(7hd) Scientific Computing and Mathematical Modelling for Multiscale Nonlinear Systems

Process synthesis, optimization, and design of energy-production systems are becoming increasingly challenging as they rapidly grow in size and complexity. Successful and sustainable development of energy infrastructures hinges on integrated energy and water systems, in which all safety, environmental, and economical considerations are accounted for. Polygeneration of energy can significantly improve efficiency and reduce capital investment cost by combining processes that involve similar intermediate products and operation units. Strategic planning for projects of such magnitude requires accurate and predictive mathematical models and a systematic multi-scale decision-making framework to provide the best plan among numerous alternatives (e.g. feedstocks, products, and technologies) that satisfies a prescribed set of objectives. Formulation of such problems often leads to large-scale nonlinear dynamic problems that are computationally challenging to solve for systems of practical importance. My overall approach is to tackle these problems from two fronts: (i) Developing robust and fast computational algorithms for the optimization of process-level models and (ii) leverage advanced mathematical techniques to derive macro/microscopic unit-process models, which are simple enough to be computationally tractable and realistic enough to capture the essential underlying physics.

Research Experiences: I am currently a postdoctoral fellow in the Process Systems Engineering Laboratory at MIT under the supervision of Prof. Paul Barton (successful proposal: NSERC Postdoctoral Fellowship). I am currently working on the multi-scale design and analysis of carbon capture, utilization, and storage networks, focusing on algae cultivation for fuel production and carbon sequestration. Since I started, I have worked on (i) fast and robust multi-parametric programming algorithms for the flux balance analysis of genome-scale metabolic networks and (ii) superstructure optimization for techno-economic analysis of carbon sequestration networks. In the first, I have achieved more than six-fold improvement in computational speed of large-scale parametric linear and quadratic programs over current parametric programming tools. In the second, using explicit solutions from the foregoing parametric study, I incorporated detailed metabolic models into superstructure models, demonstrating the computational viability of integrated metabolic-network and process-level optimization models.

I obtained my PhD from the Chemical Engineering Department at McGill under the supervision of Prof. Reghan Hill and Theo ven de Ven (successful proposal: NSERC Strategic Green Fibre Network), where I studied the stability and dynamics of wood-fibre collapse upon drying. I developed an idealized model that captures the underlying physics of drying-induced collapse, demonstrating the connection between elastocapillary stability and dry-state conformations. I rigorously established a connection between stability loss and the shape of bifurcation diagrams, providing an alternative means to identify the stability of elastocapillary systems, which is much less costly than the eigenvalue computations in conventional linear stability analyses.

Future Directions: As faculty, I would like to continue working on the development of mathematical-models and computational tools for the simulation and optimization of multi-scale biological and chemical processes with emphasis on polygeneration systems. I am particularly interested in mass production of renewable fuels, where algal bio-refineries are integrated with power and steam generation, water treatment, carbon capture, and enhanced oil recovery (EOR) plants within a large-scale carbon-sequestration networks. My future efforts are classified into three categories: (i) Improving mathematical models for existing technologies (e.g. EOR), (ii) developing new theories, models, and computational tools for studying biological systems to uncover their potential application in renewable-fuel production, and (iii) developing robust global optimization tools for superstructure modelling and techno-economic analysis of polygeneration networks. Among these, the first and last are short-term projects, where fast progress can be made by extending the research efforts from my postdoctoral training. The second is a long-term and challenging project with potentially high impact on energy systems. The potential of microbial communities in the production of clean fuels and other value-added products is not fully understood. This is due the lack of mathematical tools to characterize their complex metabolism that can quantify the behavior of micro-organisms in response to environmental stimuli. A comprehensive mathematical framework must be developed to coherently describe steady-states and transients of metabolic networks and the dynamics of the transition between these two modes.

Teaching Interests: Optimization, nonlinear dynamics, fluid mechanics, transport phenomena, computational fluid dynamics.

One of my motivations for pursuing an academic career besides research is teaching. A successful research career can be complemented by satisfying teaching responsibilities. My teaching philosophy is based on three principles: (i) maintaining students’ interest, (ii) being accessible and accountable, and (iii) valuing concepts and fundamentals over case studies and memorization. During my PhD, I was a teaching assistant and lab instructor for several undergraduate- and graduate level courses on most chemical-engineering core subjects. My experiences include preparing course material, handling lab sessions, holding tutorials and group discussions, and lecturing small (fewer than 20 students) and medium-sized classes (around 80 students).

Selected Publications:

A. Akbari, R.J. Hill, Liquid-bridge stability and breakup on surfaces with contact-angle hysteresis, Soft matter, 12, 6868-6882, 2016 (preprint arXiv:1507.06549).

A. Akbari, R.J. Hill, T.G.M. van de Ven, Stability and folds in an elastocapillary system, SIAM J. Appl. Math., 76(1):87-109, 2016 (preprint arXiv:1505.07315).

A. Akbari, R.J. Hill, T.G.M. van de Ven, Catenoid stability with a free contact line, SIAM J. Appl. Math., 75(5):2110-2127, 2015 (preprint arXiv:1505.07159).

A. Akbari, R.J. Hill, T.G.M. van de Ven, Liquid bridge breakup in contact-drop dispensing: Liquid bridge stability with a free contact line, Phys. Rev. E, 92:022404, 2015.

A. Akbari, R.J. Hill, T.G.M. van de Ven, An elastocapillary model of wood-fibre collapse upon drying, Proc. Roy. Soc. A, 471:20150184, 2015.

A. Akbari, M. Akbari, R.J. Hill, Effective thermal conductivity of two-dimensional anisotropic two-phase media, Int. J. Heat Mass Transfer, 63:41-50, 2013.