Order parameter fluctuations and thermodynamic phase transitions in finite spin systems and fragmenting nuclei

We show that in small and low density systems described by a lattice gas model with fixed number of particles the location of a thermodynamic phase transition can be detected by means of the distribution of the fluctuations related to an order parameter which is chosen to be the size of the largest fragment. We show the correlation between the size of the system and the observed order of the transition. We discuss the implications of this correlation on the analysis of experimental fragmentation data.Comment: 9 pages including 5 figures. Final version to appear in PL

Yield scaling, size hierarchy and fluctuations of observables in fragmentation of excited heavy nuclei

Multifragmentation properties measured with INDRA are studied for single sources produced in Xe+Sn reactions in the incident energy range 32-50 A MeV and quasiprojectiles from Au+Au collisions at 80 A MeV. A comparison for both types of sources is presented concerning Fisher scaling, Zipf law, fragment size and fluctuation observables. A Fisher scaling is observed for all the data. The pseudo-critical energies extracted from the Fisher scaling are consistent between Xe+Sn central collisions and Au quasi-projectiles. In the latter case it also corresponds to the energy region at which fluctuations are maximal. The critical energies deduced from the Zipf analysis are higher than those from the Fisher analysis.Comment: 30 pages, accepted for publication in Nuclear Physics A, references correcte

Moment Analysis and Zipf Law

The moment analysis method and nuclear Zipf's law of fragment size distributions are reviewed to study nuclear disassembly. In this report, we present a compilation of both theoretical and experimental studies on moment analysis and Zipf law performed so far. The relationship of both methods to a possible critical behavior or phase transition of nuclear disassembly is discussed. In addition, scaled factorial moments and intermittency are reviewed.Comment: Caption of Fig.6 was corrected. Review paper for WCI (World Consensus Initiative) Book "Dynamics and Thermodynamics with Nuclear Degrees of Freedom", published in Euorpean Physics Journal A as part of the Topical Volume. 16 pages, 21 figure

Survey of ultrasound practice amongst podiatrists in the UK

Background: Ultrasound in podiatry practice encompasses musculoskeletal ultrasound imaging, vascular hand-held Doppler ultrasound and therapeutic ultrasound. Sonography practice is not regulated by the Health and Care Professions Council (HCPC), with no requirement to hold a formal qualification. The College of Podiatry does not currently define ultrasound training and competencies. This study aimed to determine the current use of ultrasound, training received and mentorship received and/or provided by podiatrists using ultrasound. Methods: A quantitative study utilising a cross-sectional, on-line, single-event survey was undertaken within the UK. Results: Completed surveys were received from 284 podiatrists; 173 (70%) use ultrasound as part of their general practice, 139 (49%) for musculoskeletal problems, 131 (46%) for vascular assessment and 39 (14%) to support their surgical practice. Almost a quarter (n=62) worked for more than one organisation; 202 (71%) were employed by the NHS and/or private sector (n=118, 41%). Nearly all (93%) respondents report using a hand-held vascular Doppler in their daily practice; 216 (82%) to support decisions regarding treatment options, 102 (39%) to provide diagnostic reports for other health professionals, and 34 (13%) to guide nerve blocks. Ultrasound imaging was used by 104 (37%) respondents primarily to aid clinical decision making (n=81) and guide interventions (steroid injections n=67; nerve blocks n=39). Ninety-three percent stated they use ultrasound imaging to treat their own patients, while others scan at the request of other podiatrists (n=28) or health professionals (n=18). Few use ultrasound imaging for research (n=7) or education (n=2). Only 32 (11%) respondents (n=20 private sector) use therapeutic ultrasound to treat patients presenting with musculoskeletal complaints, namely tendon pathologies. Few respondents (18%) had completed formal post-graduate CASE (Consortium for the Accreditation of Sonographic Education) accredited ultrasound courses. Forty (14%) respondents receive ultrasound mentorship; the majority from fellow podiatrists (n=17) or medical colleagues (n=15). Over half (n=127) who do not have ultrasound mentorship indicated they would like a mentor predominantly for ultrasound imaging. Fifty-five (19%) report they currently provide ultrasound mentorship for others. Conclusions: Understanding the scope of ultrasound practice, the training undertaken and the requirements for mentorship will underpin the development of competencies and recommendations defined by the College of Podiatry to support professional development and ensure safe practice.</p

Bimodality: a possible experimental signature of the liquid-gas phase transition of nuclear matter

We have observed a bimodal behaviour of the distribution of the asymmetry between the charges of the two heaviest products resulting from the decay of the quasi-projectile released in binary Xe+Sn and Au+Au collisions from 60 to 100 MeV/u. Event sorting has been achieved through the transverse energy of light charged particles emitted on the quasi-target side, thus avoiding artificial correlations between the bimodality signal and the sorting variable. Bimodality is observed for intermediate impact parameters for which the quasi-projectile is identified. A simulation shows that the deexcitation step rather than the geometry of the collision appears responsible for the bimodal behaviour. The influence of mid-rapidity emission has been verified. The two bumps of the bimodal distribution correspond to different excitation energies and similar temperatures. It is also shown that it is possible to correlate the bimodality signal with a change in the distribution of the heaviest fragment charge and a peak in potential energy fluctuations. All together, this set of data is coherent with what would be expected in a finite system if the corresponding system in the thermodynamic limit exhibits a first order phase transition.Comment: 30 pages, 31 figure

Multifragmentation and the liquid-gas phase transition: an experimental overview

Two roads are presently being followed in order to establish the existence of a liquid-gas phase transition in finite nuclear systems from nuclear reactions at high energy. The clean experiment of observing the thermodynamic properties of a finite number of nucleons in a container is presently only possible with the computer. Performed with advanced nuclear transport models, it has revealed the first-order character of the transition and allowed the extraction of the pertinent thermodynamic parameters. The validity of the applied theory is being confirmed by comparing its predictions for heavy-ion reactions with exclusive experiments. The second approach is experimentally more direct. Signals of the transition are searched for by analysing reaction data within the framework of thermodynamics of small systems. A variety of potential signals has been investigated and found to be qualitatively consistent with the expectations for the phase transition. Many of them are well reproduced with percolation models which places the nuclear fragmentation into the more general context of partitioning phenomena in finite systems. A wealth of new data on this subject has been obtained in recent experiments, some of them with a new generation of multi-detector devices aiming at higher resolutions, isotopic identification of the fragments, and the coincident detection of neutrons. Isotopic effects in multifragmentation were addressed quite intensively, with particular attention being given to their relation to the symmetry energy and its dependence on density.Comment: 10 pages, 7 figures, Contribution to Proceedings of INPC2004, Goeteborg, Sweden, June 27 - July 2, 200

Isotopic and Microcanonical Temperatures in Nuclear Multifragmentation

A systematic comparison of different isotopic temperatures with the thermodynamical temperature of a multifragment system is made on the basis of the Statistical Multifragmentation Model. It is demonstrated that isotopic temperatures are strongly affected by the secondary decays of hot primary fragments and the population of particle-stable excited states in final fragments. The He-Li temperatures, measured recently by the ALADIN group, are reproduced fairly well both as a function of excitation energy and bound charge. Our analysis confirms the anomaly in the nuclear caloric curve.Comment: 10 pages in LaTeX, 3 ps figures, accepted for publication in Phys. Rev.

Humin Formation on SBA-15-pr-SO3H Catalysts during the Alcoholysis of Furfuryl Alcohol to Ethyl Levulinate: Effect of Pore Size on Catalyst Stability, Transport, and Adsorption

Herein, the alcoholysis of furfuryl alcohol in a series of SBA-15-pr-SO3H catalysts with different pore sizes is reported. Elemental analysis and NMR relaxation/diffusion methods show that changes in pore size have a significant effect on catalyst activity and durability. In particular, the decrease in catalyst activity after catalyst reuse is mainly due to carbonaceous deposition, whereas leaching of sulfonic acid groups is not significant. This effect is more pronounced in the largest-pore-size catalyst C3, which rapidly deactivates after one reaction cycle, whereas catalysts with a relatively medium and small average pore size (named, respectively, C2 and C1) deactivate after two reaction cycles and to a lesser extent. CHNS elemental analysis showed that C1 and C3 experience a similar amount of carbonaceous deposition, suggesting that the increased reusability of the small-pore-size catalyst can be attributed to the presence of SO3H groups mostly present on the external surface, as corroborated by results on pore clogging obtained by NMR relaxation measurements. The increased reusability of the C2 catalyst is attributed to a lower amount of humin being formed and, at the same time, reduced pore clogging, which helps to maintain accessible the internal pore space

Fragment properties of fragmenting heavy nuclei produced in central and semi-peripheral collisions

Fragment properties of hot fragmenting sources of similar sizes produced in central and semi-peripheral collisions are compared in the excitation energy range 5-10 AMeV. For semi-peripheral collisions a method for selecting compact quasi-projectiles sources in velocity space similar to those of fused systems (central collisions) is proposed. The two major results are related to collective energy. The weak radial collective energy observed for quasi-projectile sources is shown to originate from thermal pressure only. The larger fragment multiplicity observed for fused systems and their more symmetric fragmentation are related to the extra radial collective energy due to expansion following a compression phase during central collisions. A first attempt to locate where the different sources break in the phase diagram is proposed.Comment: 23 pages submitted to NP