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VERSION:2.0
PRODID:-//University of Liverpool Computer Science Seminar System//v2//EN
BEGIN:VEVENT
DTSTAMP:20260921T211555Z
UID:Seminar-MIF-1388@lxserverM.csc.liv.ac.uk
ORGANIZER:CN=Othon Michail:MAILTO:Othon.Michail@liverpool.ac.uk
DTSTART:20220520T140000
DTEND:20220520T150000
SUMMARY:MIF Series
DESCRIPTION:Cyril Cayron: A method to reduce N-dimensional lattices and solve N-dimensional Bézout's identities.\n\nIn order to predict deformation twins in metals and minerals, simple shears on different integral (reticular) planes should be determined. Calculating the shear vectors associated with a given shear plane requires to find a reduced unit cell attached to this plane. Different connected mathematical problems thus emerge: Bézout's identities, integer relations, and cell/lattice reduction. Quite ironically, instead of applying a pre-established lattice reduction method such as LLL, it appeared that simple shearing itself (hyperplanar shearing in dimension N > 3) can be used to reduce the unit cell, and solve the associated N-dimensional Bézout's identity. When applied recursively on different integral planes, hyperplane shearing also permits to reduce N-dimensional lattices by minimizing their metric "rhombicity". The talk will explain the different steps of the method and their geometrical meanings. Some examples with real crystals (N = 3) will be given to explain how the reduction method permits determine the Bravais lattice from diffraction measurements.\n\nhttps://www.csc.liv.ac.uk/research/seminars/abstract.php?id=1388
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