Tricritical point in heterogeneous k-core percolation

k-core percolation is an extension of the concept of classical percolation and is particularly relevant to understanding the resilience of complex networks under random damage. A new analytical formalism has been recently proposed to deal with heterogeneous k-cores, where each vertex is assigned a local threshold k(i). In this Letter we identify a binary mixture of heterogeneous k-cores which exhibits a tricritical point. We investigate the new scaling scenario and calculate the relevant critical exponents, by analytical and computational methods, for Erd?s-Rényi networks and 2D square lattices.     

Probabilistic prediction in scale-free networks: diameter changes

In complex systems, responses to small perturbations are too diverse to definitely predict how much they would be, and then such diverse responses can be predicted in a probabilistic way. Here we study such a problem in scale-free networks, for example, the diameter changes by the deletion of a single vertex for various in silico and real-world scale-free networks. We find that the diameter changes are indeed diverse and their distribution exhibits an algebraic decay with an exponent zeta asymptotically. Interestingly, the exponent zeta is robust as zeta approximately 2.2(1) for most scale-free networks and insensitive to the degree exponents gamma as long as 2相似文献   

Resistance of Feynman diagrams and the percolation backbone dimension

We present an alternative view of Feynman diagrams for the field theory of random resistor networks, in which the diagrams are interpreted as being resistor networks themselves. This simplifies the field theory considerably as we demonstrate by calculating the fractal dimension D(B) of the percolation backbone to three loop order. Using renormalization group methods we obtain D(B)=2+epsilon/21-172epsilon(2)/9261+2epsilon(3)[-74 639+22 680zeta(3)]/4 084 101, where epsilon=6-d with d being the spatial dimension and zeta(3)=1.202 057... .     

Origin of the universal roughness exponent of brittle fracture surfaces:stress-weighted percolation in the damage zone

We suggest that the observed large-scale universal roughness of brittle fracture surfaces is due to the fracture propagation being a damage coalescence process described by a stress-weighted percolation phenomenon in a self-generated quadratic damage gradient. We use the quasistatic 2D fuse model as a paradigm of a mode I fracture model. We measure for this model, which exhibits a correlated percolation process, the correlation length exponent nu approximately 1.35 and conjecture it to be equal to that of classical percolation, 4/3. We then show that the roughness exponent in the 2D fuse model is zeta=2nu/(1+2nu)=8/11. This is in accordance with the numerical value zeta=0.75. Using the value for 3D percolation, nu=0.88, we predict the roughness exponent in the 3D fuse model to be zeta=0.64, in close agreement with the previously published value of 0.62+/-0.05. We furthermore predict zeta=4/5 for 3D brittle fractures, based on a recent calculation giving nu=2. This is in full accordance with the value zeta=0.80 found experimentally.     

Roughness of stylolites: implications of 3D high resolution topography measurements

Stylolites are natural pressure-dissolution surfaces in sedimentary rocks. We present 3D high resolution measurements at laboratory scales of their complex roughness. The topography is shown to be described by a self-affine scaling invariance. At large scales, the Hurst exponent is zeta(1) approximately 0.5 and very different from that at small scales where zeta(2) approximately 1.2. A crossover length scale at around L(c)=1 mm is well characterized. Measurements are consistent with a Langevin equation that describes the growth of a stylolitic interface as a competition between stabilizing long range elastic interactions at large scales or local surface tension effects at small scales and a destabilizing quenched material disorder.     

A Mixture Model of Truncated Zeta Distributions with Applications to Scientific Collaboration Networks

The degree distribution has attracted considerable attention from network scientists in the last few decades to have knowledge of the topological structure of networks. It is widely acknowledged that many real networks have power-law degree distributions. However, the deviation from such a behavior often appears when the range of degrees is small. Even worse, the conventional employment of the continuous power-law distribution usually causes an inaccurate inference as the degree should be discrete-valued. To remedy these obstacles, we propose a finite mixture model of truncated zeta distributions for a broad range of degrees that disobeys a power-law behavior in the range of small degrees while maintaining the scale-free behavior. The maximum likelihood algorithm alongside the model selection method is presented to estimate model parameters and the number of mixture components. The validity of the suggested algorithm is evidenced by Monte Carlo simulations. We apply our method to five disciplines of scientific collaboration networks with remarkable interpretations. The proposed model outperforms the other alternatives in terms of the goodness-of-fit.     

Master integrals for four-loop massless propagators up to weight twelve

We evaluate a Laurent expansion in dimensional regularization parameter ?=(4−d)/2 of all the master integrals for four-loop massless propagators up to weight twelve, using a recently developed method of one of the present coauthors (R.L.) and extending thereby results by Baikov and Chetyrkin obtained at weight seven. We observe only multiple zeta values in our results. Therefore, we conclude that all the four-loop massless propagator integrals, with any integer powers of numerators and propagators, have only multiple zeta values in their epsilon expansions up to weight twelve.     

Fluctuation and relaxation properties of pulled fronts: A scenario for nonstandard kardar-parisi-zhang scaling

We argue that while fluctuating fronts propagating into an unstable state should be in the standard Kardar-Parisi-Zhang (KPZ) universality class when they are pushed, they should not when they are pulled: The 1/t velocity relaxation of deterministic pulled fronts makes it unlikely that the KPZ equation is their proper effective long-wavelength low-frequency theory. Simulations in 2D confirm the proposed scenario, and yield exponents beta approximately 0.29+/-0.01, zeta approximately 0.40+/-0.02 for fluctuating pulled fronts, instead of the (1+1)D KPZ values beta = 1/3, zeta = 1/2. Our value of beta is consistent with an earlier result of Riordan et al., and with a recent conjecture that the exponents are the (2+1)D KPZ values.     

Renormalization of pinned elastic systems: how does it work beyond one loop?

We study the field theories for pinned elastic systems at equilibrium and at depinning. Their beta functions differ to two loops by novel "anomalous" terms. At equilibrium we find a roughness zeta = 0.208 298 04 epsilon + 0.006 858 epsilon(2) (random bond), zeta = epsilon/3 (random field). At depinning we prove two-loop renormalizability and that random field attracts shorter range disorder. We find zeta = epsilon/3(1 + 0.143 31 epsilon), epsilon = 4 - d, in violation of the conjecture zeta = epsilon/3, solving the discrepancy with simulations. For long range elasticity zeta = epsilon/3(1 + 0.397 35 epsilon), epsilon = 2 - d, much closer to the experimental value (approximately 0.5 both for liquid helium contact line depinning and slow crack fronts) than the standard prediction 1/3.     

Creep motion of an elastic string in a random potential

We study the creep motion of an elastic string in a two-dimensional pinning landscape by means of Langevin dynamics simulations. We find that the velocity-force characteristics are well described by the creep formula predicted from phenomenological scaling arguments. We analyze the creep exponent mu and the roughness exponent zeta. Two regimes are identified: when the temperature is larger than the strength of the disorder, we find mu approximately 1/4 and zeta approximately 2/3, in agreement with the quasi-equilibrium-nucleation picture of creep motion; on the contrary, when lowering the temperature enough, the values of mu and zeta increase, showing a strong violation of the latter picture.     

On the location of poles of Ruelle's zeta function

We discuss examples of one-dimensional lattice spin systems of classical statistical mechanics whose generalized zeta function has all its poles and zeros on the real axis. The close relation between certain hyperbolic dynamical systems and these spin systems lets one expect that this is also true for some of the dynamical systems. In fact, we have found several one-dimensional expansive systems, among them the Gauss map whose zeta functions have their zeros, respectively their poles, on the real axis. Such a behaviour is closely related to the spectral properties of the sytems transfer operator which in the cases considered is a positive nuclear operator in a Banach space of holomorphic functions. We formulate a general conjecture concerning the spectrum of this class of operators.     

Higher Selberg Zeta Functions

In the paper [KW2] we introduced a new type of Selberg zeta function for establishing a certain identity among the non-trivial zeroes of the Selberg zeta function and of the Riemann zeta function. We shall call this zeta function a higher Selberg zeta function. The purpose of this paper is to study the analytic properties of the higher Selberg zeta function z(s), especially to obtain the functional equation. We also describe the gamma factor of z(s) in terms of the triple sine function explicitly and, further, determine the complete higher Selberg zeta function with having a discussion of a certain generalized zeta regularization.Work in part supported by Grant-in Aid for Scientific Research (B) No.11440010, and by Grant-in Aid for Exploratory Research No.13874004, Japan Society for the Promotion of Science     

Can nonlinear elasticity explain contact-line roughness at depinning?

We examine whether cubic nonlinearities, allowed by symmetry in the elastic energy of a contact line, may result in a different universality class at depinning. Standard linear elasticity predicts a roughness exponent zeta = 1/3 (one loop), zeta = 0.388 +/- 0.002 (numerics) while experiments give zeta approximately = 0.5. Within functional renormalization group methods we find that a nonlocal Kardar-Parisi-Zhang-type term is generated at depinning and grows under coarse graining. A fixed point with zeta approximately = 0.45 (one loop) is identified, showing that large enough cubic terms increase the roughness. This fixed point is unstable, revealing a rough strong-coupling phase. Experimental study of contact angles theta near pi/2, where cubic terms in the energy vanish, is suggested.     

Electron spin torque in atoms

The spin torque and zeta force, which govern spin dynamics, are studied by using monoatoms in their steady states. We find nonzero local spin torque in transition metal atoms, which is in balance with the counter torque, the zeta force. We show that d-orbital electrons have a crucial effect on these torques. Nonzero local chirality density in transition metal atoms is also found, though the electron mass has the effect to wash out nonzero chirality density. Distribution patterns of the chirality density are the same for Sc–Ni atoms, though the electron density distributions are different.     

Nonperturbative results for the spectrum of surface-disordered waveguides

We calculated the spectrum of normal scalar waves in a planar waveguide with absolutely soft randomly rough boundaries. Our approach is beyond perturbation theories in the roughness heights and slopes and is based instead on the exact boundary scattering potential. The spectrum is proved to be a nearly real nonanalytic function of the dispersion zeta(2) of the roughness heights (with square-root singularity) as zeta(2)?0 . The opposite case of large boundary defects is summarized.     

Thermodynamics and bulk viscosity of approximate black hole duals to finite temperature quantum chromodynamics

We consider classes of translationally invariant black hole solutions whose equations of state closely resemble that of QCD at zero chemical potential. We use these backgrounds to compute the ratio zeta/s of bulk viscosity to entropy density. For a class of black holes that exhibits a first-order transition, we observe a sharp rise in zeta/s near Tc. For constructions that exhibit a smooth crossover, like QCD does, the rise in zeta/s is more modest. We conjecture that divergences in zeta/s for black hole horizons are related to extrema of the entropy density as a function of temperature.     

Calculation of the bulk viscosity in SU(3) gluodynamics

We perform a lattice Monte Carlo calculation of the trace-anomaly two-point function at finite temperature in the SU(3) gauge theory. We obtain the long distance properties of the correlator in the continuum limit and extract the bulk viscosity zeta via a Kubo formula. Unlike the tensor correlator relevant to the shear viscosity, the scalar correlator depends strongly on temperature. If s is the entropy density, we find that zeta/s becomes rapidly small at high T, zeta/s<0.15 at 1.65T(c), and zeta/s<0.015 at 3.2T(c). However, zeta/s rises dramatically just above T(c), with 0.5相似文献   

Multi-loop zeta function regularization and spectral cutoff in curved spacetime

We emphasize the close relationship between zeta function methods and arbitrary spectral cutoff regularizations in curved spacetime. This yields, on the one hand, a physically sound and mathematically rigorous justification of the standard zeta function regularization at one loop and, on the other hand, a natural generalization of this method to higher loops. In particular, to any Feynman diagram is associated a generalized meromorphic zeta function. For the one-loop vacuum diagram, it is directly related to the usual spectral zeta function. To any loop order, the renormalized amplitudes can be read off from the pole structure of the generalized zeta functions. We focus on scalar field theories and illustrate the general formalism by explicit calculations at one-loop and two-loop orders, including a two-loop evaluation of the conformal anomaly.     

Roughness of interfacial crack fronts: stress-weighted percolation in the damage zone

We study numerically the roughness exponent zeta of an in-plane fracture front slowly propagating along a heterogeneous interface embedded in an elastic body, using a model based on the evolution of a process zone rather than a fracture line. We find zeta=0.60+/-0.05. For the first time, simulation results are in close agreement with experimental results. We then show that the roughness exponent is related to the correlation length exponent nu of a stress-weighted percolation problem through zeta=nu/(1+nu). A numerical study of the stress-weighted percolation problem yields nu=1.54 giving zeta=0.61 in close agreement with our numerical results and with experimental observations.     

First observation of nonreciprocal X-Ray gyrotropy

We report the first observation of a nonreciprocal x-ray linear dichroism caused by the time-reversal odd, real part zeta of the complex gyrotropy tensor zeta(*) which is dominated by electric dipole-electric quadrupole E1E2 interference terms. A nonreciprocal transverse anisotropy was observed in the low temperature insulating phase of a Cr doped V2O3 Mott crystal when a single antiferromagnetic domain was grown by magnetoelectric annealing along the hexagonal c axis. This new element (edge) specific spectroscopy could nicely complement x-ray magnetic circular dichroism which is silent for antiferromagnetic materials.