Master's degree in
Engineering Physics
Why study this master?
Pre-enrolment

MOTIVATION

The master's degree in Engineering Physics is oriented towards frontier engineering based on advanced education in physics. Specialist engineering fields such as nanotechnology, nanoelectronics and biomedical engineering require an ever-growing number of professionals who have extensive training in advanced physics and sound knowledge of quantum physics, complex system physics and device physics, which can be applied both at the nanoscopic scale and in large-scale facilities.

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A MASTER WITH PROFESSIONAL OPPORTUNITIES

The master's degree in Physical Engineering is associated to content with a high labor demand.



From senior researcher or technical staff, to management and management positions, going through a project, area or department, with the possibility of becoming an entrepreneur entrepreneur

Industries with a strong technology component.

Basic and applied research centres.

Frontier engineering in the field of nanotechnology.

Doctoral training in research centres and universities.

COURSES

The master program comprises 23 ECTS of common subjects, 20 ECTS of elective subjects and a master thesis of 17 ECTS. Elective subjects can be chosen among different Physics and Engineering courses.

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Common Subjects

23 ECTS

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Elective Subjects in Physics

20 ECTS

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Elective Subjects in Engineering

Max 12 ECTS

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Master Thesis

17 ECTS

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GRANTS

The Department of Physics will offer 3 grants of 1000€ for students who complete the Master's Thesis in research groups of the Department, therefore, the resolution will be passed after enrollment.

The Academic Committee of the Master will award scholarships according to the academic quality parameters of the candidates.

ADMISSION

Duration and start date

One academic year, 60 ECTS credits.

Starting September.

Fees

Approximate fees for the master’s degree, excluding academic fees and degree certificate fee, €3,200 (€5,400 for non-EU residents).

More information about fees and payment options.

Grants

The Department of Physics will offer 3 grants of € 1000 for students who complete the Master's Thesis in research groups of the Department, therefore, the resolution will be passed after enrollment.

The Academic Committee of the Master will award scholarships according to the academic quality parameters of the candidates.

Timetable and delivery

Afternoons. Face-to-face.

Language of instruction

English.

Location

Barcelona School of Telecommunications Engineering (ETSETB)

Contact the master coordinator or the managing team for further information or guidance.

Student Profile

Holders of a degree, or students in the last year of studies of a degree, can apply for admission to the master in Engineering Physics. An official degree certificate is necessary the day of registration, in September. Please check the general academic requirements for master's degrees at UPC-Barcelona Tech.

The master in Engineering Physics The master in Engineering Physics is mainly oriented to graduates in engineering physics and physicists willing to broaden their education in cutting edge engineering applications and advanced physics. Other graduates in engineering or applied sciences are also invited to apply.

Pre-enrolment is now open!

Pre-enrolment

Related Companies

The master in Engineering Physics, due to its standing has various agreements with many companies and research centers. Below you will find a non-exhaustive list of companies related to the master

Ph.D. Program

PhD studies in Computational and Applied Physics provide a high level training in the fields of Computational Physics and Applied Physics, as well as supplying an appropriate background in the general methodologies of the scientific and technical research. Our aim is that future PhDs have the capacity to lead both research and technological innovation in the fields indicated above.

Please visit the PhD in Computational and Applied Physics website

ACADEMIC INFORMATION

Relevant information on the present schoolyear will be posted here.



Academic Calendar

The Academic year consists in 2 semesters, for a more detailed information check the following PDF

Academic Calendar

Timetables

Subjects are usually taught in the afternoons, for a more detailed information check the following link

Master Degree Timetables

Master Degree Theses

The MEF Master Theses are governed by the following regulations

Theses regulations

Academic coordination:

Prof. Jordi Boronat jordi.boronat@upc.edu

Administrative coordinator:

Alicia Sanchez-Nabau alicia.sanchez.nabau@upc.edu

Secretary:

93 405 4174 / 93 401 6772 / 93 401 5966 / 93 401 6750 secretaria@etsetb.upc.edu

Syllabus

  1. Critical phenomena
    • Mean Field
    • Scaling and renormalization group
    • Kinetic Ising models
    • Continuum models
    • Growth Models
    • Percolation
  2. Dynamical Systems
    • Flows and maps
    • Normal Forms
    • Stability; Bifurcations
    • Intermittency; Chaos
    • Pattern formation
  3. Stochastic Processes
    • Markov processes
    • Master equations
    • Stochastic differential equations
    • Fokker-Planck equations
    • Relaxation and First-passage times
  4. Introduction to complex networks
    • Small-world networks
    • Scale-free networks
    • Characterization of networks

Syllabus

  1. Approximate methods in Quantum Mechanics.
    • Description of the problem. Mathematical formulation.
    • Solution of the problem using variational methods. Time-independent perturbation theory approach.
  2. Introduction to Scattering theory in Quantum Mechanics.
    • Formulation of the problem, differential cross section and Lipmann-Schwinger equation. T-matrix, Born approximation and partial wave expansions. Low-energy scattering.
  3. The many-body problem in Quantum Mechanics.
    • Bose and Fermi statistics, wave functions and simmetries.
    • Second quantization: creation and anihilation operators. Operators and observables in second quantization.
    • Hartree-Fock approximation, Gross-Pitaevskii equation and the Bogoliubov approximation.
  4. Magnetic systems
    • Polarized and unpolarized free Systems.
    • Ferromagnetic states. Single-particle excitations and particle-hole pairs. Magnons. Superconductivity and Cooper pairs. Introduction to BCS theory.
  5. Lattice systems: Bose- and Fermi-Hubbapop-contentrd models.

Syllabus

  1. Physical Chemistry of surfaces
    • Introduction to surfaces
    • Structure of surfaces
    • Solid-liquid and solid-gas interphases
    • Characterization techniques
    • Applications in sensors and catalysis
    • Functionalization of nano- and microreactors
  2. Mechanics and Fluid mechanics at micron scale
    • Introduction to micromechanic and microfluidic behavior.
    • Biosensor structure
    • Design and simulation of the biosensor fluidic behavior
    • Design and simulation of the biosensor mechanic behavior
    • Case studies in bioengineering and comunications.
  3. MEMS microdevices applied to communication circuits
    • Introduction to MEMS micro-devices. Materials and structures.
    • Ohmic- and capacitive-contact micro-switches.
    • MEMS micro-switch electromagnetic simulation
    • Application of MEMS micro-switches to reconfigurable communication circuits.
    • Circuit simulation.
    • Experimental characterization of MEMS micro-switches.

Syllabus

  1. Sources of Synchrotron and neutron radiation.
    • Continuous and pulsed sources.
  2. Safety in large facilities.
  3. Design of main devices in Sinchrotron and neutron sources:
    • focusing of photons and neutrons
    • dispersion and detection
  4. Design and use of special sample environments:
    • High pressure
    • high and low temperature
    • magnetic fields.
  5. Experimenal techniques available in large facilities.
    • Complementarity between experimental techniques
  6. Generation, storage and analysis of large facilities:
    • Experimental data

Syllabus

  1. Project planning.
  2. Planning methods based on critical path.
  3. Precedence analysis, PERT and GANTT chart.
  4. Time and cost estimation.
  5. Risk identification and mitigation plans.
  6. Stakeholders communication management.
  7. Project execution management: earned value.
  8. Project closure: success criteria and lessons learned.

Syllabus

  1. Basics of condensed matter
    • Microscopic constituents and effective interactions; condensed phases: normal and supercritical fluids, crystals, glasses, mesophases; classification and examples of transitions (first order, continuous, glassy); van der Waals theory and isomorphic states; miscibility and binary systems
    • Molecular disorder and dynamics; linear response theory, dielectric and mechanical spectroscopy, other experimental methods (thermodynamic and optical probes, scattering)
  2. Single-component systems
    • Small-molecule condensed phases; crystallization kinetics & polymorphism; structural glasses, ultrastable & aged glasses; orientationally disordered solids & plastic crystals; primary & secondary relaxations; charge conduction in molecular solids and liquids
    • Amorphous & semicrystalline linear homopolymers; ideal chain statistics and entanglement effects, entropic forces, Rouse modes and reptation; viscoelasticity, glass transition, and crystallization of linear polymers; branched polymers, gelation and rubber elasticity, affine network model for elastomers; conjugated and conductive polymers
    • Thermotropic liquid crystals (nematic, smectic, columnar) and liquid crystal polymers; optical properties and applications
  3. Multicomponent and aqueous systems
    • Polymer solutions: non-ideal chains, theta-solutions, hydrogels, swelling phenomena; superhydrophobic/hydrophilic, superolephobic, superamphiphilic, and self-healing polymer coatings; biopolymers, helix-coil and coil-globule transitions
    • Self-assembly in condensed matter: specific and non-specific interactions; block copolymers; colloidal systems (glasses, crystals, gels), surfactant-water systems, biomembranes, lyotropic liquid crystals, emulsions; semiflexible polymers & cytoskeleton

Syllabus

  1. Introduction: the hydrogen atom
  2. Interaction between atoms and external fields (static and oscillatory)
  3. Fine and hyperfine structure. Selection rules
  4. Symmetries of the wave function
  5. Many-electron atoms. Thomas-Fermi model, and Hartree-Fock method
  6. Understanding the periodic table of elements
  7. Molecular structure and degrees of freedom
  8. Advanced spectroscopic techniques: infra-red, Raman, and nuclear magnetic resonance
  9. Laser cooling, manipulation and detection of ultracold dilute quantum gases

Syllabus

  1. Mechanical properties of materials
    • Elasticity and related properties
    • Non-linear mechanical properties
    • Thermal expansion and isothermal compressibility
  2. Dielectric and optical properties of materials
    • Polarization and polarization mechanisms
    • Ferroelectricity
    • Pyroelectricity
    • Piezoelectricity
    • Dielectric response to variable frequency electric fields
    • Optical response of materials
  3. Magnetic properties of materials
    • Diamagnetism
    • Paramagnetism
    • Ferromagnetism
    • Other types of magnetism: ferrimagnetism, antiferromagnetism and non-collinear ferromagnetism
  4. Ferroic and multiferroic materials
    • Ferroic transitions
    • Multiferroic coupling: Magnetoelasticity and magnetoelectricity
    • Applications

Syllabus

  1. Biological networks
    • Examples in systems biology (metabolic networks, interactome, regulatory and signalling networks)
    • Biological neural networks
    • Networks in ecology and epidemiology
  2. Complex spatio-temporal dynamics in biology
    • Oscillations, excitability, bistability
    • Synchronization in biological systems: neural networks
    • Spatio-temporal chaos: cardiac fibrillation
  3. Complex biosignal analysis
    • Deterministic and stochastic signals
    • Statistical properties
    • Nonlinear time series analysis
  4. Self-organization in biological systems
    • Morphogenesis
    • Self-assembly (protein folding, membrane formation)
    • Growth processes (chemotaxis, tumour growth)
  5. Collective motion and active matter
    • Flocking, swarming and herd behaviour
    • Cell migration

Syllabus

  1. Introduction to Machine Learning
    • Fundamental problem of Machine Learning
    • Description of the inherent complexity of the problem
    • General approximations to the solution.
  2. Classical models of Neural Networks
    • Hopfield model
    • Recurrent Boltzmann Machines (BM) and Restricted Boltzmann Machines (RBM)
    • Learning with BM and RBM: gradient descent, Contrastive Divergence and variations
    • Single-layer Perceptrons (SLP): lineal regression, logistic regression, Rosenblat perceptron
    • Multi-layer Perceptrons (MLP)
    • Learning with MLP: Back-propagation
    • Convolutional Neural Networks (CNN): model, link with MLP and learning
  3. Deep Learning: link with classical models and modern learning techniques

Syllabus

  1. Introducción. Métodos de discretización del continuo: diferencias finitas, elementos y volúmenes finitos, métodos espectrales y métodos sin malla o de partículas
  2. Formulaciones débiles, variacionales, de Galerkin, de Petrov-Galerkin, de colocación, etc. de diferentes problemas de la Física (Termodinámica, Elasticidad, Mecánica de Fluidos, Electromagnetismo, Mecánica Cuántica, etc.)
  3. El método de los elementos finitos. Aproximación lagrangiana a trozos. Tipología de elementos finitos. Elementos nodales y modales. Elementos isoparamétricos. Errores de interpolación y convergencias h, p i hp
  4. Implementación del método de elementos finitos. Mallado de dominios. Ensamblaje de matrices. Fórmulas de cuadratura. Estimación del error de las soluciones. Ejemplos de aplicación en Matlab/Octave o Python
  5. Complementos de álgebra lineal numérica. Almacenamiento matricial. Técnicas para sistemas lineales y problemas de valores propios para problemas de dimensión elevada.
  6. Librerías de elementos finitos. Introducción a FeniCS-Python
  7. Integración temporal. Métodos de semi-discretización, de líneas, de splitting, etc. Dificutades en problemas de tipo advección-diffusión
  8. Introducción a los métodos de volúmenes finitos y de Galerkin discontinuos. Aplicaciones
  9. Métodos de orden alto. Elementos espectrales. Integración temporal de orden alto.

Syllabus

  1. Monte Carlo integration: distribution functions and their sampling. Crude Monte Carlo and rejection methods. Improving efficiency: variance reduction methods. Multidimensional integrals and Metropolis sampling.
  2. Monte Carlo methods for the study of many-particle systems: discrete systems (Ising), continuous systems in different statistical collectivities. Finite-size scaling. Advanced Monte Carlo methods.
  3. Stochastic optimization: simulated annealing and genetic algorithms.
  4. Dynamic Monte Carlo: randowm walks and the diffusion equation. Fokker-Planck and Langevin methods. Brownian dynamics.
  5. Application of Monte Carlo methods to quantum systems. Wave functions for bosons and fermions. Variational Monte Carlo. Diffusion Monte Carlo. Path integral Monte Carlo for the study at finite temperature.

Syllabus

  1. Finite difference methods applied to stellar evolution
    • Finite difference approximations
    • Von Neumann stability criterion
    • Initial values and boundary conditions
    • Explicit vs. Implicit methods
    • Lagrangian and Eulerian formalisms
    • Nuclear reaction networks. Adaptive networks
    • Relativistic hydrodynamics
  2. Smoothed-Particle Hydrodynamics
    • Fluid dynamics interpolation schemes
    • Eulerian SPH equations
    • Variable resolution in space and time
    • Lagrangian SPH equations
    • Applications of the Eulerian equations
    • Heat conduction and mass diffusion
    • Viscosity
    • Application to shocks and rarefaction problems
    • Astrophysical applications
    • Other applications
    • SPH in special and general relativity
    • Future developments
  3. Astrophysical applications of Monte Carlo and classification methods
    • Overview of basic concepts
    • Simple applications of the Monte Carlo methods
    • Classification methods: data analysis
    • Examples of classification