Mathematical simulation is a computational method that uses formal mathematical models—such as systems of differential equations, stochastic processes, or optimization formulations—to numerically approximate the behavior of complex systems under specified conditions. It enables investigation of system dynamics, sensitivity to parameters, and emergent properties when analytical solutions are infeasible or intractable. Typical workflows include model specification, parameterization, numerical integration or iteration, and validation against empirical data. Mathematical simulations are central in fields such as physics, engineering, systems biology, and economics, supporting hypothesis testing, scenario analysis, and predictive inference while explicitly encoding assumptions about structure, interactions, and boundary conditions.
An international study published in Communications Earth & Environment has advanced earthquake simulations to better anticipate the rupture process of large earthquakes.
Earth Sciences
Apr 15, 2025
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AI has created a sea change in society; now, it is setting its sights on the sea itself. Researchers at Osaka Metropolitan University have developed a machine learning-powered fluid simulation model that significantly reduces ...
General Physics
Apr 3, 2025
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In-situ resource utilization will likely play a major role in any future long-term settlement of the moon. However, designing such a system in advance with our current level of knowledge will prove difficult, mainly because ...
Space Exploration
Apr 1, 2025
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New theoretical physics research introduces a simulation method of machine-learning-based effective Hamiltonian for super-large-scale atomic structures. This effective Hamiltonian method could simulate much larger structures ...
General Physics
Mar 17, 2025
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Researchers are creating advanced simulations that will provide a deeper understanding of Mars's climatic history and help to determine whether it was once able to sustain life.
Astrobiology
Feb 28, 2025
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Skyrmions are nanometer- to micrometer-sized magnetic whirls that exhibit particle-like properties and can be moved efficiently by electrical currents. These properties make skyrmions an excellent system for new types of ...
Condensed Matter
Jan 30, 2025
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Many science fiction authors try to incorporate scientific principles into their work, but Ian Tregillis, who is a contributing author of the Wild Cards book series when he's not working as a physicist at Los Alamos National ...
General Physics
Jan 23, 2025
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Computer scientists at the University of California San Diego have developed a method for generating highly realistic computer-generated images of fluid dynamics in elements such as smoke.
Soft Matter
Jan 6, 2025
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171
The close relationship between AI and highly complicated scientific computing can be seen in the fact that both the 2024 Nobel Prizes in Physics and Chemistry were awarded to scientists for devising AI for their respective ...
Quantum Physics
Oct 30, 2024
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134
Research that eliminates the guesswork in developing advanced 3D printed materials could help accelerate the development of new forms of "self-sensing" airplanes, robots, bridges and more.
Nanophysics
Oct 7, 2024
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