Mathematical Problems of Orientationally Ordered Soft Solids (16w5021)

Arriving in Oaxaca, Mexico Sunday, September 4 and departing Friday September 9, 2016

Organizers

Alejandro Rey (McGill Univercity)

(International School for Advanced Studies, Trieste, Italy)

(Technion)

Objectives

The general objective of this workshop is to bring together the leading researchers in the field across several disciplines, including physicists, mathematicians, polymer scientists and engineers, to foster awareness and cross-disciplinary transfer of ideas in this fast evolving field and facilitate conversation among the different communities of scientists.

The workshop will bring together different, so far disconnected aspects of state-of-art knowledge: elasticity theory, pattern formation, mesoscopic aspects of soft matter physics, and biological or biomimetic morphogenesis. Their interconnections have to be developed and elaborated for the stated aim. It will alert the participants to novel methodologies that go beyond existing methods and processes, bringing attention to so far unexplored combinations of properties of active soft matter and their feedback interactions.

The following is an incomplete list of topics pertaining to the subject of the workshop that illustrates its multidisciplinary nature:

- Mechanics of soft matter and living tissues

- Rheology, combining viscoelasticity, anisotropy, and multiphase features, coupled to chemical transformations and transport

- Relation of equilibrium and non-equilibrium behavior of soft matter;

- Analysis of nonlinear evolution equations and pattern formation.

- Asymptotic and numerical methods for kinetic equations describing orientable soft matter

- Role and description of defects and topological phases.

- Mathematical description of artificial crawlers and microswimmers; collective dynamics ]

- Dynamics and growth of biological and biomimetic films and membranes;

- Interface dynamics of soft matter, coupling of bulk and interfacial properties

- Structural and interfacial instabilities

- Mechanoresponsiveness and shear-induced transitions in soft solids, shear-banding, micro-structural rearrangement.

- Control through boundary conditions and external forcing.

The three organizers come from physics, applied mathematics, and engineering backgrounds.

Len Pismen is Emeritus J. & B. Naiman Professor of Fluid Mechanics at the Technion - Israel Institute of Technology. His research is in a wide area of applied physics, including pattern formation in non-equilibrium systems (summarised in two monographs published in 1999 and 2006), dynamic capillarity, and, most recently, theory of soft solids and biological tissues. He is an editor of European Physical Journal - Special Topics, and a former member of the Board of Directors and the Scientific Council of the International Centre for Mechanical Sciences. He was an organiser of a number of scientific events, most recently, the programme on Mathematical Modelling and Analysis of Complex Fluids and Active Media in Evolving Domains at the Newton Institute for Mathematical Sciences (Cambridge UK, 2013) and the workshop "Tissue Growth and Morphogenesis: from Genetics to Mechanics and Back" (Banff, 2012).

Antonio DeSimone is Professor of Structural Mechanics and director of the Applied Mathematics research group SISSA-MathLab at the International School for Advanced Studies in Trieste, Italy. His research focuses on the mechanics of phase transforming solids, and on the mechanics of soft and biological matter, with special emphasis on shape control, self-propulsion, and motility. He has been recently awarded an Advanced Grant by the European Research Council for research on biological and bio-inspired motility at microscopic scales. He has been the organiser of several scientific events, most recently the workshop on “Liquid Crystal Defects and their Geometry, Active and Solid Liquid Crystals, and Related Systems” during the programme on the Mathematics of Liquid Crystals at the Newton Institute for Mathematical Sciences (Cambridge, UK, 2013), the workshop “Mathematics and Mechanics in the search for new materials” (Banff, 2013), and the Advanced School “Mechanobiology of cells and tissues: motility and morphogenesis” at CISM, the International Centre for Mechanical Sciences (Udine, Italy, 2014).

Alejandro Rey, James McGill Professor of Chemical Engineering, McGill, is a world leader in soft material sciences including research in liquid crystals and elastomers and the application of computational methods to develop advanced biological materials and biomimetic approaches to polymer production and manufacturing based on biological self-assembly and biological polymer processing. Dr. Rey is an executive member of McGill’s Advanced Materials Institute, a Fellow of the Royal Chemical Society (UK) and American Physical Society, former associate editor of Soft Matter, currently in the editorial boards of Liquid Crystals and Colloids and Surfaces Communications and director of the Materials Modeling Research Group.

We expect the following concrete outcomes from the workshop:

(1) To survey the state of the art on theory of orientable soft solids, and highlight it as an important emerging area in applied mathematics. Experimentalists will bring to theoreticians' attention recent developments in creating novel biomimetic materials and building up artificial mesoscopic structures, and direct them to the development of analytical and computational tools that may serve for understanding and better controlling these processes. Theoreticians and numerical analysts will summarize the predictive capabilities of their models, including continuum and discrete numerical methods. We will encourage the two sides to "compare notes" and come up with a common understanding of our current knowledge in this area.

(2) To identify the most pressing scientific problems. Experimentalists will underscore phenomena that cannot be readily rationalized or explained. Theoreticians and numerical analysts will define the limitations of various theoretical and numerical methods, and explore multi-scale modeling for prototypical problems such as the patterning and creation of three-dimensional forms.

(3) To develop promising research strategies for the future, to conduct an inventory of the cutting-edge observational, modeling and computational techniques, and suggest the most appropriate approaches to each problem. These can be combinations of existing approaches developed for separate aspects of theory of soft matter and natural morphogenesis, and combination of mechanical models and transport models. In the best case, the discussion may produce completely novel concepts and ideas to be explored in the future.

(4) To facilitate the pursuit of these strategies by initiating inter-disciplinary collaborations. We envision broad and lively discussions of all the theoretical developments, computational methodologies and experimental discoveries. Out of the discussions, we hope, collaborations will naturally grow between researchers with complementary skills and expertise. In particular, younger scientists will benefit from direct interactions with more established experts, and from the opportunity to integrate or distinguish themselves in this exciting multi-disciplinary community. We have compiled a stellar and diverse roster for the workshop. We have invited the physicists of various specializations related to mechanics of soft solids, biophysics, and nonlinear science, mathematical authorities on modeling and computations, and leading polymer physicists for their expertise in characterization of materials. So far 34 invitees have accepted the invitation. We expect to also include a significant number of younger researchers, with the aim of providing them with essential tools and techniques that they would not normally encounter within their own institutions and research groups. We are confident that this workshop will gather an exceptionally strong group of scientists.