Numerical techniques are computational methods for approximating solutions to mathematical problems that lack closed-form expressions or are analytically intractable. They encompass algorithms for root finding, numerical integration and differentiation, solution of linear and nonlinear systems, eigenvalue problems, optimization, and numerical solution of ordinary and partial differential equations. These techniques rely on discretization, iteration, and error analysis, with careful attention to stability, convergence, conditioning, and computational complexity. They are implemented using floating-point arithmetic and often exploit matrix factorizations, interpolation, finite difference, finite element, or spectral methods to achieve controllable accuracy within specified tolerances.
Before rain begins to fall, scientists and engineers can predict where a storm might cause flooding thanks to advanced modeling and digital simulations that help guide billion-dollar decisions involving infrastructure design, ...
Earth Sciences
Mar 12, 2026
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19
Estimating things that exist is generally easy, but when it comes to estimating things that do not exist, it's more difficult. This is something physicists from Poland and the UK are well aware of. To improve current simulations ...
General Physics
Mar 5, 2026
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73
Crystalline nanomaterials are valuable because their highly ordered structures give them useful properties for technologies such as data storage and optical devices. But forming nanoparticles from those orderly crystals is ...
Nanophysics
Mar 3, 2026
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14
A new computational method allows modern atomic models to learn from experimental thermodynamic data, according to a University of Michigan Engineering and Université Paris-Saclay study published in Nature Communications. ...
General Physics
Mar 3, 2026
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21
Researchers from the National University of Singapore (NUS) have developed CellScope, a high-performance single-cell analysis framework that uses manifold fitting to analyze single-cell RNA sequencing (scRNA-seq) data. This ...
Cell & Microbiology
Mar 1, 2026
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62
Quantum technologies are anticipated to transform computing, communication, and sensing by harnessing the unusual behavior of matter at the atomic scale. Translating quantum's promise into practical devices will require physical ...
Condensed Matter
Feb 25, 2026
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75
Keeping high-power particle accelerators at peak performance requires advanced and precise control systems. For example, the primary research machine at the U.S. Department of Energy's Thomas Jefferson National Accelerator ...
General Physics
Feb 13, 2026
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48
In biology, many RNA molecules act as sophisticated microscopic machines. Among them, riboswitches function as tiny biological sensors, changing their 3D shape upon binding to a specific metabolite. This shape-change acts ...
Biotechnology
Feb 5, 2026
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17
Researchers at the California NanoSystems Institute at UCLA published a step-by-step framework for determining the three-dimensional positions and elemental identities of atoms in amorphous materials. These solids, such as ...
Nanophysics
Jan 28, 2026
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28
An old puzzle in particle physics has been solved: How can quantum field theories be best formulated on a lattice to optimally simulate them on a computer? The answer comes from AI.
General Physics
Jan 26, 2026
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