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CATEGORIES:Seminar
DESCRIPTION:Joseph Indekeu\nInstitute for Theoretical Physics\nKU Leuven\nB
elgium\n\nBLUES Function Method in Physics\n\nA computational method in phy
sics is proposed that goes "beyond linear use of equation superposition" (B
LUES). A BLUES function is defined as a solution of a nonlinear differentia
l equation (DE) with a delta source that is at the same time a Green's func
tion for a related linear DE. For an arbitrary source\, the BLUES function
can be used to construct an exact solution to the nonlinear DE with a diffe
rent\, but related source. Alternatively\, the BLUES function can be used t
o construct an approximate piecewise analytical solution to the nonlinear D
E with an arbitrary source.\n\nSummary:\n\nIn the 17th century\, with the i
nvention of calculus\, Newton and Leibniz introduced differential equations
. In linear differential equations the unknown function appears to the firs
t power. There are very few methods of solving other\, nonlinear\, differen
tial equations. These can describe complex behavior and chaos. They can al
so predict growth\, diffusion and extinction of biological populations\, an
d fit observations in the 21st century of dramatic cosmic events anticipate
d by Einstein’s general theory of relativity. They are also used to model n
onlinear optical properties of metamaterials\, and can depict interface dyn
amics in inanimate condensed matter. Linear differential equations permit s
uperposition of solutions\, one of the most powerful tools in computational
science\, paradigmed by the Fourier transform. Also the Green’s function m
ethod exploits the superposition principle of the linear theory\, using Dir
ac’s delta-function as the mathematical atom for building the material syst
em. Now\, a new function method that goes beyond linear use of equation sup
erposition and is therefore named BLUES\, is jointly proposed by a KU Leuve
n statistical physicist and a Stellenbosch University biophysicist. Superpo
sition of solutions of a nonlinear problem is normally not permitted. Surpr
isingly\, however\, the transgression may be only lightly penalized or even
rewarded. The demonstration of a case in point is given in Joseph O. Indek
eu and Kristian K. Müller-Nedebock\, “BLUES function method in computationa
l physics”\, 2018 J. Phys. A: Math. Theor. 51\, 165201. The research was ca
rried out under a bilateral agreement between KU Leuven and Stellenbosch Un
iversity. \n\n\nHosted by Carl Franck\n\nPoster available
DTEND:20180713T160000Z
DTSTAMP:20180925T153846Z
DTSTART:20180713T150000Z
GEO:42.449699;-76.481903
LOCATION:Physical Sciences Building\, 416
SEQUENCE:0
SUMMARY:LASSP Seminar with Joseph Indekeu
UID:tag:localist.com\,2008:EventInstance_3723384
URL:http://events.cornell.edu/event/lassp_seminar_with_joseph_indekeu
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