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Multiscale modeling

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Multiscale modeling or multiscale mathematics is the field of solving problems that have important features at multiple scales of time and/or space. Important problems include multiscale modeling of fluids, solids, polymers, proteins, nucleic acids as well as various physical and chemical phenomena (like adsorption, chemical reactions, diffusion). Statistical modeling techniques are increasingly integrated into multiscale modeling frameworks to bridge information between scales and quantify uncertainty.

Arieh WarshelArieh WarshelArieh Warshel (Hebrew: אריה ורשל; born November 20, 1940) is an Israeli-American biochemist and biophysicist. He is a pioneer in computational studies on functional properties of biological molecules, Distinguished Professor of Chemistry and Biochemistry, and holds the Dana and David Dornsife Chair in Chemistry at the University of Southern California.Martin KarplusMartin KarplusMartin Karplus (German:; March 15, 1930 – December 28, 2024) was an Austrian and American theoretical chemist. He was the Theodore William Richards Professor of Chemistry at Harvard University. He was also the director of the Biophysical Chemistry Laboratory, a joint laboratory between the French National Center for Scientific Research and the University of Strasbourg, France.Michael BaskesMichael I. Baskes is an American engineer. Baskes earned a degree in engineering from the California Institute of Technology in 1965, and remained at the institution through 1970 to pursue doctoral study in materials science. He worked at the Los Alamos National Laboratory for 29 years, until 2005, then started a teaching career.Michael Levitt (biophysicist)Michael Levitt (biophysicist)Michael Levitt, FRS (Hebrew: מיכאל לויט; born 9 May 1947) is a South African-born biophysicist and a professor of structural biology at Stanford University, a position he has held since 1987. Levitt received the 2013 Nobel Prize in Chemistry, 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 of the Annual Review of Biomedical Data Science.Nobel Prize in ChemistryNobel Prize in ChemistryThe Nobel Prize in Chemistry is awarded annually by the Royal Swedish Academy of Sciences to scientists in the various fields of chemistry. It is one of the five Nobel Prizes established by the will of Alfred Nobel in 1895, awarded for outstanding contributions in chemistry, physics, literature, peace, and physiology or medicine.Complex fluidComplex fluids are mixtures that have a coexistence between two phases: solid–liquid (suspensions or solutions of macromolecules such as polymers), solid–gas (granular), liquid–gas (foams) or liquid–liquid (emulsions). They exhibit unusual mechanical responses to applied stress or strain due to the geometrical constraints that the phase coexistence imposes. The mechanical response includes transitions between solid-like and fluid-like behavior as well as fluctuations.Branches of scienceBranches of scienceThe branches of science, also referred to as sciences, scientificfields or scientific disciplines, are commonly divided into three major groups: Formal sciences: the study of formal systems, such as those under the branches of logic and mathematics, which use an a priori, as opposed to empirical, methodology.DiffusionDiffusionTransport of dissolved species from the highest to the lowest concentration region Some particles are dissolved in a glass of water. At first, the particles are all near one top corner of the glass.Navier–Stokes equationsNavier–Stokes equationsEquations of motion for viscous fluids Part of a series onContinuum mechanics J = − D d φ d x {\displaystyle J=-D{\frac {d\varphi }{dx}}} Fick's laws of diffusion Laws Conservations Mass Momentum Energy Inequalities Clausius–Duhem (entropy) Solid mechanics Deformation Elasticity linear Plasticity Hooke's law Stress Strain Finite strain Infinitesimal strain Compatibility Bending Contact mechanics frictional Material failure theory Fracture mechanics Fluid mechanics Fluids Statics · Dynamics Archimedes' principle · Bernoulli's principle Navier–Stokes equations Poiseuille equation · Pascal's law Viscosity (Newtonian · non-Newtonian) Buoyancy · Mixing · Pressure Liquids Adhesion Capillary action Chromatography Cohesion (chemistry) Surface tension Gases Atmosphere Boyle's law Charles's law Combined gas law Fick's law Gay-Lussac's law Graham's law Plasma Magnetohydrodynamics Rheology Viscoelasticity Rheometry Rheometer Smart fluids Electrorheological Magnetorheological Ferrofluids Scientists Bernoulli Boyle Cauchy Charles Euler Fick Gay-Lussac Graham Hooke Newton Navier Noll Pascal Stokes Truesdell vte The Navier–Stokes equations (/nævˈjeɪ ˈstoʊks/ nav-YAY STOHKS) describe the motion of viscous fluids.AdsorptionAdsorptionAdsorption is the adhesion of atoms, ions, or molecules from a gas, liquid, or dissolved solid to a surface. This process creates a film of the adsorbate on the surface of the adsorbent. This process differs from absorption, in which a fluid (the absorbate) is dissolved by or permeates a liquid or solid (the absorbent).Quantum mechanicsQuantum mechanicsDescription of physical properties at the atomic and subatomic scaleWave functions of the electron in a hydrogen atom at different energy levels. Quantum mechanics cannot predict the exact location of a particle in space, only the probability of finding it at different locations.Nucleic acidNucleic acidNucleic acids are large biomolecules that are crucial in all cells and viruses. They are composed of nucleotides, which are the monomer components: a 5-carbon sugar, a phosphate group and a nitrogenous base. The two main classes of nucleic acids are deoxyribonucleic acid (DNA) and ribonucleic acid (RNA). If the sugar is ribose, the polymer is RNA; if the sugar is deoxyribose, a variant of ribose, the polymer is DNA.

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