Seminari - Dipartimento Computer Science Seminari - Dipartimento Computer Science validi dal 14.12.2019 al 14.12.2020. Mathematical modelling of liquid crystals and industrial applications [2ECTS, MAT/05] UPDATED Relatore: Prof. Apala Majumdar; Provenienza: Strathclyde (UK); Data inizio: 2019-12-15; Note orario: 15/12-21/12/2019; Referente interno: Giandomenico Orlandi; Riassunto: Course title: Mathematical modelling of liquid crystals and industrial applications Lecturer: Prof. Apala Majumdar (Strathclyde, UK) Dates: 15-21/12/2019 TIMETABLE: MON 16/12 13.40-15.20 room M TUE 17/12 13.40-15.20 room M / lab Alpha (to be confirmed) WED 18/12 9.20 - 11.00 Seminar room 2nd floor Ca Vignal 2 THU 19/12 9.20-11.10 room M FRI 20/12 15.20-17.00 room M OVERVIEW: Materials science and engineering has witnessed unprecedented growth in recent years with the advent of biological materials, colloids, metamaterials, topological materials etc. Soft matter is at the forefront of contemporary materials research. Soft matter is a phrase used for materials that are intermediate between conventional solids and liquids in terms of their physical properties. Soft matter is fairly ubiquitous in our everyday lives and can be found in display devices, pharmaceuticals, agrochemicals, cosmetics, fibres, and are even found in the human body as biological soft matter e.g. the cell cytoskeleton. Collectively, soft matter products contribute over 200 billion GBP to the world economy and relevant industries employ over 900,000 people. Nematic liquid crystals are paradigm examples of soft matter. They are complex liquids with a degree of long-range orientational order i.e. they have certain distinguished directions and consequently, direction-dependent physical, optical, mechanical and rheological properties. Indeed, it is the directional nematic response to external light and electric fields that makes them the working material of choice for the multi-billion dollar liquid crystal display industry. Nematic liquid crystals today have applications far beyond the display industry in the health industry, microfluidics and nano-technologies. The mathematics and theory of nematic liquid crystals is deep and challenging. In fact, Pierre de Gennes was awarded the Nobel Prize for Physics in 1991, partially for his theories for nematic liquid crystals and these theories have a profound role in science and technology too. In this mini-course, we review the mathematical theories theories for nematic liquid crystals and how they can be applied to display devices, as practical case studies. We will review the celebrated Landau-de Gennes and Oseen-Frank theories for nematic liquid crystals, the key concepts of birefringence, response to external fields, anchoring and topological defects. We will then apply these concepts to the Post Aligned Bistable Nematic Device designed by Hewlett Packard, the Zenithally Bistable Nematic Device and the Planar Bistable Nematic Device, with a discussion of the static and time-dependent properties. The course has a two fold purpose. Firstly, the course will serve as an introductory course to the multi-faceted field of nematic liquid crystals and their applications in an interdisciplinary setting. Secondly, the course will describe certain generic concepts for soft matter, the rich underpinning mathematical frameworks and how mathematics can transform materials research into a predictive science. LECTURE PLAN : The course is compressed into 7 lectures of 50 minutes each. The lecture slides will be made publicly available through the university website. Day 1 : Lecture 1 : Introduction to the theory and physics of nematic liquid crystals - history, different phases and introduction to concept of partial order. Lecture 2 : The Oseen Frank theory for nematic liquid crystals - definition of director and the Oseen-Frank free energy. Day 2 : Lecture 3: Birefringence and Dielectric Anisotropy; the classical Freedericksz Transition for Nematic Liquid Crystals. Lecture 4 : The Landau-de Gennes theory for nematic liquid crystals - the Q-tensor order parameter, the free energy and the equilibrium equations. Day 3: Lecture 5 : Case Study I - Mathematical Modelling of the Post Aligned Bistable Nematic Device and Topological Mechanisms for Multistability. Day 4 :Lecture 6: Case Study II - Mathematical Modelling of the Planar Bistable Nematic Device ndash; static equilibria Lecture 7 : Case Study II ndash; Switching Mechanisms for the Planar Bistable Nematic Device REFERENCES: Gennes and J.Prost. The physics of liquid crystals. Oxford University Press. 1995 I.W.Stewart. The static and dynamic continuum theories for nematic liquid crystals. Taylor&Francis, 2004. A.Majumdar, C.J.P.Newton, J.M.Robbins & M.Zyskin. Topology and Bistability in Liquid Crystal Devices. Physical Review E, 75, 2007. G.Canevari, A.Majumdar & A.Spicer. Order reconstruction for nematics on squares and hexagons: a Landau-de Gennes study. SIAM Journal of Applied Mathematics, 77, 2017. Y.Wang, G.Canevari and A.Majumdar. Order reconstruction for nematics on squares with isotropic inclusions: a Landau-de Gennes study. SIAM Journal of Applied Mathematics, 79, 2019. C.Luo, A.Majumdar & R.Erban. Multistability in planar liquid crystal wells. Physical Review E, 85, 2012. contact person: Giandomenico Orlandi. Sun, 15 Dec 2019 00:00:00 +0100 Essentials of reaction-diffusion equations in Mathematical Biology [2ECTS, MAT/07] UPDATED Relatore: Prof. Tommaso Lorenzi; Provenienza: St Andrews (UK); Data inizio: 2020-01-07; Note orario: starting date 07/01; Referente interno: Giandomenico Orlandi; Riassunto: WARNIG:THE COURSE IS REPORTED TO ANOTHER TIME SLOT TO BE SUBSEQUENTLY FIXED Title: Essentials ofreaction-diffusion equationsin Mathematical Biology Lecturer: Tommaso Lorenzi (St. Andrews) dates: 7/1-10/1/2020 Abstract This course will provide a gentle introduction to reaction-diffusion equations in mathematical biology. The course will be organised into five related parts as follows: 1) Conservation equations 2) Linear reaction-diffusion equations 3) Nonlinear reaction-diffusion equations 4) Systems of nonlinear reaction-diffusion equations 5) Nonlocal reaction-diffusion equations Recommended Books J.D. Murray, Mathematical Biology I: An Introduction, Springer, 3rd ed. 2003 J.D. Murray, Mathematical Biology II: Spatial Models and Biomedical Applications, Springer, 3rd ed. 2003 B. Perthame, Transport Equations in Biology, Birkh auser, 2007 B. Perthame, Parabolic Equations in Biology -- Growth, Reaction, Movement and Diffusion, Springer, 2015 Contact person: Giandomenico Orlandi. Tue, 7 Jan 2020 00:00:00 +0100 Combinatorial Strategies for Modern Biology [2 ECTS, MAT/03] Relatore: Margherita Maria Ferrari; Provenienza: University of South Florida; Data inizio: 2020-04-15; Note orario: Starting date; Referente interno: Giuseppe Mazzuoccolo; Riassunto: The purpose of these lectures is twofold. On one hand, we want to highlight how classical notions in combinatorics are applied to advance our understanding of biological/chemical processes. On the other hand, we want to show that such processes lead to new mathematical objects and drive new areas of research. We will give the biological background for DNA self-assembly and DNA recombination processes, as well as RNA structure formation. We will provide the combinatorial tools, mainly graph-theoretic approaches, to model and analyze such problems, and discuss some open questions related to these models. Wed, 15 Apr 2020 00:00:00 +0200 Euler-Poincaré variational principles and applications to fluid dynamics - [1 ECTS, MAT/07] Relatore: Prof. Cesare Troncy; Provenienza: University of Surrey - UK -; Data inizio: 2020-04-20; Referente interno: Nicola Sansonetto; Riassunto: Starting from Poincareacute;#39;soriginal work from 1901, this lecture series offers a brief overview of the reduction by symmetry for Hamilton#39;s variational principle on Lie groups. After considering the simple case of a free rigid body, different types of examples will be covered before focusing on fluid dynamics. Eventually, the last lectures present a brief introduction to the application of these methods to the dynamics of nematic liquid crystals, in both ideal and dissipative cases. Mon, 20 Apr 2020 00:00:00 +0200