oxinitride (AlON), Aluminum Oxide $({\mathrm{\text{Al}}}_2{\mathrm{\text{O}}}_3)$ and Silicon Carbide (SiC), performed at the Fraunhofer Ernst-Mach-Institute (EMI). Additionally, we present initial simulation results where we use our particle–based model to simulate a second type of high-speed impact experiments where an accelerated sphere strikes a thin aluminum plate. Such experiments are done at our institute to investigate the debris clouds arising from such impacts, which constitute a miniature model version of a generic satellite structure that is hit by debris in the earth’s orbit. Our findings are that a discrete particle based method leads to very stable, energy-conserving simulations of high–speed impact scenarios. Our chosen interaction model works particularly well in the velocity range where the local stresses caused by impact shock waves markedly exceed the ultimate material strength.

In this paper, the multiscale boundary element formulation presented in Ref. 1 for modeling material degradation and fracture is extended to mixed-mode fracture problems. The case study is a spur gear tooth fracture. The inter-granular crack initiation and propagation at the microscale is considered to lead to the formation and propagation of macrocracks under mixed-mode failure conditions. Information from the microscale to the macroscale are transferred using averaging theorems. An integral nonlocal approach is employed to avoid the pathological localization of microdamage at the macroscale. Both micro- and macroscales are modeled using recently developed boundary cohesive element and stress decremental formulations. The obtained results are in good agreement with experimental findings and other reported numerical results.

A rate- and lengthscale-dependent crystal plasticity model is employed with a representative volume element for a two-phase austenitic steel under hot-forming conditions to investigate the role of austenite and MnS particle crystallographic orientation on local stress and slip conditions at austenite–MnS interfaces.

It was found that austenite–MnS particle interfacial stress magnifications are determined largely by the crystallographic orientation of the MnS and not significantly by the austenite orientations. However, the crystallographic orientation of an austenite grain neighboring a MnS particle has a dramatic effect on slip localization and slip magnitude in the absence of any significant change in interfacial stress magnitude. The results suggest that it is the crystallographic orientation of the MnS rather than that of the austenite which determines the onset and rapidity of void nucleation. The results also show that there are very particular combinations of austenite–MnS particle orientations which lead to the highest interfacial stresses, and that the peak stress magnification arises not from the properties of the second phase particles but from their orientation. Micromechanical models based on isotropic plasticity will not capture correctly the interfacial stresses.

This paper develops three components contributing to the overall framework of multiscale modeling of ductile fracture in aluminum alloys. The first module is morphology-based domain partitioning (MDP) as a pre-processor to the multiscale modeling. This module delineates regions of statistical homogeneity and inhomogeneity with a systematic three-step process that is based on geometric features of morphology. The second module is detailed micromechanical analysis of particle fragmentation and matrix cracking of heterogeneous microstructures. A locally enriched VCFEM or LE-VCFEM is developed to incorporate ductile failure through matrix cracking in the form of void growth and coalescence using nonlocal Gurson–Tvergaard–Needleman (GTN) model. The third module develops a homogenized anisotropic plasticity-damage model in the form of GTN model for macroscopic analysis. Parameters in this GTN model are calibrated from results of homogenization of microstructural variables obtained from microstructural RVE. Numerical examples elucidate the strength of components of the overall framework.

In critical conditions of variable stress-state, fluctuating temperature and hostile environment, where the objective is to design components and structures for longevity, durability, and reliability — structural integrity — then the balance between empirical engineering design based on continuum and mathematical modeling (sometimes called "distilled empiricism"), and physical modeling (sometimes called "mechanism modeling" or simply "micromechanics"), is shifted in favor of physical modeling. When combined with experimental evidence, physical modeling has the economic advantage of reducing the high cost of vast experimental programs of duration of many thousands of hours. Furthermore, existing empirical design methodologies at the higher (macroscopic) structural size scales can be supported and justified by fundamental understanding at lower (microscopic) size scales through the physical model. Armed with this information, together with knowledge of the mechanical behavior of the material over time, we follow the path of "physical model-informed empiricism", sometimes called "intelligent-informed design". Proof of identity of individual cracking processes based on their direct observation and an understanding of coupling between them is the first step in formulating a complete physical model of fracture.

This paper presents a variety of modeling and simulation methods for complex multiphase flow at microscopic, mesoscopic and macroscopic scales. Each method is discussed in terms of its scale-resolving capability and its relationship with other approaches. Examples of application are provided using a liquid–gas system, in which complex multiscale interactions exist among flow, turbulence, combustion and droplet dynamics. Large eddy simulation (LES) is employed to study the effects of a very large number of droplets on turbulent combustion in two configurations in a fixed laboratory frame. Direct numerical simulation (DNS) in a moving frame is then deployed to reveal detailed dynamic interactions between droplets and reaction zones. In both the LES and the DNS, evaporating droplets are modeled in a Lagrangian macroscopic approach, and have two-way couplings with the carrier gas phase. Finally, droplet collisions are studied using a multiple-relaxation-time lattice Boltzmann method (LBM). The LBM treats multiphase flow with real-fluid equations of state, which are stable and can cope with high density ratios. Examples of successful simulations of droplet coalescence and off-center separation are given. The paper ends with a summary of results and a discussion on hybrid multiscale approaches.