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Mathematical field
Multiscale modeling or multiscale mathematics is the field of solving problems that have important features at multiple scales of time and/or space. Important
Multiscale_modeling
The National Academies report describes the need for using multiscale materials modeling to capture the process-structures-properties-performance of
Integrated computational materials engineering
Integrated_computational_materials_engineering
Generalized version of classical Green's function
MSGF technique is in modeling of nanomaterials. These materials are very small – of the size of few nanometers. Mathematical modeling of nanomaterials requires
Multiscale_Green's_function
Weather forecasting and data assimilation system
The Global Environmental Multiscale Model (GEM), often known as the CMC model in North America, is an integrated forecasting and data assimilation system
Global Environmental Multiscale Model
Global_Environmental_Multiscale_Model
American materials scientist and engineer
for his research in computational materials science, multiscale modeling, phase-field modeling, and the design of shape-memory ceramics, metallic alloys
Mohsen_Asle_Zaeem
Type of simplified mathematical model
Coarse-grained models are presently often used as components of multiscale modeling protocols in combination with reconstruction tools (from coarse-grained
Coarse-grained_modeling
Chinese mathematician
has worked on multiscale modeling and the study of rare events. He has also made contributions to homogenization theory, theoretical models of turbulence
Weinan_E
Academic association dedicated to the use of mathematics in industry
1991 SIAM Journal on Applied Dynamical Systems (SIADS), since 2002 Multiscale Modeling and Simulation (MMS), since 2003 SIAM Journal on Imaging Sciences
Society for Industrial and Applied Mathematics
Society_for_Industrial_and_Applied_Mathematics
Scottish mathematical oncologist
to mathematical oncology, particularly in the development of multiscale and hybrid modeling approaches to tumor growth, invasion, and treatment response
Alexander_R._A._Anderson
American applied mathematician
methods, model order reduction, multiscale modeling, computational fluid dynamics of compressible flow, Earth system modeling, and concurrent multiscale coupling
Irina_Tezaur
Computational model of cells and tissues
intracellular dynamics using CompuCell3D and Bionetsolver: applications to multiscale modelling of cancer cell growth and invasion". PLOS ONE. 7 (3) e33726. Bibcode:2012PLoSO
Cellular_Potts_model
American scientist (born 1962)
author, and educator best known for his contributions to the field of multiscale modeling, pattern formation, and morphogenesis in biological systems. Glazier
James_A._Glazier
forefront of MSDT theory and applications. Multiscale decision theory is related to: Multiscale modeling Decision analysis Cooperative distributed problem
Multiscale_decision-making
Carlo molecular modeling List of software for nanostructures modeling Molecular design software Molecular dynamics Molecular modeling on GPUs Molecule
Comparison of software for molecular mechanics modeling
Comparison_of_software_for_molecular_mechanics_modeling
Mathematics researcher
developmental biology, stem cells, computational single-cell genomics, multiscale modeling, deep learning, fluid mechanics & materials, and scientific computing
Qing_Nie
Design method of discrete wavelet transforms
A multiresolution analysis (MRA) or multiscale approximation (MSA) is the design method of most of the practically relevant discrete wavelet transforms
Multiresolution_analysis
Finite-element mesh generator
version of Gmsh is integrated with SwiftComp, a general-purpose multiscale modeling software. The modified version, called Gmsh4SC, is compiled and deployed
Gmsh
Interlacing algorithm for raster images
first pass consists of a single pixel), as is usual in scale-free multiscale modeling. In the context that PNG was developed (i.e., for the image sizes
Adam7_algorithm
Skin peeling
Miller, Claire; Crampin, Edmund; Osborne, James M. (August 2022). "Multiscale modelling of desquamation in the interfollicular epidermis". PLOS Computational
Desquamation
Type of statistical model
Mixed-design analysis of variance Multiscale modeling Random effects model Nonlinear mixed-effects model Bayesian hierarchical modeling Restricted randomization
Multilevel_model
Molecular simulation method
Karplus, won the 2013 Nobel Prize in Chemistry for "the development of multiscale models for complex chemical systems". An important advantage of QM/MM methods
QM/MM
Concept from evolutionary biology
Hans (2008), "Models of Biological Pattern Formation: From Elementary Steps to the Organization of Embryonic Axes", Multiscale Modeling of Developmental
Turing_pattern
Classes of computational models
technique for multiscale modeling of nanomaterials is based upon the use of multiscale Green's function. In contrast, microscale models can simulate a
Microscale and macroscale models
Microscale_and_macroscale_models
decarbonization products for various industries. He has research interests on Multiscale Modeling, Condensed Matter Theory, Molecular Dynamics. Chaudhuri leads a research
Santanu_Chaudhuri
Sense of self-movement, force, and body position
Röhrle O, Yavuz UŞ, Klotz T, Negro F, Heidlauf T (November 2019). "Multiscale modeling of the neuromuscular system: Coupling neurophysiology and skeletal
Proprioception
Swedish mathematician (born 1945)
Texas at Austin. He has been a leading contributor in the areas of multiscale modeling and scientific computing, and a productive educator of applied mathematicians
Björn_Engquist
Computer modelling of a petroleum reservoir
In the oil and gas industry, reservoir modeling involves the construction of a computer model of a petroleum reservoir, for the purposes of improving estimation
Reservoir_modeling
Equation-free modeling is a method for multiscale computation and computer-aided analysis. It is designed for a class of complicated systems in which
Equation-free_modeling
Topics referred to by the same term
Methyl methanesulfonate Moment magnitude scale of earthquake energy Multiscale Modeling and Simulation journal Modern Montessori School, Amman, Jordan Marshall
MMS
American mechanical engineer and computational scientist
framework known as HiDeNN-AI. His work spans the finite element method, multiscale modeling and simulation, additive and advanced manufacturing, and materials
Wing_Kam_Liu
Prehistoric landslide off Norway
does multiscale modelling and inclusion of realistic palaeobathymetry affect numerical simulation of the Storegga Slide tsunami?". Ocean Modelling. 83:
Storegga_Slide
Type of climate model
transcripts on climate models "Flexible Modeling System (FMS)". Geophysical Fluid Dynamics Laboratory. – GFDL's Flexible Modeling System containing code
General_circulation_model
Colombian-American scientist
and multiscale modeling of complex biophysical systems. His work with Michael L. Klein was highly influential in the growth of Coarse-grained modeling for
Carlos_F._López
Approximations that apply at multiple scales
transforms and invariant manifolds provide a sounder support for multiscale modelling (for example, see center manifold and slow manifold). As an example
Multiple-scale_analysis
Physical property when materials or objects return to original shape after deformation
Jian; Gan, Yixiang; Hanaor, Dorian AH; Chen, C.Q. (1 May 2019). "Multiscale modeling of the effective elastic properties of fluid-filled porous materials"
Elasticity_(physics)
Modeler NEMO 3-D Quantum Dot Lab nextnano.com Materials Design MedeA Materials Square I.A. Solov'yov; A.V. Korol; A.V. Solov'yov (2017). Multiscale Modeling
List of software for nanostructures modeling
List_of_software_for_nanostructures_modeling
Software used for simulations and modeling in materials science
Database Computational materials science Modelling and Simulation in Materials Science and Engineering Multiscale modeling List of computational physics software
List of materials science software
List_of_materials_science_software
Italian mathematician
Editor-in-Chief of SIAM Multiscale Modeling and Simulation". The Maxwell Institute. 10 September 2025. Retrieved 12 April 2026. "Multiscale Modeling & Simulation
Lorenzo_Pareschi
polymer Crystallization of polymers Path integrals in polymer science Multiscale modeling M. Kotelyanskii; D. N. Theodorou, eds. (March 15, 2004). "11". Simulation
Modeling_of_polymer_crystals
Scientific activity that produces models
method) will always be more reliable than modeled estimates of outcomes. Within modeling and simulation, a model is a task-driven, purposeful simplification
Scientific_modelling
Weather prediction using mathematical models of the atmosphere and oceans
Environmental Multiscale Model both run out to ten days into the future, and the Global Forecast System model run by the Environmental Modeling Center is
Numerical_weather_prediction
Immunoglobulin-binding protein expressed in group C and G Streptococcal bacteria
2008). "Folding pathway of the b1 domain of protein G explored by multiscale modeling". Biophys J. 94 (3): 726–36. Bibcode:2008BpJ....94..726K. doi:10
Protein_G
Biological process that causes an organism to develop its shape
499–500. ISBN 978-0-19-967814-3. Miura, T (2008). "Modeling Lung Branching Morphogenesis". Multiscale Modeling of Developmental Systems. Current Topics in Developmental
Morphogenesis
Chinese-Canadian mechanical engineer
University of Alberta, where she holds a tier 1 Canada Research Chair in Multiscale Modeling of Soft Materials and Interfaces. Tang was born in 1980 in Pingjiang
Tian_Tang
Probabilistic problem-solving algorithm
1515/mcma-2016-0102. S2CID 30198383. Baeurle, Stephan A. (2009). "Multiscale modeling of polymer materials using field-theoretic methodologies: A survey
Monte_Carlo_method
American engineer
research focuses on the mechanics of materials, computational and multiscale modeling, and the failure behavior of crystalline and heterogeneous materials
Mohammed_A._Zikry
Venezuelan mathematical biologist
in Science". Santiago Schnell; Ramon Grima; Philip Maini (2007). "Multiscale Modeling in Biology". American Scientist. "Dr. Santiago Schnell becomes Dean
Santiago_Schnell
Austrian-American chemist (1930–2024)
together with Michael Levitt and Arieh Warshel, for "the development of multiscale models for complex chemical systems". Martin Karplus was born on March 15
Martin_Karplus
German computer physicist and academic
German-born American computational physicist and academic, working in multiscale modeling and computational co-design. He is currently the group leader of
Christoph_Junghans
Ability of bacteria to move independently using metabolic energy
A.; Juckeland, Guido; Biais, Nicolas; Zaburdaev, Vasily (2017). "Multiscale modeling of bacterial colonies: How pili mediate the dynamics of single cells
Bacterial_motility
Israeli chemist, biochemist and biophysicist (born 1940)
together with Michael Levitt and Martin Karplus for "the development of multiscale models for complex chemical systems". Warshel was born to a Jewish family
Arieh_Warshel
Ukrainian physicist
whose research interests include spintronics and the dynamics and multiscale modeling of magnetic materials and magnetic nanoparticles. She works in Spain
Oksana_Chubykalo-Fesenko
Biology software
solving environment for constructing two- and three-dimensional multiscale agent-based models of multicellular biology, including morphogenesis, homeostasis
CompuCell3D
Numerical method for solving physical or engineering problems
"High-dimensional finite elements for elliptic problems with multiple scales". Multiscale Modeling & Simulation. 3 (1). SIAM: 168–194. doi:10.1137/030601077. hdl:20
Finite_element_method
American biophysicist
2021-09-27. Villa Rodriguez, Elizabeth; Schulten, Klaus J (2008). Multiscale Modeling of Biomolecular Complexes (Thesis). University of Illinois at Urbana-Champaign
Elizabeth_Villa
White blood cell that secretes large volumes of antibodies
Jeroen E. J.; Hoefsloot, Huub; van Kampen, Antoine H. C. (2020). "Multiscale Modeling of Germinal Center Recapitulates the Temporal Transition From Memory
Plasma_cell
Supercomputer manufactured by Cray Research
X-MP 1985 brochure Steinhauser, Martin Oliver (2008). Computational Multiscale Modeling of Fluids and Solids: Theory and Applications. Springer. p. 21. ISBN 9783540751168
Cray_X-MP
Center for Multiscale Modeling of Biological Systems (MMBioS) - Active as of 2023 Virtual Cell Challenge - competition to develop predictive models of single-cell
Cellular_model
State of matter
ISBN 978-3-319-44649-3. OCLC 963198053. Steinhauser, M. O. (2022). Computational multiscale modeling of fluids and solids: theory and applications. Cham, Switzerland:
Liquid
South African-born biophysicist (born 1947)
together with Martin Karplus and Arieh Warshel, for "the development of multiscale models for complex chemical systems". In 2018, Levitt was a founding co-editor
Michael_Levitt_(biophysicist)
Measure of local oscillation behavior
solutions of the TV denoising problem and some extensions, SIAM, Multiscale Modeling and Simulation, vol. 6 n. 3, archived from the original on 2011-09-27
Total_variation
Primary organ of the respiratory system
Retrieved 23 February 2016. Miura T (2008). "Modeling Lung Branching Morphogenesis". Multiscale Modeling of Developmental Systems. Current Topics in Developmental
Lung
vast database of materials-related information for use in research, multiscale modeling, simulation implementation, and an array of other activities in support
ICME_cyberinfrastructure
Crystallographic defect of atoms within gaps in a lattice
1016/0022-3115(78)90261-1. Derlet, P. M.; D. Nguyen-Manh; S. L. Dudarev (2007). "Multiscale modeling of crowdion and vacancy defects in body-centered-cubic transition
Interstitial_defect
The variational multiscale method (VMS) is a technique used for deriving models and numerical methods for multiscale phenomena. The VMS framework has been
Variational_multiscale_method
Dean of the School of Engineering at Liberty University
National Laboratories for fifteen years (1987-2002) in the area of multiscale modeling for design. Horstemeyer became dean of the School of Engineering
Mark_Horstemeyer
American chemical engineer and physicist
matter physicist whose research involves computational simulation, multiscale modeling, and molecular dynamics of interfaces, thin films, colloids, catalysis
Kristen_Fichthorn
Computer simulations to discover and understand chemical properties
Young's modulus of the gel. Such nanoscale insights contribute to multiscale modeling frameworks that link atomic-scale properties of cement hydrates to
Molecular_dynamics
Type of infrastructure
Materials Engineering (ICME) cyberinfrastructure in 2010 that focuses on multiscale modeling. The United States Department of Energy supports e-Science through
Cyberinfrastructure
Form of matter
Mingchao; Wu, Jian; Gan, Yixiang; Hanaor, Dorian; Chen, C. Q. (2019). "Multiscale modeling of effective elastic properties of fluid-filled porous materials"
Foam
Neural network that learns efficient data encoding in an unsupervised manner
(2005). "A Review of Image Denoising Algorithms, with a New One". Multiscale Modeling & Simulation. 4 (2): 490–530. doi:10.1137/040616024. S2CID 218466166
Autoencoder
Four NASA robots studying Earth's magnetosphere (2015-present)
The Magnetospheric Multiscale (MMS) Mission is a NASA robotic space mission to study the Earth's magnetosphere, using four identical spacecraft flying
Magnetospheric Multiscale Mission
Magnetospheric_Multiscale_Mission
Functions for calculating potential energy
Potentials: A Class of Systematically Improvable Interatomic Potentials". Multiscale Modeling & Simulation. 14 (3): 1153–1173. arXiv:1512.06054. doi:10.1137/15M1054183
Interatomic_potential
US federally funded research and development center
Madden–Julian oscillation; Stephen Schneider. Greg Holland initiated the multiscale modeling project "Predicting the Earth System Across Scales". NCAR is currently
National Center for Atmospheric Research
National_Center_for_Atmospheric_Research
Several challenges span multiple material classes and applications: Multiscale modeling: Developing computational materials science approaches that link
Energy_materials
American materials scientist and engineer
science. Before joining MIT in 2005, he served as the director of multiscale modeling and software integration at Caltech's Materials and Process Simulation
Markus_J._Buehler
Modeling the body's responses to drugs
Physiologically based pharmacokinetic (PBPK) modeling is a mathematical modeling technique for predicting the absorption, distribution, metabolism and
Physiologically based pharmacokinetic modelling
Physiologically_based_pharmacokinetic_modelling
British chemist
Suter, J.; Groen, D.; Coveney, P. V. (2015). "Chemically specific multiscale modeling of clay-polymer nanocomposites reveals intercalation dynamics, tactoid
Peter_Coveney
David; Ying, Lexing (Jan 2006). "Fast Discrete Curvelet Transforms". Multiscale Modeling & Simulation. 5 (3): 861–899. doi:10.1137/05064182X. ISSN 1540-3459
Curvelet
Graph-based mathematical model
(2012-01-01). "Diffuse Interface Models on Graphs for Classification of High Dimensional Data". Multiscale Modeling & Simulation. 10 (3): 1090–1118. CiteSeerX 10
Phase-field_models_on_graphs
Approximate method for the simulation of a stochastic system
Raul; Vilanova, Pedro (2014-04-24). "Hybrid Chernoff Tau-Leap". Multiscale Modeling & Simulation. 12 (2): 581–615. CiteSeerX 10.1.1.756.9799. doi:10
Tau-leaping
Martin Karplus (1930–2024) Austrian American "for the development of multiscale models for complex chemical systems" Michael Levitt (b. 1947) South African
2013_Nobel_Prizes
Spanish Materials Scientist
Rodríguez, M.; Sádaba, S.; Muñoz, R.; Canal, L. P. (2011-11-23). "Multiscale Modeling of Composite Materials: a Roadmap Towards Virtual Testing". Advanced
Javier_Llorca
Chinese mathematician
M., Deng, Y., & Bluestein, D. (2010). Particle-Based Methods for Multiscale Modeling of Blood Flow in the Circulation and in Devices: Challenges and Future
Yuefan_Deng
American materials scientist
science and theoretical physics, including the mechanics of materials, multiscale modeling, and the properties of metal alloys and composites. He is the author
William_Curtin
Mathematical Earth system model
Model for Prediction Across Scales (MPAS) is an Earth system modeling software that integrates atmospheric, oceanographic, and cryospheric modeling across
Model for Prediction Across Scales
Model_for_Prediction_Across_Scales
Global numerical weather prediction system
(GFS), the Canadian Global Environmental Multiscale Model (GEM and GDPS) and the UK Met Office's Unified Model. ECMWF runs the IFS in several configurations
Integrated_Forecast_System
Mathematical model of atmospheric motions
Meteorological Modeling. Academic Press. pp. 48–49. ISBN 978-0-12-554766-6. Pielke, Roger A. (2002). Mesoscale Meteorological Modeling. Academic Press
Atmospheric_model
American scientist and advocate for the blind
Computational Modeling for Biointerface Engineering (COMBINE) Lab. Minkara’s research uses molecular dynamics and multiscale computational modeling to investigate
Mona_Minkara
Polish mathematician
Dundee in Scotland. She was also a member of the Cooperation Group "Multiscale Modeling of Tumor Initiation, Growth and Progression" at the Center for Interdisciplinary
Urszula_Alicja_Foryś
Distributed computing project simulating protein folding
Folding Dynamics from Short-Time Molecular Dynamics Simulations". Multiscale Modeling & Simulation. 5 (4): 1214–1226. doi:10.1137/06065146X. S2CID 17825277
Folding@home
Representation learning method
Elad, M. (2008-01-01). "Learning Multiscale Sparse Representations for Image and Video Restoration". Multiscale Modeling & Simulation. 7 (1): 214–241. CiteSeerX 10
Sparse_dictionary_learning
Framework to describe phase transitions
ISBN 978-0-521-84223-5. Baeurle SA, Usami T, Gusev AA (2006). "A new multiscale modeling approach for the prediction of mechanical properties of polymer-based
Statistical_field_theory
Applied mathematician and computational biologist
ISBN 978-1-4939-3102-6 David Holcman (editor), Stochastic Processes, Multiscale Modeling, and Numerical Methods for Computational Cellular Biology, 2017-10-04
David_Holcman
Weather prediction computer model
the Canadian Global Environmental Multiscale Model (GEM) it is one of several synoptic scale medium-range models in general use. NOGAPS Portal Archived
Navy Operational Global Atmospheric Prediction System Model
Navy_Operational_Global_Atmospheric_Prediction_System_Model
Singular perturbation problem dealing with confinement of Brownian particles
First Passage Time for Narrow Escape Problems: Part II: The Sphere". Multiscale Modeling & Simulation. 8 (3). Society for Industrial & Applied Mathematics
Narrow_escape_problem
Bosnian engineer
A. Ibrahimbegovic (eds.), ‘From Microstructure Investigations to Multiscale Modeling’, ISTE Wiley, ISBN 978-1-786-30259-5, pp. 1–273, (2018) Ibrahimbegovic
Adnan_Ibrahimbegovic
Numerical technique for bioelectromagnetic modeling
these charges will depend on the environment; In application to multiscale modeling, a field E i {\displaystyle \mathbf {E} ^{i}} obtained from any other
Charge based boundary element fast multipole method
Charge_based_boundary_element_fast_multipole_method
American mathematician (born 1962)
and biology[citation needed]. Hou was founder of "SIAM Journal on Multiscale Modeling and Simulation", and he served as the editor-in-chief from 2002 to
Thomas_Hou
Scientific conferences about composite materials
conference include, among others, fracture and damage, multiscale modeling, durability, aging, process modeling, simulation, additive manufacturing, bio-sourced
European Conference on Composite Materials
European_Conference_on_Composite_Materials
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