PhD on mathematical modeling of scattering

Eindhoven, Noord-Brabant
€ 3.059-3.881 per maand
Tijdelijk
Voltijds

1 maand geleden

IntroductionAre you eager to use your mathematical skills to model and design optical systems for sustainable high-tech devices for billions of people? Do you like to develop and analyze numerical methods for partial differential equations?Job DescriptionThe Computational Illumination Optics group is one of the few mathematics groups worldwide working on mathematical models of optical systems. They develop and analyze numerical methods to solve the resulting differential equations. The team has a healthy portfolio of PhD positions and close collaborations with industrial partners. It consists of four full FTEs at Eindhoven University of Technology and one part-time professor.The group has three research tracks: freeform design, imaging optics and improved direct methods; for more details see . The following mathematical disciplines are important in our work: geometrical optics, ray tracing, (numerical) PDEs, transport theory, nonlinear optimization, Lie operators and Hamiltonian systems.PhD vacancyAs part of the research program Optical coherence; optimal delivery and positioning (OPTIC) we offer you a PhD project on Surface scattering with 3D Monge-Ampère. The full OPTIC program has 12 PhD students, 4 of them employed in the Computational Illumination Optics group in Eindhoven.
The goal in freeform design is to compute the shapes of optical surfaces (reflector/lens) that convert a given source distribution, typically LED, into a desired target distribution. For ideal sources and optical surfaces we can solve the so-called Monge-Ampère equation to find the freeform shapes of the surfaces. Scattering elements however send light rays in multiple directions. They are used to reduce glare in optical systems. Current design methods that include scattering use a slow iterative process. In this project we will develop fast design methods for 3D optical systems with scattering surfaces.Research line on freeform design: The goal in freeform design is to compute the shapes of optical surfaces (reflector/lens) that convert a given source distribution, typically LED, into a desired target distribution. The surfaces are referred to as freeform since they do not have any symmetries. The governing equation for these problems is a fully nonlinear PDE of Monge-Ampère type.Key publication: Anthonissen, M. J. H., Romijn, L. B., ten Thije Boonkkamp, J. H. M., & IJzerman, W. L. (2021).Unified mathematical framework for a class of fundamental freeform optical systems. Optics Express, 29(20), 31650-31664.Research line on imaging optics: The second research track is imaging, where the goal is to form a very precise image of an object, minimizing aberrations. Light propagation is described in terms of Lie transformations.Key publication: Barion, A., Anthonissen, M. J. H., ten Thije Boonkkamp, J. H. M., & IJzerman, W. L. (2022). Alternative computation of the Seidel aberration coefficients using the Lie algebraic method. Journal of the Optical Society of America A, Optics, Image Science and Vision, 39(9), 1603-1615.Research line on improved direct methods: Direct methods, such as ray tracing, compute the target distribution given the source distribution and the layout of the optical system. These methods must be embedded in an iterative procedure to compute the final design and are based on Monte-Carlo simulation. They are known to have slow convergence. Using the Hamiltonian structure of the system and advanced numerical schemes for PDEs, we are working on more efficient and accurate methods.Key publication: van Gestel, R. A. M., Anthonissen, M. J. H., ten Thije Boonkkamp, J. H. M., & IJzerman, W. L. (2021). An energy conservative hp-method for Liouville’s equation of geometrical optics. Journal of Scientific Computing, 89, [27].Job RequirementsWe are looking for talented enthusiastic PhD candidates who meet the following requirements:

A master’s degree in (applied) mathematics or (applied) physics with a background in mathematical modeling and scientific computing
Experience with solving ordinary and partial differential equations numerically
Experience with programming (C, C++, Python, Matlab or alike)
Creative pro-active team player with good analytical skills
A research-oriented attitude
Ability to work in an interdisciplinary team and interested in collaborating with industrial partners
Motivated to develop your teaching skills and coach students
Fluent in spoken and written English (C1 level)

Conditions of EmploymentA meaningful job in a dynamic and ambitious university, in an interdisciplinary setting and within an international network. You will work on a beautiful, green campus within walking distance of the central train station. In addition, we offer you:

Full-time employment for four years, with an intermediate assessment after nine months. You will spend a minimum of 10% of your four-year employment on teaching tasks, with a maximum of 15% per year of your employment.
Salary and benefits (such as a pension scheme, paid pregnancy and maternity leave, partially paid parental leave) in accordance with the Collective Labour Agreement for Dutch Universities, scale P (min. € 3,059 max. € 3,881).
A year-end bonus of 8.3% and annual vacation pay of 8%.
High-quality training programs and other support to grow into a self-aware, autonomous scientific researcher. At TU/e we challenge you to take charge of your own

. * An excellent technical infrastructure, on-campus children's day care and sports facilities.

An allowance for commuting, working from home and internet costs.
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and a tax compensation scheme (the 30% facility) for international candidates.Information and applicationAbout usEindhoven University of Technology is an internationally top-ranking university in the Netherlands that combines scientific curiosity with a hands-on attitude. Our spirit of collaboration translates into an open culture and a top-five position in collaborating with advanced industries. Fundamental knowledge enables us to design solutions for the highly complex problems of today and tomorrow.InformationDo you recognize yourself in this profile and would you like to know more? Please contact the hiring manager dr.ir. Martijn Anthonissen ( ).Visit our website for more information about the or the . You can also contact HR Services ( ).Are you inspired and would like to know more about working at TU/e? Please visit ourApplicationWe invite you to submit a complete application by using the apply button. The application should include a:

Cover letter in which you describe your motivation and qualifications for the position.
Curriculum vitae, including a list of your publications and the contact information of three references.
Grade lists of your bachelor and master programs.

Eindhoven University of Technology

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