Access profile

The doctoral programme in Applied Mathematics is designed for students with abstract reasoning abilities and interest in solving problems, in addition to having good work habits, being dedicated to studying and having a passion for mathematics. Applicants must have a solid background in mathematics. Along this line, the main undergraduate and master’s degrees that will provide access to this doctoral programme are the following:

Undergraduate degrees:
• Bachelor’s degree in Mathematics
• Bachelor’s degree in Physics
Engineering:
• Bachelor’s degree in Computer Science
• Bachelor’s degree in Statistics

Output profile

Doctoral candidates who complete a doctoral degree will have acquired the following competencies, which are needed to carry out quality research (Royal Decree 99/2011, of 28 January, which regulates official doctoral studies):

a) A systematic understanding of the field of study and a mastery of the research skills and methods related to the field.
b) An ability to conceive, design or create, put into practice and adopt a substantial process of research or creation.
c) An ability to contribute to pushing back the frontiers of knowledge through original research.
d) A capacity for critical analysis and an ability to assess and summarise new and complex ideas.
e) An ability to communicate with the academic and scientific community and with society in general as regards their fields of knowledge in the manner and languages that are typical of the international scientific community to which they belong.
f) An ability to foster scientific, technological, social, artistic and cultural progress in academic and professional contexts within a knowledge-based society.

The award of a doctoral degree must equip the graduate for work in a variety of settings, especially those requiring creativity and innovation. Doctoral graduates must have at least acquired the personal skills needed to:

a) Develop in contexts in which there is little specific information.
b) Find the key questions that must be answered to solve a complex problem.
c) Design, create, develop and undertake original, innovative projects in their field.
d) Work as part of a team and independently in an international or multidisciplinary context.
e) Integrate knowledge, deal with complexity and make judgements with limited information.
f) Offer criticism on and intellectually defend solutions.

Finally, with respect to competencies, doctoral students must:
a) have acquired advanced knowledge at the frontier of their discipline and demonstrated, in the context of internationally recognised scientific research, a deep, detailed and well-grounded understanding of theoretical and practical issues and scientific methodology in one or more research fields;
b) have made an original and significant contribution to scientific research in their field of expertise that has been recognised as such by the international scientific community;
c) have demonstrated that they are capable of designing a research project that serves as a framework for carrying out a critical analysis and assessment of imprecise situations, in which they are able to apply their contributions, expertise and working method to synthesise new and complex ideas that yield a deeper knowledge of the research context in which they work;
d) have developed sufficient autonomy to set up, manage and lead innovative research teams and projects and scientific collaborations (both national and international) within their subject area, in multidisciplinary contexts and, where appropriate, with a substantial element of knowledge transfer;
e) have demonstrated that they are able to carry out their research activity in a socially responsible manner and with scientific integrity;
f) have demonstrated, within their specific scientific context, that they are able to make cultural, social or technological advances and promote innovation in all areas within a knowledge-based society;
g) have demonstrated that they are able to participate in scientific discussions at the international level in their field of expertise and disseminate the results of their research activity to audiences of all kinds.

Number of places

20

Duration of studies and dedication regime

Duration
The maximum period of study for full-time doctoral studies is three years, counted from the date of admission to the programme to the date of submission of the doctoral thesis. The academic committee of the doctoral programme may authorise a doctoral candidate to pursue doctoral studies on a part-time basis. In this case, the maximum period of study is five years, counting from the date of admission to the programme to the date of submission of the doctoral thesis. For calculating these periods, the date of admission is considered to be the date of the first enrolment for tutorials, and the date of submission the moment in which the Doctoral School officially deposits the doctoral thesis.

For full-time doctoral candidates, the minimum period of study is two years, counted from the date of an applicant's admission to the programme until the date on which the doctoral thesis is deposited; for part-time doctoral candidates it is four years. When there are justified grounds for doing so, and the thesis supervisor and academic tutor have given their authorisation, doctoral candidates may request that the academic committee of their doctoral programme exempt them from the minimum period of study requirement.

The calculation of periods of study will not include periods of absence due to illness, pregnancy or any other reason provided for in the regulations in force. Students who find themselves in any of these circumstances must notify the academic committee of the doctoral programme, which, where appropriate, must inform the Doctoral School. Doctoral candidates may also temporarily withdraw from the programme for up to one year, and this period may be extended for an additional year. Doctoral candidates who wish to interrupt their studies must submit a justified request to the academic committee of the doctoral programme, which will decide whether or not to approve the request. Each programme will establish conditions for readmission to doctoral studies.

Extension
If full-time doctoral candidates have not applied to deposit their thesis by the end of the three-year period of study, the academic committee of the programme may authorise an extension of up to one year. In exceptional circumstances, a further one-year extension may be granted, subject to the conditions established by the corresponding doctoral programme. In the case of part-time doctoral candidates, an extension of two years may be authorised. In both cases, in exceptional circumstances a further one-year extension may be granted by the Doctoral School's Standing Committee, upon the submission of a reasoned application by the academic committee of the doctoral programme.

Dismissal from the doctoral programme
A doctoral candidate may be dismissed from a doctoral programme for the following reasons:

• The doctoral candidate submitting a justified application to withdraw from the programme.
• The maximum period of study and of extensions thereof ending.
• The doctoral candidate not having enrolled every academic year (unless he or she has been authorised to temporarily withdraw).
• The doctoral candidate failing two consecutive assessments.
• The doctoral candidate having disciplinary proceedings filed against him or her that rule that he or she must be dismissed from the UPC.

Dismissal from the programme implies that doctoral candidates cannot continue studying at the UPC and the closing of their academic record. This notwithstanding, they may apply to the academic committee of the programme for readmission and the committee must reevaluate them in accordance with the criteria established in the regulations.

Organization

• Ventura Capell, Enric

• Burillo Puig, Pep
• Fuste Pratdesaba, Jaume
• Guardia Rubies, Jordi
• Huguet Casades, Gemma
• Martin de la Torre, Pau
• Muñoz Romero, Jose Javier
• Saludes Closa, Jordi
• Serra Albo, Oriol
• Ventura Capell, Enric

• School of Mathematics and Statistics (PROMOTORA)
• Barcelona Supercomputing Center-Centro Nacional de Supercomputación
• Department of Civil and Environmental Engineering
• Department of Mathematics
• Institute of Robotics and Industrial Informatics

Agreements with other institutions

Access profile

The doctoral programme in Applied Mathematics is designed for students with abstract reasoning abilities and interest in solving problems, in addition to having good work habits, being dedicated to studying and having a passion for mathematics. Applicants must have a solid background in mathematics. Along this line, the main undergraduate and master’s degrees that will provide access to this doctoral programme are the following:

Undergraduate degrees:
• Bachelor’s degree in Mathematics
• Bachelor’s degree in Physics
Engineering:
• Bachelor’s degree in Computer Science
• Bachelor’s degree in Statistics

Access requirements

Applicants must hold a Spanish bachelor’s degree or equivalent and a Spanish master’s degree or equivalent, provided they have completed a minimum of 300 ECTS credits on the two degrees (Royal Decree 43/2015, of 2 February)

In addition, the following may apply:

• Holders of an official degree awarded by a university in Spain or any other country in the European Higher Education Area, pursuant to the provisions of Article 16 of Royal Decree 1393/2007, of 29 October, which establishes official university course regulations, who have completed a minimum of 300 ECTS credits on official university degrees, of which at least 60 must be at the master's degree level.
• Holders of an official Spanish bachelor’s degree comprising at least 300 credits, as provided for by EU regulations. Holder of degrees of this kind must complete bridging courses unless the curriculum of the bachelor’s degree in question included research training credits equivalent in value to those which would be earned on a master's degree.
• Holders of an official university qualification who, having passed the entrance examination for specialised medical training, have completed at least two years of a training course leading to an official degree in a health-sciences specialisation.
• Holders of a degree issued under a foreign education system. In these cases, homologation is not required, but the UPC must verify that the degree certifies a level of training equivalent to an official Spanish master's degree and qualifies the holder for admission to doctoral studies in the country where it was issued. Admission on this basis does not imply homologation of the foreign degree or its recognition for any purpose other than admission to doctoral studies.
• Holders of a Spanish doctoral qualification issued under previous university regulations.

Note 1: Doctoral studies entrance regulations for holders of an undergraduate degree awarded before the introduction of the EHEA (CG 47/02 2014)

Note 2: Governing Council Decision 64/2014, which approves the procedure and criteria for assessing the fulfilment of academic admission requirements for doctoral studies by holders of non-homologated foreign degrees (CG 25/03 2014)

Admission criteria and merits assessment

During the admission process, the following elements will be considered (with their associated weights):

• Academic transcript from the applicant’s undergraduate and master’s programmes (70%).

• CV (10%).

• Motivation letter and/or personal interview (10%).

• Two letters of recommendation from professors/researchers (10%).

These criteria will be published on the programme’s web page. The final score will be used as the admission criteria in the case that demand exceeds the number of available seats.

There is no provision for entrance exams or any specific entrance tests. If candidates’ backgrounds in mathematics or the subject of the candidates’ doctoral theses so require, they will be required to take bridging courses in the master’s programme in Advanced Mathematics and Mathematical Engineering (MAMME), the official master’s programme offered by the FME that is associated with this doctoral programme.

Training complements

The academic committee for the programme may require that doctoral students pass specific bridging courses. In such cases, the committee will keep track of the bridging courses completed and establish appropriate criteria to limit their duration. The courses could involve training in research or transversal education, but in no case will candidates be required to enrol in 60 or more ECTS credits.

Depending on the doctoral student activity report, the programme’s Academic Committee may propose measures, in addition to those established by current regulations, that would disassociate candidates who do not meet the established requisites.

Additionally, students who require it based on their previous education and the subject of their thesis, will have to take courses from the master’s programme in Advanced Mathematics and Mathematical Engineering (MAMME) offered by the School of Mathematics and Statistics. A detailed list of the subjects offered is listed hereafter:

Enrolment period for new doctoral students

All up-to-date information can be found on the FME’s web page: https://fme.upc.edu/ca/curs-actual/matricula/estudiants-de-doctorat

More information at the registration section for new doctoral students

Enrolment period

All up-to-date information can be found on the FME’s web page: https://fme.upc.edu/ca/curs-actual/matricula/estudiants-de-doctorat

More information at the general registration section

Procedure for the preparation and defense of the research plan

Doctoral candidates must submit a research plan, which will be included in their doctoral student activity report, before the end of the first year. The plan may be improved over the course of the doctoral degree. It must be endorsed by the tutor and the supervisor, and it must include the method that is to be followed and the aims of the research.

At least one of these annual assessments will include a public presentation and defence of the research plan and work done before a committee composed of three doctoral degree holders, which will be conducted in the manner determined by each academic committee. The examination committee awards a Pass or Fail mark. A Pass mark is a prerequisite for continuing on the doctoral programme. Doctoral candidates awarded a Fail mark must submit a new research plan for assessment by the academic committee of the doctoral programme within six months.

The committee assesses the research plan every year, in addition to all of the other activities in the doctoral student activity report. Doctoral candidates who are awarded two consecutive Fail marks for the research plan will be obliged to definitely withdraw from the programme.

If they change the subject of their thesis, they must submit a new research plan.

Formation activities

Procedure for assignment of tutor and thesis director

The academic committee of the doctoral programme assigns a thesis supervisor to each doctoral candidate when they are admitted or enrol for the first time, taking account of the thesis supervision commitment referred to in the admission decision.

The thesis supervisor will ensure that training activities carried out by the doctoral candidate are coherent and suitable, and that the topic of the candidate’s doctoral thesis will have an impact and make a novel contribution to knowledge in the relevant field. The thesis supervisor will also guide the doctoral candidate in planning the thesis and, if necessary, tailoring it to any other projects or activities undertaken. The thesis supervisor will generally be a UPC professor or researcher who holds a doctoral degree and has documented research experience. This includes PhD-holding staff at associated schools (as determined by the Governing Council) and UPC-affiliated research institutes (in accordance with corresponding collaboration and affiliation agreements). When thesis supervisors are UPC staff members, they also act as the doctoral candidate’s tutor.

PhD holders who do not meet these criteria (as a result of their contractual relationship or the nature of the institution to which they are attached) must be approved by the UPC Doctoral School's Standing Committee in order to participate in a doctoral programme as researchers with documented research experience.

The academic committee of the doctoral programme may approve the appointment of a PhD-holding expert who is not a UPC staff member as a candidate’s thesis supervisor. In such cases, the prior authorisation of the UPC Doctoral School's Standing Committee is required. A UPC staff member who holds a doctoral degree and has documented research experience must also be proposed to act as a co-supervisor, or as the doctoral candidate’s tutor if one has not been assigned.

A thesis supervisor may step down from this role if there are justified reasons (recognised as valid by the committee) for doing so. If this occurs, the academic committee of the doctoral programme will assign the doctoral candidate a new thesis supervisor.

Provided there are justified reasons for doing so, and after hearing any relevant input from the doctoral candidate, the academic committee of the doctoral programme may assign a new thesis supervisor at any time during the period of doctoral study.

If there are academic reasons for doing so (an interdisciplinary topic, joint or international programmes, etc.) and the academic committee of the programme gives its approval, an additional thesis supervisor may be assigned. Supervisors and co-supervisors have the same responsibilities and academic recognition.

The maximum number of supervisors of a doctoral thesis is two: a supervisor and a co-supervisor.

For theses carried out under a cotutelle agreement or as part of an Industrial Doctorate, if necessary and if the agreement foresees it this maximum number of supervisors may not apply. This notwithstanding, the maximum number of supervisors belonging to the UPC is two.

More information at the PhD theses section

Permanence

The academic committee of the programme may authorise an extension of up to one year for full-time doctoral candidates who have not applied to deposit their thesis by the end of the three-year period of study, in the terms outlined in the Academic Regulations for Doctoral Studies of the Universitat Politècnica de Catalunya. In the case of part-time candidates, an extension of two years may be authorised. In both cases, in exceptional circumstances a further one-year extension may be granted by the Doctoral School's Standing Committee, upon the submission of a reasoned application by the academic committee of the doctoral programme.

A doctoral candidate may be dismissed from a doctoral programme for the following reasons:

• The doctoral candidate submitting a justified application to withdraw from the programme.
• The maximum period of study and of extensions thereof ending.
• The doctoral candidate not having enrolled every academic year (unless he or she has been authorised to temporarily withdraw).
• The doctoral candidate failing two consecutive assessments.
• The doctoral candidate having disciplinary proceedings filed against him or her that rule that he or she must be dismissed from the UPC.

Dismissal from the programme implies that doctoral candidates cannot continue studying at the UPC and the closing of their academic record. This notwithstanding, they may apply to the academic committee of the programme for readmission and the committee must reevaluate them in accordance with the criteria established in the regulations.

International Mention

The doctoral degree certificate may include International Doctorate mention. In this case, the doctoral candidate must meet the following requirements:

a) During the period of study leading to the award of the doctoral degree, the doctoral candidate must have spent at least three months at a respected higher education institution or research centre outside Spain to complete courses or do research work. The stays and activities carried out must be endorsed by the thesis supervisor and authorised by the academic committee of the programme. The candidate must provide a certifying document issued by the person responsible for the research group of the body or bodies where the stay or activity was completed. This information will be added to the doctoral student’s activity report.
b) Part of the thesis (at least the summary and conclusions) must be written and presented in one of the languages commonly used for science communication in the relevant field of knowledge, which must not be an official language of Spain. This rule does not apply to stays and reports in Spanish or to experts from Spanish-speaking countries.
c) At least two PhD-holding experts belonging to a higher education institution or research centre outside Spain must have issued officially certified reports on the thesis.
d) The thesis examination committee must have included at least one PhD-holding expert from a higher education or research institution outside Spain who was not responsible for the candidate’s stay abroad (point a) above).
e) The thesis defence must have taken place on UPC premises or, in the case of joint programmes, at the location specified in the collaboration agreement.

List of authorized thesis for defense

• FINOGINA, TAMARA: Coercion-resistant cast-as-intended verifiability in electronic voting systems
  
  Author: FINOGINA, TAMARA
  Thesis file: (contact the Doctoral School to confirm you have a valid doctoral degree and to get the link to the thesis)
  Programme: DOCTORAL DEGREE IN APPLIED MATHEMATICS
  Department: Department of Mathematics (MAT)
  Mode: Normal
  Deposit date: 26/07/2023
  Reading date: 02/10/2023
  Reading time: 11:00
  Reading place: Sala d'Actes de la Facultat de Matemàtiques i Estadística, Edifici U, Campus Sud
  Thesis director: HERRANZ SOTOCA, JAVIER
  Committee:
       PRESIDENT: RONNE, PETER BROWNE
       SECRETARI: VILLAR SANTOS, JORGE LUIS
       VOCAL: HAENNI, ROLF
  Thesis abstract: One of the most common fears regarding electronic voting is that a voting device will disregard the voter's intent and cast a different vote instead. An undetectable attack like that on a large scale will allow the adversary to control the election result completely. Therefore, the cast-as-intended verification, which ensures that the ballot contains the voter's choice and not something else, is crucial. Another common fear when introducing electronic voting is coercion, which captures a variety of ways the coercer can use to prevent voters from expressing their will. Hence, coercion resistance is a valuable property of electronic voting as well. One particularly challenging task is to find a trade-off between ensuring a voter cannot be coerced and, at the same time, preventing a malicious voting device from cheating. This thesis explores this trade-off to find how we can provide coercion-resistant cast-as-intended verification. The contributions can be roughly divided into three parts: (1) study in the standard settings, (2) exploration of post-quantum cryptography, and (3) practical constructions and search for the limitations of both properties. In the first part, we give an extensive overview of the current state of the art in electronic voting literature regarding those properties. Then, we put forward two formal definitions for achieving coercion-resistant cast-as-intended verification in settings without pre-exchanged data. After that, we present two practical constructions and prove their security under the proposed definitions. We also show the efficiency of our proposals by providing proof of the concept implementations. In the second part, we switch to post-quantum settings and identify the usability issues rooted in the lattice-based math affecting both proposed solutions. To address those issues, we present a generic transformation that departs from an interactive zero-knowledge system (that might require multiple re-runs to complete the protocol) and obtains a 3-move zero-knowledge system (without re-runs). The transformation combines the well-known Fiat-Shamir technique with several initially exchanged messages. The resulting 3-move system enjoys honest-verifier zero-knowledge and can be easily turned into a fully deniable proof using standard methods. In the final part, we focus on the practical aspects of the coercion-resistant cast-as-intended verification. First, we present the case of a computationally limited voter, which we consider the most realistic. We show that even a computationally limited voter can enjoy coercion-resistant cast-as-intended verification, but a help of a simple aid device for nonce generation is required. Also, we demonstrate that our generic definition easily adapts to the constraints of the limited voter. After that, we present ongoing work that focuses on the cases of extreme coercion based on new and unexplored mechanisms such as delay encryption and blockchain. We show an advanced coercive attack on our first construction and describe an improvement to the second solution that reduces the number of interactions to an optimal three rounds. To summarize, we start by studying coercion-resistant cast-as-intended verification in standard settings, which results in formal definitions and two practical solutions. Then we move into the post-quantum world, where we learn that an extra step is needed to preserve the usability of our previously proposed constructions, which results in the generic transformation to avoid protocol re-runs. After that, we concentrate on a computationally limited voter, which leads to another simple solution and shows the adaptability of our original definitions. Finally, we explore the extreme coercion threats, which result in a new coercion attack on the first construction and upgrade of the second solution.
  
• MARTÍNEZ PINILLA, RAMIRO: Lattice-Based Zero-Knowledge Proofs of Knowledge
  
  Author: MARTÍNEZ PINILLA, RAMIRO
  Thesis file: (contact the Doctoral School to confirm you have a valid doctoral degree and to get the link to the thesis)
  Programme: DOCTORAL DEGREE IN APPLIED MATHEMATICS
  Department: Department of Mathematics (MAT)
  Mode: Normal
  Deposit date: 14/07/2023
  Reading date: 29/09/2023
  Reading time: 11:00
  Reading place: Sala d'Actes de l'FME, Edifici U, Campus Sud
  Thesis director: MORILLO BOSCH, MARIA PAZ
  Committee:
       PRESIDENT: RÀFOLS SALVADOR, CARLA
       SECRETARI: HERRANZ SOTOCA, JAVIER
       VOCAL: GUASCH CASTELLÓ, SANDRA
  Thesis abstract: The main goal of this dissertation is to develop new lattice-based cryptographic schemes. Most of the cryptographic protocols that each and every one of us use on a daily basis are only secure under the assumption that two mathematical problems, namely the discrete logarithm on elliptic curves and the factorization of products of two primes, are computationally hard. That is believed to be true for classical computers, but quantum computers would be able to solve these problems much more efficiently, demolishing the foundations of plenty of cryptographic constructions. This reveals the importance of post-quantum alternatives, cryptographic schemes whose security relies on different problems intractable for both classical and quantum computers. The most promising family of problems widely believed to be hard for quantum computers are lattice-based problems. We increase the supply of lattice-based tools providing new Zero-Knowledge Proofs of Knowledge for the Ring Learning With Errors (RLWE) problem, perhaps the most popular lattice-based problem. Zero-Knowledge proofs are protocols between a prover and a verifier where the prover convinces the verifier of the validity of certain statements without revealing any additional relevant information. Our proofs extend the literature of Stern-based proofs, following the techniques presented by Jacques Stern in 1994. His original idea involved a code-based problem, but it has been reiteratedly improved and generalized to be used with lattices. We illustrate our proposal defining a variant of the commitment scheme, a cryptographic primitive that allows us to ensure some message was already determined at some point without revealing it until a future time, defined by Benhamouda et al. in ESORICS 2015, and proving in Zero-Knowledge the knowledge of a valid opening. Most importantly we also show how to prove that the message committed in one commitment is a linear combination, with some public coefficients, of the committed messages from two other commitments, again without revealing any further information about the messages. Finally, we also present a Zero-Knowledge proof analogous to the previous one but for multiplicative relations, something much more involved that allows us to prove any arithmetic circuit. We give first an interactive version of these proofs and then show how to construct a non-interactive one. We diligently prove that both the commitment and the companion Zero-Knowledge Proofs of Knowledge are secure under the assumption of the hardness of the underlying lattice problems. Furthermore, we specifically develop such proofs so that the arising conditions can be directly used to compute parameters that satisfy them. This way we provide a general method to instantiate our commitment and proofs with any desired security level. Thanks to this practical approach we have been able to implement all the proposed schemes and benchmark the prototype implementation with actually secure parameters, which allows us to obtain meaningful results and compare its performance with the existing alternatives. Moreover, provided that multiplication of polynomials in the quotient ring Z¿[x]/<xn+1>, with p prime and n a power of two, is the most basic operation when working with ideal lattices we comprehensively study what are the necessary and sufficient conditions needed for applying (a generalized version of) the Fast Fourier Transform (FFT) to obtain an efficient multiplication algorithm in quotient rings as Z¿[x]/<xn-a> (where we consider any positive integer m and generalize the quotient), as we think it is of independent interest. We believe such a theoretical analysis is fundamental to be able to determine when a given generalization can also be applied to design an efficient multiplication algorithm when the FFT is not defined for the ring we are considering. That is the case of the rings used for the commitment and proofs described before, where only a partial FFT is available.
  

Last update: 27/09/2023 04:45:27.

List of lodged theses

Last update: 27/09/2023 04:30:23.

List of defended theses by year

• APARICIO ESTREMS, GUILLERMO: Metric-aware optimization of high-order meshes for curved adaptivity
  
  Author: APARICIO ESTREMS, GUILLERMO
  Thesis file: (contact the Doctoral School to confirm you have a valid doctoral degree and to get the link to the thesis)
  Programme: DOCTORAL DEGREE IN APPLIED MATHEMATICS
  Department: (DECA)
  Mode: Normal
  Reading date: 26/04/2023
  Thesis director: ROCA NAVARRO, FRANCISCO JAVIER | GARGALLO PEIRO, ABEL
  

  Committee:
       PRESIDENT: MOXEY, DAVID
       SECRETARI: SARRATE RAMOS, JOSE
       VOCAL: MITTAL, KETAN
  Thesis abstract: To enhance the simulation accuracy when the solution presents sharp curved features, the community of high-order methods has started to curve not only the boundary but also the interior of unstructured high-order meshes. Many of these approaches contribute to curved high-order adaptivity based on error estimators. The error estimators determine a discrete metric that is used to modify the curved high-order mesh. Unfortunately, although all these approaches must modify the mesh coordinates, no approach considers metric-aware optimization of curved high-order meshes for a high-polynomial degree. Furthermore, the existing approaches neither explicitly enforce unitary Riemannian measures for all mesh entities nor specifically devise a specific-purpose solver for curved sharp features. To address these issues, this thesis aims to demonstrate metric-aware optimization of high-order meshes on curved geometry with the coordinates as design variables. To this end, it proposes the following contributions. First, to verify and optimize the stretching and alignment deviation between the mesh and an analytic metric, we define a differentiable shape distortion measure for curved high-order meshes. Second, to enforce unitary Riemannian measures of the mesh entities, we define a differentiable size-shape distortion measure for curved high-order meshes. Third, to efficiently minimize with tight tolerances a point-wise metric-aware distortion measure for curved high-order meshes, we devise a specific-purpose solver. Fourth, to apply Newton¿s method for the distortion minimization of meshes equipped with a discrete target metric, we derive up to second-order the derivatives for a high-order metric interpolation. Finally, to also match curved boundaries, we derive up to second-order the derivatives for an implicit CAD representation. In conclusion, this thesis demonstrates metric-aware optimization of high-order meshes on curved geometry. To this end, it proposes a novel metric- and geometry- aware mesh optimization framework and a specific-purpose optimization solver. These novelties will contribute to error-driven curved high-order adaptivity. Hence, they will help to enhance the simulation accuracy for solutions presenting sharp curved features.
  

• BARCELÓ MERCADER, JORDI: Mathematical and computational modeling of flexoelectricity at fixed and moving interfaces, fracture surfaces and contact
  
  Author: BARCELÓ MERCADER, JORDI
  Thesis file: (contact the Doctoral School to confirm you have a valid doctoral degree and to get the link to the thesis)
  Programme: DOCTORAL DEGREE IN APPLIED MATHEMATICS
  Department: (DECA)
  Mode: Normal
  Reading date: 08/09/2023
  Thesis director: ARIAS VICENTE, IRENE
  

  Committee:
       PRESIDENT: RÓDENAS GARCÍA, JUAN JOSÉ
       SECRETARI: RODRIGUEZ FERRAN, ANTONIO
       VOCAL: PANDOLFI, ANNA MARINA
  Thesis abstract: Flexoelectricity is a two-way coupling between strain gradient and polarisation or strain and polarization-gradient. Harnessing flexoelectricity as a functional property requires gradient engineering. This is a major step from the uniform-field configurations of piezoelectric devices, since piezoelectricity couples strains and polarisation. Gradients can be generated by non-uniform deformation, such as bending and torsion, or through non-uniform material distributions, electrode configurations and complex geometries. Gradient engineering thus requires accurate quantitative modelling tools capable of efficiently dealing with all these elements with high-physical fidelity in order to build engineering tools for the design of flexoelectric devices. From a mathematical point of view, flexoelectricity is modelled as a system of coupled high-order PDEs. This poses important challenges to computationally solving boundary value problems in general multi-material samples with complex geometries and electrode configurations.In this thesis, a theoretical and computational model for flexoelectricity in the presence of interfaces has been developed and implemented in the context of the hierarchical B-spline immersed boundary approach. This framework has been used to study physical material interfaces, as well as fictitious interfaces such as generalised periodicity unit cell boundaries. The former has been used in multimaterial symmetry-breaking arrangements up-scaling flexoelectricity in electromechanical devices. For the latter case, an elegant and efficient implementation making use of the periodicity of the B-spline bases functions has been derived and used for the design and analysis of flexoelectric architected periodic lattice metamaterials. Moving interfaces such as cracks and ferroelectric domain boundaries have also been studied by coupling phase-field models for fracture and ferroelectric microstructure accounting for flexoelectricity. Finally, flexoelectricity has been shown as a plausible cause for the asymmetric tribology observed in ferroelectrics in tight collaboration with experimentalists.
  

• CHAHARE, NIMESH RAMESH: Mechanics of Epithelial tissue subjected to controlled pressure
  
  Author: CHAHARE, NIMESH RAMESH
  Thesis file: (contact the Doctoral School to confirm you have a valid doctoral degree and to get the link to the thesis)
  Programme: DOCTORAL DEGREE IN APPLIED MATHEMATICS
  Department: (DECA)
  Mode: Normal
  Reading date: 20/06/2023
  Thesis director: ARROYO BALAGUER, MARINO | TREPAT GUIXER, XAVIER
  

  Committee:
       PRESIDENT: TRIVEDI, VIKAS
       SECRETARI: MUÑOZ ROMERO, JOSE JAVIER
       VOCAL: SUZANNE, MAGALI
  Thesis abstract: Epithelial sheets form specialized 3D structures suited to their physiological roles, such as branched alveoli in the lungs, tubes in the kidney, and villi in the intestine. To generate and maintain these structures, epithelia must undergo complex 3D deformations across length and time scales. How epithelial shape arises from active stresses, viscoelasticity, and luminal pressure remains poorly understood. To address this question, we developed a microfluidic chip and a computational framework to engineer 3D epithelial tissues with controlled shape and pressure. In the setup, an epithelial monolayer is grown on a porous surface with circular low adhesion zones. On applying hydrostatic pressure, the monolayer delaminates into a spherical cap from the circular zone. This simple shape allows us to calculate epithelial tension using Laplace's law. Through this approach, we subject the monolayer to a range of lumen pressures at different rates and hence probe the relation between strain and tension in different regimes while computationally tracking actin dynamics and their mechanical effect at the tissue scale. Slow pressure changes relative to the actin dynamics allow the tissue to accommodate large strain variations. However, under sudden pressure reductions, the tissue develops buckling patterns and folds with different degrees of symmetry-breaking to store excess tissue area. These insights allow us to pattern epithelial folds through rationally directed buckling. Our study establishes a new approach for engineering epithelial morphogenetic events.
  

• COLTRARO IANNIELLO, FRANCO: Robotic manipulation of cloth: mechanical modeling and perception
  
  Author: COLTRARO IANNIELLO, FRANCO
  Thesis link: http://hdl.handle.net/10803/688226
  Programme: DOCTORAL DEGREE IN APPLIED MATHEMATICS
  Department: Department of Mathematics (MAT)
  Mode: Normal
  Reading date: 30/03/2023
  Thesis director: AMOROS TORRENT, JAUME | ALBERICH CARRAMIÑANA, MARIA
  

  Committee:
       PRESIDENT: GONZALEZ DIAZ, ROCIO
       SECRETARI: SUSIN SANCHEZ, ANTONIO
       VOCAL: BRIOT, SEBASTIEN
  Thesis abstract: In this work we study various mathematical problems arising from the robotic manipulation of cloth. First, we develop a locking-free continuous model for the physical simulation of inextensible textiles. We present a novel 'finite element' discretization of our inextensibility constraints which results in a unified treatment of triangle and quadrilateral meshings of the cloth. Next, we explain how to incorporate contacts, self-collisions and friction into the equations of motion, so that frictional forces and inextensibility and collision constraints may be integrated implicitly and without any decoupling. We develop an efficient 'active-set' solver tailored to our non-linear problem which takes into account past active constraints to accelerate the resolution of unresolved contacts and moreover can be initialized from any non-necessarily feasible point. Then, we embark ourselves in the empirical validation of the developed model. We record in a laboratory setting --with depth cameras and motion capture systems-- the motions of seven types of textiles (including e.g. cotton, denim and polyester) of various sizes and at different speeds and end up with more than 80 recordings. The scenarios considered are all dynamic and involve rapid shaking and twisting of the textiles, collisions with frictional objects and even strong hits with a long stick. We then, compare the recorded textiles with the simulations given by our inextensible model, and find that on average the mean error is of the order of 1 cm even for the largest sizes (DIN A2) and the most challenging scenarios. Furthermore, we also tackle other problems relevant to robotic cloth manipulation, such as cloth perception and classification of its states. We present a reconstruction algorithm based on Morse theory that proceeds directly from a point-cloud to obtain a cellular decomposition of a surface with or without boundary: the results are a piecewise parametrization of the cloth surface as a union of Morse cells. From the cellular decomposition the topology of the surface can be then deduced immediately. Finally, we study the configuration space of a piece of cloth: since the original state of a piece of cloth is flat, the set of possible states under the inextensible assumption is the set of developable surfaces isometric to a fixed one. We prove that a generic simple, closed, piecewise regular curve in space can be the boundary of only finitely many developable surfaces with nonvanishing mean curvature. Inspired on this result we introduce the dGLI cloth coordinates, a low-dimensional representation of the state of a piece of cloth based on a directional derivative of the Gauss Linking Integral. These coordinates --computed from the position of the cloth's boundary-- allow to distinguish key qualitative changes in folding sequences.
  

• FONT I REVERTER, JORDI: Mathematical and computational modeling of active cellular flows
  
  Author: FONT I REVERTER, JORDI
  Thesis file: (contact the Doctoral School to confirm you have a valid doctoral degree and to get the link to the thesis)
  Programme: DOCTORAL DEGREE IN APPLIED MATHEMATICS
  Department: (DECA)
  Mode: Normal
  Reading date: 08/06/2023
  Thesis director: ARROYO BALAGUER, MARINO
  

  Committee:
       PRESIDENT: ETIENNE, JOCELYN
       SECRETARI: SAEZ VIÑAS, PABLO
       VOCAL: HERNÁNDEZ MACHADO, AURORA
  Thesis abstract: During development, cellular tissues undergo dramatic reconfigurations as a result oforganized flows driven by active forces. Depending on the system, cellular flows and activeforces can be understood from a continuum perspective that views tissues as active fluids, whoseeffective properties depend on processes at cellular scales. Here, we develop a mathematicaland computational modeling framework to simulate and understand cellular flows of thin tissuelayers driven by active force densities, bulk tension fields, edge line tension fields, and patternsof proliferation/extrusion. This framework is capable of describing interfacial active fluidson curved geometries or in deformable domains. We first describe the mathematical models,present the finite element discretization, verify our implementation against analytical solutions,and examine tissue dynamics under prototypical active patterns. We then apply this frameworkto understand two morphogenetic cellular flows. First, we examine supra-cellular migrationby fountain flows within planar cell clusters. This mode of supra-cellular motion is quiteprevalent but its ability to drive efficient migration is unclear due to the existence of conflictingretrograde and anterograde flows organized around two vortices, both in contact with thesubstrate. We find that efficient locomotion is achieved by patterned friction and/or cellular selfpropulsion,both of which being natural consequences of the mechanism of contact inhibitionof locomotion. Second, we use our framework to infer the active forces driving morphogeneticflows on a spherical surface during gastrulation in zebrafish embryos. Starting from individualcell tracking data, we estimate density and velocity fields, and using an inverse hydrodynamicmethod, we infer first the active force density, and then the previously unmapped activetension field in the bulk of the interfacial tissue. We finally provide conclusions and proposeideas to continue from here.
  

• GUTIÉRREZ TERRADILLOS, ARMANDO: Theta correspondences and arithmetic intersections
  
  Author: GUTIÉRREZ TERRADILLOS, ARMANDO
  Thesis file: (contact the Doctoral School to confirm you have a valid doctoral degree and to get the link to the thesis)
  Programme: DOCTORAL DEGREE IN APPLIED MATHEMATICS
  Department: Department of Mathematics (MAT)
  Mode: Normal
  Reading date: 26/05/2023
  Thesis director: ROTGER CERDÀ, VICTOR | FREIXAS I MONTPLET, GERARD
  

  Committee:
       PRESIDENT: MOLINA BLANCO, SANTIAGO
       SECRETARI: RIO DOVAL, ANA
       VOCAL: LEMMA, FRANCESCO
  Thesis abstract: The thesis is mainly divided into two parts. In essence, the first one is an extension of the paper [Ter22]. Using the regularized Siege-Weil formula of [GQT14] we obtain an explicit expression for the truncated integral of the Siegel theta function. The main application of this result is an explicit formula for the integral of the logarithm of the Borcherds forms. The result involves different zeta values and coefficients of Eisenstein series. It completes the work of [Kud03]. Besides the aforementioned formula for the integral of the theta function, a detailed analysis of the Siegel theta function near the infinity is required. Chapter two is an extension of the work with Antonio Cauchi in [CT]. The purpose of this part is twofold. On the one hand, under some conditions, we show that the multiplicity of the Shalika model of unramified representations for the group GU(2, 2) is one. Using this result and following the ideas of [Sak06], we are able to find an expression of the Shalika functional in terms of the Satake parameter of a representation in GSp4. On the other hand, we use this result and to establish a relationship between a zeta integral for a group GU(2,2) and a twisted standard L-function of GSp4, where the relation between the involved automorphic representations is given by the theta correspondence.
  

• JIMÉNEZ RAMOS, ALBERT: Nodal distributions on the high-dimensional simplex for high-order interpolation and integration
  
  Author: JIMÉNEZ RAMOS, ALBERT
  Thesis file: (contact the Doctoral School to confirm you have a valid doctoral degree and to get the link to the thesis)
  Programme: DOCTORAL DEGREE IN APPLIED MATHEMATICS
  Department: (DECA)
  Mode: Normal
  Reading date: 28/06/2023
  Thesis director: ROCA NAVARRO, FRANCISCO JAVIER | GARGALLO PEIRO, ABEL
  

  Committee:
       PRESIDENT: PERSSON, PER-OLOF
       SECRETARI: FERNANDEZ MENDEZ, SONIA
       VOCAL: RAPETTI GABELLINI, FRANCESCA
  Thesis abstract: To simulate unsteady phenomena on complex moving geometry, computational scientists and engineers have been interested in unstructured space-time discretizations. These space-time discretizations aim to overcome some issues of standard time marching methods by considering a unique mesh that discretizes the steady space-time geometry described by the moving spatial geometry. Unfortunately, they have not been widely adopted for 3D unsteady high-fidelity simulations because many fundamental capabilities related to high-order approximation to geometry and solution must still be developed in 4D. These capabilities include performing high-order numerical interpolation and integration on complex space-time geometry. To address these issues, this thesis aims to demonstrate interpolation-aware optimization of nodal distributions on the high-dimensional simplex constrained to fulfill either feasible interpolation or feasible integration with the point coordinates as design variables. To this end, it proposes the following contributions. First, to interpolate a curved subdivision model obtained from a linear triangular mesh, we devise an equispaced nodal geometry representation method. Second, to additionally preserve the required simulation intent, we devise a nodal modeling method. Third, to estimate the interpolation error of a nodal distribution, we propose a point refinement method. Fourth, to explore the nodal distributions that are the heuristically best local minima of an interpolation error proxy, we propose a specific-purpose optimization method. Fifth, to minimize the interpolation error of an initial nodal distribution, we propose a constrained optimization method. Finally, to enforce small interpolation error and exact integration, we propose a constrained optimization problem. In conclusion, this thesis demonstrates interpolation-aware optimization of nodal distributions on the high-dimensional simplex for feasible interpolation or integration. To this end, it proposes novel nodal methods to model and represent the simulation intent and to explore and optimize nodal distributions. These novelties will contribute to performing high-order numerical interpolation and integration on complex 4D geometry. Hence, they will help to exploit the benefits of high-fidelity 4D space-time simulation for 3D moving complex geometries.
  

• LARRAURI BORROTO, LÁZARO ALBERTO: First Order Logic of Random Sparse Structures
  
  Author: LARRAURI BORROTO, LÁZARO ALBERTO
  Thesis file: (contact the Doctoral School to confirm you have a valid doctoral degree and to get the link to the thesis)
  Programme: DOCTORAL DEGREE IN APPLIED MATHEMATICS
  Department: Department of Mathematics (MAT)
  Mode: Normal
  Reading date: 03/03/2023
  Thesis director: NOY SERRANO, MARCOS
  

  Committee:
       PRESIDENT: DAWAR, ANUJ
       SECRETARI: ATSERIAS PERI, ALBERT
       VOCAL: FERAY, VALENTIN
  Thesis abstract: This work is dedicated to the study several models of random structures from the perspective of first-order logic. We prove that the asymptotic probabilities of first-order statements converge in a general model of random structures with linear density, extending previous results by Lynch. Additionally, we give an application of this result to the random SAT problem. We also inspect the set of limiting probabilities of first-order properties in sparse binomial graphs, binomial d-uniform hypergraphs and graphs with given degree sequences. In particular, we characterize the conditions under which this set of asymptotic probabilities is dense in the interval [0, 1]. Finally, we introduce the question of whether preservation theorems, namely Los-Tarski Theorem and Lyndon¿s Theorem, hold in a probabilistic sense in various models of random graphs. We obtain several positive results in different regimes of the binomial random graph and uniform graphs from addable minor-closed classes.
  

• MIRZA, WALEED AHMAD: A theoretical and computational study of the active self-organization of nematic patterns in thin cytoskeleton layers and their effect on curvature.
  
  Author: MIRZA, WALEED AHMAD
  Thesis file: (contact the Doctoral School to confirm you have a valid doctoral degree and to get the link to the thesis)
  Programme: DOCTORAL DEGREE IN APPLIED MATHEMATICS
  Department: (DECA)
  Mode: Normal
  Reading date: 16/02/2023
  Thesis director: ARROYO BALAGUER, MARINO
  

  Committee:
       PRESIDENT: TURLIER, HERVÉ
       SECRETARI: ORIOLA SANTANDREU, DAVID
       VOCAL: ERZBERGER, ANNA
  Thesis abstract: The structure and dynamics of important biological systems, ranging from cytoskeletal gels to tissues, are controlled by an interplay between activity, dissipation, nematic order, density, and geometry. In particular, the actin cytoskeleton is remarkably adaptable and versatile and self-organizes into a variety of architectures, notably dense nematic structures. Examples of such structures are contractile rings to accomplish cell division and wound healing, or stress fibers playing an essential role in cell spreading, force generation, and migration. However, the mechanisms leading to dense nematic bundles remain poorly understood and to our knowledge, no prior theory explains their mesoscale self-assembly. Previous hydrodynamic approaches to active nematic systems have focused on incompressible liquid crystals. However, these models are not pertinent to actin gels, which are highly porous and exhibit very large density variations controlling activity gradients and active flows. Furthermore, porous actin networks can exhibit extended isotropic states without defects, and nematic order is presumably induced by flows and active mechanisms rather than by crowding. Finally, little attention has been paid to the formulation of active nematics on deformable surfaces and to a general computational framework to address such complex problems. Finally, we lack a unified understanding of actin network polymorphism, and more specifically of the physical mechanisms that enable a single active material to adopt very different network architectures with distinct cellular functions. To address these challenges, we develop a variety of theoretical and computational models for active nematic gels. In part I of the thesis, we focus on active nematic gels confined to a plane. We develop a transparent modeling framework for density-dependent active nemato-hydrodynamics based on Onsager¿s variational formalism, according to which the dynamics result from a competition between free-energy release, dissipation and activity. We also develop a numerical finite element method based on a time-incremental version of Onsager's formalism, which inherits the nonlinear stability and thermodynamic consistency of the continuum principle. We use this numerical approach to study the assembly of a contractile ring during wound healing and the defect dynamics in a confined colony of contractile cells. We next study the active self-assembly of nematic patterns from a uniform and quiescent gel using linearized theory and nonlinear simulations. We establish the conditions for nematic bundle formation and how active gel parameters control the architecture, connectivity and dynamics of self-organized patterns of nematic bundles. Finally, using discretenetwork simulations, we substantiate the major requirements for active nematic self-organization according to our theory. We thus provide a framework to understand the emergence and dynamics of mesoscale nematic organizations in actin networks. In part II of the thesis, we develop a general model for active nematic gels on deformable surfaces. Again, Onsager's nonlinear formalism provides a simple method to transparently develop complex models. The resulting system tight couples shape dynamics, nematic dynamics, density dynamics, and interfacial hydrodynamics. We exercise this model to understand the self-organization of the cytokinetic ring using an axisymmetric numerical formulation. Finally, we provide a general 3D computational approach and apply it to an inextensible active liquid crystalline deformable surface. We examine the interplay between the motion of nematic defects and shape.
  

• MOHAMMADI, HOSSEIN: Mathematical and computational modeling of geometrically nonlinear electromechanical
  
  Author: MOHAMMADI, HOSSEIN
  Thesis file: (contact the Doctoral School to confirm you have a valid doctoral degree and to get the link to the thesis)
  Programme: DOCTORAL DEGREE IN APPLIED MATHEMATICS
  Department: (DECA)
  Mode: Normal
  Reading date: 16/06/2023
  Thesis director: ARIAS VICENTE, IRENE
  

  Committee:
       PRESIDENT: LATORRE FERRUS, MARCOS
       SECRETARI: RODRIGUEZ FERRAN, ANTONIO
       VOCAL: SHARMA, PRADEEP
  Thesis abstract: The flexoelectric effect, the two-way linear coupling between strain gradient and electric polarization (direct flexoelectricity) or electric field gradient and strain (converse flexoelectricity) universally present in any dielectric, has given rise to a new research area referred to as strain gradient engineering in which in contrast to the conventional wisdom that views strain gradients as undesirable, researchers seek to mobilize strain gradients in a smart way to design sensors, actuators, and energy harvesting devises for next-generation micro/nano electromechanical systems.Ionic crystals with high dielectricity, such as ferroelectric perovskites at their paraelectric phase, achieve the best flexoelectric properties and have thus been a favorite to explore the flexoelectric effect. Nevertheless, large strain gradients are required for the flexoelectric effect to be noticeable. In these materials, large enough strain gradients are only achieved at very small scales. Soft and deformable materials, on the other hand, can endure large strains at larger scales before failure making them suitable candidates for the development of electromechanical devices. The focus of this thesis is two-fold, on the one hand, it explores novel ways to generate electricity in soft materials, including non-piezoelectric dielectric elastomers, under non-homogeneous fields. In particular, surface instabilities in flexoelectric film/ dielectric substrate are explored in depth. On the other hand, the manifestations of flexoelectricity on material behavior, in particular around stress singularities are explored.
  

• OKS LEVIS, DAVID: High-performance computing fluid-structure interaction model of bioprosthetic aortic valve replacements
  
  Author: OKS LEVIS, DAVID
  Thesis file: (contact the Doctoral School to confirm you have a valid doctoral degree and to get the link to the thesis)
  Programme: DOCTORAL DEGREE IN APPLIED MATHEMATICS
  Department: (DECA)
  Mode: Normal
  Reading date: 17/07/2023
  Thesis director: SAMANIEGO, CRISTOBAL | HOUZEAUX, GUILLAUME PASCAL
  

  Committee:
       PRESIDENT: ARZAMENDI AIZPURUA, DABIT
       SECRETARI: SOUDAH PRIETO, EDUARDO
       VOCAL: PALMER, MARK
  Thesis abstract: Computational modeling and simulation (CM&S) provides a powerful cost- and time-efficient tool to access detailed mechanistic information of biomedical problems, which is not accessible in either clinical imaging or in vitro bench testing. This enables the efficient testing of medical devices for a wide range of design parameters and working conditions, dictated by patient-specific characteristics such as age, gender, ethnicity, or comorbidities. Furthermore, computational models can be used to simulate not only single patients or bench-test setups but also populations of virtual patients, from either clinical or synthetic databases to obtain informative statistics. These studies, known as in silico clinical trials, can be used to reduce, refine and augment both animal and bench tests. CM&S can thus reduce cost and accelerate the time-to-market of medical devices while improving their safety and efficacy before the first-in-human implantation. In this thesis, a predictive fluid-structure interaction (FSI) computational model of bioprosthetic heart valve replacements was developed to be used in supercomputing environments and applied to problems of biomedical and clinical interest. The end objective is to provide a framework to test and optimize valve prostheses. Given that transcatheter aortic valve replacements (TAVRs) are being implanted in lower-risk and younger patients, long-term effects such as leaflet thrombosis have become a critical concern for patients, doctors, and device manufacturers. This work is focused on predicting the thrombogenic risk and overall hemodynamic performance of bioprosthetic aortic valve replacements. Motivated by minimizing patient-device mismatch, the main questions of interest addressed involve evaluating the effect of multiple geometric and material parameters on prosthesis performance. Some of these parameters include aortic annulus eccentricity, the diameter of the sinotubular junction, coronary alignment, and leaflet rigidity. In this thesis, both in vitro and patient-specific settings were modeled, according to the application of interest. For the model to run in practical computational times, the immersed finite element FSI method developed was designed to meet high-performance computing (HPC) standards. The numerical method was validated against well-known FSI benchmarks, and its performance was analyzed using HPC tools and was deployed in Barcelona Supercomputing Center's in-house multi-physics code, Alya. The model solves the two-way coupling between fluid and solid mechanics, together with fluid-particle dynamics to model the risk of platelet activation. The completeness and efficiency of the tool open an array of possibilities for predicting the performance of devices in patient-specific settings. This thesis hence represents a step towards in silico medicine becoming the gold standard in R&D of novel medical devices, regulatory submissions, and clinical planning.
  

• OUZERI, ADAM AMINE: Theory and computation of multiscale epithelial mechanics : from active gels to vertex models
  
  Author: OUZERI, ADAM AMINE
  Thesis file: (contact the Doctoral School to confirm you have a valid doctoral degree and to get the link to the thesis)
  Programme: DOCTORAL DEGREE IN APPLIED MATHEMATICS
  Department: (DECA)
  Mode: Normal
  Reading date: 14/06/2023
  Thesis director: ARROYO BALAGUER, MARINO
  

  Committee:
       PRESIDENT: JOANNY, JEAN FRANÇOIS
       SECRETARI: SAEZ VIÑAS, PABLO
       VOCAL: FOUCHARD, JONATHAN
  Thesis abstract: Epithelial monolayers perform a variety of mechanical functions, which include maintaining a cohesive barrier or developing 3D shapes, while undergoing stretches over a wide range of magnitudes and loading rates. To perform these functions, they rely on a hierarchical organization, which spans molecules, cytoskeletal networks, adhesion complexes and junctional networks up to the tissue scale. While the molecular understanding and ability to manipulate cytoskeletal components within cells is rapidly increasing, how these components integrate to control tissue mechanics is far less understood, partly due to the disconnect between theoretical models of subcellular dynamics and those at a tissue scale. To fill this gap, here we propose a formalism bridging active-gel models of the actomyosin cortex and 3D vertex-like models at a tissue scale. We show that this unified framework recapitulates a number of seemingly disconnected epithelial time-dependent phenomenologies, including stress relaxation following stretch/unstretch manoeuvres, active flattening after buckling, pulsatile non-affine contractions, curling, or active superelasticity. We further apply the proposed modelling framework to understand and predict the mechanics and reshaping of 3D epithelia in the context of epithelial domes. More specifically, we examine the effect of size, shape and deformation rate on the mechanics of pressurized cell monolayers. We show how the active viscoelasticity of the actomyosin cortex enables the directed folding of rapidly deflating domes into pre-defined buckling patterns. Overall, the proposed framework systematically connects subcellular cortical dynamics and tissue mechanics, and ties a variety of epithelial phenomenologies to a common sub-cellular origin.
  

• PARADELA DIAZ, JAIME: Unstable motions in the Three Body Problem
  
  Author: PARADELA DIAZ, JAIME
  Thesis file: (contact the Doctoral School to confirm you have a valid doctoral degree and to get the link to the thesis)
  Programme: DOCTORAL DEGREE IN APPLIED MATHEMATICS
  Department: Department of Mathematics (MAT)
  Mode: Normal
  Reading date: 30/06/2023
  Thesis director: GUARDIA MUNARRIZ, MARCEL | MARTINEZ-SEARA ALONSO, MARIA TERESA
  

  Committee:
       PRESIDENT: TERRACINI, SUSANNA
       SECRETARI: DELSHAMS I VALDES, AMADEU
       VOCAL: FEJOZ, JACQUES
  Thesis abstract: The 3 Body Problem (3BP) models the motion of three bodies interacting via Newtonian gravitation. It is called restricted when one body has zero mass and the other two, the primaries, have strictly positive masses. In the region of the phase space where one body is far from the other two (the primaries for the restricted case) both models can be studied as a nearly integrable Hamiltonian system. This is the so-called hierarchical regime. The present thesis deals with the existence of unstable motions, in the 3BP and/or its restricted versions. More concretely, we analyze the existence of topological instability, non trivial hyperbolic sets and oscillatory motions (complete orbits which are unbounded but return infinitely often to some bounded region). On one hand, the existence of (a strong form of) topological instability in the N Body Problem was coined by Herman to be "the oldest question in dynamical systems". On the other hand, oscillatory motions are the unique type of complete motions for the 3BP which are not present in the integrable approximation. Their connection with the existence of non trivial hyperbolic sets have lead to the formulation of fundamental, yet unsolved, conjectures about their abundance.We establish the existence of Arnold diffusion, a robust mechanism leading to topological instability, in the Restricted 3BP for any value of the masses of the primaries. The transition chain leading to Arnold diffusion is built in the hierarchical region. We extend a previous result by Kaloshin, Delshams, De la Rosa and Seara, which applied to arbitrarily small mass ratio. Their setting, which exploits the trick, used by Arnold in his original paper, of making use of two perturbative parameters, lead to an a priori unstable model. In our setting, we face some of the challenges present in a priori stable systems.We present several results concerning the existence of oscillatory motions and non trivial hyperbolic sets in the restricted and non restricted 3 Body Problem. First, we develop new tools which blend geometric ideas with variational techniques to prove that there exist oscillatory motions in the restricted 3BP in a non nearly integrable regime. Second we show the existence of non trivial hyperbolic sets and oscillatory motions in the 3BP for all values of the masses. The non trivial hyperbolic set, contained in a subset of the hierarchical region where the inner bodies perform approximately circular motions, is associated to a transverse intersection between the stable and unstable manifolds of a Normally Hyperbolic Invariant Manifold. The existence of center directions complicates heavily both the analysis of existence of transverse intersections between these invariant manifolds and the construction of the horseshoe. The contribution of the author focuses on completing the first of these two steps.Finally, we study the existence of Arnold diffusion in the 3BP for all values of the masses. The robustness of the mechanism which we use to prove the existence of Arnold Diffusion in the Restricted 3BP implies that the obtained transition chain admits a continuation in the 3BP if one mass is sufficiently small. The substantial difference when the masses are fixed is that one can construct a transition chain along which there is a significant exchange of momentum between the inner and outer bodies, resulting in a large change of the eccentricity of the inner bodies. This requires considerably more work than in our construction of the transition chain in the Restricted 3BP and our construction of hyperbolic sets for the 3BP. The first step towards establishing this result, which constitutes the subject of the last chapter of this thesis, is the analysis of the so called Melnikov approximation associated to the aforementioned transition chain.
  

• URTIAGA ERNETA, IÑIGO: Elliptic problems: regularity of stable solutions and a nonlocal Weierstrass extremal field theory
  
  Author: URTIAGA ERNETA, IÑIGO
  Thesis file: (contact the Doctoral School to confirm you have a valid doctoral degree and to get the link to the thesis)
  Programme: DOCTORAL DEGREE IN APPLIED MATHEMATICS
  Department: Department of Mathematics (MAT)
  Mode: Normal
  Reading date: 04/07/2023
  Thesis director: CABRE VILAGUT, XAVIER
  

  Committee:
       PRESIDENT: DE PHILIPPIS, GUIDO
       SECRETARI: SAARI, OLLI
       VOCAL: SERRA MONTOLÍ, JOAQUIM
  Thesis abstract: This PhD dissertation deals with qualitative questions from the theory of elliptic Partial Differential Equations (PDE) and integro-differential equations. We are primarily interested in a distinguished class of solutions satisfying appropriate minimality conditions.The first part of the thesis provides a regularity theory for stable solutions to semilinear problems involving variable coefficients. Here, stability refers to the nonnegativity of the principal eigenvalue of the linearized equation. For variational problems, this amounts to the nonnegativity of the second variation, a necessary condition for minimality. Our main achievement is to show the boundedness of stable solutions in C11 domains in the optimal range of dimensions n < 10. This result is new even for the Laplacian, for which a C3 assumption on the domain was needed.The second part furnishes natural sufficient conditions for the minimality of critical points in a general nonlocal framework. Namely, we construct a calibration for nonlocal energy functionals, under the assumption that the critical point is embedded in a family of sub/supersolutions whose graphs produce a foliation. As a consequence, we deduce that the solution is a minimizer with respect to competitors taking values in the foliated region. Our result extends, for the first time, the classical Weierstrass extremal field theory in the Calculus of Variations to a nonlocal setting. To find a calibration for the most basic fractional functional, the Gagliardo-Sobolev seminorm, was an important open problem that we have solved.
  

Last update: 27/09/2023 05:01:46.

Research groups

• ACES-Advanced Control of Energy Systems
• ALBCOM-Algorithms, Computational Biology, Complexity and Formal Methods
• CoDAlab-Control, Dynamics and Applications
• COMBGRAPH-Combinatorics, Graph Theory and Applications
• DAMA-UPC-Data Management Group
• DCG-Discrete and Combinatorial Geometry
• gAGE-Research Group of Astronomy and Geomatics
• GEOMVAP-Geometry of Manifolds and Applications
• GIES-Geophysics and Earthquake Engineering
• GNOM-Mathematical Optimization Group
• GRAA-Research Group in Applied Analysis
• GREC-Knowledge Engineering Research Group
• GRHCT-Group of Research on History of Science and Technology
• GRTJ-Game Theory Research Group
• INSIDE-Innovation in Systems for Engineering Design and Training
• KEMLG-Knowledge Engineering and Machine Learning Group
• L'AIRE-Laboratory of Aeronautical and Industrial Research and Studies
• LACAN - UPC-Numerical Methods for Applied Sciences and Engineering
• LARCA-Laboratory of Relational Algorithmics, Complexity and Learnability
• MAK-Mathematics Applied to Cryptography
• MAPTHE-Matrix Analysis and Discrete Potential Theory
• SAC-Advanced Control Systems
• SARTI-MAR-Sistemes d'Adquisicio Remota de dades i Tractament de la Informacio en el Medi Mari
• TN-Number Theory Research Group
• VIS-Artificial Vision and Intelligent Systems

Teachers

• Alberich Carramiñana, Maria
• Alvarez Montaner, Josep
• Amoros Torrent, Jaume
• Arias Vicente, Irene
• Arroyo Balaguer, Marino
• Balbuena Martinez, M.Camino
• Baldoma Barraca, Inmaculada
• Barja Yañez, Miguel Angel
• Batlle Arnau, Carles
• Burillo Puig, Pep
• Cabre Vilagut, Xavier
• Carmona Mejias, Angeles
• Casanellas Rius, Marta
• Comellas Padro, Francesc de Paula
• Delshams i Valdes, Amadeu
• Diez Mejia, Pedro
• Encinas Bachiller, Andres Marcos
• Fabrega Canudas, Josep
• Farre Cirera, Rafel
• Fernandez Mendez, Sonia
• Fernandez Sanchez, Jesus
• Ferrer Biosca, Alberto
• Ferrer Llop, Josep
• Fiol Mora, Miguel Angel
• Franch Bullich, Jaume
• Freixas Bosch, Josep
• Garcia Planas, Maria Isabel
• Gargallo Peiró, Abel
• Giacomini, Matteo
• Gimenez Pradales, Jose Miguel
• Gracia Sabate, Xavier
• Guardia Munarriz, Marcel
• Guillamon Grabolosa, Antoni
• Herranz Sotoca, Javier
• Huerta Cerezuela, Antonio
• Huguet Casades, Gemma
• Lario Loyo, Joan C.
• Lazaro Ochoa, Jose Tomas
• Magret Planas, M. Dolors
• Martí Farré, Jaume
• Martin de la Torre, Pau
• Martinez-Seara Alonso, Maria Teresa
• Masdemont Soler, Josep Joaquim
• Miranda Galceran, Eva
• Mitjana Riera, Margarida
• Molina Blanco, Santiago
• Mora Gine, Mercè
• Morillo Bosch, Maria Paz
• Muñoz Lecanda, Miguel Carlos
• Muñoz Romero, Jose Javier
• Myers, Timothy
• Noy Serrano, Marc
• Olle Torner, Maria Mercedes
• Palacios Quiñonero, Francisco
• Pascual Gainza, Pere
• Pozo Montero, Francesc
• Puente del Campo, Maria Albina
• Quer Bosor, Jordi
• Ramirez Ros, Rafael
• Rio Doval, Anna
• Rodellar Benede, Jose
• Rodriguez Ferran, Antonio
• Roman Roy, Narciso
• Rotger Cerdà, Victor
• Rubio Massegu, Josep
• Rue Perna, Juan Jose
• Saez Viñas, Pablo
• Sainz Sapera, Luis
• Sanchez Soler, Mónica
• Sarrate Ramos, Jose
• Serra Albo, Oriol
• Silveira Isoba, Rodrigo Ignacio
• Sola-Morales Rubio, Joan
• Soler Villanueva, Jaume
• Susin Sanchez, Antonio
• Vazquez, Mariano
• Ventura Capell, Enric
• Vidal Segui, Yolanda
• Villar Santos, Jorge Luis