Comparison of Canonical and Grand Canonical Models for selected multifragmentation data

Calculations for a set of nuclear multifragmentation data are made using a Canonical and a Grand Canonical Model. The physics assumptions are identical but the Canonical Model has an exact number of particles, whereas, the Grand Canonical Model has a varying number of particles, hence, is less exact. Interesting differences are found.Comment: 12 pages, Revtex, and 3 postscript figure

Removal and recovery of nutrients by ion exchange from water and wastewater

University of Technology, Sydney. Faculty of Engineering and Information Technology.In this study, a fixed bed ion exchange system for nutrient removal and recovery for water and waste water was developed and tested for nitrate and phosphate. A post-treatment consisting of a fixed bed bed ion-exchange system with a Purolite and an HFO column in series and individually was used to remove and recover nitrate and phosphate from synthetic water and wastewater. The efficiency of the ion exchange materials incorporated into the anthracite matrix at 1, 3, 5 and 10%, in their ability to remove and recover these nutrients was investigated. Another ion exchange material, HAIX, was also investigated for the removal and recovery of nitrate and phosphate. Also, the study considered regeneration and reuse of the ion exchange media in order to see how long the system can effectively remove and recover nitrate and phosphate before saturation. Purolite was found to exhibit a higher capacity for the removal of nitrate than for phosphate. HFO was found to exhibit a higher capacity for the removal of phosphate than for nitrate. Both these media were required in series to remove both nitrate and phosphate. Increase in dose of the two ion exchange materials incurred an increased in removal efficiency of nitrate and phosphate. However, the selectivity of Purolite for nitrate and HFO for phosphate decreased with increase percentage by mass of the ion exchanger in the anthracite matrix. Regeneration was undertaken using a distilled water wash as well as 3% NaC1 wash. It was found that NaC1 successfully regenerated the exhausted media for reuse. Distilled water wash was not a successful medium for regeneration. A column experiment was also conducted with MBR effluent to investigate the possibility of removing the nitrate and phosphate. Both N and P in the MBR effluent were found in different forms (as NH₄ – N, organic N, inorganic and organic phosphorus). Other competing anions like C1⁻ and SO₄²⁻ were also present in the feed. Despite the different forms of N and P as well as competing anions, the Purolite and HFO in series system still had a removal efficiency of 87-100%. The column was able to remove almost 100% of nitrate and phosphate in the effluent. The Langmuir, Freundlich and Sips isotherm models were used to model the equilibrium isotherm of nitrate and phosphate removal by Purolite (A500PS), HAIX and HFO. The results show that the experimental data satisfactorily fitted to all three models. The kinetic data for the adsorption of both nitrate and phosphate were satisfactorily described by the Ho model. The fit for phosphate on HFO was less satisfactory than the other adsorbents

Negative specific heat in a thermodynamic model of multifragmentation

We consider a soluble model of multifragmentation which is similar in spirit to many models which have been used to fit intermediate energy heavy ion collision data. In this model $c_v$ is always positive but for finite nuclei $c_p$ can be negative for some temperatures and pressures. Furthermore, negative values of $c_p$ can be obtained in canonical treatment. One does not need to use the microcanonical ensemble. Negative values for $c_p$ can persist for systems as large as 200 paticles but this depends upon parameters used in the model calculation. As expected, negative specific heats are absent in the thermodynamic limit.Comment: Revtex, 13 pages including 6 figure

On the choice of colliding beams to study deformation effects in relativistic heavy ion collisions

It has been suggested that collisions between deformed shapes will lead to interesting effects on various observables such as K production and elliptic flow. Simple formulae can be written down which show how to choose the colliding beams which will maximise the effects of deformation.Comment: 2 pages, this version supersedes the previous on

A Model for Phase Transition based on Statistical Disassembly of Nuclei at Intermediate Energies

Consider a model of particles (nucleons) which has a two-body interaction which leads to bound composites with saturation properties. These properties are : all composites have the same density and the ground state energies of composites with k nucleons are given by -kW+\sigma k^{2/3} where W and \sigma are positive constants. W represents a volume term and \sigma a surface tension term. These values are taken from nuclear physics. We show that in the large N limit where N is the number of particles such an assembly in a large enclosure at finite temperature shows properties of liquid-gas phase transition. We do not use the two-body interaction but the gross properties of the composites only. We show that (a) the p-\rho isotherms show a region where pressure does not change as $\rho$ changes just as in Maxwell construction of a Van der Waals gas, (b) in this region the chemical potential does not change and (c) the model obeys the celebrated Clausius-Clapeyron relations. A scaling law for the yields of composites emerges. For a finite number of particles N (upto some thousands) the problem can be easily solved on a computer. This allows us to study finite particle number effects which modify phase transition effects. The model is calculationally simple. Monte-Carlo simulations are not needed.Comment: RevTex file, 21 pages, 5 figure

Incorporating Radial Flow in the Lattice Gas Model for Nuclear Disassembly

We consider extensions of the lattice gas model to incorporate radial flow. Experimental data are used to set the magnitude of radial flow. This flow is then included in the Lattice Gas Model in a microcanonical formalism. For magnitudes of flow seen in experiments, the main effect of the flow on observables is a shift along the $E^*/A$ axis.Comment: Version accepted for publication in Phys. Rev. C, Rapid Communicatio