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Doctor Study Program in Physics and Astronomy


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University of latvia


Doctor Study Program


Doctor Study Program in Physics and Astronomy

for obtaining the degree of the Doctor of Physics (Dr. Phys.)





Chairman of the Board of Doctor studies in Physics and Astronomy,

Director of the Program

Mārcis Auziņš

Prof. Dr. Habil. Phys



ADOPTED

at the meeting of the Board

of Doctor studies in Physics and Astronomy

held on ____.___.___

Minutes No ________

Chairman of DP

________________

(signature)

ADOPTED

at the meeting of the Council

of the Faculty of Physics and Mathematics

held on _____.____.____

Minutes No _______________

Chairman of the Council

_________________

(signature)




Adopted

at the meeting of the LU Scientific Council

____.____.____

Minutes No ________

Scientific Pro-rector

___________________

(signature)

Adopted

at the meeting of LU Senate

____.___.____

Resolution No _____

Chairman of the Senate

__________________

(signature)






^ Doctor Study Program in Physics and Astronomy

ANNOTATION


The aim of the Doctor study program in physics is to ensure obtaining of the scientific qualification in astronomy or the following subsections of the science of physics:




  • Solid-state physics

  • Experimental methods and instruments in physics

  • Didactics of physics

  • Physics of condensed substance

  • Chemical physics

  • Laser physics and spectroscopy

  • Physics of materials

  • Medical physics

  • Optics

  • Optometry

  • Physics of semi-conductors

  • Thermophysics

  • Fluid and gas mechanics

  • Theoretical physics



The realisation of the Doctor study program in the LU Faculty of Physics and Mathematics is organised in compliance with the laws "On Higher Educational Establishments", "On Scientific Activity", "On Education", the Constitution of LU, the Doctor study program of LU, "Regulations on the Schedule and Criteria of Promotion" (Regulations No 134 of the Cabinet of Ministers, 06.04.99.), an the present program.


In realisation of the Doctor study program there participate the professors, lecturers and employees of the Department of Physics, LU Faculty of Physics and Mathematics, employees of the LU Institute of Astronomy, employees of the LU FPhM Institute of Nuclear Physics and Spectroscopy, employees of the LU Institute of Solid-state Physics, employees of the LU Institute of Physics, employees of the LU Institute of Chemical Physics. In realisation of the program there is attracted also the material and technical resources of the aforesaid institutes, mainly in the form of experimental equipment and computers.


^

Doctor Study Program in Physics and Astronomy





The scientific degree to be taken. Doctor of physics (Dr. phys.)

Aim of the studies. To prepare highly qualified scientists and teaching staff in physics

The studies are co-ordinated by the Chairman of the Board of Doctor studies (at present prof. M. Auziņš)

^ Board of the Doctor studies in Physics:


The Board of the Doctor studies in Physics and Astronomy upon recommendation of the Council of LU FPhM is approved by the Scientific Pro-rector of LU for the term of 5 years. The Board consists of all professors of the Department of Physics. Additionally there may be elected associated professors. The candidates for a doctor’s degree from among the students of the doctor studies nominate their representative. The present composition of the Board of the Doctor studies in Physics and Astronomy is given in the Appendix 1.


The studies take place:

In the Department of Physics of the Faculty of Physics and Mathematics and in the institutes associated with the faculty:


^

Structure of LU


Main directions of research

LU Institute of Astronomy

  • Astrophysics

  • Geo-cosmic research

LU FPhM Institute of Nuclear Physics and Spectroscopy

  • Theoretical nuclear physics

  • Physics of atoms and molecules

  • Laser spectroscopy

  • Medical physics

  • Technical physics

LU Institute of Solid-state Physics

  • Physics of materials

  • Solid-state physics

  • Physics of unarranged substances

  • Physics of glass

  • Technical physics

  • Medical physics

LU Institute of Physics

  • Fluid and gas mechanics

  • Thermophysics

LU FPhM Department of Physics

  • Didactics of physics

  • Thermophysics

  • Fluid and gas mechanics

  • Theoretical physics

LU Institute of Chemical Physics

  • Chemical physics

  • Theoretical physics



Studies and research are carried out in the following subsection of physics:




Subsection

Leading professor1

Astronomy

Doc. Juris Žagars

Physics of condensed substance

Prof. Andrejs Siliņš

Experimental methods and instruments in physics

Prof. Ivars Tāle

Didactics of physics

Prof. Edvīns. Šilters

Sold-state physics

Prof. Ivars Tāle

Chemical physics

Prof. Andrejs Siliņš

Laser physics and spectroscopy

Prof. Mārcis. Auziņš

Physics of materials

Prof. Andris Krūmiņš

Physics of semi-conductors

Prof. Andris Krūmiņš

Medical physics

Prof. Jānis Spīgulis

Optics

Prof. Ruvins Ferbers

Optometry

Prof. Ivars Lācis

Fluid and gas mechanics

Prof. Andrejs Cēbers

Thermophysics

Prof. Andrejs Cēbers

Theoretical physics

Prof. Mārcis Auziņš




^ In studies and research co-operation with the following universities is carried out2:

University of Lund, University of Goteborg, University of Linchoping, Kings College of London, Moscow State University, University of Connecticut, University of Oklahoma, D.Didro University No 7 of Paris, Nica-Sophia Antipolis University, Technical University of Athens, University of Rostock, University of Kaiserslautern, University of Sussex, University of Hannover, University of Kotbuss.


^ Prerequisites for doctor studies in physics:

Master’s degree in physics (Mc.phys.), master’s degree in chemistry (Mc.chem.), master’s degree in engineering (Mc. ing) and diplomas of the higher education adequate to the said master’s degrees.


Admission to the LU program in doctor studies in physics

  • The applicant submits to the Board of the doctor studies in physics (BDS) the draft of the scientific research and during the discussions organised by DSP the level of the applicant’s knowledge in physics, respective subsection of physics and foreign language is evaluated. The commission established by BDS adopts the decision concerning the conformity of the applicant and, if necessary, indicate the additional courses to be acquired during the studies.

  • Based on the recommendations of the Board of the doctor study program in physics in the Department of LU Doctor studies the applicant is matriculated in the LU program of doctor studies.

  • The candidate for the doctor’s degree together with the scientific supervisor, taking into account the recommendations of BDS, elaborate the individual study and research program, which under leadership of the professor of the respective subsection is adopted at the meeting of the structure and is submitted to the Department of LU Doctor studies.



^ Contents of the Doctor study program in physics.

Full-time studies in the LU doctor study program in the field of physics correspond to 144 credits which are divided as follows:

  1. Acquiring of the latest research methods of the respective subsection of physics, acquiring of the methods and approaches of information technologies, data processing and presentation – 12 credits;

  2. Preparation and participation in the realisation of the Bachelor and Master study programs in physics, scientific conferences, seminars, schools – 18 credits.

  3. Acquiring of theoretical courses:

  • the main course of the subsection (see programs in the appendix) – 8 credits;

  • course of specialisation (contents is determined individually) – 6 credits;

  • individually determined additional courses (if necessary).

  1. Individual research work and elaboration of the promotion work – 100 credits.




The form of the promotion work in physics.

The form of the promotion work may be dissertation or the series of scientific articles.


1. ^ The promotion work – series of scientific articles consists of the resume, paper and at least five scientific articles of the author, which are published or accepted for publication in the editions, which are included in the list, determined by LSC.

The paper of the promotion work summarises the results, shown in the scientific articles of the author, if necessary slightly supplementing them with the works which are not yet prepared in the form of articles.

The scientific articles, included in the promotion work – the series of scientific articles, are the copies of full research publications according to the regulations of those magazines, which have accepted or have been submitted for publication.

The authors of the promotion work may add to the work also the copies of the published theses of conferences and scientific meetings, providing also with the necessary bibliographic references.


2. ^ The promotion work – dissertation is formed as a significant research in some of the subsections of physics, which makes a completed, uniform work, which due to its specifics may not be published in parts during the course of the work.

The promotion work – dissertation is an expanded scientific research where the detailed overview is given about general achievements in the respective field of science, as well as reflected the significance of the concrete work in the context of the development of the field of science, indicated and described in detail the methods and materials, which have been used in the work, as well as clearly shown the results achieved in the work and their scientific value.

For defending the promotion work – dissertation there are necessary 5 publications in the editions form the list, approved by LZP and 2 reports at international conferences.

The authors of the promotion work may add to the work also the list of other publications.


Defending of the promotion work.

The promotion work is defended in some Promotion Board of the branch of physics.


Appendices

  • Promotion examination programs of subsections with the lsit of literature

  • CVs of the leading professors with the list of latest publications.



Appendix 1. The composition of the Board of doctor studies in physics and astronmy




  1. Prof. Mārcis Auziņš

  2. Prof. Andrejs Cēbers

  3. Prof. Ruvin Ferber

  4. Prof. Andris Krūmiņš

  5. Prof. Ivars Lācis

  6. Prof. Andrejs Siliņš

  7. Prof. Edvīns Šilters

  8. Prof. Jānis Spīgulis

  9. Prof. Ivars Tāle

  10. Dr. habil. phys Juris Žagars

  11. Representative nominated by candidates for the doctor’s degree from among students



Doctor study program in physics and astronomy

The aim of this Study program is to prepare highly qualified scientists and teaching staff in physics and astronomy. The persons, who have accomplished these studies are able to successfully compete in the labour market for leading positions in various fields of science capacious national economy.

The Doctor study program envisages obtaining the higher qualification in some subsections of the science of astronomy and physics:

Solid-state physics, Experimental methods and instruments in physics, Didactics of physics, Physics of condensed substance, Chemical physics, Laser physics and spectroscopy, Physics of materials, Optics, Optometry, Physics of semi-conductors, Thermophysics, Fluid and gas mechanics, Theoretical physics.

The realisation of the Doctor study program in the Faculty of Physics and Mathematics (FPhM) of University of Latvia (LU) is organised in compliance with the laws "On Higher Educational Establishments", "On Scientific Activity", "On Education", the Constitution of LU, the Doctor study program of LU, "Regulations on the Schedule and Criteria of Promotion" (Regulations No 134 of the Cabinet of Ministers, as of 06.04.99.), the Doctor Study program in Physics and Astronomy.

In realisation of the Doctor study program there participate the professors, lecturers and employees of the Department of Physics, Faculty of Physics and Mathematics of University of Latvia, employees of the LU Institute of Astronomy, employees of the LU FPhM Institute of Nuclear Physics and Spectroscopy, employees of the LU Institute of Solid-state Physics, employees of the LU Institute of Physics, employees of the LU Institute of Chemical Physics. In realisation of the program there is attracted also the material and technical resources of the aforesaid institutes, mainly in the form of experimental equipment and computers.

Contents of the Doctor study program in physics. Full-time studies in the LU doctor study program in the field of physics correspond to 144 credits which are divided as follows:

  1. Acquiring of the latest research methods of the respective subsection of physics, acquiring of the methods and approaches of information technologies, data processing and presentation – 12 credits;

  2. Preparation and participation in the realisation of the Bachelor and Master study programs in physics, scientific conferences, seminars, schools – 18 credits.

  3. Acquiring of theoretical courses:

  • the main course of the subsection (see programs in the appendix) – 8 credits;

  • course of specialisation (contents is determined individually) – 6 credits;

  • individually determined additional courses (if necessary).

  1. Individual research work and elaboration of the promotion work – 100 credits.




The form of the promotion work in physics. The form of the promotion work may be dissertation or the series of scientific articles.

1. The promotion work – series of scientific articles consists of the resume, paper and at least five scientific articles of the author, which are published or accepted for publication in the editions, which are included in the list, determined by LSC.

The paper of the promotion work summarises the results, shown in the scientific articles of the author, if necessary slightly supplementing them with the works which are not yet prepared in the form of articles.

The scientific articles, included in the promotion work – the series of scientific articles, are the copies of full research publications according to the regulations of those magazines, which have accepted or have been submitted for publication.

The authors of the promotion work may add to the work also the copies of the published theses of conferences and scientific meetings, providing also with the necessary bibliographic references.

2. ^ The promotion work – dissertation is formed as a significant research in some of the subsections of physics, which makes a completed, uniform work, which due to its specifics may not be published in parts during the course of the work.

The promotion work – dissertation is an expanded scientific research where the detailed overview is given about general achievements in the respective field of science, as well as reflected the significance of the concrete work in the context of the development of the field of science, indicated and described in detail the methods and materials, which have been used in the work, as well as clearly shown the results achieved in the work and their scientific value.

For defending the promotion work – dissertation there are necessary 5 publications in the editions form the list, approved by LSC and 2 reports at international conferences.

The authors of the promotion work may add to the work also the list of other publications.

The process of the doctor studies is managed and controlled by the Board of Doctor studies with the following composition:

Prof. Mārcis Auziņš – Chairman of the Board, Prof. Andrejs Cēbers, Prof. Ruvin Ferber, Prof. Andris Krūmiņš, Prof. Ivars Lācis, Prof. Andrejs Siliņš, Prof. Edvīns Šilters, Prof. Jānis Spīgulis, Prof. Ivars Tāle, Dr. habil. phys Juris Žagars

As it is demonstrated by the investigation carried out in Latvia and 23 more European countries, in total more than hundred universities, by the European Physics Education Network (EUPEN), the Doctor study program in physics and astronomy of the University of Latvia correspond to the average European level of the Doctor studies in physics, see Inquiries into European Higher Education in Physics, vol. 3, Gent 1999.

Number of the students. During the last years in the study program in physics and astronomy at an average there are admitted 6 students per year. Taking into account that not always it is possible to finish studies in the envisaged three years, the total number of the students in this program is about 20. The program is finance from the resources of the State budget.

In the material and technical resources provision of the program there participate the institutes, associated in the Department of Physics of the Faculty of Physics and Mathematics and with the faculty, where the scientific researches are carried out in the enumerated subsections of physics and astronomy:


LU Institute of Astronomy Astrophysics

Geo-cosmic research

LU FPhM Institute of Nuclear Physics and Spectroscopy Theoretical Nuclear Physics

Physics of atoms and molecules

Laser spectroscopy

Medical physics

Technical physics

LU Institute of Solid-state Physics Physics of materials

Solid-state physics

Physics of unarranged substances

Physics of glass

Technical physics

Medical physics

LU Institute of Physics Fluid and gas mechanics

Thermophysics

LU FPhM Department of Physics Didactics of physics

Thermophysics

Fluid and gas mechanics

Theoretical physics

LU Institute of Chemical Physics Chemical physics

Theoretical physics


Program of doctoral examination in physics.

Specialty - theoretical physics


I General program

  1. Basic concepts of quantum mechanics.

  1. Density matrix.

  2. Angular momentum and spin. Addition of angular momenta.

  3. Perturbation theory. Perturbation theory of degenerated states. Time dependent

perturbation theory.

  1. Semiclassical approximation. Boundary conditions and theBohr-Sommerfeld

quantization. Tunneling. Semiclassical matrix elements.

  1. Hydrogen atom.

2.1. Schrodinger equation for hydrogen atom in spherical coordinates.

2.2. Rydberg states. Semiclassical wave functions. Quantum defect.

2.3. Schrodinger equation for hydrogen atom in parabolic coordinates.

  1. Dirac equation for hydrogen atom. Structure of energy levels.

  2. Vacuum polarization.The Lemb shift.

  3. Hyperfine structure. Interaction of electron with magnetic dipole and

electric quadrupole momentum of nuclei.

  1. Multielectron atoms.

  1. Central -field approximation. Classification of electronic states.

  2. Electrostatic and spin-orbit interaction. Lj and jj coupling. Periodic system

of elements.

  1. Self- consistent field theory. Hartree-Fock approximation.

  2. Tomas-Fermi equation.

  1. Molecules.

  1. Hydrogenic molecular ion H2+ . Separation of variables.

  2. Born-Oppenheimer approximation.

  3. Electronic terms of diatomic molecules. Their classification.

  4. Rotational and vibrational energies of diatomic molecules.

  5. Hund’s coupling cases.

  6. -doubling.

  7. Collision of second case. Landau-Zener formula.

  8. Variational calculations of molecules. Density functional method.

  1. Atomic nuclei.

  1. Nuclear shell model.

  2. Collective nuclear models for spherical and deformed nuclei.

  3. Generalized unified model.

  1. Atoms in external static fields.

  1. Hydrogen atom in static electric field.The linear Stark effect. Ionization by

electric field.

  1. Multielectron atoms - the squared Stark effect.

  2. Schrodinger equation in magnetic field. Electron in homogeneous

magnetic field.

  1. Zeeman effect. Paschen-Back effect.

  1. Electromagnetic field quantization.

  1. Quantization of transverse electromagnetic waves. Creation and annihilation

operators. Photonic states.

  1. Shift operator and coherent states.

  2. Squeezed quantum states.

  1. Interaction of atoms with electromagnetic field.

  1. Emission and absorption of photons. Einstein’s coefficients.

  2. Electric dipole transitions in atoms. Selection rules.

  3. Higher multipole transitions in atoms, molecules and atomic nuclei.

  4. Two-level system in periodic field.The Rabi frequency.

  5. Atoms in strong laser field. Multiphoton ionization and harmonic generation.

High order perturbation theory and “nonperturbative” methods.

  1. Scattering theory.

  1. Elastic scattering of partcles in classical physics. Cross sections. Rutherford

formula.

  1. Scattering of particles in quantum mechanics. Scattering amplitude and phase.

Differential and total cross sections.

  1. Semiclassical approximation.

  2. Born approximation.

  3. Scattering of low-energy particles.

  4. Resonance with quasidiscrete level.

  5. Nonelastic scattering. S-matrix. Resonanses in nuclear reaction.

The Breit-Wigner formula.

  1. Close-coupling equations.

  2. Scattering of fast electrons from atoms and molecules.

  3. Optical model for nuclear reactions.




References

  1. L.D.Landau and E.M.Lifshitz, Quantum Mechanics ( Pergamon, Oxford, 1977 ).

  2. H.A.Bethe and E.E.Solpeter, Quantum Mechanics of One- and Two-Electron Atoms,

2nd ed. ( Plenum/Rosetta, New York, 1977 ).

  1. I.I.Sobelman, Vvedenije v Teoriju Atomnih Spektrov ( Fizmatgiz, Moskwa, 1963 ).

  2. V.B.Berestecky, E.M.Lifsitz i L.P.Pitajevsky, Relativistskaja Kvantovaja Teorija,

Cast 1 ( Nauka, Moskwa, 1968 ).

  1. A.I.Ahijezer, Kvantovaja elektrodinamika ( Nauka, Moskwa, 1985 ).

  2. J.S.Slater, Electronic Structure of Molecules.

  3. U.Failer, Strojenije i Dinamika Molekul, ( Mir, Moskwa, 1982 ).

  4. P.W.Atkins, R.S.Friedman, Molecular Quantum Mechanics, 3rd ed. ( Oxford

University Press, 1997 ).

  1. J.M.Sirokov i N.P.Judin, Jadernaja Fizika ( Nauka, Moskwa, 1980 ).

  2. A.S.Davidov, Teorija Atomnovo Jadra ( Fizmatgiz, Moskwa, 1958 ).

  3. L.D.Landau and E.M.Lifsitz, Mechanics ( Pergamon, Oxford, 1960 ).

  4. N.F Mott and H.S.Massey, Theory of Atomic Collisions ( Oxford University

Press, London, 1965 ).


II Special program “Theory of interaction between atom and laser radiation




  1. Dipole transition probabilities for hydrogen atom. Gordon’s formulas. Semiclassical

approximation.

  1. Photoeffect and bremsstrahlung.

  2. High order perturbation theory for calculation of multiphoton transition

probabilities in atoms.

  1. Semiclassical approximation for evaluation of multiphoton processes.

  2. The Keldysh theory.

  3. Quasienergy approach.

  4. Numerical methods in the case of three-dimentional time-dependent potentials.

  5. Above-threshold ionization spectrum and its complex structure for short laser

pulses.

  1. Multiple ionization of atoms.

  2. Scattering of particles in presence of laser radiation.

  3. Harmonic generation.

  4. Microwave ionization of Rydberg atoms. Chaos phenomenon.

  5. Transitions in Rydberg atoms generated by half-cycle electromagnetic pulses.

  6. Atomic wave packets.



PHYSICS PROGRAM, subsection “Mechanics of fluids and gas”




  1. The history of the mechanics of fluids and gas [15].

  2. The notion of continuous media. Lagrange coordinates. Euler coordinates. Variation of the volume of material element. Continuity equation. Stress tensor of continuous media. The stress on the arbitrary oriented surface element. III Nuton law in the mechanics of continuous media. The equation of motion of continuous media. The ideal fluid model. The viscous fluid model. The momentum conservation law in mechanics of continuous media. The kinematics of material element of the continuous media (Cauchy theorem). The hydrodynamic vorticity vector [1], [2].

  3. Hydrostatics. The equilibrium equations. Archimed law. The equilibrium of homogeneously rotating fluid. Barometric equilibrium. Barometric formula [15].

  4. The velocity of propagation of the small perturbation. The velocity of the sound. Mach number. Abrupt density changes. One-dimensional motion of the ideal gas in tube with variable crossection. Laval nozzle [15].

  5. Potential flows. Dynamics of the region of the vortical flow in the ideal fluid (Hill’s vortex).

  6. Potential flow due to the motion of the body. D’Alembert’s paradox. Added mass effects (added mass of sphere). The dynamics of bubble in the ideal fluid. The dynamics of the bubble at impulse like motion of the fluid. Lift force and Joukowski’s formula [1], [2].

  7. The two-dimensional flows of the ideal fluid. The complex potential. The complex velocity. The complex potential in the some simplest cases. The conformal mapping method in hydrodynamics of the ideal fluids. The flow with the circulation past the cylinder. The flow past the elliptic cylinder. The flow past the plate. The flow past Joukowski airfoils. The Tschapligin- Joukowski condition and lift force. The dynamics of the boundary layer and the formation of the Joukowski vortex [1], [2].

  8. The constitutive relations in hydrodynamics of the viscous fluid. Navier-Stokes equation. Shear and dilational viscosities. The kinetic energy theorem. The energy equation of the continuos media. The equation of the internal energy. Fourrier law. The local equilibrium hypothesis. The temperature equation [1], [2].

  9. The equation of motion of the continuos media in the curvilinear co-ordinates (cylindrical and spherical). The deformation rate tensor in the curvilinear co-ordinates [1], [2].

  10. Reynolds number. Stokes approximation. Flow past sphere in the Stokes approximation. Stokes formula. The flow past rotating sphere in the Stokes approximation [1], [2], [3].

  11. Thermal convection in the flat layer. Boussinesq approximation. Prandtl, Rayleigh and Grashof numbers. The monotonous instability of fluid under the heating from below. The critical Rayleigh number in the layer with free surfaces. The character of the convective motion in flat layer [3], [4].

  12. Lagrange displacement. Deformation of the surface element due to the fluid motion. The intensity of the vortex tube. The conservation of the intensity of the vortex tube in the barotropic fluid. The circulation conservation theorem. The equation of the hydrodynamic vorticity. The dynamics of the vorticity in the flows with convergent streamlines. The principle of the frozen field lines in the magnetohydrodynamics. Magnetic Reynold’s number [1],[2].

  13. The motion of viscous fluid in capillaries and flat layers. Poiseuille’s formula. Drag coefficient (for laminar and turbulent flows). Blasius’s formula [3].

  14. Exact solutions of the Navier-Stokes equation. Landau jet. The disk rotating in motionless fluid. The rotation of the fluid near motionless disk. Flow near front critical point [16].

  15. Boundary layer. The equations of the fluid motion in the boundary layer approximation. Boundary layer on flat plate in steady case. Autosimilar solutions of the boundary layer equation. Blasius’s formula. The thickness of the boundary layer. The entrance region of the tube. The notion about the stability of the boundary layer [6].

  16. The theorem of the viscous fluid jets. Planar and axisymmetric jets. Radial Loicjansky jet from orifice [17].

  17. Turbulent flow. Linear stability theory. Orr-Sommerfeld equations. Transition from laminar to turbulent flow: flow in pipe and flow in the boundary layer past the body [16].

  18. Reynolds equations. Balance equations of the energy and second moment. Correlation functions, correlation coefficients, integral scale of turbulence. Spectral distribution of the energy. Isotropic turbulence [18].

  19. The subject of magnetohydrodynamics. The energy equation in magnetohydrodynamics. The equation of the field energy. The magnetic field stress tensor. The internal energy equation. The equation of motion of conducting media in magnetic field. Temperature equation in magnetohydrodynamics [5].

  20. 2D Hartman flow. The velocity profile of the Hartman flow. The Hartman boundary layer. The drag coefficient in the case of Hartman flow and its physical interpretation. Hartman flow between two electroconductive walls [19].

  21. Electrovortical flows. Autosimilar solutions. Electrovortical flow between two parallel walls [20].

  22. Magnetic field selfgeneration. The disk dynamo. Kauling theorem [7].

  23. The waves in the continuous media mechanics. Alven transverse waves. Sound waves. The sound wave radiation. Surface waves on the surface of heavy liquid. The notion of the dispersion of the surface waves. The approximation of the “shallow” water [5], [3], [8].

  24. The simple waves. The simple wave in the gas dynamics in the one-dimensional case. Politropic gas. The formation of the shock wave in the tube (the problem about piston). Non-linear waves in “shallow” water approximation, hydraulic jumps. Ryman invariants and the dam problem [3], [2], [8].

  25. Shock waves. The conditions on jump. Hygoniot adiabat. Problem about piston and shock wave in the tube [3].

  26. Non-linear waves on the surface of heavy liquid. Corteweg-de Vries equation. Soliton [8], [10].

  27. Convective loop and Lorentz equations. The characteristic bifurcation’s of the Lorentz equations and the deterministic chaos phenomena. Galerkin method for the description of the thermal convection in flat layer and Lorentz equations [4], [11].

  28. The motion of dynamic system. Poincare section. Attractors of dynamic systems. Scenarios of the turbulence origin. The period doubling scenario [12], [13].

  29. Hele-Shaw flows. Saffman-Taylor instability. The conformal mapping method and Saffman-Taylor solution for the free interface dynamics in the Hele-Shaw cell. Fluid motion in porous media [6], [14].

  30. The numerical simulation of the vorticity transfer equation: dicretization, conservative and monotonous finite difference schemes, stability analysis, the accuracy of the algorithm and the methods of its realization [21], [22], [25], [27], [28].

  31. The numerical simulation of the equation of the stream function: discrete and continuous problems, analytical solutions (Fourrier series), the finite difference schemes, their stability and realization.

  32. Boundary conditions for the determination of the vorticity and stream function: physical and numerical conditions for the determination of the pressure, temperature and concentration fields [21], [22], [25], [27], [28].

  33. Main numerical methods for the numerical simulation of the compressible fluid flows: shock waves, artificial viscosity, boundary conditions, convergence criteria [21], [22], [23], [25], [27], [29].

  34. The methods of the numerical simulation of the turbulent flows [25], [27], [28], [29], [30], [31].

  35. Packages Fluent and C. Their utilisation for numerical simulation.




References

  1. G.K.Batchelor. An introduction to fluid dynamics. - 1999 – Cambridge University Press; C.Pozrikidis. Introduction to theoretical and computational fluid dynamics. 1996 – Oxford University Press.

  2. L.I.Sedov. Continuos media mechanics. - 1976 – Nauka, Moscow.

  3. L.D.Landau, E.M.Lifshitz. Hydrodynamics. - 1986 – Nauka, Moscow.

  4. E.Z.Gershuni, E.M.Zhuhovicki. Convective stability of incompressible fluid. – 1972 - Nauka, Moscow.

  5. L.D.Landau, E.M.Lifshitz. Electrodynamics of Continuos media. - 1982 – Nauka, Moscow.

  6. G.Schlichting. The theory of boundary layer. – 1974 - Nauka, Moscow.

  7. G.Moffat. Magnetic field generation in conductive media. – 1980 – Mir, Moscow.

  8. D.Whitham. Linear and Non-linear Waves. – 1977 - Mir, Moscow.

  9. D.Lighthill. Waves in liquids. – 1981 - Mir, Moscow.

  10. V.I.Karpman. Non-linear waves in dispersive media. – 1973 - Nauka, Moscow.

  11. A.Lichtenberg, M.Liberman. Regular and chaotic dynamics. – 1984 - Mir, Moscow.

  12. H.G.Schuster. Deterministic chaos: An introduction. – 1995 – John Wiley Sons.

  13. F.Moon. Chaotic oscillations. – 1990 - Mir, Moscow.

  14. P.G.Saffman, G.Taylor. The penetration of a fluid into a porous medium or Hele-Shaw cell containing a more viscous liquid. – 1958 - Proc. Royal Society, v.A245, P.312-329.

  15. L.G.Loicjanskij. Mechanics of fluids and gas. – 1970 - Moscow.

  16. L.Vulis, V.Kashkarov. Theory of viscous fluid jet. – 1965 - Moscow.

  17. I.O.Hintze. Turbulence. – 1963 - Moscow.

  18. G.G.Branover, A.B.Cinober. Magnetohydrodynamics of incompressible media. – 1970 -Moscow.

  19. V.Bojarevich, J.Freibergs, E.Shilova, E.Scherbinin. Electrovortical flows. – 1985 – Zinatne, Rīga.

  20. P.Roache. Computational Fluid Dynamics. – 1980 - Moscow.

  21. P.J.Roache. Computational Fluid Dynamics. –1972 - Albuquerque, New Mexico – P.87-115.

  22. R.Richtmayer, K.Morton. Finite difference methods for solution of the boundary problems. – 1972 - Moscow.

  23. A.A.Samarskij, Yu.P.Popov. Finite difference schemes in gasdynamics. – 1975 .

  24. O.M.Belocerkovskij. Numerical simulation in mechanics of continuos media. – 1984 - Moscow.

  25. A.A.Samarskij. Theory of finite difference schemes.



The program is accepted on the meeting of the Council for promotion and habilitation of the Institute of Physics of University of Latvia (mechanics of fluids and gas, thermal and molecular physics, physics of magnetic phenomena, technical physics) at 27 May 1996.


Program for Latvian doctor degree in physics

Subprogram: Experimental methods and equipment




  1. Signal analyses and noise.

Shot noise, Jonsons noise, 1/f noise, external field induced noises. The methods of signal measuring under background noise.




  1. The methods of electrical measurements.

Direct current measurements, threshold of sensitivity. The methods of voltage averaging. The methods for periodic voltage measurement. Sinhrodetection, “boxcar” method. Voltage, current and resistance measurement methods and apparatus. Spectrum analyzer. Oscilloscoping. Frequency measurements and frequency standards. The methods and equipment for measuring of dielectric loses.




  1. The measurements of luminous flux.

Photodetectors - thermal detectors, quantum detectors. The spectral sensitivity of light detectors. The methods of the determination of spectral sensitivity. The methods for weak luminous flux measuring. Photon counting. The methods of measuring of periodic and modulated luminous flux

Time-resolved spectroscopy; the methods of time resolved spectroscopy in mili-, micro-, nano-, pico- and femtosecond time scale.




  1. Quantum detectors. CCD camera, intensificators of luminous flux. The matrix of photodiodes. Optical multichannel analysators (OMA).




  1. Light sources.

Black-body emission. A-type light sources. Discharge light sources for the line spectrum and for the continuum. The pulsed light sources. The methods for light pulses compression. The principal limit for light pulse duration. Standard light sources. The methods for radiation spectrum determination.




  1. Laser.

The amplifying media, resonator, oscillation modes. The active media for lasers. Tunable lasers. Lasers for pico- and femtosecond pulses. The modes sinchronization, compression of light pulses. The time-resolved spectroscopy of the fast processes.


7. Synchrotron as a spectral instrument.

Application of synchrotron radiation.




  1. Vacuum, methods, equipment and measuring.

The pumps :mechanical, jet, molecular, sorption. The materials for vacuum chambers. Materials for gaskets and pacing. Lead-in of electrical connections. Lead-in for mechanical drives. The methods for super - high vacuum.




  1. Low temperatures

The thermodynamics in reaching of low temperature. Cooling cycles. The equipment for cooling and production of cryogenic liquids (liquid gasses). The lead-in of electrical connections. The lead-in of mechanical movement.


10. The high temperatures in experiments.

Obtaining of high temperature. Resistive heaters. Radiative heaters, lasers. The materials and methods for isolation.


11. The manufacturing of materials and materials thermal treatment.

The methods of crystals growth from the melt, from the solution in melt: methods of Kyropulos, Chochralskii, Stocbarger. The necessary equipment for these methods.

The methods for manufacturing of thin films: vapor epitaxy, molecular beam epitaxy. The metal-organic compound chemical epitaxy. Doping of materials, introduction of activators. Preparation of high purity materials and corresponding equipment. The methods and equipment for materials annealing and quenching.


12. The magnetic field.

Superconductors, its properties. The solenoids: conventional and superconducting. Creation of the uniform field. The magnetometry. Squids, measuring of weak magnetic fields. Antimagnetic shields.


13. The microwaves in physics experiments.

The methods of magnetic resonances: ESR, NMR, ENDOR. Optically detected circular magnetic dichroism and ESR. The equipment for microwaves, wave - guides, resonators. Generators of microwaves. Inactive components of wave-guides. The detection of microwaves.




  1. The physical equipment for semiconductor technology.




15. The methods for determination of material structure and composition.

X-ray structure analysis. The tunnel and atom force microscopy. The scanning electron microscopy. Masspectrometry. The spectroscopic methods for determination of composition of materials.


16. The methods for distant measurements.

The space measurement systems. The transmission and processing of information.


17. The ionizing radiation in physics experiments.

The detection of radiation. Dosymetry. Protection from ionizing radiation.


Literature.







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