On the topological characterization of two-dimensional phase transitions

It is shown that for the two-dimensional planar-rotator model the variance of the number of vortices inside a large loop is proportional to the perimeter of the loop at all temperatures. A similar result holds for the variance of the charge inside a loop in the lattice Coulomb gas model. Hence a topological distinction between the high and low temperature phases of these models (area law versus perimeter law) is not possible.     

Equivalence of degeneracy regularizations of lattice fermions

It is shown that the recently proposed degeneracy regularization of Becher for free fermions on a lattice is completely equivalent to that of Susskind.     

Study of combined electroreflectance and double layer effects at lead electrodes

Reflectance changes at lead electrodes have been measured as a function of surface charge at 45° and 70° angles of incidence using solutions of sodium fluoride and quaternary ammonium salts. These solutions were chosen so as to provide quite different composition for the inner layer at the metal/solution interface, and hence different optical contributions there from. Linear reflectance-surface charge relation has been observed for NaF solutions only at a number of wavelengths. The optical effects from the inner layer has been recognized but could not be separated out from the main er effect by comparative measurements at two angles of incidence. This has been rationalized on the basis of similar variation of the er effect and the optical effect from the double-layer as a function of angle of incidence of light.     

Polarography of niobium : Reduction in mineral acid media

The formation and interconversion of the nitro-, chloro-, perchloro- and sulphato-complexes of niobium in mineral acid media and the reduction of the nitro-complex have been studied. Conditions for a linear proportionality between the limiting current and the concentration of niobium in the microgram range have been worked out.     

151Eu Mössbauer studies in the high Tc superconducting oxide materials

¹⁵¹Eu Mössbauer studies have been made across the respective superconductive transition temperatures in two compounds, La_1.7Eu_0.1Sr_0.2CuO_4?y and EuBa₂Cu₃O₇, having zero resistance state at 25K and 85K respectively. The¹⁵¹Eu isomer shift data establish that Eu ions are in trivalent state at all temperatures. The Mössbauer f-factor does not show any significant anomaly across the T_C.     

Gamma and π0 production by 4 GeV/cπ+p interactions

Inclusive data for the production of γ rays and π⁰ are presented from an experiment with a 4 GeV/cπ⁺ beam, using a track-sensitive target. The results are compared with data at other energies and with π⁺and π^? distributions.     

Are there low-lying,intrashell-excited,highly deformed states in the 1f-2p shell nuclei?

It is shown that the improved effective interactions in the fp shell imply the existence of an excited band of states which is much more deformed than the ground state band for some fp shell nuclei. Such states are to a certain extent analogous to the fission isomers occurring in heavy nuclei. Their experimental identification would be interesting and might also help to further improve the effective interaction.     

The energy spectra and electromagnetic transitions of odd-a titanium isotopes

The isotopes ^{55, 47, 49, 51}Ti are studied in the framework of the deformed configuration mixing shell model. The calculated spectra and electromagnetic properties agree well with the observed ones. The calculations suggest the existence of an excited $\text{K =}\text{1}\text{2}$ band of states in ^{45, 47, 49}Ti and a $\text{K =}\text{7}\text{2}$ band in ⁵¹Ti. In ⁴⁹Ti this excited $\text{K =}\text{1}\text{2}$ band is more deformed than the “ground state band”. On the basis of the overall agreement between the calculated and experimental spectra and decay properties we suggest the spin assignments $\text{J =}\text{5}\text{2}$, $\text{7}\text{2}$, $\text{9}\text{2}$, $\text{5}\text{2}$ and $\text{7}\text{2}$ to the states in ⁴⁷Ti observed at 2.168, 2.97, 2.408, 2.835 and 3.223 MeV, respectively.     

Quenched Averages for Self-Avoiding Walks and Polygons on Deterministic Fractals

We study rooted self avoiding polygons and self avoiding walks on deterministic fractal lattices of finite ramification index. Different sites on such lattices are not equivalent, and the number of rooted open walks W _n (S), and rooted self-avoiding polygons P _n (S) of n steps depend on the root S. We use exact recursion equations on the fractal to determine the generating functions for P _n (S), and W _n(S) for an arbitrary point S on the lattice. These are used to compute the averages ,, and over different positions of S. We find that the connectivity constant μ, and the radius of gyration exponent are the same for the annealed and quenched averages. However, , and , where the exponents and , take values different from the annealed case. These are expressed as the Lyapunov exponents of random product of finite-dimensional matrices. For the 3-simplex lattice, our numerical estimation gives and , to be compared with the known annealed values and .     

Scaling relation for determining the critical threshold for continuum percolation of overlapping discs of two sizes

We study continuum percolation of overlapping circular discs of two sizes. We propose a phenomenological scaling equation for the increase in the effective size of the larger discs due to the presence of the smaller discs. The critical percolation threshold as a function of the ratio of sizes of discs, for different values of the relative areal densities of two discs, can be described in terms of a scaling function of only one variable. The recent accurate Monte Carlo estimates of critical threshold by Quintanilla and Ziff [Phys. Rev. E76, 051115 (2007)] are in very good agreement with the proposed scaling relation.