Some non- linear problems in theoretical physics

An immense variety of problems in theoretical physics are of the non-linear type. Non~linear partial differential equations (NPDE) have almost become the rule rather than an exception in diverse branches of physics such as fluid mechanics, field theory, particle physics, statistical physics and optics, and the construction of exact solutions of these equations constitutes one of the most vigorous activities in theoretical physics today. The thesis entitled ‘Some Non-linear Problems in Theoretical Physics’ addresses various aspects of this problem at the classical level. For obtaining exact solutions we have used mathematical tools like the bilinear operator method, base equation technique and similarity method with emphasis on its group theoretical aspects. The thesis deals with certain methods of finding exact solutions of a number of non-linear partial differential equations of importance to theoretical physics. Some of these new solutions are of relevance from the applications point of view in diverse branches such as elementary particle physics, field theory, solid state physics and non-linear optics and give some insight into the stable or unstable behavior of dynamical Systems The thesis consists of six chapters.

physics of the Web

Science is search for the laws of underlying phenomena of the nature. Engineering constructs the nature as we wish. Interestingly the huge engineering infrastructure like world wide web has grown in such a complex structure such that we need to see the fundamental science behind the structure and behaviour of these networks. This talk covers the science behind the complex networks like web, biological, social etc. The talk aim to discuss the basic theories that govern the static as well as the dynamics of such interesting networks

Relativistic effects in physics and chemistry of element 105. [Part] I.

A detailed study of the electronic structure and bonding of the pentahalides of group 5 elements V, Nb, Ta, and element 105, hahnium (and Pa) has been carried out using relativistic molecular cluster Dirac-Slater discrete-variational method. A number of calculations have been performed for different geometries and molecular bond distances. The character of the bonding has been analyzed using the Mulliken population analysis of the molecular orbitals. It is shown that hahnium is a typical group 5 element. In a great number of properties it continues trends in the group. Some peculiarities in the electronic structure of HaCl_5 result from relativistic effects.

Relativistic effects in physics and chemistry of element 105. [Part] II.

Relativistic self-consistent charge Dirac-Slater discrete variational method calculations have been done for the series of molecules MBr_5, where M = Nb, Ta, Pa, and element 105, Ha. The electronic structure data show that the trends within the group 5 pentabromides resemble those for the corresponding pentaclorides with the latter being more ionic. Estimation of the volatility of group 5 bromides has been done on the basis of the molecular orbital calculations. According to the results of the theoretical interpretation HaBr_5 seems to be more volatile than NbBr_5 and TaBr_5.

Relativistic effects in physics and chemistry of element 105. [Part] III.

Electronic structures of MOCl_3 and MOBr_3 molecules, where M = V, Nb, Ta, Pa, and element 105, hahnium, have been calculated using the relativistic Dirac-Slater discrete variational method. The character of bonding has been analyzed using the Mulliken population analysis of the molecular orbitals. It was shown that hahnium oxytrihalides have similar properties to oxytrihalides of Nb and Ta and that hahnium has the highest tendency to form double bond with oxygen. Some peculiarities in the electronic structure of HaOCl_3 and HaOBr_3 result from relativistic effects. Volatilities of the oxytrihalides in comparison with the corresponding pentahalides were considered using results of the present calculations. Higher ionic character and lower covalency as well as the presence of dipole moments in MOX_3 (X = Cl, Br) molecules compared to analogous MX_5 ones are the factors contributing to their lower volatilities.

Relativistic effects in physics and chemistry of element 105. [Part] IV.

Results of relativistic (Dirac-Slater and Dirac-Fock) and nonrelativistic (Hartree-Fock-Slater) atomic and molecular calculations have been compared for the group 5 elements Nb, Ta, and Ha and their compounds MCl_5, to elucidate the influence of relativistic effects on their properties especially in going from the 5d element Ta to the 6d element Ha. The analysis of the radial distribution of the valence electrons of the metals for electronic configurations obtained as a result of the molecular calculations and their overlap with ligands show opposite trends in behavior for ns_1/2, np_l/2, and (n -1 )d_5/2 orbitals for Ta and Ha in the relativistic and nonrelativistic cases. Relativistic contraction and energetic stabilization of the ns_1/2 and np_l/2 wave functions and expansion and destabilization of the (n-1)d_5/2 orbitals make hahnium pentahalide more covalent than tantalum pentahalide and increase the bond strength. The nonrelativistic treatment of the wave functions results in an increase in ionicity of the MCl_5 molecules in going from Nb to Ha making element Ha an analog of V. Different trends for the relativistic and nonrelativistic cases are also found for ionization potentials, electronic affinities, and energies of charge-transfer transitions as well as the stability of the maximum oxidation state.

Cooperative Physics of Fly Swarms: An Emergent Behavior

We have simulated the behavior of several artificial flies, interacting visually with each other. Each fly is described by a simple tracking system (Poggio and Reichardt, 1973; Land and Collett, 1974) which summarizes behavioral experiments in which individual flies fixate a target. Our main finding is that the interaction of theses implemodules gives rise to a variety of relatively complex behaviors. In particular, we observe a swarm-like behavior of a group of many artificial flies for certain reasonable ranges of our tracking system parameters.

Make progress with physics and chemistry. 'Haz progresos con física y química'.

Seleccionado en la convocatoria: Licencias por estudios destinadas a funcionarios docentes no universitarios, Gobierno de Aragón 2009-10

Methods of Math Physics

Lecture notes for a course on methods of mathematical physics.

Physics Information Skills

An introduction to high quality information resources and databases in Physics and related disciplines. Refers to resources of information and methods of searching them.

Physics video for AS/A Level Science & Art Competition

A video made by physics for the AS/A Level Science & Art Competition

AS/A Level Science & Art Competition: Particle Physics

A video made by physics for the AS/A Level Science & Art Competition