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BEGIN:VEVENT
DTSTAMP:20230522T141844Z
DTSTART:20230530T140000Z
DTEND:20230530T150000Z
SUMMARY:Structures defined on the polyhedral cell complexes in their rela
tion to material processing and design
UID:{http://www.columbasystems.com/customers/uom/gpp/eventid/}r1je-lhyxnl
cq-u8pou2
DESCRIPTION:Abstract of the talk\n\nPolyhedral cell complex (PCC) is a di
screte representation of a 3D space tessellation providing an excellent
model of real polycrystalline materials [1] such as alloys and ceramics.
From the combinatorial point of view\, PCCs are just a family of sets c
ontaining graphs and hypergraphs as their subsets or skeletons. Algebrai
cally\, they can be expressed as a set of incidence matrices [2] or disc
rete operators acting on the k-cells of different dimensions k = {0\, 1\
, 2\, 3}. In addition to the scalar and vector parameters defined on a P
CC’s cells\, the present talk focuses on the labelling or indexing of se
ts in a PCC\, which means an assignment for each set a label or several
labels characterising its own type. The whole set of these labels assign
ed on each of the PCC skeletons forms a configuration state\, which can
be expressed by a single state vector encoding all the cell types simila
r to the well-known DNA sequences. The set of all such state vectors in
a PCC one can regard as a structure defined on its elements. A successio
n of related structures\, expressed by their state vectors\, can be refe
rred to as a process defined on a PCC's elements. Three different types
of structures can be distinguished: directly assigned\, imposed by the k
-cells of other dimensions and induced in due course of some kinetic pro
cess which depends on the pre-existing assigned structure. \n\nSuch a di
screte theoretical framework allows to describe and analyse appearance a
nd evolution of a particular space ordering inside real polycrystalline
materials based on their X-ray/EBSD maps by the well-developed tools of
algebraic topology\, statistics and graph theory. The present work prima
rily focuses on the processes of structure evolution\, providing both ma
thematical tools and software [3] for the simulation of structure evolut
ion of assigned\, imposed and induced defect types. In particular\, we p
erform an entropic (informational) and component (graph) analysis of gra
in structure evolution during continuous dynamic recrystallisation (CDRX
) processes in copper and aluminium alloys [4\,5] and of another structu
re of micro-cracks obtained as a result of kinetic fracture process and
induced by the spatial arrangement of graphene inclusions in ceramic com
posites [6].\n\nThe authors acknowledge the financial support from EPSRC
UK via grants EP/V022687/1 (PRISB) and EP/N026136/1 (GEMS).\n\n[1] E. N
. Borodin\, A. P. Jivkov\, Evolution of triple junctions’ network during
severe plastic deformation of copper alloys – a discrete stochastic mod
elling. Philosophical Magazine\, 100 (2019) 467-485.\n[2] K. Berbatov\,
P.D. Boom\, A.L. Hazel\, A.P. Jivkov\, Applied Mathematical Modelling 11
0 (2022) 172-192.\n[3] Elijah Borodin\, Discrete Processing Design code
(2023) URL: github.com/PRISBteam/PCC_Processing_Design\n[4] S. Zhu\, E.
Borodin\, A. P. Jivkov\, Topological phase transitions of grain boundary
networks during severe plastic deformations of copper alloys. Acta Mate
rialia (Under review)\, 2023.\n[5] S. Zhu\, E. Borodin\, A. P. Jivkov\,
Triple junctions network as the key pattern for characterisation of grai
n structure evolution in metals\, Materials & Design\, 198 (2021) 109352
.\n[6] E. Borodin\, A.P. Jivkov\, A.G. Sheinerman\, M. Yu Gutkin. Optimi
sation of rGO-enriched nanoceramics by combinatorial analysis. Materials
& Design\, 212 (2021) 110191.\n\nAbout the speaker\n\nDr. Elijah Borodi
n is a staff at the Department of Solids and Structures in the School of
Engineering.
STATUS:TENTATIVE
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CLASS:PUBLIC
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