Does sex induce a phase transition?

We discovered a dynamic phase transition induced by sexual reproduction. The dynamics is a pure Darwinian rule applied to diploid bit-strings with both fundamental ingredients to drive Darwin's evolution: (1) random mutations and crossings which act in the sense of increasing the entropy (or diversity); and (2) selection which acts in the opposite sense by limiting the entropy explosion. Selection wins this competition if mutations performed at birth are few enough, and thus the wild genotype dominates the steady-state population. By slowly increasing the average number m of mutations, however, the population suddenly undergoes a mutational degradation precisely at a transition point m_c. Above this point, the “bad” alleles (represented by 1-bits) spread over the genetic pool of the population, overcoming the selection pressure. Individuals become selectively alike, and evolution stops. Only below this point, m < m_c, evolutionary life is possible. The finite-size-scaling behaviour of this transition is exhibited for large enough “chromosome” lengths L, through lengthy computer simulations. One important and surprising observation is the L-independence of the transition curves, for large L. They are also independent on the population size. Another is that m_c is near unity, i.e. life cannot be stable with much more than one mutation per diploid genome, independent of the chromosome length, in agreement with reality. One possible consequence is that an eventual evolutionary jump towards larger L enabling the storage of more genetic information would demand an improved DNA copying machinery in order to keep the same total number of mutations per offspring.     

On the role of volatility in the evolution of social networks

We study how the volatility, node- or link-based, affects the evolution of social networks in simple models. The model describes the competition betweenorder – promoted by the efforts of agents to coordinate – and disorder induced byvolatility in the underlying social network.We find that when volatility affects mostly the decay of links, the model exhibit a sharp transition between an ordered phase with a dense network and a disordered phase with a sparse network. When volatility is mostly node-based, instead, only the symmetric (disordered) phase existsThese two regimes are separated by a second order phase transition of unusual type, characterized by an order parameter critical exponent β = 0⁺.We argue that node volatility has the same effect in a broader class of models, and provide numerical evidence in this direction.     

Interplay of noise and coupling in heterogeneous ensembles of phase oscillators

We study the effects of noise on the collective dynamics of an ensemble of coupled phase oscillators whose natural frequencies are all identical, but whose coupling strengths are not the same all over the ensemble. The intensity of noise can also be heterogeneous, representing diversity in the individual responses to external fluctuations. We show that the desynchronization transition induced by noise may be completely suppressed, even for arbitrarily large noise intensities, is the distribution of coupling strengths decays slowly enough for large couplings. Equivalently, if the response to noise of a sufficiently large fraction of the ensemble is weak enough, desynchronization cannot occur. The two effects combine with each other when the response to noise and the coupling strength of each oscillator are correlated. This combination is quantitatively characterized and illustrated with explicit examples.     

Metastability and functional integration in anisotropically coupled map lattices

Metastability is a property of systems composed of many interacting parts wherein the parts exhibit simultaneously a tendency to function autonomously (local segregation) and a tendency to cooperate (global integration). We study anisotropically coupled map lattices and discover that for specific values of the coupling control parameters the entire system transits to a metastable regime. We show that this regime manifests a quasi-stable state in which the system can flexibly switch to another such state. We briefly discuss the relevance of our findings for information processing, functional integration, metastability in the brain, and phase transitions in complex systems.     

Non-perturbative renormalization-group approach to lattice models

The non-perturbative renormalization-group approach is extended to lattice models, considering as an example a φ⁴ theory defined on a d-dimensional hypercubic lattice. Within a simple approximation for the effective action, we solve the flow equations and obtain the renormalized dispersion epsilon(q) over the whole Brillouin zone of the reciprocal lattice. In the long-distance limit, where the lattice does not matter any more, we reproduce the usual flow equations of the continuum model. We show how the numerical solution of the flow equations can be simplified by expanding the dispersion in a finite number of circular harmonics.     

Effects of random biquadratic couplings in a spin-1 spin-glass model

A spin-1 model, appropriated to study the competition between bilinear (J _ij S _i S _j ) and biquadratic (K _ij S _i ² S _j ²) random interactions, both of them with zero mean, is investigated. The interactions are infinite-ranged and the replica method is employed. Within the replica-symmetric assumption, the system presents two phases, namely, paramagnetic and spin-glass, separated by a continuous transition line. The stability analysis of the replica-symmetric solution yields, besides the usual instability associated with the spin-glass ordering, a new phase due to the random biquadratic couplings between the spins. Received 18 May 1999 and Received in final form 20 October 1999     

Power laws in zero-range processes on random networks

We study statistical properties of a zero-range process (ZRP) on random networks.We derive an analytic expression for the distribution of particles (also called node occupation distribution)in the steady state of the ZRP in the ensemble of uncorrelated random graphs. We analyze the dependence of this distribution on the node-degree distribution.In particular, we show that when the degree distribution is tuned properly, one can obtainscale-free fluctuations in the distribution of particles.Such fluctuations lead to a power law in the distribution of particles, just like in the ZRP with the hopping rate u(m) = 1+b/mon homogeneous graphs.     

Zero temperature solutions of the Edwards-Anderson model in random Husimi lattices

We solve the Edwards-Anderson model (EA) in different Husimi lattices using the cavity method at replica symmetric (RS) and 1-step of replica symmetry breaking (1RSB) levels. We show that, at T = 0, the structure of the solution space depends on the parity of the loop sizes. Husimi lattices with odd loop sizes may have a trivial paramagnetic solution thermodynamically relevant for highly frustrated systems while, in Husimi lattices with even loop sizes, this solution is absent. The range of stability under 1RSB perturbations of this and other RS solutions is computed analytically (when possible) or numerically. We also study the transition from 1RSB solutions to paramagnetic and ferromagnetic RS solutions. Finally we compare the solutions of the EA model in Husimi lattices with that on the (short loops free) Bethe lattices, showing that already for loop sizes of order 8 both models behave similarly.     

Universal behaviors of mutual information in one-dimensional ${\sf J}_1-{\sf J}_2$ model

The critical behaviors of the entropy correlation effects in the one dimensional J₁-J₂ Heisenberg model are studied. It is shown that the mutual information or the correlation entropy captures the key features of information about critical fluctuations and can be used to quantify the quantum and finite-temperature phase transitions. At the critical point, the mutual information is power-law decay and the entanglement correlation length is infinite. While far away from the critical point, the mutual information is exponential decay and the entanglement correlation length is finite. A universal property of the mutual information is also found. Based on the critical behaviors of the mutual information, a new method to quantify the infinite order phase transition in the system is proposed.     

Investigations of electron beam characteristics using an accelerator based on a magnetron gun with a secondary-emission cathode

The reliability and service life of accelerating installations are substantially determined by the lifetime of electron sources. The accelerator under consideration has a magnetron gun with a channel-free cold secondary-emission cathode in crossed fields as an electron source [1, 2]. In the present work, the data of the electron beam parameters obtained in the accelerator based on the magnetron gun with a secondary-emission cathode are given, and possible secondary uses are suggested. The text was submitted by the authors in English.     

Transition from fractal to non-fractal scalings in growing scale-free networks

Real networks can be classified into two categories: fractal networks and non-fractal networks. Here we introduce a unifying model for the two types of networks. Our model network is governed by a parameter q. We obtain the topological properties of the network including the degree distribution, average path length, diameter, fractal dimensions, and betweenness centrality distribution, which are controlled by parameter q. Interestingly, we show that by adjusting q, the networks undergo a transition from fractal to non-fractal scalings, and exhibit a crossover from ‘large’ to small worlds at the same time. Our research may shed some light on understanding the evolution and relationships of fractal and non-fractal networks.     

Spontaneous-search method and short-time dynamics: applications to the Domany-Kinzel cellular automaton

The one-dimensional Domany-Kinzel cellular automaton is investigated by two numerical approaches: (i) the spontaneous-search method, which is a method appropriated for a search of criticality; (ii) short-time dynamics. Both critical frontiers of the system are investigated, namely, the one separating the frozen and active phases, as well as the critical line determined by damage spreading between two cellular automata, that splits the active phase into the nonchaotic and chaotic phases. The efficiency of the spontaneous-search method is established herein through a precise estimate of both critical frontiers, and in addition to that, it is shown that this method may also be used in the determination of the critical exponent ν_⊥. Using the critical frontiers obtained, other exponents are estimated through short-time dynamics. It is verified that the critical exponents of both critical frontiers fall in the universality class of directed percolation.     

Laser pulse transient method for measuring the normal spectral emissivity of samples with arbitrary surface quality

A laser pulse transient method for measuring normal spectral emissivity is described. In this method, a laser pulse (λ=1064 nm) irradiates the top surface of a flat specimen. A two-dimensional temperature response of the bottom surface is measured with a calibrated thermographic camera. By solving an axisymmetric boundary value heat conduction problem, the normal spectral emissivity at 1064 nm is determined by using an iterative nonlinear least-squares estimation procedure. The method can be applied to arbitrary sample surface quality. The method is tested on a nickel specimen and used to determine the normal spectral emissivity of AISI 304 stainless steel. The expanded combined uncertainty of the method has been estimated to be 18%.     

Pairwise entanglement and geometric phase in high dimensional free-Fermion lattice systems

The pairwise entanglement, measured by concurrence and geometric phase in high dimensional free-Fermion lattice systems have been studied in this paper. When the system stays at the ground state, their derivatives with the external parameter show the singularity closed to the phase transition points, and can be used to detect the phase transition in this model. Furthermore our studies show for the free-Fermion model that both concurrence and geometric phase show the intimate connection with the correlation functions. The possible connection between concurrence and geometric phase has been also discussed.     

Urban traffic from the perspective of dual graph

Urban traffic is modeled using a dual graph representation of the urban transport network, where roads are mapped to nodes and intersections are mapped to links. The proposed model considers both the navigation of the vehicles in the network and the motion of the vehicles along roads. The vehicle-holding ability of roads and the vehicle-turning ability at intersections are also incorporated. The overall handling ability of the system can be quantified by a phase transition from free flow to congestion. Simulations show that the system's handling ability greatly depends on the topology of the transportation network. In general, a well-planned grid can hold more vehicles, and its overall handling ability is much greater than that of a growing self-organized network.     

Field-theoretical Renormalization-Group approach to critical dynamics of crosslinked polymer blends

We consider a crosslinked polymer blend that may undergo a microphase separation. When the temperature is changed from an initial value towards a final one very close to the spinodal point, the mixture is out equilibrium. The aim is the study of dynamics at a given time t, before the system reaches its final equilibrium state. The dynamics is investigated through the structure factor, S(q, t), which is a function of the wave vector q, temperature T, time t, and reticulation dose D. To determine the phase behavior of this dynamic structure factor, we start from a generalized Langevin equation (model C) solved by the time composition fluctuation. Beside the standard de Gennes Hamiltonian, this equation incorporates a Gaussian local noise, ζ. First, by averaging over ζ, we get an effective Hamiltonian. Second, we renormalize this dynamic field theory and write a Renormalization-Group equation for the dynamic structure factor. Third, solving this equation yields the behavior of S(q, t), in space of relevant parameters. As result, S(q, t) depends on three kinds of lengths, which are the wavelength q ⁻¹, a time length scale R(t) ∼ t ^1/z , and the mesh size ξ ^*. The scale R(t) is interpreted as the size of growing microdomains at time t. When R(t) becomes of the order of ξ ^*, the dynamics is stopped. The final time, t ^*, then scales as t ^* ∼ ξ ^{* z}, with the dynamic exponent z = 6−η. Here, η is the usual Ising critical exponent. Since the final size of microdomains ξ ^* is very small (few nanometers), the dynamics is of short time. Finally, all these results we obtained from renormalization theory are compared to those we stated in some recent work using a scaling argument.     

Giant monopole resonances in the statistical model

The strength functions fore ⁺ e ^– pair decay of the isoscalar and isovector giant monopole resonances in highly excited nuclei are derived and used in a statistical model calculation of thee ⁺ e ^– pair energy spectrum from compound nuclear decay in¹¹⁰Sn following a fusion evaporation reaction. This result is then compared to thee ⁺ e ^– spectrum derived from internal pair decay of the giant dipole and giant quadrupole resonances. The computation shows that the pair decay from the excited-state GDR dominates the pair spectrum over the region of all giant resonances, exceedingL=0 transitions by at least a factor of ten. We also compute the angular correlations betweene ⁺ ande ^– for theL=0, L=1 andL=2 transitions and estimate their power to discriminate between the various multipolarities.Dedicated to Prof. Dr. P. Kienle on the occasion of his 60th birthday     

Partition of excitation energy between reaction products in heavy ion collisions

In the single-particle approach a partition of the excitation energy between the reaction products in deep inelastic collisions of heavy ions are investigated. The role of the particle-hole excitations and the nucleon exchange is considered. The ratio of the projectile excitation energy to the total excitation energy for the reactions²³⁸U(1468 MeV)+¹²⁴Sn,²³⁸U(1398 MeV)+¹¹⁰Pd,⁵⁶Fe(505MeV)+¹⁶⁵Ho,⁷⁴Ge (629 MeV)+¹⁶⁵Ho and⁶⁸Ni(880 MeV)+¹⁹⁷Au is calculated. The results of calculations are in good agreement with the experimental data.We are grateful to Dr. N.V. Antonenko for valuable discussions. This work was supported partly by the Russian Minister for Education and Research under the Grant N2-61-13-28.