Recent progress in quantitative analysis of multiscale media
Venue: Department of Mathematics, Faculty of Science, University of Split
Scientific Committee: Saša Krešić-Jurić (University of Split), Stephen Shipman (Louisiana State University), Ricardo Weder (National Autonomous University of Mexico)
Organising Committee: Kirill Cherednichenko (University of Bath), Tonći Crmarić (University of Split), Luis Silva (National Autonomous University of Mexico), Igor Velčić (University of Zagreb)
The meeting will focus on recent progress in analytical techniques for the analysis of composite media, where the presence of a contrast in either geometric or material features of the problem leads to "non-classical" effective descriptions. In particular the meeting will feature a discussion of the behaviour of fluid-solid structures, where one additionally faces a change in the momentum balance equations as well as the interface conditions between different components within the composite.
Talk schedule
Monday 29 May
9:30--10:00: Arrival and coffee
10:00--11:00: Igor Velčić "..."
Abstract:
11:00--11:30: Coffee
11:30--12:30: Julius Kaplunov "Asymptotic analysis of fluid-loaded elastic plates"
12:30--14:00: Lunch
14:00--15:00: Kirill Cherednichenko "..."
Abstract:
15:00--16:30: Coffee and open research discussion
Tuesday 30 May
8:50--9:50: Marin Bužančić "Effective quasistatic evolution models for perfectly plastic plates with periodic microstructure"
10:00--11:00: Andrijana Ćurković "The interaction between a thin fluid layer and an elastic plate"
11:00--11:30: Coffee
11:30--12:30: Yi Sheng Lim "..."
Abstract:
12:30--14:00: Lunch
14:00--15:00: Josipa-Pina Milišić "Richards flow in porous media with cross diffusion"
Abstract: In this talk, we present the existence of large-data, weak entropy solutions for a non-isothermal, immiscible, compressible, unsaturated two-phase flow model in porous media. The model is thermodynamically consistent and includes temperature gradients and cross-diffusion effects. Since some terms of the total energy balance are not integrable in the classical weak sense, we consider so-called variational entropy solutions. We show a priori estimates derived from the entropy balance and the total energy balance, as well as the compactness result obtained by applying the div-curl lemma.
15:00--16:30: Coffee and open research discussion
Wednesday 31 May
10:00--11:00: Danila Prikazchikov "..."
Abstract:
11:30--12:30: Josip Žubrinić "..."
Abstract:
12:30--14:00: Lunch
14:00--15:00: Mario Bukal "Derivation of reduced models for micro-fluidic channels"
Abstract: We consider an interaction between a thin layer of an incompressible viscous fluid and an elastic structure, a phenomenon occurring in micro-fluidic channels. Our aim is to analyze the full-size nonlinear fluid-structure interaction (FSI) problem and to rigorously derive corresponding reduced models, which are favorable in engineering modeling. This is a singular limit problem in terms of the vanishing relative fluid thickness, which is carried out based on suitable energy estimates and uniform no-contact results for FSI systems. Reduced models are justified in terms of weak convergence results in the sense that weak limits of solutions to the full-size FSI problem are identified in a relation with solutions of the reduced model. The talk is based on joint work with B. Muha (University of Zagreb).
15:00--16:00: Saša Krešić-Jurić "Gauge transformations and symmetries of evolution equations"
Abstract:
16:00--17:30: Coffee and open research discussion
Thursday 1 June
10:00--11:00: Dario Bojanjac "Engineering perspective on metamaterials"
Abstract: Metamaterials are artificially made materials engineered to have a property that cannot be found in nature. They are usually constructed from assemblies of tiny plastic or metallic elements arranged in periodic patterns with characteristic length smaller than the wavelength. Using metamaterials as a building block, it is possible to produce objects such as superlense, electromagnetic cloak, ultrasound detector, high gain antenna and others. In this talk we will present recent developments and applications of metamaterials in electrical engineering, especially in problems connected to antennas. We will mention electromagnetic metasurfaces, a one-layer metamaterials, as a standard way of controlling wavefront of a radiating or receiving electromagnetic wave.
11:00--11:30: Coffee
11:30--12:30: Mikhail Cherdantsev "High-contrast random composites: homogenisation framework and new spectral phenomena"
Abstract: We study the homogenisation problem for elliptic operators in the divergence form with high-contrast random coefficients. In particular, we are interested in the behaviour of their spectra. We assume that on one of the components of the composite the coefficients are ''of order one'', the complimentary ''soft" component consists of randomly distributed inclusions, whose size and spacing are small, and the coefficients on the soft component exhibit the so called double-porosity scaling.
Our interest in high-contrast homogenisation problems is motivated by the band-gap structure of their spectra. From an intuitive point of view this phenomenon can be explained by viewing the "soft'' inclusions as micro-resonators, which may dramatically amplify of completely block the propagation of waves in the medium, depending on the frequency. From a mathematically rigorous perspective, this was first analysed by Zhikov (2000, 2004) in the periodic setting.
In this talk I will present our recent results and the ongoing work in this area, including the scalar case, linear elasticity systems and eigenfunction localisation on a defect.
12:30--14:00: Lunch
14:00--15:00: Luis Silva "..."
Abstract:
15:00--16:30: Coffee and open research discussion
Friday 2 June
10:00--10:30: Coffee
10:30--12:30: Open research discussion
12:30--14:00: Lunch and closure
Participants
| Bath | UNAM | Zagreb | Split | Other |
|---|---|---|---|---|
|
Kirill Cherednichenko
Yi Sheng Lim
|
Luis Silva
|
Dario Bojanjac
Mario Bukal
Marin Bužančić
Josipa-Pina Milišić
Igor Velčić
Josip Žubrinić
|
Andrijana Ćurković
Saša Krešić-Jurić
|
Mikhail Cherdantsev (Cardiff)
Julius Kaplunov (Keele)
Danila Prikazchikov (Keele)
|