9th Semester AMPS

Here s the translation of the text you provided: Introduction. Basic concepts and characteristic quantities of an ionized medium (density, temperature and thermal velocity, collision frequency, Debye length, plasma frequency). Propagation in a homogeneous cold multi-component plasma: Constitutive relations and determination of plasma conductivity and permittivity. Electrostatic and electromagnetic waves in unmagnetized plasma. Propagation rates in magnetized plasma along and transverse to the magnetic field (electromagnetic and whistler waves, cyclotron and hybrid resonances, cutoffs). Propagation in a magnetic fluid: Magnetohydrodynamic equations and generalized Ohm s law. Hydromagnetic waves (acoustic, Alfven and magnetoacoustic). Propagation of electrostatic waves in hot plasma: Elements of kinetic theory, distribution functions and Vlasov equation. Effect of temperature and resonant electrons on the propagation of Langmuir waves (Bohm-Gross relation and Landau damping). Ion acoustic waves. Coupling of oscillations and distinction between amplification and damping. Application to a two-electron beam system. Propagation in a medium with mild inhomogeneity and adiabatic approximation. Reflection and propagation at discontinuity surfaces.

Second Quantization Formalism: Second quantization – basic formalism – introduction. Identical fermions – electron gas. Phonons. Basic Concepts and Tools: Canonical transformations. Green s functions. Thermal Green s functions. Path integrals. Symmetries and Symmetry Breaking. Interacting Electrons: Nearly free electrons. Fermi liquid, quasi-particles, Hartree-Fock approximation. Collective excitations (random phase approximation, plasmons, excitons). Nesting properties, low-dimensional systems, Spin and charge density waves, itinerant ferromagnetism. Strongly correlated electrons, Hubbard-type Hamiltonians. Electron-ion interaction (or other bosonic fields): Jellium model, Peierls instability. Frolich Hamiltonian, Polarons. Interaction with spin fluctuations. Macroscopic Quantum States: Bose-Einstein condensates. Superfluidity, Helium 4. Superconductivity, Ginzburg-Landau and BCS Theories. Unconventional Superconductivity in Helium 3. Nambu-Eliashberg theory. Complex Quantum Order States of Matter: Inhomogeneous superconductivity, FFLO states, strong scattering with imperfections, unconventional magnetic order states and charge order states, Pomeranchuk instabilities. Coexistence and competition of quantum order states, unconventional superconductors and magnets. Contemporary problems. From new superconducting and magnetic materials to neutron stars and Laser-trapped fermionic gases.

For the description, please refer to the course with code 9187, Analysis of Surface Mechanical Systems (of the Applied Mathematics Direction).

Introduction to Composite Materials: - Historical Context and Applications: Overview of the development and uses of composite materials. - Classification of Composite Materials: Based on matrices and reinforcements: - Matrices: Brief description of polymeric systems. - Categories of Reinforcements: - Particles, fibers, and nanoinclusions. - Structured Composite Materials: Fiber classification by material, orientation, length, and distribution. - Core materials. Manufacturing with composites: - Manufacturing techniques (theory). - Laboratory (Manufacturing of Fiber Reinforced Plate with Vacuum Assisted Resin Transfer Molding). Long-Fiber Ply properties: - Curing degree, density, stiffness, strength, thermal expansion factor. - Rule of mixtures and more advanced micromechanical theories. Stress-Strain Theory of a single ply: - Stress-Strain Tensor: Examination and relevance. - Stiffness and Compliance tensorial transformation. Orthotropic and Transversely Isotropic Materials: - Multilayered composites, coding, and classical laminate theory. - Theoretical Models: For determining elastic constants and strength. Failure Criteria for Composite Materials: - Maximum stress-strain criteria, Puck, and Tsai-Wu models. - Comparisons between criteria and selecting an appropriate one.

For the description, please refer to the course with code 9138, Design and Analysis of Control Systems (of the Applied Mathematics Direction).

Scalar – vector potential: Gauge transformations. Energy. Momentum. Angular momentum. Maxwell s Electromagnetic stress tensor. E/M waves in non-conductive media, Fresnel coefficients (proof), E.M waves in conductive media. Dispersion (non-conductive, conductive, plasma). Waves on transmission lines. Waveguide (rectangular, cylindrical systems). Fields of moving point charge. Retarded potentials. Radiation (point charge, electric dipole, magnetic dipole). Antennas (linear antenna, array of antennas).

Measurement Techniques: Instruments and measurements of electronic signals. Passive Filters: High pass, low pass, and bandpass filters. Operational Amplifiers: Linear circuits of operational amplifier, nonlinear circuits of operational amplifiers, differential amplifiers. Application Circuits. Diode Applications: Diode circuit, rectifiers, power electronics. Transistor Applications: Bipolar Junction Transistor characteristics and Field Effect Transistors. Common Emitter, Common Base, and Common Collector Amplifiers. Digital Circuits I: Boolean Algebra, logical gates, combinational circuits, and systems. Digital Circuits II: Flip-Flops, sequential circuits, and systems.

Preparation of an experimental and/or theoretical-computational project with an applied character, individually or in groups. The topics are determined by the faculty members, who are responsible for supervising and grading the project. The assignment of the project can also be done in collaboration with faculty members of other Schools.

The course ENVIRONMENTAL POLICY moves along two narrative axes. The first axis specifically addresses the basic principles and concepts of Environmental Policy as institutionally reflected in European and international conventions and treaties concerning the environment. Through this statutory framework (policy), the importance and inseparable relationship of the environment or space in general with society emerges. Thus, it narratively includes references to both social movements related to the environment or to the values that fueled interest in environmental protection, and the historical evolution of the environmental crisis and its crucial cultural dimension. The second axis selectively focuses on the Philosophical contemplation of the environment and specifically on Environmental Ethics. It is addressed to students who wish to delve into areas of thought such as: moral relativism and environmental ethics, the conceptual dualisms of anthropocentric (Thomas Aquinas, Descartes, Kant, modern perspectives) and ecocentric (bio- and physiocentric). The core of the teaching is the traditional ethical theories (Utilitarianism, theory of rights, Social Contract theory): How should the interests of future generations be understood? Does intergenerational solidarity make sense? What are the consequences of including animals in the moral community? What are the ramifications of biocentric ethics? What are holistic theories and which individual interests are equivalent to the interest of the whole? Do we have moral obligations to species? What are the basic tenets of Deep Ecology? What is its relationship with Scientific Ecology? What is the critical view of Deep Ecology from the perspective of the Third World? Ecofeminism links women with nature, conceptually and empirically, symbolically and epistemologically, politically and ethically. Is there antagonism between Ecofeminists and deep ecologists? How is the New Ecological Paradigm constructed? How did Durkheim, Weber, Marx understand Environmental Sociology? What is the environmental movement? What is Ecological Modernization? What constitutes the Risk Society?

Control charts for the mean, for variance, for standard deviation, for sample range. P-charts and c-charts. Charts for controlling the number of defects. Cumulative Sum (CUSUM) charts. Moving Average and Exponentially Weighted Moving Average (EWMA) Control Charts. Acceptance sampling for lots of identical products. Single sampling plans. Average outgoing quality. Double sampling plans. Operating characteristic curve. Multiple sampling plans. Robust parametric designs. Taguchi s methodology. Alternative designs for quality control. The crossed design. The combined design. Construction of combined formations from optimal designs. Laboratories using statistical packages.

Basic notions: Topological spaces, Basis, subbasis of topology, Open sets, closed sets, closure, interior, boundary, continuous functions, relative topology, homeomorphisms. Cartesian products: Product topology, projections, general properties. Connectedness: Definitions, properties, Connective components; Path connectedness, Applications to R^n. Separation axioms: Hausdorff spaces, regular spaces, normal spaces, completely regular spaces. Countability and Metrizable topological spaces. Separability. First and second countable spaces, Lindelof spaces, Urysohn’s metrizability Theorem. Compactness: Tychonoff’s Theorem, Stone Cech compactification, Superfilters, the space N. Convergence: Convergence in topological spaces, nets, subnets.

The syllabus varies depending on the instructor.

For the description, please refer to the course with code 9321, Environmental Policy (of the Applied Mathematics Direction).

Structure and composition of the Earth s atmosphere: Composition and structure of the Earth s atmosphere and biosphere. Troposphere-Stratosphere. Ideal gas law - Equation of hydrostatic equilibrium. Principles of radiation propagation in the atmosphere: Mie scattering, Rayleigh scattering. Molecular absorption - Absorption lines of molecular pollutants. Black-gray body radiation. Earth s energy balance - Modeling. Equations of motion in the atmosphere: Continuity equation - The differential D. Equations of motion of the atmosphere (inertial, rotating, and special reference frames). General atmospheric circulation. Geostrophic wind - Geopotential height. Atmospheric ozone - Ultraviolet solar radiation: Ultraviolet solar radiation - measurement techniques. Stratospheric - Tropospheric, total ozone - measurement techniques. Global Climate Change (GCC) - Greenhouse Effect: The carbon cycle. Global Climate Change - Physical/chemical processes. Predictive models - Preventive measures against GCC. Stability conditions in the atmosphere: Adiabatic lapse rate of dry atmosphere. Entropy and potential temperature. Stability - instability criterion in the atmosphere. Atmospheric Boundary Layer: Basic structure of the Atmospheric Boundary Layer. Temperature inversions - Urban heat island - Sea and land breeze. Atmospheric Pollution: Primary - secondary gaseous pollutants - Photochemical reactions. Suspended particulate matter - Air quality index. Mathematical models for predicting atmospheric pollution. Experiments and devices for recording gaseous pollutants.

Bayesian statistical theory for pattern recognition, Decision functions, Categorization with decision functions, Bayes classifiers with training, Neyman-Pearson classifier, Learning algorithms, Cluster finding, ManMin algorithms, K-means, Non-Parametric Decision Theory - connection to optimization theory, Unsupervised learning, Dimensionality reduction - Fisher technique, divergence criterion, entropy, Karunen-Loeve, Introduction to the basic concepts of neural networks, Perceptron, Basic architectures: Feedforward networks, Feedback networks, Pattern recognition with Neural systems.

Microsystems and Nanosystems: Definitions and examples. Relationships: Between microelectronic, micro-optical, and micro-electro-mechanical technology. Basic Microelectronic Technology Processes and Modeling: Thermal oxidation Dopant diffusion Ion implantation Physical and chemical deposition Lithography Etching Fabrication: Examples of microelectronic device fabrication. Special Processes: For micromechanics and microsensor fabrication. Micromachining: Surface and bulk processes. Physical Principles of Sensors: Operation Examples of fabrication and operation of physical and biochemical microsensors. Lab-on-chip technology. Nanotechnology: Methods of fabrication at the nanoscale. Top-down and bottom-up nanofabrication. Fabrication and quantum properties of nanoparticles and nanowires. Applications in sensors.

Dielectrics: Electric insulators. Dielectric materials for capacitors and microelectronic applications. Active Dielectrics: Ferroelectric, piezoelectric, and pyroelectric materials. Electrets. Smart Materials: Electroactive polymers – Dielectric elastomers. Energy harvesting. Additional Topics: Solid-state electrolytes. Liquid crystals. Photovoltaic materials. Materials for energy applications and environmental pollution management.

The role of the Medical Physicist in health care. Biomechanics, muscle and forces. Physics of the skeleton. Pressure in the body. Osmosis and the kidneys. Physics of the lungs and breathing. Physics of the cardiovascular system and electric signals. Sound, speech, and hearing. Interaction of mechanical waves with living matter and applications (e.g., extracorporeal lithotripsy). Physics of the eyes and vision, artificial vision. Introduction to Bionics, biosensors, and bioactivators.

Biophotonics section: Basic principles of the interaction of laser radiation with living matter. Biophysical action mechanisms. Diagnostic applications of lasers. Surgical applications of lasers. Photodynamic therapy. Medical lasers and dosimetry. Laser safety. Environment section: Basic principles of the propagation of laser radiation in the atmosphere. Atmospheric Optics: Mie, Rayleigh, and Raman scattering. LIDAR technique (radiation propagation equation, setup geometry, signal recording techniques). DIAL technique, LIF technique. Measurement of pollutants in the atmosphere and the hydrosphere.

Nuclear reactions with neutrons. Nuclear fission. Scattering, diffusion, absorption, thermalization of neutrons. Criticality calculations of bare homogeneous thermal neutron systems. Nuclear power reactors. Construction of nuclear power plants. Nuclear fuel. Heat removal from the core of nuclear power reactors in steady state. Thermodynamic cycles and energy production. Safety of nuclear installations and nuclear accidents. Dispersion of fission products in the atmosphere. Basic principles of radiation protection and Radioenvironmental studies. Industrial applications of nuclear technology.

Introduction to Fracture Mechanics. Fatigue of metallic materials. Laws for calculating crack growth. Fatigue of composite materials. Use of finite element programs for crack problems. Basic principles of the Damage Tolerance philosophy. Analysis of crack growth mechanism based on the Damage Tolerance philosophy. Methodology for predicting remaining structural life. Example of structural calculation with the damage tolerance philosophy. Crack growth calculation programs (AFGROW–NASGRO – RAPID). Smart Materials and Structures. Introduction to Structural Health Monitoring. Laboratory:  Demonstration of fatigue experiment on an INSTRON testing machine.  Numerical applications using the finite element method.

Elements of differential geometry of three-dimensional surfaces: Oblique and orthogonal reference systems, applications. General bending theory of smooth thick shells: Applications. General bending theory of smooth thin-walled shells: Applications. Bending theory of shells: Applications. Methodology for decoupling partial linear systems of higher order. Membrane analysis of shells: Applications. Analysis of cylindrical shells subjected to bending and membrane stresses. Analysis of shells of revolution subjected to bending and membrane stresses: Applications.

Finite Fields. Modular arithmetic. Number Theory. The sieve of Eratosthenes and other factoring methods. The extended Eulidean algorithm. The Euler function. Linear Diophantine equations and congruences. The fundamental theorems: The fundamental theorem of Arithmetic, Euler, Fermat, Wilson, the Chinese remainder theorem the prime number theorem. Quadratic congruences, Legendre and Jacobi symbols. The Quadratic reciprocity law. Numbers: perfect, Mersenne, Fermat and amicable numbers. Cryptology. Historical overview. Classical cryptosystems: encryption, decryption and cryptanalysis of the cryptosystems: additive, multiplicative, affine, Vigenere, Playfair and Hill. The Discrete logarithm problem (D.L.P.). Public Key cryptosystems: The R.S.A., Merkle, Hellman- the Diffie-Hellman problem, Elgamal, Massey – Omura. Digital Signatures. Elliptic Curves. Combinatorial Designs and Cryptography.

Continuum hypothesis. Development of basic principles of fluid mechanics: kinematics of flows, forces and deformation of fluids, basic equations (conservation of mass, momentum, energy) in integral and differential form, constitutive laws, solutions of Navier-Stokes equations. Dimensional analysis and similarity. Inviscid flow: circulation, vortex dynamics, dynamic flow. Viscous flows: significance of Reynolds number, wake, boundary layers, boundary layer separation. Turbulent flows.

Nonlinear operators. Compact operators and applications to the existence of solutions to integral equations. Monotone operators. Basic properties. Nemitsky operators. Brower and Shaudar fixed point theorems. Applications. The Ekeland variational principle. Differentiability in Banach spaces. Gateaux and Frechet derivatives. Critical point theory. Applications.

Introduction: The problem of measure. Classes of sets: Algebras, σ-algebras, Dynkin classes. Measure spaces: Outer measures, complete measures, and completion of a measure space, regular measures, Lebesgue measure. Measurable sets: Structure of measurable sets, non-measurable sets. Measurable functions: Sequences of measurable functions, Egorov and Lusin Theorems. Lebesgue integral: Integral of simple functions, integral of non-negative measurable functions, basic properties of the integral. Monotone convergence theorem, Fatous lemma. Lebesgue integral in general: Dominated convergence theorem, Beppo Levi theorem. Comparison: Riemann and Lebesgue integration. Topics: Modes of convergence of sequences of measurable functions, L p L p spaces. Product measures, Fubini theorem. Signed measures, Radon-Nikodym theorem.

From the Schrödinger equation to the Klein-Gordon equation. Probability density and current. Negative energies. Antiparticles. The Klein-Gordon equation with Coulomb potential. Electrodynamics of spin=0 particles. Feynman diagrams. Scattering, cross-section, invariant amplitude, Mandelstam variables. The Dirac equation. Gamma matrices. Probability density and current. The antiparticle wave function. Invariant quantities. Electrodynamics of spin=1/2 particles. Feynman diagrams. Scattering and invariant amplitude calculation. Introduction to second quantization.

Banach spaces. Geometric forms of the Hahn–Banach theorem. Separation of convex sets. Definition and basic properties of the weak topology σ (E, E). The weak topology σ (E, E). Reflexive spaces. Uniformly convex spaces. Definition and basic properties of compact operators. The Riesz–Fredholm theory. Spectrum of a compact operator. Spectral analysis of compact operators. Unbounded operators in Banach spaces and applications. Sobolev spaces (in R) and applications to boundary value problems.

Basic concepts and results from dynamic systems theory: Stability, Lyapunov, La Salle, and Chetaev theorems. Linear control systems: Reachable sets, Controllability, Observability. Equivalence of Linear systems through coordinate change and feedback, Canonical forms. Stabilization of linear systems. Infinite horizon quadratic cost optimization problem. Observers and dynamic feedback design. Realization theory. Algebraic stability criteria (Routh, Hurwitz). The concept of input-output stability, results and applications. Introduction to design and analysis problems in nonlinear systems. An introduction to design and analysis issues in the case of stochastic control systems.

Electrical noise and measurement limits of physical quantities. Electrical signal conditioning and processing with passive and active elements. Protection of sensitive instruments from electromagnetic and microseismic interference. Magnetic field generation. Secondary electron emission, Faraday cage and two basic functions of the photomultiplier tube. Electron beam shaping, electrostatic lens. Electrical discharges in gases, electrical discharge devices and sputtering technique. Basic techniques for high vacuum generation and measurement. The course includes: 1. Electrical signal and pulse propagation in transmission lines. 2. Temperature control of specimens. 3. Improving the signal-to-noise ratio, Lock-In Amplifier. 4. Constant voltage sources. 5. Constant current sources. 6. Study of electrical discharge in a Neon lamp. 7. Standing waves in transmission lines. 8. Weak light flux measurement with a photomultiplier.