Phys.org: Phys.org news tagged with: partial differential equations
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Heat distributions help researchers to understand curved spaceThe heat equation is one of the most important partial differential equations. The behavior of the solution to the equation reflects the geometry of the underlying space very well. Therefore, this equation has been investigated very extensively in both analysis and geometry. The solution evolves over time so that the Dirichlet's energy functional decreases most efficiently. Recently, F. Otto introduced another characterization: the solution evolves so that the Boltzmann entropy increases most efficiently from the viewpoint of optimal transportation. Both of these characterizations enable us to study the heat equation on spaces admitting singularities, where usual differential calculus does not work. However, their identification in such spaces is unknown.
http://phys.org/news328255083.html
Other SciencesTue, 26 Aug 2014 07:50:06 ESTnews328255083The brain could be key to a better computerYour brain is incredibly well-suited to handling whatever comes along, plus it's tough and operates on little energy. Those attributes—dealing with real-world situations, resiliency and energy efficiency—are precisely what might be possible with neuro-inspired computing.
http://phys.org/news319361126.html
TechnologyThu, 15 May 2014 08:40:01 ESTnews319361126Light knots: Physicists use Maxwell's equations to describe field lines that encode torus knots and links(Phys.org) —A team of physicists, two from the U.S., and one each from Poland and Spain has used Maxwell's equations to describe field lines that encode all torus knots and links. As they describe in their paper published in the journal Physical Review Letters, the result of using the equations could lead to a method of creating light in the real world that can be tied into knots.
http://phys.org/news301302916.html
PhysicsFri, 18 Oct 2013 08:15:37 ESTnews301302916The secret lives of bubbles: Mathematicians describe evolution, dissolution of clusters of bubbles (w/ video)Bubble baths and soapy dishwater, the refreshing head on a beer and the luscious froth on a cappuccino. All are foams, beautiful yet ephemeral as the bubbles pop one by one.
http://phys.org/news287313104.html
Other SciencesThu, 09 May 2013 14:00:08 ESTnews287313104Biophysicists model the behavior of a protein critical to cell motion(Phys.org) -- Physicists at Lehigh have created a mathematical model that could benefit researchers who study cell motion, including cancerous cell motion, tissue healing processes and human embryonic development.
http://phys.org/news261633305.html
PhysicsMon, 16 Jul 2012 04:55:14 ESTnews261633305Mathematics: First-ever image of a flat torus in 3DJust as a terrestrial globe cannot be flattened without distorting the distances, it seemed impossible to visualize abstract mathematical objects called flat tori in ordinary three-dimensional space. However, a French team of mathematicians and computer scientists has succeeded in constructing and visually representing an image of a flat torus in three-dimensional space. This is a smooth fractal, halfway between fractals and ordinary surfaces. The results are published in PNAS.
http://phys.org/news254640881.html
Other SciencesThu, 26 Apr 2012 06:35:24 ESTnews254640881