Course Code

Course Title/ Contents Course Description/ synopsis

No of Contact hours (T:P)/ Units

PHY 701

Electromagnetic Theory Electrostatic potential problems.  Poission and Laplace's equation method of images, Green's theorem, multiple expansions.  Magnetic fields. Stokes theorem, vector potential. Electromagnetic Maxwell's equation. Propagation of electromagnetic waves in different ionized and non-ionized media, phase velocity, group velocity and pulse propagation, attenuation, refraction, energy propagation and transfer, polarization and dispersion. Green function methods, diffraction theory, simple radiating systems, Lagrangian derivation of Maxwell's equations and the covariant structure of electromagnetism.

(45,0) 3, R

PHY 705

Analysis of Data

 Nature of observations: errors of observations; mean and median, weighted and adjusted means. Precision and accuracy. Parameters of frequency distributions.  Measure of dispersion, skewness, kurtosis. Standard errors of parameters.  Significance tests.  Theory of errors. Binomial, Gaussian and Poisson distribution. Other one-dimensional empirical distributions, unbounded and bounded distributions. Time series. Persistence; periodicity, quasi-periodicity; harmonic analysis.  Simple correlation ratio. Partial correlation. Smoothing and interpolation. Curve fitting; method of least squares, statistical analysis. Tests of fit, the x-square distribution; comparison of averages, student's t-distribution; analysis of variance, the F-distribution; errors of correlation coefficients, Fisher's Z-transformation

(45,0) 3 R

PHY 703

Electromagnetic Theory

 Electrostatic potential problems.  Poission and Laplace's equation method of images, Green's theorem, multiple expansions.  Magnetic fields. Stokes theorem, vector potential. Electromagnetic Maxwell's equation. Propagation of electromagnetic waves in different ionized and non-ionized media, phase velocity, group velocity and pulse propagation, attenuation, refraction, energy propagation and transfer, polarization and dispersion. Green function methods, diffraction theory, simple radiating systems, Lagrangian derivation of Maxwell's equations and the covariant structure of electromagnetism.

(45,0) 3, R 

PHY 702

Thermodynamics and Statistical Mechanics

Basic Postulates of thermodynamics of simple, homogeneous systems. Thermodynamic potentials and stability of thermodynamic systems. Gibb’s theory of thermodynamics with interaction effects. Partition functions of different ensembles. Fundamental equilibrium theory; Liouville’s theorem and the Ergodic hypothesis. Distribution Functions, entropy and connections with thermodynamics, Microcanonical, canonical and grand canonical ensembles. Boltzmann and Maxwell-Boltzmann distributions. Fermi Dirac and Bose-Einstein statistics. Equilibrium phases and transitions; phenomenology of phase equilibria; First and second order transitions. Applications to classical and quantum systems. Boltzmann equation. Einstein transition probability. Random variables. Brownian motion and their applications. Universality and scaling. Critical indices.

(45,0) 3 E

PHY 703

Quantum Theory     

Fundamental of quantum mechanics-operators in Hilbert Space, basic axioms, Matrix formulation of quantum mechanisms -  state vectors, observables, equations of motion.  Approximation methods in quantum mechanics.  Many-electron systems.  Scattering theory. Relativistic theory.       

(45,0) 3 R

PHY 704

Basic Fluid Dynamics          

Basic equations - definition of a perfect fluid, fluid pressures and body forces. Langrangian and Eulerian representation of fluid motion in an inertial system. Equations of conservation of matter and energy, for both adiabatic and non-adiabatic motions.

Diffusion in Fluids - viscosity, tangential stresses in a real fluid and the stress tensor.  The Navier-Strokes equation of conservation of energy.

Elementary Application of Basic Equation -Bernoulli's equation. Archimedes principle. Equation of motion relative to the rotating earth.  The Coriolis force, centrifugal force and effective gravity. Solutions of equations - difficulties of solution, non-linearity; orders of magnitude, 'ill-conditioned' form of some of the equations.  Approximations by orders of magnitude, method of perturbation and linearisation boundary conditions with examples. Vorticity and divergence - concepts of vorticity and divergence, vorticity equation, factors contributing to changes in vorticity.

Applications of basic equations to some physical problems.    

(30,0) 2 R

PHY 706

Quantum Field Theory

Classical Field Theory:The Electromagnetic Field, Interactions of a point particle, Symmetries and conservation laws, fundamental invriants, energy-momentum tensor. Noether’s theorem. Green’s functions. Radiation. Relativistic Wave equations:the Klein-Gordon equation, Dirac equation and the Weyl equation. Dirac propagator. Quantization of fields:scalar field, charged scalar field, quantized radiation field, massive vector fields. Interaction with external fields: emission probabilities, Compton effect, Pair creation & annihilation, Bremmstrahlung etc. Perturbation theory, Feynmann rules. Feynmann diagrams. Radiative corrections and renormalization: vacuum corrections, electron propagator, vertex functions, the Lamb shift, the anomalous magnetic moment. Functional methods. Introduction to Gauge Field theories.

(45,0) 3 E

PHY 707

General Relativity

Generalization of special relativity. Effects of gravity, curved spacetimes, metrics, particle paths as geodesics, light and null geodesics. Curved Spacetimes: Tensors as a general tool in curved spacetime, geodesic equations, curvature and its description, geodesic deviation. Distributed matter and the stress-energy tensor. Einstein equations in general and in vacuum. Lambda term. Spherically-symmetric vacuum solution: Schwarzschild metric, equation of motion in the Schwarzschild metric. Properties of the orbits of particles and photons. Infall into a black hole. Event horizon and infinite redshift surfaces. Weak-field limits: Gravitational lenses, time delays and periastron advance. Binary pulsar. Gravitational collapse. Rotating black holes. The Kerr metric, its singularities and horizons, properties of particles and photon orbits, inertial frame dragging.

(45,0) 3 E

PHY 708

Particle Physics

The Standard Model: Elementary particles (quarks, leptons, antiparticles & hadrons). Forces of nature (electromagnetic, strong, weak, gravity), Gauge Bososns (photons, gluons, W+ and Zo, graviton). Strength and range of interactions. Theoretical framework. Natural limits. Four vectors. Electromagnetic Interaction: QED. Feynman diagrams. Vertices. Perturbation theory. Renormalization. Weak Interactions: Charged currents. Parity violations. Weak interaction of leptons and quarks. Neutral currents. Electroweak unification and the Glashow-Weinberg-Salam model. W+ and Zo bosons. Precision tests of the standard models in e+e-. Strong Interaction: QCD. Gluons and colour. Properties of QCD (quarks confinement, asymptotic freedom and hadrons) Strong interacion vertices. Running coupling constants. Quark model of hadrons: light quark meson, Baryons: Mesons, masses and magnetic moments. Hadron resonances. The c and b-quarks. Beyond the Standard Model: the Higgs boson, Neutrino oscillations. Grand Unification (proton decay). Supersymmetry.

(45,0) 3 E

PHY 809

Non-linear Dynamical Systems

Types of non-linear dynamical systems and connections between them. Poincare sections, conjugacy and flow equivalence. Review of portraits and the geometry of solutions to ordinary differential equations. Stability: Liapunov, quasi-asymptotic stability, Liapunov functions. Liapunov stability theorems and linerar stability (for distinct eigenvalues). Stationary points in R2. Population models as examples. Periodic orbits in ordinary differential equations. Statement and explanation of Poincare-Bendixson theorem. Poincare index and Dulacs criterion. Bifurcations: Introduction to bifurcation theory (by Taylor’s series) and Hopf bifurcation. Maps of the interval. Fixed points, periodic points and stability. Saddle-mode and periodic doubling bifurcations. Chaos: Piecewise linear maps; the tent map. Transivity and chaos (sensitive dependence on initial conditions). Brief description of the maps x – nx (1 – x), particularly for n=4, and topological conjugacy. Period three inplies existence of all periods. Statement of Sharkovskii theorem.

(45,0) 3

PHY 711

Basic Model Concepts and Manifest Properties of Solids:

Properties of Energy Bands in Solids: Wave function for an electron in a periodic potential, energy bands in a perturbed nearly free electron systems. Energy band calculations, density of states in energy bands. Introduction to energy bands in solids. Optical processes in solids: Absorption and reflection phenomena. Carrier recombination and luminescence, direct and indirect transitions. Excitations, colour centres and lasers. Photoelectric phenomena.

(45,0) 3 E

PHY 712

Semi-Conductor Physics

General introduction: Energy bands, free and localized levels scattering. Electronic transitions, recombination, trapping lifetime, Maxwellian distribution function Boltzmann’s equation, continuity and conductivity equation. Carrier injection into semiconductors.Ambipolar flow, “field-free” diffusion. Current flows in semiconductors: contacts blocking and injecting, p-n junction. Application to device technology.

(45,0) 3 E

PHY 714

Rock Physics

Physical characteristics of rocks with relevance to geo-engineering and geo-exploration applications. Mechanical properties of rocks - strength, deformability, porosity, permeability of sample and in-situ rocks. Electrical properties of rocks - the conduction mechanism in sedimentary, crystalline rocks and magmas. Cross-coupling (electromechanical) phenomena in rocks with applications.

Generalized theory of cracks in rocks. Applications of theoretical and laboratory studies of rock to field phenomena. Solid testing techniques.

(45,0) 3 E

PHY 715

Vacuum Techniques

Rotary pump, diffusion pump, Iron pump, different methods of cleaning surfaces and methods of material preparation for sample analysis in vacuum.

(30,0) 2 E

PHY 717

 Alloys, Surface and Interface Physics

Theories of Binary and Ternary liquid alloys:  Classification of liquid alloys, Calculation of thermodynamic properties of liquid alloys (bulk and surface properties) within the various framework of theoretical models.

Surface and Interface Physics : Reconstruction and relaxation, Surface Crystallography, Surface electronic structure, Magneto-resistance in a two-dimensional channel, P-N Junctions, Hetero-structures , Semiconductor lasers, Light emitting diodes and Scanning tunneling microscopy.

(45,0) 3 E

PHY 731

Applications of Physics in Meteorology

This course covers in an elementary manner the basic concepts in meteorology and illustrates the application of physical and mathematical techniques to meteorological problems.

Scales of motion: the structure and composition of the atmosphere the general circulation, energy sources and sinks, the balances of angular momentum, heat, water vapour and mass; the mean pressure field and air flow; Rossby waves; monsoon circulations; semi

(30,0)2 R

PHY 732

Phenomena in Natural Plasma:

Basic concepts and common phenomena: Debye shieldings, dielectric constant, charge and current densities, conservation laws, dispersion relations in a magneto-plasma. Equations of continuity, diffusion. Equations of motion and transport of ionization, adiabatic invariants. Collusion, ionization and conductivity. Instabilities in plasmas and waves in plasma:. Ionosphere; the earth's ionosphere. Altitude distribution of charged particles. Collisions and conductivity, plasma instabilities and generation of electron density irregularities such as spradic E and spread F. Artificial modification of the ionosphere. The ionosphere's of other planets. Magnetosphere: earth's radiation belts. Geomagnetic trapping of solar wind. Ionospheric and magnetic storms. Sun: reactions in the sun. Solar flux and omission of energetic particles.

(45,0) 3 E

PHY 718 

Ionospheric Physics I                                                                                                                                                                                                    (2units)

Constitution of the atmosphere. Formation and structure of D-, E-, and F-layers of the ionosphere. Vertical and oblique propagation of radio waves in the ionosphere. Ionospheric absorption and fading, magneto-ionic theory. Ionospheric disturbances. Special features of the equatorial ionosphere.

(30,0)2 E

PHY 719 

Ionospheric Physics II          

The earth’s magnetic field. Secular and transient variations. Aurorae. Conjugate point relationships. Winds and movements. Rockets and satellites. Other special techniques.

(30,0)2 E

PHY 783

Solar Physics                         

Solar interior equations. Energy generation rate. The core and envelope. Model of the Sun. Energy transfer. The photosphere. The chromosphere. Radiative transfer equation. Solar-Earth geometry. Motion of the Earth in space. Extraterrestrial solar energy. Scattering in the Earth’s atmosphere. Solar energy variation at ground level. Total global diffuse. Direct irradiances. Solar energy availability predictions from climatological data.

(30,0)2 E

PHY 733

Structure and Dynamics of the Upper Atmosphere Atmospheric nomenclature. Hydrostatic equations of atmospheric structure, scale height. Heat balance in the thermosphere, dissociation and diffusion. Production and loss processes of ions and electrons. Chapman theory. Attitude distribution and temporal variations of neutral and ionized constituents, temperature and collision frequency in the mesosphere and thermosphere. 

Winds and tidal oscillations. Gravity waves. Drift motions of irregularities. E-region electric current and the dynamics of the ionosphere.    

Propagation of electromagnetic waves in the ionosphere. Measuring techniques for the parameter of the neutral constituents, ions and electrons, winds and drifts of irregularities, and temperature with special emphasis on those used locally. 

(45,0) 3 E

PHY 734

Dynamic Meteorology                      

Equations and fundamental laws governing atmospheric motion on rotating earth. Orders of magnitude for different scale of motion. The hydrostatic and geostropic approximations. The thermal wind surfaces of discontinuity. Gravity waves, acoustic waves and Rossby waves. Tidal oscillations Transformation of basic equations into pressure and potential temperature coordinates formulation. Vorticity and divergence equations. Kelvins's Bjerkness' theorem , quasi-geostrophic models. The Omega equation. The boundary layer: the Ekman

(30,2)2 C

PHY 735

Electrical Processes in the Fair Weather Atmosphere      

Atmospheric composition and ionization. Ions, nuclei and aerosols. Vertical profiles of fair weather atmospheric and meteorological parameters. The exchange layer. The atmosphere as a passive electric network. Relaxation time. Basic electrical relations for quasi-stationary changes. The effects of sudden changes. Surface measurements of atmospheric parameters. Free air measurements of electric parameters. Global representatively of stations. Solar terrestrial relations. Experimental techniques in the measurement of atmospheric electric parameters.

(45,45) 4 E

PHY 745

Radioactivity in the Atmosphere.      

Natural and artificial radioactivity; radioactive presentation and variations in air, surface soil, water and rain. The cosmic-induced radioactive contaminants. Detection and characterization of atmospheric radioactive effects. Relations of atmospheric electric effects and radioactivity in the atmosphere. Measurements, experimental investigations and instrumentation requirements. Applications to installations and hazard detection.

(45,0) 3 E

PHY 746

Transient effects in equipment and structural protection from lightning.                                                                                                                                                                                                                                                          The nature and characteristics of transients. Response characteristics of networks to transients. Transient effects on equipment and degradation induced by transients. Fourier frequency characterization of transients. Protection of installations. Distinctions between voltage, current and frequency surges and its relationship wit natural phenomena. Protection of structures and equipment from transients

(45,0) 3 E

PHY 736

Atmospheric Electricicity in Disturbed Weather

Thundercloud structure and dynamics. Optical and electric characteristics of ground and air discharges. Recovery curves. Radiation from lightning channels. Lightning currents. Accoustics of thunder and application to lightning path reconstruction. Characteristics of natural point-discharge. Precipitation electricity. Charge magnitudes and arrangement in thunderclouds. Theories of charge generation in thunderclouds. Warm cloud electrification. Experimental technique in the measurement of disturbed weather atmospheric parameters.

(45,45) 4 E

PHY 737

Surface Energy Budget: Large scale energy budgets and annual hemispheric mean. Equation for the surface energy budget and relative sizes of the terms. Short wave radiation; methods or measurement and the distribution of the radiation. Long wave radiation; Stefan's law, and Win's law, emission of E.M. radiation by the atmospheric gases; the measurements and typical values; soil diffusivities and temperature waves. Altent and sensible heat fluxes; eddy fluxes and eddy diffusivities. Direct and profile measurement of vertical fluxes; Bowen ration, Penman's formula. Advection: the importance and practicability of Advection measurements in case studies. 

Cloud Physics: Condensation and evaporation: growth equation for droplets, ice crystals and precipitation, thermodynamic control. Super-saturation spectra of natural aerosol particles. Simple model on condensation in a steady updraguht. Freezing processes: freezing nuclei, the role of freezing process in precipitation. Coalescence continuos and stochastic growth models; properties of the 'collision kernel'. Cloud modeling; continuity equation applied to cloud and rain.

(30,2) 2 R

PHY 743

Satellite and Radar Meteorology: Physical principles of earth satellites and their sensors; radiometers, limits of resolution, interpretation of LR and visible images, inversion of CO₂ emission data.

Principles of radar, the radar equation, limits of detection and resolution, reflectivity of hydirmeteors, estimation of precipitation rates, iso-echo contoured displays, radar in cloud physics research. 

(30,0) 2 R

PHY 738

Synoptic Meteorology

Pressure systems: the formation and maintenance of anticyclones; the polar front; air masses, air mass characteristic; frontal depressions, slope and characteristics of frontal surfaces; non-frontal low pressure systems' convergence, divergence and vorticity advection and development. Laboratory classes in analyzing synoptic surface and upper air charts, thickness charts, frontal area sections and the T/f diagram.

(15,45)2 C

PHY 739

Atmospheric Models, Numerical Weather Prediction and             Models of the Tropical Atmosphere

Scale analysis of basic equations. Eady's model. Structure of Eady wave comparison with structure of cyclonic wave in atmosphere, selection principle description of GFDL numerical model. Energetics of real atmosphere and energy levels and conversions. Use of models in study of general circulation. Richardson's model. The filter problem. Inclusion of physical processes in numerical models and subgrid scale parameterization. Objective analysis, the balance equation, omega equation. Limitations of numerical  prediction models. The problems of using exciting models in low latitudes, parameterization of radiation and conversation in tropical models. Comparison of existing numerical models of the tropical atmosphere. The modeling of synoptic and sub-synoptic tropical meteorological phenomena.

(45,0) 3 E

PHY 749

Tropical Meteorology, Weather Analysis, Frontogenesis and symbolic Representations

Climatology and general circulation in the tropics, mean wind and temperature fields at the surface and in the troposphere, monsoon circulations, the inter-tropical discontinuity (I.T.D.), the heat and water balance of the tropics. Meteorology of West Africa; mean patterns; the tropical easterly jet, the African easterly jet, easterly wave, and vortices, their propagation and characteristics the I.T.D. over West Africa. Weather systems affecting West Africa, dust haze. Line squalls, thunderstorms monsoon rain fog; the interactions between the monsoon flow and zonally propagating perturbations resulting in the observed weather. 

Methods of analyzing meteorological data in the tropics forecasting techniques, forecasts for specific purposes, use of satellite and radar data.

Laboratory exercises include the streamline analysis of West African weather systems, use of satellite vis. and I.R. data, computations of divergence and vorticity in tropical synoptic systems and the use of the T/f gram in the tropics.

Fronto-genesis and symbolic representations

(15,45)2 R

PHY 741

Physical Meteorology II

Atmospheric Radiation: Physics of electromagnetic radiation; simple quantum theory, the shape and width of spectral lines Radian flux, intensity and radiance, the laws of Kirchoff, Lambert, Stefan Wien, Planck and Swartchild; Rayleig and Mie scattering.

Solar radiation: the origin of the observed solar spectrum, the solar constant and its measurements; the geometry of received solar radiation; the absorption of solar radiation in the atmosphere and the distribution of the radiation received at the earth surface.  Terrestrial radiation; the absorption bands in the free atmosphere, monochromatic fluxes, heating rates, the diffusive approximation; the application of band models, Simpson's method, Elsasser charts.

Radiation climatology: the distribution of radiative sources and sinks, net radiation computations, the parameterization of radiation in numerical models of the atmosphere.      

Boundary layer: Reynold's stresses, momentum and heat transport by turbulence. Eddy transfer coefficients, Prandtl's mixing length hypothesis. Logarithmic wind profile in the neutral boundary layer. The atmospheric boundary layer, the constant flux layer, the Ekman layer, similarly techniques for describing the boundary layer. Stability parameters; Richard Richardson's number, the Monin Ubokhof parameter, Deacon's law and the power law. Comparison of the theoretical and observed wind temperature and humidity profiles.

Turbulence and Diffusion: Atmospheric turbulence and relationships with velocity correlation's; energy transfer by turbulence, the universal equilibrium range, the inertial and viscous sub-ranges.

Diffusion in the lower atmosphere: the dispersion of tracers in the lower atmosphere described by classical theory, the statistical approach and empirically. The application of these descriptions to atmospheric pollution.

(30,0)2

PHY 742

Special Topics in Meteorology        

Introductory courses of fifteen lectures may be given on a variety of specialized topics related to meteorology. Students may register for from 2 to 4 topics.

Meteorology of East Africa -  Climatology of East Africa and the Indian Ocean tropical cyclones of the Arabian Sea and Indian Ocean, the inter-tropical discontinuity the effects of mid-latitude systems, dynamic considerations, primary models of the bridge and dust system, secondary models of the East African wind regions.

Applied Climatology - Application of Climatology methods and date to agriculture, environmental studies, industry, civil engineering, aviation and town planning. Processing and presentation of data for different applications, benefit analysis of applied climatology.

Atmospheric Electricity - Vertical electric field and current in fine weather; field changes due to lightning discharges and recovery after a discharge; the structure of a lightning flash; the electrical structure of a thunderstorm. Mechanisms for cloud electrification.

Upper Atmospheric Physics: Atmospheric nomenclature, the ozonosphere, ozone distribution; ozone and weather. Heat balance in the thermosphere; atmospheric compositions, temperature and density distribution. The ionosphere. The magnetosphere.

Hydrology: Concept of the hydrological cycle, precipitation estimates, measurements; water surplus and deficit, soil moisture, infiltration, storage, movement and seasonal variations; ground-water, aquifer characteristics; surface water measurements of flow in natural channels, base flow and regression curves, storm run off; effect of vegetation on water balance; hydrological forecasting.

(30 – 60,0)

(2 – 4)

PHY 751

Fundamentals of Nuclear Physics.

Introduction and basic concepts: Definitions, Nuclear properties, Nuclear potential and energy levels. Radioactivity and transformation kinematics. Nuclear collisions.

Nuclear Instability: b^- decay, b⁺ decay, electron capture (EC), a-decay and semi classical theory of a-decay, gamma -decay and yield selection rules, Internal conversion (IC), Auger electron emission.

Interaction of Radiation with matter: specific ionization, linear energy transfer (LET). Mechanisms and energy transfer of Heavy changed particles (Bethe-Bloch formula, Bragg curve, energy requirements etc), fast electrons, gamma-rays, neutrons including attenuation and moderation. Nuclear reactions: General features of nuclear reactions, elastic scattering, direct reaction, compound nucleus reaction, Heavy ions reaction. Brief review of concepts and principles of reactors and criticality.

(45,0) 3

PHY 752

Radiation Detection and Dosimetry:

Radiation quantities: Definitions and Units

Radiation detection methods: Ionization in gases; Ionization in semiconductors, Scintillation Gamma spectrometry, Neutron detection, Thermoluminescence, Film Dosimetry, Chemical dosimeter (Fricke), Particle Track detection, calorimetry, etc.Counting statisticsDosimetry: External dosimetry (gamma ), Internal dosimetry, Reference Man Patient Dosimetry in radiographicexamination, mammography, fluoroscopy and computed tomography

(45,0) 3

PHY 753

Radiation Biology:

Cellular Radiation Damage: Single strand break, Double strand break, Repair, DNA Degeneracy, Stochastic and Non-stochastic Effects: Somatic and Genetic Effects, Late Effects, Latency Period, Radiation Carcinogenesis Mutations.

Radiation Modifying Agents: Radiosensitizers and Radioprotectors, Linear Energy Transfer Oxygen Effect, Sulphides and other agents.

Cell Cycle (Mitoses, Mioses)

Acute Radiation Syndrome: LD₅₀

Prenatal Radiation Exposure:

Risk and comparison of Risks:

(45,0) 3

PHY 754

Radiation protection Guides:

The External Radiation Hazard and Protection: Time, distance and shielding, Monitoring for external radiations (areas and personal).

The Internal Radiation Hazard and Protection: Sources and type of airborne contaminants, control of the internal radiation hazard, exposure reduction, internal dosimetry. Waste Management: Contamination, protection against contamination (protective clothing, decontamination), Waste disposal, packaging and safe transport of radioactive materials. Principles of Radiation Protection: Justification, optimization, dose limit, international safety standards –ICRP, BSS, NNRA.Elements of Radiation Protection Programmed in Medicine and Industry: Monitoring, Emergency preparedness planning and response, QA and QC for equipment, Training, Audit, Safety of equipment.

(45,0) 3

PHY 755

Nuclear Applications in Medicine, Industry and Research

Physics and Principles of diagnostic imaging equipment: radiographic x-ray unit, fluoroscopic unit, computed tomography, mammographic units.Principles of radiation therapy (teletherapy and brachytherapy). Physics of radiotherapy equipment: C0-60 unit and Linear accelerator.

Physics and operational principles of Gamma camera. Physics of Positron (b⁺) Emission Tomography (PET). Physics and operational principles of Magnetic Resonance Imaging (MRI). Industrial Uses: Industrial radiography, Tracing, Gauging, Material Modification, Sterilization food preservation and others. Research Uses: Neutron Activation Analysis, Particle-induced x-ray Emission (PIXE) and others.

(45,0) 3

PHY 756

Non-ionizing radiation:

Radiometric Units Lasers: Laser operations, Lasing Actions, TEM modes, Biological effects: eye damage, skin damage, Protection Guides and Standards, Maximum Permissible Exposure (MPE), Safety Measurements, power and energy, Beam divergence

Radiofrequency (RF) and Microwave:

Communications, antennas and antenna gain, G, Penetration depth. GSM hand-sets and base stations, Biological Effects, Thermal and Non Thermal Effects, temperature-humidity index. Microwave Measurements, survey meters Protection Guides and Standards, Maximum permissible exposure (MPE) Safety

(45,0) 3

PHY 760

Laboratory & Field Experiments in Geophysics Basic techniques of laboratory and field research in geophysics. Geophysical instrumentation and design. Actual data acquisition and analysis. (Involving laboratory experiments or field trips).

15,90)3s

PHY 761

Laboratory and Field Experiments in Meteorology A series of experiments designed to illustrate meteorological phenomena and the use of meteorological research tools. Experiments in instrument errors and characteristics and the measurement of ground of heat flux, solar radiation measurements, drop size distribution in precipitation, the vertical wind profile, the turbulence spectrum near the ground.

(0,90) 2 R

PHY 762

Operational Meteorological and Climatology

A three part practical orientation programme conducted in collaboration with the Meteorological Research and Training Institute, Oshodi:

(i) Meteorological observing plotting and the use of routine instruments.

(ii) Operational analyses and aviation forecasting techniques.

(iii)       Climatological methods: statistical concepts, distributions and probabilities, coefficients of variation, estimation of extremes, regression, coefficients; significance, student's Fisher's and chi-squared tests. 

(30,90)4

PHY 771

Fundamentals of Electronics: Designs and Analysis. Circuit theory network synthesis and analysis. Basic theory of amplifiers. Feedback systems and application. Equivalent electrical circuits for physical and biological systems.

(3,0) 2

PHY 772

Physical Instrumentation

The electronics of instrumentation. Circuit elements, laws and networks. Signal and amplification and noise elimination. Operational amplifiers and applications. Methods and techniques of scientific measurements: sensor processors, storage and retrieval systems. Display and recording of signals. Basic principles of the D'Arsoncal meter VTBM, the generalized meter and the C.R.O. automatic synchronization's mechanism and stability. Analog and diagonal recording systems and converters. Computer compatible data logging. DC and AC bridges. Electrical transducers and applications in servo-control, remote sensing and scientific measurements. Special applications in instrumentation. (The application will involve the design of instrument prototypes).

(30,90) 3

PHY 773

Methods and Techniques of Geophysical Prospecting

A classification of geophysical techniques for investigating the earth's crust. Unified approach to geophysical data acquisition, analysis and interpretation: Planning, staking, mapping, presentation of results, analysis and interpretation techniques. Gravity methods. Seismic refraction and reflection techniques. Magnetics and geo-electric's. Field and laboratory techniques. Generalized interpretation techniques and geophysical instrumentation. (Instrumentation will involve particular geophysical instrument which will be selected every year).

(30,90) 3

PHY 774

Applied Electronics and Workshop Practices Workshop - safety precautions. Basic hand tolls and bench work practice. Plain and cylindrical generation of smooth surface using power operated machines. Selection and properties of materials used for construction - metallic and non-metallic. Metal joining devices and adhesives in common use. Soldering techniques and wrap joints. Multi-meters and oscilloscopes. Auto-ranging in measuring instruments. A survey of the use of electronics circuit devices e.g. diodes, transistors including FET, integrated circuits, photocells. Selection, use and care of test instruments. Survey of pick-ups and transducer devices. Basic circuit synthesis and analysis. Pulse circuits. Instrumentation and measuring techniques: impedance matching. Probes - active and input and output impedance using the scope.

(0,90) 2 C

PHY 781

Numerical and Computational Methods Interpolation schemes, the Lagrangian representation, Aitkin algorithm least square fit. Interactive processes. Solution of linear equations, Gaussian elimination, inversion of matrices. Fourier series and harmonic analysis. Difference equations. Numerical integration and differentiation - Trapezium, Simpson's limitation of size of grid. Solution of ordinary differential equation, step by step methods, Kutta predictor methods. Partial differential equation; simple wave propagation forward difference, backward difference, central difference in time, the implicit scheme, conditions for stability; e.g. diffusion equation; hyperbolic equation method of relaxation and other interactive schemes applied to simultaneous equations; ill-conditioned equations. Elliptic equations - interactive methods, spectral series method.

Functional representation, minimization and telescoping. Computer solution of equations.

(30,90) 3 R

PHY 782

Mathematical Methods of Physics Functions of a complex variable and the properties and consequences of analyticity; techniques of analytical continuation and applications, calculus of residues. Complex integration. Conformal transformations, 'Systematic' methods of obtaining 'exact' solutions of O.D.E., in closed forms. Local and global analysis of initial and boundary values problems Applications will include solutions of Eigenvalues of schroedinger type equations, the classical Anharmonic oscillator. Introduction to partial differential equation methods of characteristics for solving first order p.d.e. Transform methods and application to the solution of initial and boundary value problems.

PHY 790

M.Sc. Project                         6 units

Registration in consultation with staff in any area of their options. Candidates will also be required to present their reports orally.

6 units C

PHY 790

Diploma Project

In consultation with their supervisors, candidates may either carry out a directed research project in meteorology or prepare a review of selected papers on a chosen meteorological topic. Candidates may be also required to present their reports orally.

(30,0) 2 C

PHY 802

Statistical Mechanics

Gibbs theory of thermodynamics with emphasis on interactions among the constituents of the ensemble; thermodynamics limit, stability and suitable interaction potentials. Cooperative phenomena; models of ferromagnetism, spin correlations, long range order, Universality. Models: Ising and Lattice-gas Hamiltonians. Exact solutions to one dimensional Ising model. Mean-field theories. Curie-Weiss theory. Landau theory and the order-parameter. Scaling and critical exponents relations. Introduction to the renormalisation group. Critical non-equilibrium systems; earthquakes, sand piles and rice piles, biological evolution. Simple numerical models; the sand pile cellular automaton, Lattice gas, Extremum dynamics model of evolution. Analytic formalism; mean field theory of branching ratios, stochastic diffusion equations. Renormalisation group. Introduction to “generalized homogenous functions”, convexity, and renormalization techniques. Quantum-field theoretic method.

(30,45) 3

PHY 804

Many-body Theory

Basic notions of quantum statistics, partition functions and the field theoretic method. Approximation scheme. Hartree-Fock. R.P.A. Application to lattice dynamics: Electrons, Phonons and their quantization, phonon modes in perfect crystals. description of one- and two- body forces. Second quantization. Ground states in Hartree-Fock approximation.

Greens Function Formalism. Schrodinger, Heisenberg and Interaction Representations. Evolution in Complex time. Linear response functions and Green’s Functions. Wick’s theorem for operator products and averages. Feynmann diagrams. Thermodynamic Feynman diagram. Ward identities. Transport Phenomena and Disorder effects: Boltzmann description of Electron transport. Einstein relations and stationary transport coefficients. Resistivity due to electron-phonon interaction. Low-temperature resistivity due to electron-electron interaction. Kubo formula. Impurity scattering. Disorder; localization and length scaling. Superconductivity; Effective electron attraction – Cooper pairs and Schafroth pairs. BCS ground state. Gap equation and Bogoliubov transformation. London equation and Critical field. Ginzburg-Landau equations. Type-1 and II superconductors. Flux quantization, Critical coupling. Magnetism: Magnetism of local moments. Weiss’ Molecular Field theory. Ground State and Magnons of the Heisenberg model. Ground state, excitations and symmetries of the Hubbard model. Weak itinerant electron Magnetism. Itinerant-electron Ferromagnetism and antiferromagnetism. Magnetization fluctuations. Spin-density waves.

(30,0) 2

PHY 811

Thin Solid Films                   

Preparation of thin films, high vacuum techniques, vacuum evaporation, cathodix sputtering, chemical vapour disposition. Nature of thin films - condensation nuclation and growth of thin films, epitaxy of metals and semiconductors. Electron microscopy of thin films - microstructural determination by electron microscope - electron diffraction studies - analysis of complex diffraction patterns -  reflection and scanning electron microscopy. Electrical properties of metal films - transport phenomena in semi-conductor films. Thin film superconductors. Metal - semi-contacts. Application of thin films - thin film resistors, capacitors and conductors in integrated circuit. Various methods for the measurement of thickness of thin films. Optical properties of thin film.

(30,0) 2

PHY 812

Surface Physics of Solid Materials

Atomic structure of surfaces. Electronic structure of solid surfaces and electronic transport at surfaces. Surface states, and space charge layer. Techniques and measurements - experimental methods. Application in semi-conductor devices.

(30,0) 2

PHY 813

Geo-Potential Fields and the Earth's Interior

Potential field theory of geophysics: multiple expansion, method of images, upward/downward continuation, introduction geomathematics. Electrical properties of the earth's interior. Investigations of the upper mantle and mantlecore system; seismology long wavelength geomagnetic E.M., and gravity fields and geothermal fields. Phase transitions, equation of state and cross coupled properties thermoelastic, thermovisco-elastic, magneto elastic etc.

(30,0) 2

PHY 832

Ionosphere Physics               

Detailed treatment of the magneotionic theory (both Appleton-Hartee and the generalized theory of Sen-Wyller) - dispersion, absorption, phase and group velocity, virtual height, true height, ray tracing and full wave theory. Introduction to the magnetosphere. Selected research topics (with emphasis on ionospheric research topics in progress in the Department): ionospheric storms; spread F; sporadic E; drifts, waves and irregularities; absorption and the lower ionosphere; ionospheric propagation of h.f., l.f., and v.l.f., radio waves; v.h.f. scatter propagation; incoherent scattering; artificial heating and modification of the ionosphere; total electron content; solar effects on the ionosphere. Sample calculations and analysis techniques.

(15,45)2

PHY 873

Advanced Methods of Applied Geophysics

Time sequence analysis in geophysics-convolutions, transforms deconvolutions and filtering techniques-applications in seismic methods. Conduction mechanism in porous materials and silicate melts. Double layer and associated phenomena, and cross-coupling effects in crystal materials. Paleomagnetism and magnetic characteristics of rocks. Geophysical inversion techniques using linear pregnostic and diagnostic iterations. Laboratory and field techniques. (Selected topics).

(30,0) 2

PHY 874

 Sources and Utilization of Energy

Importance of energy. Sources of energy. Methods of conversion and harnessing of energy. Solar cells as a solar energy; converter - characteristics, efficiency and technology of the devices. Direct conversion of energy and applications in technology. Other forms of energy-nuclear, fossil, geothermal tidal and hydro, and wind.

(30,0) 2

PHY 883

Applied Group Theory

Elementary differential geometry. Elements of Lie algebra and Lie group theory.  Symmetric spaces. Elementary fibre-bundle theory. Applications to quantum mechanics and relativity theory.

(30,0) 2