Tag: Topology
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A New Bridge: How Manifolds Link Infinity with Computer Science
Introduction: A Concept That Reframed Space In the mid-19th century, the mathematician Bernhard Riemann began rethinking space itself. His idea of a manifold — a shape that locally resembles familiar Euclidean space but can twist and warp in surprising ways — opened a new way to understand geometry, physics, and beyond. While the term may…
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A Bridge Between Infinity and Computer Science: The Manifold
Introduction: Why a Mathematical Concept Changes Everything In the annals of mathematics, certain ideas do more than solve equations. They reshape entire fields of study. The manifold—born from the work of Bernhard Riemann in the 19th century—did exactly this. By providing a flexible way to think about space, manifolds bridged abstract geometry with the real-world…
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Topology Reveals Hidden Rules Of Amorphous Materials
New insights into the softness of amorphous materials For decades, scientists have puzzled over why glass and other amorphous materials deform more easily in some regions than in others. A collaborative study from major Japanese institutions—The University of Osaka, the National Institute of Advanced Industrial Science and Technology (AIST), Okayama University, and the University of…
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Topology Uncovers Hidden Rules Governing Softness in Amorphous Materials
New Insight into the Mechanics of Amorphous Materials For decades, the origin of “soft spots” in amorphous materials like glass has puzzled scientists. A collaborative study by researchers from The University of Osaka, AIST, Okayama University, and the University of Tokyo now attributes this softness to hidden hierarchical structures unveiled through topology. Using a mathematical…
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Topology Reveals Hidden Rules Of Amorphous Materials: Softness From Hierarchical Structures
New topological lens explains why some regions of amorphous materials soften more easily Topology is transforming our understanding of materials that have long frustrated scientists: amorphous solids such as glass, rubber, and certain plastics. A recent multidisciplinary study uses persistent homology, a mathematical tool from topology, to uncover the hidden hierarchical structures that govern mechanical…