General Scaling Behavior Research Articles

The minority game with variable payoffs

In the standard minority game, each agent in the minority group receives the same payoff regardless of the size of the minority group. Of great interest for real social and biological systems are cases in which the payoffs to members of the minority group depend on the size of the minority group. This latter includes the fixed sum game. We find, remarkably, that the phase structure and general scaling behavior of the standard minority game persists when the payoff function depends on the size of the minority group. There is still a phase transition at the same value of z, the ratio of the dimension of the strategy space to the number of agents playing the game. We explain the persistence of the phase structure and argue that it is due to the absence of temporal cooperation in the dynamics of the minority game. We also discuss the behavior of average agent wealth and the wealth distribution in these variable payoff games.

Variable Payoffs in the Minority Game

In the standard minority game, each agent in the minority group receives the same payoff regardless of the size of the minority group. Of great interest for real social and biological systems are cases in which the payoffs to members of the minority group depend on the size of the minority group. This latter includes the fixed sum game. We find, remarkably, that the phase structure and general scaling behavior of the standard minority game persists when the payoff function depends on the size of the minority group. There is still a phase transition at the same value of z, the ratio of the dimension of the strategy space to the number of agents playing the game. We explain the persistence of the phase structure and argue that it is due to the absence of temporal cooperation in the dynamics of the minority game. We also discuss the behavior of average agent wealth and the wealth distribution in these variable payoff games.

Angular dependence of the magnetoresistivity in (Bi,Pb)2Sr2Ca2Cu3O/Ag tape

Measurements of the magnetoresistance R(H) as functions of the temperature and the angle θ between the applied magnetic field and the plane of a (Bi,Pb)2Sr2Ca2Cu3O/Ag tape have been performed in a low magnetic field region below Tc. Contrary to the two-dimensional vortex pancake model, the data do not scale well with H sin(θ) for small angles. Instead, our results show a general three-dimensional scaling behavior based on the anisotropy in the upper critical field Hc2 over entire angular range. From the scaling, the dissipation anisotropy is found to be unchanged at lower temperatures and decreases with increasing temperature at temperatures close to Tc.

Meson mT-scaling in heavy-ion collisions at SIS energies

We perform systematical studies on transverse-mass spectra of $\pi^0$, $\eta$, $\omega$, $\phi$, $K^+$ and $K^-$ mesons for C + C, Ni + Ni, Au + Au collisions at SIS energies within the HSD transport approach. We find that the $m_T$-spectra sensitively reflect the in-medium properties of the mesons. The 'bare mass' scenario leads to a general scaling behaviour for the meson $m_T$-spectra when including a mass shift due to the associate strangeness production threshold for kaons and antikaons whereas a 'dropping' mass scheme violates this $m_T$-scaling. The relative slope parameters, however, provide valuable information about the average meson potentials in the nuclear medium.

Solar wind low-frequency magnetohydrodynamic turbulence: extended self-similarity and scaling laws

Abstract. In this paper we review some of the work done in investigating the scaling properties of Magnetohydrodynamic turbulence, by using velocity fluctuations measurements performed in the interplanetary space plasma by the Helios spacecraft. The set of scaling exponents ξq for the q-th order velocity structure functions, have been determined by using the Extended Self-Similarity hypothesis. We have found that the q-th order velocity structure function, when plotted vs. the 4-th order structure function, displays a range of self-similarity which extends over all the lengths covered by measurements, thus allowing for a very good determination of ξq. Moreover the results seem to show that the scaling exponents are the same regardless the various observation periods considered. The obtained scaling exponents have been compared with the results of some intermittency models for Kraichnan's turbulence, derived in the framework of infinitely divisible fragmentation processes, showing the good agreement between these models and our observations. Finally, on the basis of the actually available data sets, we show that scaling laws in Solar Wind turbulence seem to be different from turbulent scaling laws in the ordinary fluid flows. This is true for high-order velocity structure functions, while low-order velocity structure functions show the same scaling laws. Since our measurements involve length scales which extend over many order of magnitude where dissipation is practically absent, our results show that Solar Wind turbulence can be regarded as a testing bench for the investigation of general scaling behaviour in turbulent flows. In particular our results strongly support the point of view which attributes a key role to the inertial range dynamics in determining the intermittency characteristics in fluid flows, in contrast with the point of view which attributes intermittency to a finite Reynolds number effect.

Coupled-cluster expansions for the lattice O(3) sigma model.

The coupled-cluster method with the eigenvalue equations truncated according to the continuum limit is applied to the Hamiltonian lattice O(3) {sigma} model. The long wavelength approximation of the vacuum wave function and mass gaps are calculated up to order 8. The results show general scaling behavior according to the full {beta} function. {copyright} {ital 1996 The American Physical Society.}

A quantitative theory of linear chain polymer dynamics in the melt. I. General scaling behavior

A theory of melt polymer dynamics for linear chain systems is developed. This theory generalizes recent work, which considers the lateral motion of the chains. A description is provided of the short time dynamics and of the crossover from this early time regime to a highly entangled dynamics. In both of these regimes, an effective friction coefficient for the lateral motion is evaluated by considering the extent of correlation between the displacements of the beads. This correlation is required due to the chain connectivity and the noncrossability of the chain backbones. The crossover time between these two regimes is found to be independent of chain length. In the early time regime, the bead mean squared displacement is found to have a time dependence between g∼t0.4 and g∼t0.5. In the highly entangled regime, g has a t2/7 dependence. The reptative motion of the chains along their own backbones and the coupling between this motion and the lateral chain motion is also included. It is found that the inclusion of these features results in a shorter terminal time in the long chain limit than would be the case otherwise. Long range correlated many chain motions are also considered in this work. These motions are expected to dominate the chain diffusion in the long chain limit. This theory predicts a terminal time that scales as N3.3 and a diffusion constant that scales as N−2.1, where N is the number of monomer units per chain.

Third-harmonic-generation spectroscopy of poly(p-phenylenevinylene): A comparison with oligomers and scaling laws for conjugated polymers.

The third-order nonlinear optical susceptibility ${\mathrm{\ensuremath{\chi}}}^{(3)}$(-3\ensuremath{\omega};\ensuremath{\omega},\ensuremath{\omega},\ensuremath{\omega}) of thin films of poly(p-phenylenevinylene) (PPV) and several corresponding oligomers (OPV-n) has been investigated by third-harmonic generation using variable laser wavelengths from 900 to 1520 nm. The oligomers show a single three-photon resonance of ${\mathrm{\ensuremath{\chi}}}^{(3)}$(-3\ensuremath{\omega};\ensuremath{\omega},\ensuremath{\omega},\ensuremath{\omega}) which is closely related to the linear absorption spectrum. We can identify, however, two maxima in the ${\mathrm{\ensuremath{\chi}}}^{(3)}$ spectrum of PPV. They are assigned to three-photon resonances with the maximum of the exciton absorption and with the threshold of the continuum of states, which can be located at 3.2\ifmmode\pm\else\textpm\fi{}0.1 eV. This corresponds to an exciton binding energy of 0.7\ifmmode\pm\else\textpm\fi{}0.1 eV. We observe a general scaling behavior for PPV, OPV-n, and other one-dimensional conjugated \ensuremath{\pi}-electron systems in their neutral form. Their ${\mathrm{\ensuremath{\chi}}}^{(3)}$ values, evaluated at comparable resonant or low-resonant conditions, follow an empirical scaling relationship ${\mathrm{\ensuremath{\chi}}}^{(3)}$/${\mathrm{\ensuremath{\alpha}}}_{\mathrm{max}}$\ensuremath{\sim}${\ensuremath{\lambda}}_{\mathrm{max}}^{\mathit{x}}$, where ${\mathrm{\ensuremath{\alpha}}}_{\mathrm{max}}$ and ${\ensuremath{\lambda}}_{\mathrm{max}}$ denote the absorption coefficient and wavelength of the low-energy absorption maximum. We obtain an exponent x=10\ifmmode\pm\else\textpm\fi{}1 which is much larger than expected from an earlier theory. Possible reasons for the difference between theory and experimental results are discussed. \textcopyright{} 1996 The American Physical Society.

Temperature dependence of low angle structure factors of liquid alkali metals using electron-ion plasma model

The analytic solution of EIP model in the MSA via the OCP criterion yields temperature dependent results in RPA quite satisfactorily at high temperatures. The same set of parameters produces low and high angle structural properties. The model can work almost near to the critical point if the ion-core radius is allowed to vary systematically in the regionρ<2ρc,ρc being the critical density. The model can also accommodate the general scaling behaviour observed for the structure factors of liquid alkali metals.

Transport currents and magnetic properties of textured Bi(2223) tape

Magnetic and transport properties of textured Bi(2223) tape with high critical transport current density (jc(77 K, 0 T)=2.8*104 A cm-2) were studied. Magnetic measurements show nongranular behaviour of shielding and transport currents for the magnetic field orientation perpendicular to the tape plane B perpendicular to p at low temperatures and low fields. At high magnetic fields and temperatures, however, quite large differences were observed, which depend on magnetic field sweep rate B and voltage criteria Ec. This is connected with granularity and inhomogeneity of the current flow. It was established that the magnetic field dependence of the critical current has a general scaling behaviour: jc(B, B, T)=jc(0, B, T) f(B/B0(B, T)) where the scaling function f becomes exp(-B/B0) for B/B0>or=1. The scaling parameter B0 is proportional to the irreversibility field Birr. Both B0 and Birr show an exponential temperature dependence.

Equilibrium morphology of block copolymer melts. 3

The field theoretical approach developed in an earlier work (Kawasaki, K.; et al. Macromolecules 1988, 21, 2972) was recast in such a way as to avoid power series expansion in the concentration variable. The general scaling behavior was found, which naturally gives rise to the well-known two-thirds power law of the domain size. The theory is related to other approaches by Helfand and co-workers and by Semenov. Numerical consequences of the theory are aslo presented that clearly demonstrate approach to the correct asymptotic behavior

Equilibrium morphology of block copolymer melts

The field theoretical approach developed in an earlier work (Kawasaki, K.; et al. Macromolecules 1988, 21, 2972) was recast in such a way as to avoid power series expansion in the concentration variable. The general scaling behavior was found, which naturally gives rise to the well-known two-thirds power law of the domain size. The theory is related to other approaches by Helfand and co-workers and by Semenov. Numerical consequences of the theory are aslo presented that clearly demonstrate approach to the correct asymptotic behavior

The β function of the two-dimensional non-linear σ model

Improved MCRG methods are used to determine the β function of the two-dimensional O(3) standard action σ model. We argue that the previously observed anomalous behavior of the mass gap can be understood as a general scaling behavior according to the full β function.