Probing the Nuclear Symmetry Energy with Heavy Ion Collisions

Heavy Ion Collisions (HIC) represent a unique tool to probe the in-medium nuclear interaction in regions away from saturation. In this report we present a selection of new reaction observables in dissipative collisions particularly sensitive to the symmetry term of the nuclear Equation of State ($Iso-EoS$). We will first discuss the Isospin Equilibration Dynamics. At low energies this manifests via the recently observed Dynamical Dipole Radiation, due to a collective neutron-proton oscillation with the symmetry term acting as a restoring force. At higher beam energies Iso-EoS effects will be seen in an Isospin Diffusion mechanism, via Imbalance Ratio Measurements, in particular from correlations to the total kinetic energy loss. For fragmentation reactions in central events we suggest to look at the coupling between isospin distillation and radial flow. In Neck Fragmentation reactions important Iso-EoS information can be obtained from fragment isospin content, velocity and alignement correlations. The high density symmetry term can be probed from isospin effects on heavy ion reactions at relativistic energies (few AGeV range), in particular for high transverse momentum selections of the reaction products. Rather isospin sensitive observables are proposed from nucleon/cluster emissions, collective flows and meson production. The possibility to shed light on the controversial neutron/proton effective mass splitting in asymmetric matter is also suggested. A large symmetry repulsion at high baryon density will also lead to an "earlier" hadron-deconfinement transition in n-rich matter. The binodal transition line of the (T,\rho_B) diagram is lowered to a region accessible through heavy ion collisions in the energy range of the new planned facilities, e.g. the FAIR/NICA projects. Some observable effects of the formation of a Mixed Phase are suggested, in particular a Neutron Trapping mechanism. The dependence of the results on a suitable treatment of the isovector part of the interaction in effective QCD Lagrangian approaches is critically discussed. We stress the interest of this study in nuclear astrophysics, in particular for supernovae explosions and neutron star structure, where the knowledge of the Iso-EoS is important at low as well as at high baryon density.Comment: 52 pages, 28 figures, topical review submitted to J. Phys. G: Nucl. Phys (IOP Latex

Isospin in fragment production

Based on a general approach to binary systems we show that in the low density region asymmetric nuclear matter (ANM) is unstable only against isoscalarlike fluctuations. The physical meaning of the thermodynamical chemical and mechanical instabilities is related to the inequality relations verified by the strength of interaction among different components. Relevance of these results in bulk and neck fragmentation is discussed.Comment: 8 pages, 5 Postscript figures, talk at Cortona 2002 Conference, Oct.7-Oct.12, Italy, World Scientific (in press

Reaction Dynamics with Exotic Beams

We review the new possibilities offered by the reaction dynamics of asymmetric heavy ion collisions, using stable and unstable beams. We show that it represents a rather unique tool to probe regions of highly Asymmetric Nuclear Matter ($ANM$) in compressed as well as dilute phases, and to test the in-medium isovector interaction for high momentum nucleons. The focus is on a detailed study of the symmetry term of the nuclear Equation of State ($EOS$) in regions far away from saturation conditions but always under laboratory controlled conditions. Thermodynamic properties of $ANM$ are surveyed starting from nonrelativistic and relativistic effective interactions. In the relativistic case the role of the isovector scalar $\delta$-meson is stressed. The qualitative new features of the liquid-gas phase transition, "diffusive" instability and isospin distillation, are discussed. The results of ab-initio simulations of n-rich, n-poor, heavy ion collisions, using stochastic isospin dependent transport equations, are analysed as a function of beam energy and centrality. The isospin dynamics plays an important role in all steps of the reaction, from prompt nucleon emissions to the final fragments. The isospin diffusion is also of large interest, due to the interplay of asymmetry and density gradients. In relativistic collisions, the possibility of a direct study of the covariant structure of the effective nucleon interaction is shown. Results are discussed for particle production, collective flows and iso-transparency. Perspectives of further developments of the field, in theory as well as in experiment, are presented.Comment: 167+5 pages, 77 figures, general revie

SPICE model of memristive devices with threshold

Although memristive devices with threshold voltages are the norm rather than the exception in experimentally realizable systems, their SPICE programming is not yet common. Here, we show how to implement such systems in the SPICE environment. Specifically, we present SPICE models of a popular voltage-controlled memristive system specified by five different parameters for PSPICE and NGSPICE circuit simulators. We expect this implementation to find widespread use in circuits design and testing

On the validity of memristor modeling in the neural network literature

An analysis of the literature shows that there are two types of non-memristive models that have been widely used in the modeling of so-called "memristive" neural networks. Here, we demonstrate that such models have nothing in common with the concept of memristive elements: they describe either non-linear resistors or certain bi-state systems, which all are devices without memory. Therefore, the results presented in a significant number of publications are at least questionable, if not completely irrelevant to the actual field of memristive neural networks

Teaching Memory Circuit Elements via Experiment-Based Learning

The class of memory circuit elements which comprises memristive, memcapacitive, and meminductive systems, is gaining considerable attention in a broad range of disciplines. This is due to the enormous flexibility these elements provide in solving diverse problems in analog/neuromorphic and digital/quantum computation; the possibility to use them in an integrated computing-memory paradigm, massively-parallel solution of different optimization problems, learning, neural networks, etc. The time is therefore ripe to introduce these elements to the next generation of physicists and engineers with appropriate teaching tools that can be easily implemented in undergraduate teaching laboratories. In this paper, we suggest the use of easy-to-build emulators to provide a hands-on experience for the students to learn the fundamental properties and realize several applications of these memelements. We provide explicit examples of problems that could be tackled with these emulators that range in difficulty from the demonstration of the basic properties of memristive, memcapacitive, and meminductive systems to logic/computation and cross-bar memory. The emulators can be built from off-the-shelf components, with a total cost of a few tens of dollars, thus providing a relatively inexpensive platform for the implementation of these exercises in the classroom. We anticipate that this experiment-based learning can be easily adopted and expanded by the instructors with many more case studies.Comment: IEEE Circuits and Systems Magazine (in press