Isospin in Reaction Dynamics. The Case of Dissipative Collisions at Fermi Energies

A key question in the physics of unstable nuclei is the knowledge of the $EOS$ for asymmetric nuclear matter ($ANM$) away from normal conditions. We recall that the symmetry energy at low densities has important effects on the neutron skin structure, while the knowledge in high densities region is crucial for supernovae dynamics and neutron star properties. The $only$ way to probe such region of the isovector $EOS$ in terrestrial laboratories is through very dissipative collisions of asymmetric (up to exotic) heavy ions from low to relativistic energies. A general introduction to the topic is firstly presented. We pass then to a detailed discussion on the $neck-fragmentation$ process as the main dissipative mechanism at the Fermi energies and to the related isospin dynamics. From Stochastic Mean Field simulations the isospin effects on all the phases of the reaction dynamics are thoroughly analysed, from the fast nucleon emission to the mid-rapidity fragment formation up to the dynamical fission of the $spectator$ residues. Simulations have been performed with an increasing stiffness of the symmetry term of the $EOS$. Some differences have been noticed, especially for the fragment charge asymmetry. New isospin effects have been revealed from the correlation of fragment asymmetry with dynamical quantities at the freeze-out time. A series of isospin sensitive observables to be further measured are finally listed.Comment: 16 pages, 6 figures, Contribution to the 5th Italy-Japan Symposium, Recent Achievements and Perspectives in Nuclear Physics, Naples Nov.3-7 2004, World Sci. in press. Latex in WorldSci/proc/styl

On vanishing theorems for Higgs bundles

We introduce the notion of Hermitian Higgs bundle as a natural generalization of the notion of Hermitian vector bundle and we study some vanishing theorems concerning Hermitian Higgs bundles when the base manifold is a compact complex manifold. We show that a first vanishing result, proved for these objects when the base manifold was K\"ahler, also holds when the manifold is compact complex. From this fact and some basic properties of Hermitian Higgs bundles, we conclude several results. In particular we show that, in analogy to the classical case, there are vanishing theorems for invariant sections of tensor products of Higgs bundles. Then, we prove that a Higgs bundle admits no nonzero invariant sections if there is a condition of negativity on the greatest eigenvalue of the Hitchin-Simpson mean curvature. Finally, we prove that invariant sections of certain tensor products of a weak Hermitian-Yang-Mills Higgs bundle are all parallel in the classical sense.Comment: 10 Pages, some typos corrected and minor change

Heavy Quark Dynamics in the QGP

We assess transport properties of heavy quarks in the Quark-Gluon Plasma (QGP) that show a strong non-perturbative behavior. A T-matrix approach based on a potential taken from lattice QCD hints at the presence of heavy-quark (HQ) resonant scattering with an increasing strength as the temperature, $T$, reaches the critical temperature, T_c \simeq 170 \; \MeV for deconfinement from above. The implementation of HQ resonance scattering along with a hadronization via quark coalescence under the conditions of the plasma created in heavy-ion collisions has been shown to correctly describe both the nuclear modification factor, $R_{AA}$, and the elliptic flow, $v_2$, of single electrons at RHIC and have correctly predicted the $R_{AA}$ of D mesons at LHC energy.Comment: 10 pages, 4 figures, Proceedings of EPIC@LHC Workshop, 6-8 July, Bar

Quantum Energy Expectation in Periodic Time-Dependent hamiltonians via Green Functions

Let $U_F$ be the Floquet operator of a time periodic hamiltonian $H(t)$. For each positive and discrete observable $A$ (which we call a {\em probe energy}), we derive a formula for the Laplace time average of its expectation value up to time $T$ in terms of its eigenvalues and Green functions at the circle of radius $e^{1/T}$. Some simple applications are provided which support its usefulness.Comment: 31 page

The Affine Structure of Gravitational Theories: Symplectic Groups and Geometry

We give a geometrical description of gravitational theories from the viewpoint of symmetries and affine structure. We show how gravity, considered as a gauge theory, can be consistently achieved by the nonlinear realization of the conformal-affine group in an indirect manner: due the partial isomorphism between $CA\left( 3,1\right)$ and the centrally extended $Sp\left( 8\right)$, we perform a nonlinear realization of the centrally extended (CE)$Sp\left( 8\right)$ in its semi-simple version. In particular, starting from the bundle structure of gravity, we derive the conformal-affine Lie algebra and then, by the non-linear realization, we define the coset field transformations, the Cartan forms and the inverse Higgs constraints. Finally we discuss the geometrical Lagrangians where all the information on matter fields and their interactions can be contained.Comment: 21 pages. arXiv admin note: text overlap with arXiv:0910.2881, arXiv:0705.460

Artemether resistance in vitro is linked to mutations in PfATP6 that also interact with mutations in PfMDR1 in travellers returning with Plasmodium falciparum infections.

BACKGROUND: Monitoring resistance phenotypes for Plasmodium falciparum, using in vitro growth assays, and relating findings to parasite genotype has proved particularly challenging for the study of resistance to artemisinins. METHODS: Plasmodium falciparum isolates cultured from 28 returning travellers diagnosed with malaria were assessed for sensitivity to artemisinin, artemether, dihydroartemisinin and artesunate and findings related to mutations in pfatp6 and pfmdr1. RESULTS: Resistance to artemether in vitro was significantly associated with a pfatp6 haplotype encoding two amino acid substitutions (pfatp6 A623E and S769N; (mean IC50 (95% CI) values of 8.2 (5.7 - 10.7) for A623/S769 versus 623E/769 N 13.5 (9.8 - 17.3) nM with a mean increase of 65%; p = 0.012). Increased copy number of pfmdr1 was not itself associated with increased IC50 values for artemether, but when interactions between the pfatp6 haplotype and increased copy number of pfmdr1 were examined together, a highly significant association was noted with IC50 values for artemether (mean IC50 (95% CI) values of 8.7 (5.9 - 11.6) versus 16.3 (10.7 - 21.8) nM with a mean increase of 87%; p = 0.0068). Previously described SNPs in pfmdr1 are also associated with differences in sensitivity to some artemisinins. CONCLUSIONS: These findings were further explored in molecular modelling experiments that suggest mutations in pfatp6 are unlikely to affect differential binding of artemisinins at their proposed site, whereas there may be differences in such binding associated with mutations in pfmdr1. Implications for a hypothesis that artemisinin resistance may be exacerbated by interactions between PfATP6 and PfMDR1 and for epidemiological studies to monitor emerging resistance are discussed

Sharp Hardy inequalities in the half space with trace remainder term

In this paper we deal with a class of inequalities which interpolate the Kato's inequality and the Hardy's inequality in the half space. Starting from the classical Hardy's inequality in the half space \rnpiu =\R^{n-1}\times(0,\infty), we show that, if we replace the optimal constant $\frac{(n-2)^2}{4}$ with a smaller one $\frac{(\beta-2)^2}{4}$, $2\le \beta <n$, then we can add an extra trace-term equals to that one that appears in the Kato's inequality. The constant in the trace remainder term is optimal and it tends to zero when $\beta$ goes to $n$, while it is equal to the optimal constant in the Kato's inequality when $\beta=2$

"Magic" numbers in Smale's 7th problem

Smale's 7-th problem concerns N-point configurations on the 2-dim sphere which minimize the logarithmic pair-energy V_0(r) = -ln r averaged over the pairs in a configuration; here, r is the chordal distance between the points forming a pair. More generally, V_0(r) may be replaced by the standardized Riesz pair-energy V_s(r)= (r^{-s} -1)/s, which becomes - ln r in the limit s to 0, and the sphere may be replaced by other compact manifolds. This paper inquires into the concavity of the map from the integers N>1 into the minimal average standardized Riesz pair-energies v_s(N) of the N-point configurations on the 2-sphere for various real s. It is known that v_s(N) is strictly increasing for each real s, and for s<2 also bounded above, hence "overall concave." It is (easily) proved that v_{-2}(N) is even locally strictly concave, and that so is v_s(2n) for s<-2. By analyzing computer-experimental data of putatively minimal average Riesz pair-energies v_s^x(N) for s in {-1,0,1,2,3} and N in {2,...,200}, it is found that {v}_{-1}^x(N) is locally strictly concave, while v_s^x(N) is not always locally strictly concave for s in {0,1,2,3}: concavity defects occur whenever N in C^{x}_+(s) (an s-specific empirical set of integers). It is found that the empirical map C^{x}_+(s), with s in {-2,-1,0,1,2,3}, is set-theoretically increasing; moreover, the percentage of odd numbers in C^{x}_+(s), s in {0,1,2,3}, is found to increase with s. The integers in C^{x}_+(0) are few and far between, forming a curious sequence of numbers, reminiscent of the "magic numbers" in nuclear physics. It is conjectured that the "magic numbers" in Smale's 7-th problem are associated with optimally symmetric optimal-energy configurations.Comment: 109 pages, of which 30 are numerical data tables. Thoroughly revised version, to appear in J. Stat. Phys. under the different title: `Optimal N point configurations on the sphere: "Magic" numbers and Smale's 7th problem

Temporal shifts of Bois Noir phytoplasma types infecting grapevine in South Tyrol (Northern Italy)

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