ARCADES is a Marie Sklodowska-Curie Innovative Training Network offering a comprehensive training program at the crossroads of mathematical foundations, CAD technology, and software development.
ARCADES offers 13 Early-Stage-Researcher (ESR) positions which allow the researcher to work towards a PhD. The ESRs will be recruited within 2016 for a duration of 36 months. All positions are already filled in. Every ESR will work on an independent research project (detailed below) which will be flexible enough to match the competence and goals of the student.
The ESRs will have secondment visits (internships) to other members of the Network, including industrial partners. The planned secondments are listed below but may change as the individual projects evolve. ESRs will also attend the generic viagra mastercard accepted throughout Europe. A bayer levitra 20mg will be established by the time of recruitment describing the scientific goals and methods, the secondments, any courses to be taken, and the personal, professional and career development of the ESR, and how it shall be achieved.
Marie Sklodowska-Curie ESRs are paid a competitive gross salary of 3,110 €/month, adjusted for their host country, a Mobility Allowance of 600 €/month and, for researchers who have a family, a Family Allowance of 500 €/month. All amounts are subject to deductions and taxes. Family is defined as persons linked to the researcher by (i) marriage, or (ii) a relationship with equivalent status to a marriage recognised by the national legislation of the country of the beneficiary or of nationality of the researcher, or (iii) dependent children who are actually being maintained by the researcher; family status is determined at recruitment and does not evolve.
The applicant must:
- Have a Master’s degree in Computer Science, Mathematics or Engineering (or any equivalent diploma).
- Should be — at the date of recruitment — an ‘early stage researcher (ESR)’, i.e. have less than 4 years of a research career, and not have a doctoral degree. The 4 years are measured from the date when they obtained the degree which would formally entitle them to embark on a PhD, either in the country where the degree was obtained or in the country where the PhD is provided.
- Trans-national mobility: The applicant should not have resided in the country where the research training takes place for more than 12 months in the 3 years immediately prior to recruitment, and not have carried out their main activity (work, studies, etc.) in that country. For refugees under the Geneva Convention , the refugee procedure (i.e. before refugee status is conferred) will not be counted as ‘period of residence/activity in the country of the beneficiary’.
- Be able to communicate fluently in English (speaking and writing). Oral interview with the prospective advisor may be required.
To apply for the position, please provide:
- a letter of motivation regarding the position as well as the ARCADES network;
- a detailed CV including education, work experience, skills, dissertations, research interests, career objectives, names and contact details of two referees, including the supervisor of the master thesis, willing to provide confidential letters of recommendation, and list of publications if any; Please also provide the English language certificates, if any.
- a transcript of his/hers master studies’ grades (including the overall grade and an explanation of the grading system) and the master’s thesis if available;
- letter of recommendation, preferably of the Master’s thesis supervisor, sent directly to the contact persons below.
- fill in the eligibility form and include it with your application.
Items i,ii, and iii should be emailed as a single PDF file (<5 Mb) to the head of the Educational Committee Laurent Busé, cc to arcades AT athena-innovation.gr, with ‘PhD application Arcades′ in the subject line.
Students and researchers from countries affected by conflicts and having their careers interrupted are encouraged to apply. Researchers faced by these circumstances can also visit: http://ec.europa.eu/research/mariecurieactions/news-events/news/2015/1216-researchers-at-risk_en.htm.
ESR1; Institution: ATHENA Research and Innovation Center, Athens, Greece; Start Date: 2016
|Title: Compact and efficient implicit representations
|We design algorithms and develop implementations for powerful implicit representations, and methods to obtain them from other representations. Sparse implicitisation reduces geometric operations on curves and (hyper)surfaces to manipulating an interpolation matrix. The method relies on a point sample on the object, given in two alternative representations:
Parameterised objects: Sparse implicitisation by interpolation has been studied in a series of articles by the supervisor and his team, e.g. [1,2]. This PhD advances the state-of-the-art in one or more of the following ways: (i) numerically improve the definition of the implicit equation, (ii) handle objects of higher codimension, namely space curves, (iii) exploit information about the normals to the curve/surface. In collaboration with SINTEF (and INRIA) we juxtapose the method to other approaches, including those developed in ESR4, ESR8.
Point clouds: Modern technology, such as scanners, is increasingly leading CAD developers to represent objects as point clouds, which offer flexibility for web applications. RISC-Software (also Missler) studies point samples defining solids swept along a path, and the resulting triangular mesh. Our goal is to reconstruct approximate boundary surfaces by point sampling with feature-aware distribution, segmenting the mesh to a graph of implicit, low-degree patches based on surface fitting, and recovering geometric features like edges or corners, for NC tool verification (cf. ESR2).
The project will take place at ATHENA RC under the supervision of generic cialis india, at the ErGA Lab. The PhD will be awarded by the Dept. of Informatics and Telecoms of the University of Athens.
Secondments are planned at SINTEF (Oslo, Norway) and at industrial partner RISC-Software (Linz, Austria).
ESR2; Institution: ATHENA Research and Innovation Center, Athens, Greece; Start Date: 2016
|Title: Algebraic elimination for modelling motion
|Sparse (or toric) elimination theory and, in particular, sparse resultants and matrix-based methods for system solving, have complexity that scales with the sparseness of the equations and the actual number of roots of the polynomial system. A related application is in change of representation of geometric objects (ESR1). ATHENA has used these tools to obtain efficient solutions for serial and parallel robot kinematics and calibration. Algebraic systems model the workspace of mechanisms, such as machine tools, with prescribed degrees of freedom, including the case of over-constraint mechanisms. We develop prototype software that efficiently solves specific instances, such as those provided by our industrial partners. Sparse elimination is employed to reveal the sparseness of motion polynomials. These have coefficients in the dual quaternions. Quaternions have been successfully used with sparse elimination to exploit the sparseness of the forward kinematics of the Stewart/Gough parallel robot. Secondments to Missler, and JKU.
The project will take place at ATHENA RC under the supervision of Ioannis Emiris, at the ErGA Lab. The PhD will be awarded by the Dept. of Informatics and Telecoms of the University of Athens.
Secondments are planned at JKU (Linz, Austria) and at industrial partner Missler (France).
ESR3; Institution: U. Barcelona, Barcelona, Spain; Start Date: 2016
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|This project is at the crossroad of commutative algebra and geometric modelling. Detection and analysis of
singularities of curves and surfaces are at the core of Computer Aided Design of shapes. The aim of this PhD proposal is to approach this geometric problem with tools of Commutative Computational Algebra which are being explored at this moment with very satisfactory results. More concretely, we will study the relation between parameterisations of curves and surfaces and algebraic features of the module of syzygies (or higher syzygies) of the coordinates of the parameterisation.
This “geometry of syzygies” approach is a rich research area in commutative algebra which already provided interesting and promising results in the case of plane curves, and we expect to extend its results to surfaces and spatial curves. The final goal of this project is to unravel these results for space curves and surfaces, highlighting those that would provide applications in geometric modelling and visualisation. It is also expected to find more compact formulas for implicitisation of rational parameterisations, which we also expect to achieve.The project will take place at the Mathematics Dept of the University of Barcelona under the supervision of Carlos D’Andrea.
Secondments will take place at INRIA (Sophia-Antipolis, France) and at JKU (Linz, Austria).
ESR4; Institution: INRIA, France; Start Date: 2016
|Title: Distances between points, rational Bézier curves & surfaces by means of matrix-based implicit representations.
|Computing the orthogonal projection of a point onto a NURBS curve or surface is a critical problem in geometric modelling that allows, for instance, to determine closest points. State-of-the-art approaches are mainly based on a “flattening” step which provides an initial guess that is refined by applying Newton-Raphson’s method. The main difficulty here is to get good initial values for which Newton iterations will converge successfully. In order to avoid it, we propose to develop a new algebraic approach based on the use of matrix representations of Bézier patches. This representation has been designed to provide an alternative implicit representation that allows not only to replace the classical polynomial implicit equation, but also to answer the point inversion problem, i.e., the computation of the parameter value of a given point on the Bézier patch. Given a Bézier patch, one builds a matrix whose entries are typically linear forms in the variables of the ambient space and such that its rank drops exactly on this patch, yielding a new matrix-based implicit representation. Besides the fact of being almost always valid, these representations can be very easily coupled with numerical linear algebra and hence provide a very interesting tool for treating geometric problems in the context of approximate computations.
The goal of this PhD topic is to develop new algorithms for solving the closest point problem by means of matrix representations. Taking into account that inversion can be solved by matrix representations, the main idea will be to rely on inversion of a parameterisation which is built from the normal lines of a Bézier patch (normal congruence maps). As a natural extension, the second objective will be to investigate new methods for computing distances between two distinct Bézier patches, which has important applications in geometric modelling, but also in other areas. The theoretical aspects of matrix representations, in particular the complexity of this approach (in terms of computations and size) and their generalisation to toric Bézier patches will be investigated in collaboration with the University of Barcelona. The new distance function will be analysed and experimented on geometric problems, such as surface fitting, in collaboration with the Missler company.
The project will take place at Inria Sophia Antipolis, in the team GALAAD under the supervision of viagra 50 mg sildenafil. The PhD will be awarded by the University of Nice.
Secondments are planned at the U.Barcelona (Barcelona, Spain) and at industrial partner Missler (France).
ESR5; Institution: INRIA, France; Start Date: 2016
|Title: New geometric models for the design and computation of complex shapes.
|The representation of complex shapes is a major bottleneck in geometric modelling. Classical representations are based on bspline surfaces, which are trimmed and assembled to describe shapes. But these models have several drawbacks: weak connection between topology and geometry, inaccuracies along trimmed curves, obstacles in their local refinement. They induce a high computational cost in many geometric operations and in the use and transformation of these models.The objective of the Ph.D. project is to investigate new geometric representations, based on new types of spline functions, which extend the standard bspline representation used in CAD. We will study the space of piecewise polynomial functions of bounded degree on domains with arbitrary topology. We will analyze their dimension and determine bases with good geometric properties. These functional spaces will be used to construct families of models with a prescribed topology, which automatically satisfy regularity constraints along edges or across surfaces. We will also investigate local refinement properties for adaptive methods in geometric representation problems.
We aim to demonstrate the impact of the approach in specific modelling problems. Several applications are foreseen: fitting and reconstruction of structured shapes from point clouds, description of computational domains for isogeometric analysis and numerical simulations, deformation of models for shape optimization, shape design from sketchs and curve networks. Some of these applications such as modelling problems for ship hull, bulb, propellers and for architecture will be investigated in collaboration with industrial partners of the network.
The project will take place at Inria Sophia Antipolis, in the team GALAAD under the supervision of levitra doses recommendation. The PhD will be awarded by the University of Nice.
Secondments are planned at the industrial partners Evolute (Vienna, Austria) and HRS (Athens, Greece).
ESR6; Institution: INRIA, France; Start Date: 2016
|Title: Skeleton paradigm for intuitive modelling of complex shapes
|A skeleton defines a shape and makes intelligible its organisation while helping to visualise its deformations. It is a union of lower dimensional manifolds that is homotopy equivalent to the shape and characterises its topology. Implicit surfaces obtained by convolution are defined in a natural way around a skeleton, like a wire generating an electric field: most level sets of the field are smooth independently of the smoothness of the wire. Global topology changing modifications are easily amenable to the model by manipulating the skeleton. Those implicit models, used in computer graphics, thus support the intuitive and creative design of complex shapes. The goal of this project is to bring those models to meet the reliability, accuracy and precision required in an industrial context. One requires there topologically accurate shapes and standard CAD parametric descriptions. Both those aspects are the challenge to be answered.
The ideal candidate will have a solid background in applied mathematics or computer science, with a taste for computational experiments.The project will take place at Inria Sophia Antipolis, in the team GALAAD under the supervision of Evelyn Hubert. The PhD will be awarded by the University of Nice.
Secondments are planned at ATHENA (Athens, Greece) and at industrial partner Hue (Oslo, Norway and/or Houston company’s office).
ESR7; Institution: JKU, Austria; Start Date: 2016
|Title: An algebraic framework for motion design
|Construction of a framework for the design of motions modelling prescribed tasks.
An essential idea of CAD is the use of control structures, for instance control points. The designer adapts/optimises a shape by adjusting elements of the control structure, which defines the shape that is then calculated in real time by algebraic algorithms. The situation is more complicated when we deal with movable linkages (kinematic chains). When a motion for performing a certain task is designed, one often also has a numerical function in the middle, namely the forward kinematics or the backward kinematics (depending on the type of the control of the kinematic chain), bridging the control structure adapted by the designer and the constraints resulting from the model such as the necessity to avoid collisions. In this ambitious project, we aim for an algebraic framework with algebraic interpolation algorithms for computing motions directly from a control structure with maximum flexibility. The underlying idea is the theory of motion polynomials, which have coefficients in the dual quaternions that parameterise all motions that can be rationally parameterised. Up to now, collision problems have hardly been considered with dual quaternions, so that a main challenge of this project will be the algebraic treatment of collisions. Collaborators include ATHENA, RISC-Soft, Missler.The project will take place at the Research Institute for Symbolic Computation, JKU, under the supervision of Josef Schicho.
Secondments are planned at ATHENA (Athens, Greece) and at industrial partner RISC-Software (Linz, Austria).
ESR8; Institution: SINTEF, Norway; Start Date: 2016
|Title: Refinement strategies and linear independence for LR-splines
|Providing refinement strategies for LR-splines that ensure linear independence, numerical stability and the anticipated error reduction of LR-spline approximations.
In its general form, LR-splines are incredibly versatile: the only restriction in the refinement process is that at each step at least one B-spline is refined. Even so, experiments have shown that care has to be take to maintain linear independence and a numerically stable B-spline basis. Currently, this is managed through restrictive rules of thumb, such as avoiding overloaded elements or B-splines, and avoiding B-splines with nested support. Refinements are often restricted to the midpoint of knot intervals. This project will develop refinement strategies incorporating these informal rules. One of the challenges this project will address is how the choice of refinement direction can be optimised in order to maximise the approximation power of LR-splines. A second challenge is refinements strategies for big data, where typically the size of both the original data and of the approximate LR-spline model requires tiling into manageable pieces. Different application areas will typically require different refinement strategies. This will be incorporated into the project through the two secondment periods. At UoS, the focus will be on refinement strategies suitable for isogeometric analysis, i.e., for creating geometric models suitable both for design and simulation purposes. At Hue, the focus will be on adapting LR-spline algorithms for modelling and visualisation of very large seismic datasets. The development of a plugin for their HueSpace software platform will enable testing of the refinement strategies on complex real-world seismic workflows.The project will take place at the Dept of Applied Mathematics, SINTEF under the supervision of Tor Dokken. The PhD will be awarded by the University of Oslo.
Secondments are planned at U. Strathclyde (Glasgow, UK) and at industrial partner Hue (Oslo, Norway).
ESR9; Institution: SINTEF, Norway; Start Date: 2016
|Title: Locally refined approximate implicitisation for design and manufacturing
|Approximate implicitisation of curves and surfaces has until now focused on approximation by a single polynomial. However, when addressing composite shapes composed of multiple curves or surfaces, implicitisation by a single polynomial is inadequate, because it inevitably requires a high polynomial degree. To avoid this, one resorts to a piecewise algebraic representation. The simplest such representation, tensor product B-splines, defines piecewise polynomials over a regular grid. The main challenge for this representation comes from the required regularity of the grid: any refinements to increase the level of local detail will span the whole width of the grid. In contrast, the refinements of locally refined LR-splines are truly local, thus facilitating the approximation of local detail and the introduction of additional degrees of freedom only where needed. LR piecewise algebraic surfaces provide a watertight representation, and offer an alternative to the boundary representations of traditional CAD systems. The representation is also highly suitable for layered manufacturing, since plane sections can be extracted as algebraic curves. The project will, among others: study of the approximation properties of locally refined algebraic representations, address the question of how to implement an inside/outside notion across a complex volume, and look at the challenges of representing boundary representation CAD models in this new format.
The project will take place at the Dept of Applied Mathematics, SINTEF under the supervision of Tor Dokken. The PhD will be awarded by the University of Oslo.
Secondments are planned at ATHENA (Athens, Greece) (3 Months: Investigate the application of sparse elimination theory to implicitisation of LR-Splines) and at industrial partner RISC-Software (Linz, Austria).
ESR10; Institution: U. Strathclyde, UK; Start Date: 2016
|Title: Novel representations for modelling free-form objects under geometric, volumetric, internal-layout constraints
|Development of a parametric modeller enabling the robust and low-cost generation of smooth freeform 3D objects under constraints that occur in the engineering-design practice, such as: (i) adequate geometric smoothness (G 1 −G 2 ) and fairness (non-oscillatory distribution of curvatures) of the bounding surfaces, (ii) shape-preserving control curves lying on the bounding surfaces (iii) volumetric (moment) constraints, and (iv) internallayout constraints. Parametric modelling will be based on surface T-splines for obtaining at a low-cost, in terms of the required degrees of freedom, representation of the object to be designed.
The project will take place at the Dept of Naval Architecture, Ocean and Marine Engineering, U. Strathclyde under the supervision of Panagiotis Kaklis.
Secondments are planned at TUW (Vienna, Austria) and at industrial partner HRS (Athens, Greece).
ESR11; Institution: U. Strathclyde, UK; Start Date: 2016;
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|Design of engineering systems is becoming increasingly complex and demanding due to a plethora of requirements regarding efficiency, economy, safety, comfort and lower-carbon footprint. Realistic simulation of the associated physical phenomena, processes and subsystems places a premium on tightly integrated Design-Through-Analysis (DTA) tools. According to a study undertaken by T. Blacker, Manager of Simulation Sciences at SNL (Sandia National Labs), almost 80% of the overall model and analysis time is devoted to the creation of analysis-suitable geometry and meshing. Decreasing this 80% substantially is vital for developing optimisation frameworks that can provide robust results in reasonable time scale.
The aim of the proposed PhD thesis is to enhance a commercial CAD-CAE tool (CADfix), developed by our industrial partner TranscenData, with isogeometric (IGA) functionality, that will enable the low-cost construction of geometrically accurate and locally refinable meshes suitable for isogeometric (IGA) BEM/FEM solvers. The new functionality will be also exploited for improving the meshes used by conventional BEM/FEM solvers through improving their geometric accuracy and reducing their spatial redundancy.
The IGA-enhanced CAD-CAE tool will be used for handling two challenging research problems: (a) Modelling and analysing the effects of shape modifications on the performance of the ship-hull-propeller or renewable energy-device system through the development of novel T-spline IGA-BEM solvers. (b) Automatic construction of geometrically accurate and locally refinable T-/LR-spline based volumetric meshing of complex computational domains such as the 3D domain bounded by the stern of the ship hull, her propeller and their appendages or the 3D domain interface between a fluid and a deforming structural domain, which arises in various industrial applications, such as the aero/hydro-elasticity problem of large scale wind/tidal turbine, and ship propellers.The project will take place at the Dept of Naval Architecture, Ocean and Marine Engineering, U. Strathclyde under the supervision of Panagiotis Kaklis.
Secondments are planned at INRIA (Sophia-Antipolis, France) and at industrial partner International TechneGroup (Cambridge, UK).
ESR12; Institution: TUW, Austria; Start Date: 2016
|Title: Interactive geometric design under constraints imposed by function and fabrication.
|The goal of this research is to develop methodology for an integrated interactive design approach which takes constraints arising from function and fabrication already in the geometric design phase into account. Starting from our interactive form-finding tool for polyhedral surfaces, we will aim at deeper insight into the extent to which the method of simplifying the constraint variety through sparse quadratic constraints is applicable to other scenarios. As a practically important example, we will develop a prototypical system for interactive control-point based design and approximation with models composed of developable rational B-spline surfaces, with capabilities of handling as-isometric-as-possible deformations of developable NURBS models, designing curved-folded objects, and incorporating constraints on the bending behaviour of the underlying material.
The project will take place at the Institute of Discrete Mathematics and Geometry at TU Wien under the supervision of Helmut Pottmann.
Secondments are planned at U. Strathclyde (Glasgow, UK) and at industrial partner Missler (France).
ESR13; Institution: Evolute, Austria; Start Date: 2016
|Title: Computational design for architecture.
|The general theme of this research are new algorithms and methodology for modelling systems which combine architectural shape modelling with aspects of fabrication, statics and function. We will focus on two novel directions within Architectural Geometry: (i) panel layouts which follow certain patterns (in particular, semi-regular patterns and their duals; Evolute has already encountered polyhedral patterns in their work for the Museum of Islamic Arts in the Louvre, and in their research on circle packing meshes, (ii) support structures such as space frames which do not only follow the panel boundaries, but create themselves 3D patterns which are part of the design and provide increased flexibility to achieve structural stability.
The project will take place at Evolute’s office at Vienna under the supervision of Alexander Schiftner. The PhD will be awarded by TU Wien.
Secondments are planned at INRIA (Sophia-Antipolis, France) and at SINTEF (Oslo, Norway).