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.

• Formulation of the problem, differential cross section and Lipmann-Schwinger equation. T-matrix, Born approximation and partial wave expansions. Low-energy scattering.

• 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.

• Polarized and unpolarized free Systems.
• Ferromagnetic states. Single-particle excitations and particle-hole pairs. Magnons. Superconductivity and Cooper pairs. Introduction to BCS theory.

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

• 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.

• 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.

• focusing of photons and neutrons
• dispersion and detection

• High pressure
• high and low temperature
• magnetic fields.

• Complementarity between experimental techniques

• 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)

• 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

• 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

• Polarization and polarization mechanisms
• Ferroelectricity
• Pyroelectricity
• Piezoelectricity
• Dielectric response to variable frequency electric fields
• Optical response of materials

• Diamagnetism
• Paramagnetism
• Ferromagnetism
• Other types of magnetism: ferrimagnetism, antiferromagnetism and non-collinear ferromagnetism

• 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

• Oscillations, excitability, bistability
• Synchronization in biological systems: neural networks
• Spatio-temporal chaos: cardiac fibrillation

• Deterministic and stochastic signals
• Statistical properties
• Nonlinear time series analysis

• Morphogenesis
• Self-assembly (protein folding, membrane formation)
• Growth processes (chemotaxis, tumour growth)

• 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.

• 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

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.