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SUMMARY:CECAM Workshop: "Innovations in fractional calculus and applicatio
 ns to functional and biological materials"
DTSTART:20230913T090000
DTEND:20230915T140000
DTSTAMP:20260928T180759Z
UID:d998301bb5f4ab5e91fea2bd4a4d59c2737f3afa29b7419761781037
CATEGORIES:Conferences - Seminars
DESCRIPTION:You can apply to participate and find all the relevant informa
 tion (speakers\, abstracts\, program\,...) on the event website: https://
 www.cecam.org/workshop-details/1198\n\nDescription\nFractional partial dif
 ferential equations (FPDEs) are emerging as a powerful tool for modeling c
 hallenging multiscale phenomena including microstructure in materials\, ov
 erlapping microscopic and macroscopic scales\, anomalous transport\, and l
 ong-range time memory or spatial interactions. Furthermore\, fractional ca
 lculus is an excellent framework for modelling nonconventional fractal and
  non-local media\, opening valuable prospects on future engineered materia
 ls. Compared to integer-order PDEs\, the fractional order of the derivativ
 es in FPDEs may be a function of space and time or even a distribution\, o
 pening up great opportunities for modeling and simulation of multi-physics
  phenomena\, e.g. seamless transition from wave propagation to diffusion\
 , or from local to non-local dynamics. In addition\, data-driven fractiona
 l differential operators may be constructed to fit data from a particula
 r experiment or specific phenomenon\, including the effect of uncertaint
 ies\, in which the fractional orders are determined directly from the data
 \, and introducing nonlinearities leading to more complex operators\, with
  one or more fractional orders\, capable to model less typical phenomena (
 such as\, for instance\, wave propagation in heterogeneous systems). Simil
 arly\, in imaging applications the variable and even distributed fractiona
 l order that may change in space offer great flexibility that can be used 
 to suppress noise while preserving edge sharpness.\n In short\, FPDEs lea
 d to a paradigm shift\, according to which data-driven fractional operator
 s may be constructed to model a specific phenomenon instead of the curren
 t practice of tweaking free parameters that multiply pre-set integer-order
  differential operators. Also important is that the misspecification of p
 hysical models using integer order derivatives leads to a variable coeffic
 ient fit (struggling to fit the data at each location\, for example) whe
 reas it was shown in the literature that the “correct” fractional orde
 r model can fit all the data with a constant coefficient model.\nThe main
  reasons that FPDE modeling has not been used extensively so far is that F
 PDEs are non-unique and that they are quite expensive to solve numerically
  as they typically generate dense linear algebraic systems due to the nonl
 ocality of fractional differential operators. Furthermore\, FPDEs present 
 additional mathematical and numerical difficulties\, which are not encount
 ered in the context of integer-order PDEs.\nThis workshop will focus on th
 e use of fractional calculus in different areas of materials\, addressing
   multiscale structure\, porous media\, crack propagation\, visco-elasto-
 plasticity\, wave propagation\, non-local continua\, dynamic fracture in b
 rittle and quasi-brittle solids.etc.. We will invite researchers who work 
 on multiscale modeling of materials as well as applied mathematicians who 
 have made significant progress in advancing the fundamentals of FPDEs.
LOCATION:BCH 2103 https://plan.epfl.ch/?room==BCH%202103
STATUS:CONFIRMED
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