Competition between isoscalar and isovector pairing correlations in N=Z nuclei

We study the isoscalar (T=0) and isovector (T=1) pairing correlations in N=Z nuclei. They are estimated from the double difference of binding energies for odd-odd N=Z nuclei and the odd-even mass difference for the neighboring odd-mass nuclei, respectively. The empirical and BCS calculations based on a T=0 and T=1 pairing model reproduce well the almost degeneracy of the lowest T=0 and T=1 states over a wide range of even-even and odd-odd N=Z nuclei. It is shown that this degeneracy is attributed to competition between the isoscalar and isovector pairing correlations in N=Z nuclei. The calculations give an interesting prediction that the odd-odd N=Z nucleus 82Nb has possibly the ground state with T=0.Comment: 5 pages, 4 figures, to be published in Phys. Rev. C (R

Diversity, Stability, Recursivity, and Rule Generation in Biological System: Intra-inter Dynamics Approach

Basic problems for the construction of a scenario for the Life are discussed. To study the problems in terms of dynamical systems theory, a scheme of intra-inter dynamics is presented. It consists of internal dynamics of a unit, interaction among the units, and the dynamics to change the dynamics itself, for example by replication (and death) of units according to their internal states. Applying the dynamics to cell differentiation, isologous diversification theory is proposed. According to it, orbital instability leads to diversified cell behaviors first. At the next stage, several cell types are formed, first triggered by clustering of oscillations, and then as attracting states of internal dynamics stabilized by the cell-to-cell interaction. At the third stage, the differentiation is determined as a recursive state by cell division. At the last stage, hierarchical differentiation proceeds, with the emergence of stochastic rule for the differentiation to sub-groups, where regulation of the probability for the differentiation provides the diversity and stability of cell society. Relevance of the theory to cell biology is discussed.Comment: 19 pages, Int.J. Mod. Phes. B (in press

Macroscopic chaos in globally coupled maps

We study the coherent dynamics of globally coupled maps showing macroscopic chaos. With this term we indicate the hydrodynamical-like irregular behaviour of some global observables, with typical times much longer than the times related to the evolution of the single (or microscopic) elements of the system. The usual Lyapunov exponent is not able to capture the essential features of this macroscopic phenomenon. Using the recently introduced notion of finite size Lyapunov exponent, we characterize, in a consistent way, these macroscopic behaviours. Basically, at small values of the perturbation we recover the usual (microscopic) Lyapunov exponent, while at larger values a sort of macroscopic Lyapunov exponent emerges, which can be much smaller than the former. A quantitative characterization of the chaotic motion at hydrodynamical level is then possible, even in the absence of the explicit equations for the time evolution of the macroscopic observables.Comment: 24 pages revtex, 9 figures included. Improved version also with 1 figure and some references adde

Differentiation and Replication of Spots in a Reaction Diffusion System with Many Chemicals

The replication and differentiation of spots in reaction diffusion equations are studied by extending the Gray-Scott model with self-replicating spots to include many degrees of freedom needed to model systems with many chemicals. By examining many possible reaction networks, the behavior of this model is categorized into three types: replication of homogeneous fixed spots, replication of oscillatory spots, and differentiation from `m ultipotent spots'. These multipotent spots either replicate or differentiate into other types of spots with different fixed-point dynamics, and as a result, an inhomogeneous pattern of spots is formed. This differentiation process of spots is analyzed in terms of the loss of chemical diversity and decrease of the local Kolmogorov-Sinai entropy. The relevance of the results to developmental cell biology and stem cells is also discussed.Comment: 8 pages, 12 figures, Submitted to EP

An alternative understanding of mass formulas in terms of nuclear structure

A typical form of mass formula is re-explained in terms of nuclear structure. For $N \approx Z$ nuclei, we propose to start with the shell model picture and to consider the T=0 $2n-2p$ ($\alpha$-like) correlations as the fundamental concept, instead of the symmetry energy. Subsequently, the symmetry energy is described on the basis of the $\alpha$-like superfluidity caused by the T=0 $2n-2p$ correlations, in parallel with the pairing energy described on the basis of the pairing superfluidity. This re-explanation gives useful insight for understanding the nuclear mass formula. The origin of the Wigner energy is also explained in an interacting boson model for the Cooper pairs in the $\alpha$-like superfluid vacuum. Adding a correction term due to the T=0 $2n-2p$ correlations, which determines the T=0 base level for nuclear masses, can improve the mass formulas in practice.Comment: to be published in Prog. Theor. Phys. Vol. 113, No.

Global features of proton-neutron interactions and symmetry energy

We study global features of proton-neutron (p-n) interactions and symmetry energy over a wide range of nuclei, using a schematic model interaction with four forces proposed recently. Calculations are performed by the BCS approximation in N,Z=20-50 and N,Z=50-82 regions. The experimental double differences of binding energies and symmetry energy are reproduced quite well. It is shown that the isoscalar p-n interactions with all J are indispensable for explaining the binding energies of not only $N\approx Z$ but also N>Z nuclei in the A=40-160 region.Comment: 15 pages, 4 figures, submitted to Phys. Lett.