Radial flow has little effect on clusterization at intermediate energies in the framework of the Lattice Gas Model

The Lattice Gas Model was extended to incorporate the effect of radial flow. Contrary to popular belief, radial flow has little effect on the clusterization process in intermediate energy heavy-ion collisions except adding an ordered motion to the particles in the fragmentation source. We compared the results from the lattice gas model with and without radial flow to experimental data. We found that charge yields from central collisions are not significantly affected by inclusion of any reasonable radial flow.Comment: 8 pages, 2 figures, submitted to PRC; Minor update and resubmitted to PR

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

Model of multifragmentation, Equation of State and phase transition

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. We draw a p-V diagram for the model and compare with a p-V diagram obtained from a mean-field theory. We investigate the question of chemical instability in the multifragmentation model. Phase transitions in the model are discussed.Comment: Revtex, 9 pages including 6 figures: some change in the text and Fig.

A study of the phase transition in the usual statistical model for nuclear multifragmentation

We use a simplified model which is based on the same physics as inherent in most statistical models for nuclear multifragmentation. The simplified model allows exact calculations for thermodynamic properties of systems of large number of particles. This enables us to study a phase transition in the model. A first order phase transition can be tracked down. There are significant differences between this phase transition and some other well-known cases

Nuclear Chemical and Mechanical Instability and the Liquid-Gas Phase Transition in Nuclei

The thermodynamic properties of nuclei are studied in a mean field model using a Skryme interaction. Properties of two component systems are investigated over the complete range of proton fraction from a system of pure neutrons to a system of only protons. Besides volume, symmetry, and Coulomb effects we also include momentum or velocity dependent forces. Applications of the results developed are then given which include nuclear mechanical and chemical instability and an associated liquid/gas phase transition in two component systems. The velocity dependence leads to further changes in the coexistence curve and nuclear mechanical and chemical instability curves.Comment: 21 pages, 9 figures, Results are changed due to error in progra

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

P 097—Metabolic cost of transport in over-ground and treadmill walking of healthy elderly and effects of a treadmill familiarization protocol

Background: Previous research has shown that the mechanics of walking on a treadmill is similar to walking overground. However it might be true that the energetics of walking is not similar between overground and treadmill, especially for older adults. We hypothesized that a lack of or inadequate familiarization on a treadmill would increase the Metabolic Cost of Transport (MCoT) in older adults due to increased levels of anxiety and the novelty of the locomotor task. Methods: 10 healthy elderly (5 males and 5 females, mean age of 75.3 SD(6.3) years) were recruited and they walked first at their overground Preferred Walking Speed (PWS) for 8 min to reach a steady state of oxygen consumption in the morning. After that the same speed was imposed on a dual-belt treadmill and they walked for 15 min to properly familiarize themselves with the treadmill. This was called the familiarization session (Session 1). In the afternoon they repeated both the overground and treadmill walking again in the same order and with the same protocol. This session was called the post-familiarization session (Session 2). Results: The group average of the overground PWS was 1.28 SD(0.11) m/s (4.61 SD(0.40) km/hr). During the familiarization session, the group average of the Gross Cost of Transport (GCoT) was 3.47 SD(0.35) J/kg/m while walking overground and 4 SD(0.65) J/kg/m while walking on a treadmill. The Net Cost of Transport (NCoT) was 2.64 SD(0.37) J/kg/m while walking overground and 3.14 SD(0.64) J/kg/m while walking on a treadmill. During the post-familiarization session, the group average of the GCoT was 3.84 SD(0.35) J/kg/m while walking overground and 3.94 SD(0.67) J/kg/m while walking on a treadmill. The NCoT was 2.76 SD(0.39) J/kg/m while walking overground and 2.90 SD(0.68) J/kg/m while walking on a treadmill. Both the GCoT and NCoT were statistically significantly higher on a treadmill than overground during the familiarization session. This elevation was not present during the post-familiarization session. There were also no statistically significant differences in the Resting Metabolic Rate (RMR) between before walking overground and before walking on a treadmill in either the familiarization or the post-familiarization session. Discussion and Conclusion: This shows that the energetics of walking can be different for even healthy elderly on a treadmill if they are not or inadequately familiarized to it. This underlines the importance of adequate familiarization to treadmill walking for elderly in trying to understand the MCoT in this population

Tracking the phase-transition energy in disassembly of hot nuclei

In efforts to determine phase transitions in the disintegration of highly excited heavy nuclei, a popular practice is to parametrise the yields of isotopes as a function of temperature in the form $Y(z)=z^{-\tau}f(z^{\sigma}(T-T_0))$, where $Y(z)$'s are the measured yields and $\tau, \sigma$ and $T_0$ are fitted to the yields. Here $T_0$ would be interpreted as the phase transition temperature. For finite systems such as those obtained in nuclear collisions, this parametrisation is only approximate and hence allows for extraction of $T_0$ in more than one way. In this work we look in detail at how values of $T_0$ differ, depending on methods of extraction. It should be mentioned that for finite systems, this approximate parametrisation works not only at the critical point, but also for first order phase transitions (at least in some models). Thus the approximate fit is no guarantee that one is seeing a critical phenomenon. A different but more conventional search for the nuclear phase transition would look for a maximum in the specific heat as a function of temperature $T_2$. In this case $T_2$ is interpreted as the phase transition temperature. Ideally $T_0$ and $T_2$ would coincide. We invesigate this possibility, both in theory and from the ISiS data, performing both canonical ($T$) and microcanonical ($e=E^*/A$) calculations. Although more than one value of $T_0$ can be extracted from the approximate parmetrisation, the work here points to the best value from among the choices. Several interesting results, seen in theoretical calculations, are borne out in experiment.Comment: Revtex, 10 pages including 8 figures and 2 table

Entropy Corrections for Schwarzschild and Reissner-Nordstr\"om Black Holes

Schwarzschild black hole being thermodynamically unstable, corrections to its entropy due to small thermal fluctuations cannot be computed. However, a thermodynamically stable Schwarzschild solution can be obtained within a cavity of any finite radius by immersing it in an isothermal bath. For these boundary conditions, classically there are either two black hole solutions or no solution. In the former case, the larger mass solution has a positive specific heat and hence is locally thermodynamically stable. We find that the entropy of this black hole, including first order fluctuation corrections is given by: {\cal S} = S_{BH} - \ln[\f{3}{R} (S_{BH}/4\p)^{1/2} -2]^{-1} + (1/2) \ln(4\p), where $S_{BH}=A/4$ is its Bekenstein-Hawking entropy and $R$ is the radius of the cavity. We extend our results to four dimensional Reissner-Nordstr\"om black holes, for which the corresponding expression is: {\cal S} = S_{BH} - \f{1}{2} \ln [ {(S_{BH}/\p R^2) ({3S_{BH}}/{\p R^2} - 2\sqrt{{S_{BH}}/{\p R^2 -\a^2}}) \le(\sqrt{{S_{BH}}/{\p R^2}} - \a^2 \ri)}/ {\le({S_{BH}}/{\p R^2} -\a^2 \ri)^2} ]^{-1} +(1/2)\ln(4\p). Finally, we generalise the stability analysis to Reissner-Nordstr\"om black holes in arbitrary spacetime dimensions, and compute their leading order entropy corrections. In contrast to previously studied examples, we find that the entropy corrections in these cases have a different character.Comment: 6 pages, Revtex. References added, minor changes. Version to appear in Class. Quant. Gra