The equations obtained by Yang while discussing the condition of self-duality of $SU(2)$ gauge fields on Euclidean four-dimensional space have been generalized. Exact solutions and their graphical representations for the generalized equation (for some particular values of the parameters) have been reported. They represent interesting physical characteristics like waves with spreading solitary profile, spreading wave packets, waves with pulsating solitary profile (between zero and a maximum), waves with oscillatory solitary profile and chaos.

An irreversible model of an Ericsson cryogenic refrigeration cycle working with an ideal Fermi gas is established, which is composed of two isothermal and two isobaric processes. The influence of both the quantum degeneracy and the finite-rate heat transfer between the working fluid and the heat reservoirs on the performance of the cycle is investigated, based on the theory of statistical mechanics and thermodynamic properties of an ideal Fermi gas. The inherent regeneration losses of the cycle are analyzed. Expressions for several important performance parameters such as the coefficient of performance, cooling rate and power input are derived. By using numerical solutions, the cooling rate of the cycle is optimized for a given power input. The maximum cooling rate and the corresponding parameters are calculated numerically. The optimal regions of the coefficient of performance and power input are determined. Especially, the optimal performance of the cycle in the strong and weak gas degeneracy cases and the high temperature limit is discussed in detail. The analytic expressions of some optimized parameters are derived. Some optimum criteria are given. The distinctions and connections between the Ericsson refrigeration cycles working with the Fermi and classical gases are revealed.

Heavy flavor baryons containing single and double charm (beauty) quarks with light flavor combinations are studied using the hypercentral description of the three-body problem. The confinement potential is assumed as hypercentral Coulomb plus power potential with power index 𝜈. The ground state masses of the heavy flavor, $J^{P} = \dfrac{1}{2}^{+}$ and $\dfrac{3}{2}^{+}$ baryons are computed for different power indices, 𝜈 starting from 0.5 to 2.0. The predicted masses are found to attain a saturated value in each case of quark combinations beyond the power index $\nu = 1.0$.

In this work, we analyse the positive parity of states of odd-mass nucleus within the framework of interacting boson-fermion model. The result of an IBFM-1 multilevel calculation with the 2d_5/2, 1g_7/2, 3s_1/2, 2d_3/2 and 1h_11/2, single particle orbits is reported for the positive parity states of the odd-mass nucleus ^125-129Xe. Also, an IBM- 1 calculation is presented for the low-lying states in the even-even ^124-128Xe core nucleus. The energy levels and $B(E2)$ transition probabilities were calculated and compared with the experimental data. It was found that the calculated positive parity low-spin state energy spectra of the odd-mass ^125-129Xe isotopes agree quite well with the experimental data.

The yrast bands of even-even selenium isotopes with $A = 68-78$ are studied in the framework of projected shell model, by employing quadrupole plus monopole and quadrupole pairing force in the Hamiltonian. The oblate and prolate structures of the bands have been investigated. The yrast energies, backbending plots and reduced $E2$ transition probabilities and 𝑔-factors are calculated and compared with the experimental data. The calculated results are in reasonably good agreement with the experiments.

A four-detector perturbed angular correlation (PAC) spectrometer has been developed with ultra-fast BaF₂ detectors to acquire four coincidence spectra simultaneously, two at 180° and two at 90°. This spectrometer has double efficiency compared to that of a three-detector set-up. Higher efficiency is desirable for PAC studies in solid state physics where large number of coincidences are required to obtain the PAC spectra with good statistics and is particularly useful when the half-lives of the parent probe nuclei used for PAC measurements are $\sim 2-3$ days or less as in ¹¹¹In (2.8 d), ⁹⁹Mo (2.7 d) and ¹⁴⁰La (1.7 d). The performance of the spectrometer has been tested for the HfO₂ monoclinic crystal in the temperature range from 77 to 873 K and for the HfF₄.3H₂O crystal at room temperature. The polycrystalline HfO₂ has been synthesized from Hf metal by heating in air. The hydrated hafnium fluoride has been crystallized by dissolving Hf metal in 40% HF and drying slowly at room temperature.

The resonance states in ¹⁶O + ¹⁶O, ₁₂C + ¹⁶O, 𝛼 + ¹⁶O and 𝛼 + ₁₂C are described using modified Morse potential proposed earlier whose success has already been demon-strated in the case of ₁₂C + ₁₂C system. The general validity of such a potential with long range, shallow depth and repulsive soft core determined from the resonance data itself is being examined through the present study of the resonances in the above four systems. In each system, the experimental data of a large number of states have been successfully described with a modified Morse potential. The success points out a common mechanism of the origin of these states, and reaffirms authentically the diatomic-like rotational and vibrational picture of the nuclear molecular resonances proposed previously. The close resemblance between the physics of diatomic molecules and nuclear molecular resonances extending to the level of potential which is Morse type in both the cases - although belong to two different areas of physics - is further strengthened through the present study.

In this work the dependence of intrinsic effciency of a NaI(Tl) detector of radius 3.82 cm and height 7.62 cm on source{detector distance $(d)$, source-off-axis distance $(d_{0})$ and 𝛾-photon energy have been investigated using analytical and Monte Carlo methods. The results showed that, for a given off-axis distance, there exists a value of the ratio of source-detector distance $(d)$ to detector radius $(R)$ where intrinsic efficiency is minimum. This $d/R$ value at which minimum e±ciency occurs approaches zero as off-axis distance increases and it is almost constant with increase in energy. In the region where $d/R < 0:01$, a criteria given by Jehouani et al [1] for good photon detection, intrinsic efficiency decreases with increasing off-axis distance. The implications of the results for radioactivity measurement and radiation protection are discussed. Chacteristics of intrinsic e±ciency in the regions $d/R < 0:01$ and $d/R > 10$ are also compared.

Detection of periodic structures, hidden in random surfaces has been addressed by us for some time and the `extended matched filter' method, developed by us, has been shown to be effective in detecting the hidden periodic part from the light scattering data in circumstances where conventional data analysis methods cannot reveal the successive peaks due to scattering by the periodic part of the surface. It has been shown that if $r_{0}$ is the coherence length of light on scattering from the rough part and 𝛬 is the wavelength of the periodic part of the surface, the extended matched filter method can detect hidden periodic structures for $(r_{0}/\Lambda) \geq 0:11$, while conventional methods are limited to much higher values ($(r_{0}/\Lambda) \geq 0:33)$. In the method developed till now, the detection of periodic structures involves the detection of the central peak, first peak and second peak in the scattered intensity of light, located at scattering wave vectors $v_{x} = 0, Q, 2Q$, respectively, where $Q = 2\pi/\Lambda$, their distinct identities being obfuscated by the fact that the peaks have width $\Delta v_{x} = 2\pi/r_{0} \gg Q$. The relative magnitudes of these peaks and the consequent problems associated in identifying them is discussed. The Kolmogorov-Smirnov statistical goodness test is used to justify the identification of the peaks. This test is used to `reject' or `not reject' the null hypothesis which states that the successive peaks do exist. This test is repeated for various values of $r_{0}/\Lambda$, which leads to the conclusion that there is really a periodic structure hidden behind the random surface.

A simple procedure to solve two fully quantized non-linear Jaynes-Cummings models is presented, one in which an atom interacts with a two-mode radiation field in a Raman-type process and the other involving multiphoton interaction between the two-mode field and the atom. Effect of intensity-dependent coupling between the field and the atom in both the above-mentioned cases has also been investigated. The unitary transformation method presented here not only solves the time-dependent problem but also permits a determination of the eigensolutions of the interacting Hamiltonian at the same time. Graphical features of the time dependence of the population inversion have been analysed when one of the field modes is prepared initially in a coherent state while the other one in a vacuum state.

An entry length is always observed before laminar flow is achieved in fluid flowing in a conduit. This depends on the Reynolds number of the flow and the degree of smoothness of the conduit. This work examined this region and the point where laminar flow commences in the context of flow through conduit packed with porous material like beads, of known porosity. Using some theoretical assumptions, it is demonstrated that permeability varies from zero at wall-fluid boundary to maximum at mid-stream, creating a permeability profile similar to the velocity profile. An equation was obtained to establish this. We also found that peak values of permeability increase with increasing porosity, and therefore entry length increases with increasing porosity with all other parameters kept constant. A plot of peak permeability versus porosity revealed that they are linearly related.

We study some typical defect problems in one-dimensional (1D) hexagonal and two-dimensional (2D) octagonal quasicrystals. The first part of this investigation addresses in detail a uniformly moving screw dislocation in a 1D hexagonal piezoelectric quasicrystal with point group $6mm$. A general solution is derived in terms of two functions $\varphi_{1}$, $\varphi_{2}$, which satisfy wave equations, and another harmonic function $\varphi_{3}$. Elementary expressions for the phonon and phason displacements, strains, stresses, electric potential, electric fields and electric displacements induced by the moving screw dislocation are then arrived at by employing the obtained general solution. The derived solution is verified by comparison with existing solutions. Also obtained in this part of the investigation is the total energy of the moving screw dislocation. The second part of this investigation is devoted to the study of the interaction of a straight dislocation with a semi-infinite crack in an octagonal quasicrystal. Here the crack penetrates through the solid along the period direction and the dislocation line is parallel to the period direction. We first derive a general solution in terms of four analytic functions for plane strain problem in octagonal quasicrystals by means of differential operator theory and the complex variable method. All the phonon and phason displacements and stresses can be expressed in terms of the four analytic functions. Then we derive the exact solution for a straight dislocation near a semi-infinite crack in an octagonal quasicrystal, and also present the phonon and phason stress intensity factors induced by the straight dislocation and remote loads.

Polystyrene (PS) films are used in packaging and biomedical applications because of their transparency and good environmental properties. The present investigation is centered on the antifungal and antibacterial activities involved in the film surface. Subsequently, microbial formations were immobilized on the modified PS films. Living microorganisms such as bacteria and yeast were used. Untreated PS films show very fast rate of growth of bacteria within few hours. The study involves developments of polymer surfaces with bacterial growth and further studies after giving antibacterial treatment such as plasma treatment. Major emphasis has been given to study the effect of various parameters which can affect the performance of the improved material. Films were prepared by two methods: plasma treatment under vacuum and under ongoing He-Ne laser source. The parameters such as (1) surface area by contact angle measurements, (2) quality of material before and after treatment by SEM and FTIR spectra and (3) material characterization by UV-vis spectra were studied. It was observed that plasma treatment of

The fragmentation of deuteron, ⁶He and ¹¹Be have been studied during interaction with the ²⁰⁸Pb nucleus at various projectile energies. The Coulomb dissociation cross-sections and the momentum distribution of the break-up fragments have been analysed within the framework of the direct fragmentation model. The post-acceleration effect of deuteron during break-up and the halo structures of both the ⁶He and ¹¹Be have been investigated.