How pairs of partners emerge in an initially fully connected society

A social group is represented by a graph, where each pair of nodes is connected by two oppositely directed links. At the beginning, a given amount $p(i)$ of resources is assigned randomly to each node $i$. Also, each link $r(i,j)$ is initially represented by a random positive value, which means the percentage of resources of node $i$ which is offered to node $j$. Initially then, the graph is fully connected, i.e. all non-diagonal matrix elements $r(i,j)$ are different from zero. During the simulation, the amounts of resources $p(i)$ change according to the balance equation. Also, nodes reorganise their activity with time, going to give more resources to those which give them more. This is the rule of varying the coefficients $r(i,j)$. The result is that after some transient time, only some pairs $(m,n)$ of nodes survive with non-zero $p(m)$ and $p(n)$, each pair with symmetric and positive $r(m,n)=r(n,m)$. Other coefficients $r(m,i\ne n)$ vanish. Unpaired nodes remain with no resources, i.e. their $p(i)=0$, and they cease to be active, as they have nothing to offer. The percentage of survivors (i.e. those with with $p(i)$ positive) increases with the velocity of varying the numbers $r(i,j)$, and it slightly decreases with the size of the group. The picture and the results can be interpreted as a description of a social algorithm leading to marriages.Comment: 7 pages, 3 figure

Combined potential and spin impurity scattering in cuprates

We present a theory of combined nonmagnetic and magnetic impurity scattering in anisotropic superconductors accounting for the momentum-dependent impurity potential. Applying the model to the d-wave superconducting state, we obtain a quantitative agreement with the initial suppression of the critical temperature due to Zn and Ni substitutions as well as electron irradiation defects in the cuprates. We suggest, that the unequal pair-breaking effect of Zn and Ni may be related to a different nature of the magnetic moments induced by these impurities.Comment: 5 pages, 3 tables, RevTex, to be published in Phys. Rev.

Avalanches in complex spin networks

We investigate the magnetization reversal processes on classes of complex spin networks with antiferromagnetic interaction along the network links. With slow field ramping the hysteresis loop and avalanches of spin flips occur due to topological inhomogeneity of the network, even without any disorder of the magnetic interaction [B. Tadic, et al., Phys. Rev. Lett. 94 (2005) 137204]. Here we study in detail properties of the magnetization avalanches, hysteresis curves and density of domain walls and show how they can be related to the structural inhomogeneity of the network. The probability distribution of the avalanche size, N_s(s), displays the power-law behaviour for small s, i.e. N_s(s)\propto s^{-\alpha}. For the scale-free networks, grown with preferential attachment, \alpha increases with the connectivity parameter M from 1.38 for M=1 (trees) to 1.52 for M=25. For the exponential networks, \alpha is close to 1.0 in the whole range of M.Comment: 16 pages, 10 figures in 29 eps file

Escape rate and Hausdorff measure for entire functions

The escaping set of an entire function is the set of points that tend to infinity under iteration. We consider subsets of the escaping set defined in terms of escape rates and obtain upper and lower bounds for the Hausdorff measure of these sets with respect to certain gauge functions.Comment: 24 pages; some errors corrected, proof of Theorem 2 shortene

Are Devaney hairs fast escaping?

Beginning with Devaney, several authors have studied transcendental entire functions for which every point in the escaping set can be connected to infinity by a curve in the escaping set. Such curves are often called Devaney hairs. We show that, in many cases, every point in such a curve, apart from possibly a finite endpoint of the curve, belongs to the fast escaping set. We also give an example of a Devaney hair which lies in a logarithmic tract of a transcendental entire function and contains no fast escaping points.Comment: 22 pages, 1 figur

Impurity and strain effects on the magnetotransport of La1.85Sr0.15Cu(1-y)Zn(y)O4 films

The influence of zinc doping and strain related effects on the normal state transport properties(the resistivity, the Hall angle and the orbital magneto- resistance(OMR) is studied in a series of La1.85Sr0.15Cu(1-y)Zn(y)O4 films with values of y between 0 and 0.12 and various degrees of strain induced by the mismatch between the films and the substrate. The zinc doping affects only the constant term in the temperature dependence of cotangent theta but the strain affects both the slope and the constant term, while their ratio remains constant.OMR is decreased by zinc doping but is unaffected by strain. The ratio delta rho/(rho*tan^2 theta) is T-independent but decreases with impurity doping. These results put strong constraints on theories of the normal state of high- temperature superconductors

Magnetic polarons in weakly doped high-Tc superconductors

We consider a spin Hamiltonian describing $d$-$d$ exchange interactions between localized spins $d$ of a finite antiferromagnet as well as $p$-$d$ interactions between a conducting hole ($p$) and localized spins. The spin Hamiltonian is solved numerically with use of Lanczos method of diagonalization. We conclude that $p$-$d$ exchange interaction leads to localization of magnetic polarons. Quantum fluctuations of the antiferromagnet strengthen this effect and make the formation of polarons localized in one site possible even for weak $p$-$d$ coupling. Total energy calculations, including the kinetic energy, do not change essentially the phase diagram of magnetic polarons formation. For parameters reasonable for high-$T_c$ superconductors either a polaron localized on one lattice cell or a small ferron can form. For reasonable values of the dielectric function and $p$-$d$ coupling, the contributions of magnetic and phonon terms in the formation of a polaron in weakly doped high-$T_c$ materials are comparable.Comment: revised, revtex-4, 12 pages 8 eps figure