Forthcoming events in this series
Composite membranes comprised of an ultra-thin coating film formed over a porous support membrane are the basis for state-of-the-art reverse osmosis (RO) and nanofiltration (NF) membranes, offering the possibility to independently optimize the support membrane and the coating film. However, limited information exists on transport through such composite membrane structures. Numerical calculations have been carried out in order to probe the impacts of the support membrane skin-layer pore size and porosity, support membrane bulk micro-porosity, and coating film thickness and morphology (i.e. surface roughness) on solvent and solute transport through composite membranes. Results suggest that the flux and rejection of a composite membrane may be fine-tuned, by adjusting support membrane skin layer porosity and pore size, independent of the properties of the coating film. Further, the water flux over the membrane surface is unevenly distributed, creating local ‘hot spots’ of high flux that may govern initial stages of membrane fouling and scaling. The analysis provides important insight on how the non-trivial interaction of support properties and film roughness may result in widely varying transport properties of the composite structure. In particular, the simulations reveal inherent trade-offs between flux, rejection and fouling propensity (the latter due to ‘hot spots’), which are purely consequences of geometrical factors, irrespective of materials chemistry.
Topological defects (TDs) are unavoidable consequence of continuous symmetry breaking phase transitions. They exhibit several universal features and often span apparently completely different systems. Particularly convenient testing ground to study basic physics of TDs are liquid crystals (LCs) due to their softness, liquid character and optical anisotropy. In the lecture I will present our recent theoretical studies of TDs in nematic LCs, which are of interest also to other branches of physics.
I will first focus on coarsening dynamics of TDs following the isotropic-nematic phase transition. Among others we have tested the validity of the Kibble-Zurek [1,2] prediction on the size of the so called protodomains, which was originally derived to estimate density of TDs as a function of inflation time in the early universe. Next I will consider nematic LC shells [3]. These systems are of interest because they could pave path to mm sized scaled crystals exhibiting different symmetries. Particular attention will be paid to curvature induced unbinding of pairs of topological defects. This process might play important role in membrane fission processes.
[1] W.H. Zurek, Nature 317, 505 (1985).
[2] Z. Bradac et al., J.Chem.Phys 135, 024506 (2011)
[3] S. Kralj et al., Soft Matter 7, 670 (2011); 8, 2460 (2012).
Stability plays an important role in engineering, for it limits the load carrying capacity of all kinds of structures. Many failure mechanisms in advanced engineering materials are stability-related, such as localized deformation zones occurring in fiber-reinforced composites and cellular materials, used in aerospace and packaging applications. Moreover, modern biomedical applications, such as vascular stents, orthodontic wire etc., are based on shape memory alloys (SMA’s) that exploit the displacive phase transformations in these solids, which are macroscopic manifestations of lattice-level instabilities.
The presentation starts with the introduction of the concepts of stability and bifurcation for conservative elastic systems with a particular emphasis on solids with periodic microstructures. The concept of Bloch wave analysis is introduced, which allows one to find the lowest load instability mode of an infinite, perfect structure, based solely on unit cell considerations. The relation between instability at the microscopic level and macroscopic properties of the solid is studied for several types of applications involving different scales: composites (fiber-reinforced), cellular solids (hexagonal honeycomb) and finally SMA's, where temperature- or stress-induced instabilities at the atomic level have macroscopic manifestations visible to the naked eye.
We discuss new symmetry results for nonconstant entire local minimizers of the standard Ginzburg-Landau functional for maps in ${H}^{1}_{\rm{loc}}(\mathbb{R}^3;\mathbb{R}^3)$ satisfying a natural energy bound.
Up to translations and rotations, such solutions of the Ginzburg-Landau system are given by an explicit map equivariant under the action of the orthogonal group.
More generally, for any $N\geq 3$ we characterize the $O(N)-$equivariant vortex solution for Ginzburg-Landau type equations in the $N-$dimensional Euclidean space and we prove its local energy minimality for the corresponding energy functional.
As Herb Sutter predicted in 2005, "The Free Lunch is Over", software programmers can no longer rely on exponential performance improvements from Moore's Law. Computationally intensive software now rely on concurrency for improved performance, as at the high end supercomputers are being built with millions of processing cores, and at the low end GPU-accelerated workstations feature hundreds of simultaneous execution cores. It is clear that the numerical software of the future will be highly parallel, but what language will it be written in?
Over the past few decades, high-level scientific programming languages have become an important platform for numerical codes. Languages such as MATLAB, IDL, and R, offer powerful advantages: they allow code to be written in a language more familiar to scientists and they permit development to occur in an evolutionary fashion, bypassing the relatively slow edit/compile/run/plot cycle of Fortran or C. Because a scientist’s programming time is typically much more valuable than the computing cycles their code will use, these are substantial benefits. However, programs written in such languages are not portable to high performance computing platforms and may be too slow to be useful for realistic problems on desktop machines. Additionally, the development of such interpreted language codes is partially wasteful in the sense that it typically involves reimplementation (with associated debugging) of some algorithms that already exist in well-tested Fortran and C codes. Python stands out as the only high-level language with both the capability to run on parallel supercomputers and the flexibility to interface with existing libraries in C and Fortran.
Our code, PyClaw, began as a Python interface, written by University of Washington graduate student Kyle Mandli, to the Fortran library Clawpack, written by University of Washington Professor Randy LeVeque. PyClaw was designed to build on the strengths of Clawpack by providing greater accessibility. In this talk I will describe the design and implementation of PyClaw, which incorporates the advantages of a high-level language, yet achieves serial performance similar to a hand-coded Fortran implementation and runs on the world's fastest supercomputers. It brings new numerical functionality to Clawpack, while making maximal reuse of code from that package. The goal of this talk is to introduce the design principles we considered in implementing PyClaw, demonstrate our testing infrastructure for developing within PyClaw, and illustrate how we elegantly and efficiently distributed problems over tens of thousands of cores using the PETSc library for portable parallel performance. I will also briefly highlight a new mathematical result recently obtained from PyClaw, an investigation of solitary wave formation in periodic media in 2 dimensions.
Boundary conditions in pseudospectral collocation methods
are imposed by removing rows of the discretised differential operator and
replacing them with others to enforce the required conditions at the boundary.
A new approach, based upon projecting the discrete operator onto a lower-degree
subspace to create a rectangular matrix and applying the boundary condition
rows to ‘square it up’, is described.
We show how this new projection-based method maintains
characteristics and advantages of both traditional collocation and tau methods.
When attempting to homogenise a large number of dislocations, it becomes important to express the stress in a body due to the combined effects of many dislocations. Assuming linear elasticity, this can be written as a simple sum over all the dislocations. In this talk, a method for obtaining an asymptotic approximation to this sum by simple manipulations will be presented. This method can be generalised to approximating one-dimensional functions defined as sums, and work is ongoing to achieve the same results in higher dimensions.
A great number of works about the tear film behaviour was published. The majority of these works based on modelling with the use of the lubrication approximation. We explore the relevance of the lubrication tear film model compare to the 2D Navier-Stokes model. Our results show that the lubrication model qualitatively describe the tear film evolution everywhere except region close to an eyelid margin. We also present the tear film behaviour using Navier-Stokes model that demonstrates that here is no mixing near the MCJ when the eyelids move relative to the eyeball.
Multiscale differential equations arise in the modelling of many important problems in the science and engineering. Numerical methods for such problems have been extensively studied in the deterministic case. In this talk, we will discuss numerical methods for (mean-square stable) stiff stochastic differential equations. In particular we will discuss a generalization of explicit stabilized methods, known as Chebyshev methods to stochastic problems.
Strong explosive volcanic eruptions could inject in the lower stratosphere million tons of SO2, which being converted to sulfate aerosols, affect radiative balance of the planet for a few years. During this period the volcanic radiative forcing dominates other forcings producing distinct detectable climate responses. Therefore volcanic impacts provide invaluable natural test of climate nonlinearities and feedback mechanisms. In this talk I will overview volcanic impacts on tropospheric and strsatospheric temperature, ozone, high-latitude circulation, stratosphere-troposphere dynamic interaction, and focus on the long-term volcanic effect on ocean heat content and sea level.
1. "Approximate approximations" and accurate computation of high dimensional potentials.
2. Iteration procedures for ill-posed boundary value problems with preservation of the differential equation.
3. Asymptotic treatment of singularities of solutions generated by edges and vertices at the boundary.
4. Compound asymptotic expansions for solutions to boundary value problems for domains with singularly perturbed boundaries.
5. Boundary value problems in perforated domains without homogenization.
We have recently found a way to describe large-scale neural
activity in terms of non-equilibrium statistical mechanics.
This allows us to calculate perturbatively the effects of
fluctuations and correlations on neural activity. Major results
of this formulation include a role for critical branching, and
the demonstration that there exist non-equilibrium phase
transitions in neocortical activity which are in the same
universality class as directed percolation. This result leads
to explanations for the origin of many of the scaling laws
found in LFP, EEG, fMRI, and in ISI distributions, and
provides a possible explanation for the origin of various brain
waves. It also leads to ways of calculating how correlations
can affect neocortical activity, and therefore provides a new
tool for investigating the connections between neural
dynamics, cognition and behavior
