The problem of a bubble moving steadily in a HeleShaw cell goes back to Taylor and Saffman in 1959. It is analogous to the wellknown selection problem for SaffmanTaylor fingers in a HeleShaw channel. We apply techniques in exponential asymptotics to study the bubble problem in the limit of vanishing surface tension, confirming previous numerical results, including a previously predicted surface tension scaling law. Our analysis sheds light on the multiple tips in the shape of the bubbles along solution branches, which appear to be caused by switching on and off exponentially small wavelike contributions across Stokes lines in a conformally mapped plane.
Past Industrial and Applied Mathematics Seminar
In biological cells, genomic DNA is complexed with proteins, forming socalled chromatin structure, and packed into the nucleus. Not only the nucleotide (A, T, G, C) sequence of DNA but also the 3D structure affects the genomic function. For example, certain regions of DNA are tightly packed with proteins (heterochromatin), which inhibits expression of genes coded there. The structure sometimes changes drastically depending on the state (e.g. cell cycle or developmental stage) of the cell. Hence, the structural dynamics of chromatin is now attracting attention in cell biology and medicine. However, it is difficult to experimentally observe the motion of the entire structure in detail. To combine and interpret data from different modes of observation (such as live imaging and electron micrograph) and predict the behavior, structural models of chromatin are needed. Although we can use molecular dynamics simulation at a microscopic level (~ kilo basepairs) and for a short time (~ microseconds), we cannot reproduce longterm behavior of the entire nucleus. Mesoscopic models are wanted for that purpose, however hard to develop (there are fundamental difficulties).
In this seminar, I will introduce our recent theoretical/computational studies of chromatin structure, either microscopic (molecular dynamics of DNA or single nucleosomes) or abstract (polymer models and reactiondiffusion processes), toward development of such a mesoscopic model including local "states" of DNA and binding proteins.
References:
T. Kameda, A. Awazu, Y. Togashi, "Histone Tail Dynamics in Partially Disassembled Nucleosomes During Chromatin Remodeling", Front. Mol. Biosci., in press (2019).
Y. Togashi, "Modeling of Nanomachine/Micromachine Crowds: Interplay between the Internal State and Surroundings", J. Phys. Chem. B 123, 14811490 (2019).
E. Rolls, Y. Togashi, R. Erban, "Varying the Resolution of the Rouse Model on Temporal and Spatial Scales: Application to Multiscale Modelling of DNA Dynamics", Multiscale Model. Simul. 15, 16721693 (2017).
S. Shinkai, T. Nozaki, K. Maeshima, Y. Togashi, "Dynamic Nucleosome Movement Provides Structural Information of Topological Chromatin Domains in Living Human Cells", PLoS Comput. Biol. 12, e1005136 (2016).

The dynamics of many physical systems often evolve to asymptotic states that exhibit periodic spatial and temporal variations in their properties such as density, temperature, etc. Such regular patterns look the same when moved by a basic unit and/or rotated by certain special angles. They possess both translational and rotational symmetries giving rise to discrete spatial Fourier transforms. In contrast, an aperiodic crystal displays long range spatial order but no translational symmetry.
Recently, quasicrystals which are related to aperiodic crystals have been observed to form in diverse physical systems such as metallic alloys (atomic scale) and dendritic, star, and block copolymers (molecular scale). Such quasicrystals lack the lattice symmetries of regular crystals, yet have discrete Fourier spectra. We look to understand the minimal mechanism which promotes the formation of such quasicrystalline structures using a phase field crystal model. Direct numerical simulations combined with weakly nonlinear analysis highlight the parameter values where the quasicrystals are the global minimum energy state and help determine the phase diagram.
By locating parameter values where multiple patterned states possess the same free energy (Maxwell points), we obtain states where a patch of one type of pattern (for example, a quasicrystal) is present in the background of another (for example, the homogeneous liquid state) in the form of spatially localized dodecagonal (in 2D) and icosahedral (in 3D) quasicrystals. In two dimensions, we compute several families of spatially localized quasicrystals with dodecagonal structure and investigate their properties as a function of the system parameters. The presence of such metastable localized quasicrystals is significant as they may affect the dynamics of the crystallisation in soft matter.
The talk will begin with an introduction to the science of what determines the behaviour of a liquid on a on a surface and giving an overview of some of the different theories that can be used to describe the shape and structure of the liquid in the drop. These include microscopic density functional theory (DFT), which describes the liquid structure on the scale of the individual liquid molecules, and mesoscopic thin film equation (PDE) and kinetic MonteCarlo models. A DFT based method for calculating the binding potential đť‘”(h) for a film of liquid on a solid surface, where h is the thickness of the liquid film, will be presented. The form of đť‘”(h) determines whether or not the liquid wets the surface. Calculating drop profiles using both DFT and also from inputting đť‘”(h) into the mesoscopic theory and comparing quantities such as the contact angle and the shape of the drops, we find good agreement between the two methods, validating the coarsegraining. The talk will conclude with a discussion of some recent work on modelling evaporating drops with applications to inkjet printing.
One of the key unsolved challenges at the interface of physical and life sciences is to formulate comprehensive computational modeling of cells of higher organisms that is based on microscopic molecular principles of chemistry and physics. Towards addressing this problem, we have developed a unique reactive mechanochemical forcefield and software, called MEDYAN (Mechanochemical Dynamics of Active Networks: http://medyan.org). MEDYAN integrates dynamics of multiple mutually interacting phases: 1) a spatially resolved solution phase is treated using a reactiondiffusion master equation; 2) a polymeric gel phase is both chemically reactive and also undergoes complex mechanical deformations; 3) flexible membrane boundaries interact mechanically and chemically with both solution and gel phases. In this talk, I will first outline our recent progress in simulating multimicron scale cytosolic/cytoskeletal dynamics at 1000 seconds timescale, and also highlight the outstanding challenges in bringing about the capability for routine molecular modeling of eukaryotic cells. I will also report on MEDYANâ€™s applications, in particular, on developing a theory of contractility of actomyosin networks and also characterizing dissipation in cytoskeletal dynamics. With regard to the latter, we devised a new algorithm for quantifying dissipation in cytoskeletal dynamics, finding that simulation trajectories of entropy production provide deep insights into structural evolution and selforganization of actin networks, uncovering earthquakelike processes of gradual stress accumulation followed by sudden rupture and subsequent network remodeling.
Thin film flows of nematic liquid crystal will be considered, using the LeslieEricksen formulation for nematics. Our model can account for variations in substrate anchoring, which may exert a strong influence on patterns that arise in the flow. A number of simulations will be presented using an "in house" code, developed to run on a GPU. Current modeling directions involving flow over interlaced electrodes, socalled "dielectrowetting", will be discussed.
During this seminar, we will present a new mathematical model describing the transport of nitric oxide (NO) in a realistic geometrical representation of the lungs. Nitric oxide (NO) is naturally produced in the bronchial region of the lungs. It is a physiological molecule that has antimicrobial properties and allows the relaxation of muscles. It is well known that the measurement of the molar fraction of NO in the exhaled air, the socalled FeNO, allows a monitoring of asthmatic patients, since the production of this molecule in the lungs is increased in case of inflammation. However, recent clinical studies have shown that the amount of NO in the exhaled air can also be affected by Â« noninflammatory Â» processes, such as the action of a bronchodilator or a respiratory physiotherapy session for a patient with cystic fibrosis. Using our new model, we will highlight the complex interplay between different transport phenomena in the lungs. More specifically, we will show why changes taking place in the deepest part of the lungs are expected to impact the FeNO. This gives a new light on the clinical studies mentioned below, allowing to confer a new role to the NO for the management of various pulmonary pathologies.
Further Information:
Our new Hooke fellow will introduce her research.
Tensors are higher dimensional analogues of matrices; they are used to record data with multiple changing variables. Interpreting tensor data requires finding low rank structure, and the structure depends on the application or context. Often tensors of interest define semialgebraic sets, given by polynomial equations and inequalities. I'll give a characterization of the set of tensors of real rank two, and answer questions about statistical models using probability tensors and semialgebraic statistics. I will also describe work on learning a path from its threedimensional signature tensor. This talk is based on joint work with Guido MontĂşfar, Max Pfeffer, and Bernd Sturmfels.
When a liquid drop is deposited over a solid surface whose temperature is sufficiently above the boiling point of the liquid, the drop does not experience nucleate boiling but rather levitates over a thin layer of its own vapor. This is known as the Leidenfrost effect. Whilst highly undesirable in certain cooling applications, because of a drastic decrease of the energy transferred between the solid and the evaporating liquid due to poor heat conductivity of the vapor, this effect can be of great interest in many other processes profiting from this absence of contact with the surface that considerably reduces the friction and confers an extreme mobility on the drop. During this presentation, I hope to provide a good vision of some of the knowledge on this subject through some recent studies that we have done. First, I will present a simple fittingparameterfree theory of the Leidenfrost effect, successfully validated with experiments, covering the full range of stable shapes, i.e., from small quasispherical droplets to larger puddles floating on a pocketlike vapor film. Then, I will discuss the end of life of these drops that appear either to explode or to takeoff. Finally, I will show that the Leidenfrost effect can also be observed over hot baths of nonvolatile liquids. The understanding of the latter situation, compare to the classical Leidenfrost effect on solid substrate, provides new insights on the phenomenon, whether it concerns levitation or its threshold.