Universal Behavior of Lyapunov Exponents in Unstable Systems

We calculate the Lyapunov exponents in a classical molecular dynamics framework. The system is composed of few hundreds particles interacting either through Yukawa (Nuclear) or Slater-Kirkwood (Atomic) forces. The forces are chosen to give an Equation of State that resembles the nuclear and the atomic $^4He$ Equation Of State respectively near the critical point for liquid-gas phase transition. We find the largest fluctuations for an initial "critical temperature". The largest Lyapunov exponents $\lambda$ are always positive and can be very well fitted near this "critical temperature" with a functional form $\lambda\propto |T-T_c|^{-\omega}$, where the exponent $\omega=0.15$ is independent of the system and mass number. At smaller temperatures we find that $\lambda\propto T~ ^{0.4498}$, a universal behavior characteristic of an order to chaos transition.Comment: 11 pages, RevTeX, 3 figures not included available upon reques

Generalized entropy and temperature in nuclear multifragmentation

In the framework of a 2D Vlasov model, we study the time evolution of the "coarse-grained" Generalized Entropy (GE) in a nuclear system which undergoes a multifragmentation (MF) phase transition. We investigate the GE both for the gas and the fragments (surface and bulk part respectively). We find that the formation of the surface causes the growth of the GE during the process of fragmentation. This quantity then characterizes the MF and confirms the crucial role of deterministic chaos in filling the new available phase-space: at variance with the exact time evolution, no entropy change is found when the linear response is applied. Numerical simulations were used also to extract information about final temperatures of the fragments. From a fitting of the momentum distribution with a Fermi-Dirac function we extract the temperature of the fragments at the end of the process. We calculate also the gas temperature by averaging over the available phase space. The latter is a few times larger than the former, indicating a gas not in equilibrium. Though the model is very schematic, this fact seems to be very general and could explain the discrepancy found in experimental data when using the slope of light particles spectra instead of the double ratio of isotope yields method in order to extract the nuclear caloric curve.Comment: 26 pages, 9 postscript figures included, Revtex, some figures and part of text changed, version accepted for publication in PR

Gene expression profile predicts response to the combination of tosedostat and low-dose cytarabine in elderly AML

Tosedostat is an orally administered metalloenzyme inhibitor with antiproliferative and antiangiogenic activity against hematological and solid human cancers. Clinical activity has been demonstrated in relapsed acutemyeloid leukemia (AML). Thirty-three elderly patients with AML (median age, 75 years) received 120mgtosedostat orally once daily combinedwith subcutaneous low-dose cytarabine (20 mg twice per day for 10 days, up to 8 cycles), until disease progression. Inductionmortality was 12%. According to an intention-to-treat analysis, the complete remission (CR) rate was 48.5%, and thus the primary end point of the study was reached (expected CR, 25%). The partial remission rate was 6.1%,with an overall response rate of 54.5%. Furthermore, 4 of 33 patients had stable disease (median: 286 days). Themedian progression-free survival and overall survival (OS)were 203 days and 222 days, respectively. Responding patients had a longer median OS than nonresponding patients (P=.001). Amicroarray analysis performed in 29 of 33 patients identified 188 genes associated with clinical response (CR vs no CR). Three of them (CD93, GORASP1, CXCL16) were validated by quantitative polymerase chain reaction, which correctly classified 83% of the patients. Specifically, CR achievement was efficiently predicted by the gene expression patterns, with an overall accuracy exceeding 90%. Finally, a negative predictive value of 100% was validated in an independent series, thus representing the first molecular predictor for clinical response to a specific combination drug treatment for AML

Studies in the statistical and thermal properties of hadronic matter under some extreme conditions

The thermal and statistical properties of hadronic matter under some extreme conditions are investigated using an exactly solvable canonical ensemble model. A unified model describing both the fragmentation of nuclei and the thermal properties of hadronic matter is developed. Simple expressions are obtained for quantities such as the hadronic equation of state, specific heat, compressibility, entropy, and excitation energy as a function of temperature and density. These expressions encompass the fermionic aspect of nucleons, such as degeneracy pressure and Fermi energy at low temperatures and the ideal gas laws at high temperatures and low density. Expressions are developed which connect these two extremes with behavior that resembles an ideal Bose gas with its associated Bose condensation. In the thermodynamic limit, an infinite cluster exists below a certain critical condition in a manner similar to the sudden appearance of the infinite cluster in percolation theory. The importance of multiplicity fluctuations is discussed and some recent data from the EOS collaboration on critical point behavior of nuclei can be accounted for using simple expressions obtained from the model.Comment: 22 pages, revtex, includes 6 figures, submitted to Phys. Rev.

Isotopic composition of fragments in multifragmentation of very large nuclear systems: effects of the chemical equilibrium

Studies on the isospin of fragments resulting from the disassembly of highly excited large thermal-like nuclear emitting sources, formed in the ^{197}Au + ^{197}Au reaction at 35 MeV/nucleon beam energy, are presented. Two different decay systems (the quasiprojectile formed in midperipheral reactions and the unique source coming from the incomplete fusion of projectile and target in the most central collisions) were considered; these emitting sources have the same initial N/Z ratio and excitation energy (E^* ~= 5--6 MeV/nucleon), but different size. Their charge yields and isotopic content of the fragments show different distributions. It is observed that the neutron content of intermediate mass fragments increases with the size of the source. These evidences are consistent with chemical equilibrium reached in the systems. This fact is confirmed by the analysis with the statistical multifragmentation model.Comment: 9 pages, 4 ps figure

Exactly Solvable Models: The Road Towards a Rigorous Treatment of Phase Transitions in Finite Systems

We discuss exact analytical solutions of a variety of statistical models recently obtained for finite systems by a novel powerful mathematical method, the Laplace-Fourier transform. Among them are a constrained version of the statistical multifragmentation model, the Gas of Bags Model and the Hills and Dales Model of surface partition. Thus, the Laplace-Fourier transform allows one to study the nuclear matter equation of state, the equation of state of hadronic and quark gluon matter and surface partitions on the same footing. A complete analysis of the isobaric partition singularities of these models is done for finite systems. The developed formalism allows us, for the first time, to exactly define the finite volume analogs of gaseous, liquid and mixed phases of these models from the first principles of statistical mechanics and demonstrate the pitfalls of earlier works. The found solutions may be used for building up a new theoretical apparatus to rigorously study phase transitions in finite systems. The strategic directions of future research opened by these exact results are also discussed.Comment: Contribution to the ``World Consensus Initiative III, Texas A & M University, College Station, Texas, USA, February 11-17, 2005, 21

Heated nuclear matter, condensation phenomena and the hadronic equation of state

The thermodynamic properties of heated nuclear matter are explored using an exactly solvable canonical ensemble model. This model reduces to the results of an ideal Fermi gas at low temperatures. At higher temperatures, the fragmentation of the nuclear matter into clusters of nucleons leads to features that resemble a Bose gas. Some parallels of this model with the phenomena of Bose condensation and with percolation phenomena are discussed. A simple expression for the hadronic equation of state is obtained from the model.Comment: 12 pages, revtex, 1 ps file appended (figure 1