Domain wall roughness in epitaxial ferroelectric PbZr0.2Ti0.8O3 thin films

The static configuration of ferroelectric domain walls was investigated using atomic force microscopy on epitaxial PbZr(0.2)Ti(0.8)O(3) thin films. Measurements of domain wall roughness reveal a power-law growth of the correlation function of relative displacements B(L) alpha L(2zeta) with zeta approximately 0.26 at short length scales L, followed by an apparent saturation at large L. In the same films, the dynamic exponent mu was found to be approximately 0.6 from independent measurements of domain wall creep. These results give an effective domain wall dimensionality of d = 2.5, in good agreement with theoretical calculations for a two-dimensional elastic interface in the presence of random-bond disorder and long-range dipolar interactions.     

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   

Roughening of fracture surfaces: the role of plastic deformation

Post mortem analysis of fracture surfaces of ductile and brittle materials on the microm-mm and the nm scales, respectively, reveal self-affine cracks with anomalous scaling exponent zeta approximately 0.8 in three dimensions and zeta approximately 0.65 in two dimensions. Attempts to use elasticity theory to explain this result failed, yielding exponent zeta approximately 0.5 up to logarithms. We show that when the cracks propagate via plastic void formations in front of the tip, followed by void coalescence, the void positions are positively correlated to yield exponents higher than 0.5.     

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.     

Probing the largest scale structure in the universe with polarization map of galaxy clusters

We introduce a new formalism to describe the polarization signal of galaxy clusters on the whole sky. We show that a sparsely sampled, half-sky map of the cluster polarization at z approximately 1 would allow us to better characterize the very large scale density fluctuations. While the horizon length is smaller in the past, two other competing effects significantly remove the contribution of the small scale fluctuations from the quadrupole polarization pattern at z approximately 1. For the standard LambdaCDM universe with vanishing tensor mode, the quadrupole moment of the temperature anisotropy at z = 0 is expected to have an approximately 32% contribution from fluctuations on scales below 6.3 h(-1) Gpc. This percentage would be reduced to approximately 2% level for the quadrupole moment of polarization pattern at z approximately 1. A cluster polarization would shed light on the potentially anomalous features of the largest scale fluctuations.     

Discretization dependence of criticality in model fluids: a hard-core electrolyte

Grand-canonical simulations at various levels, zeta=5-20, of fine-lattice discretization are reported for the near-critical 1:1 hard-core electrolyte or restricted primitive model (RPM). With the aid of finite-size scaling analyses, it is shown convincingly that, contrary to recent suggestions, the universal critical behavior is independent of zeta (> or approximately 4), thus the continuum (zeta--> infinity ) RPM exhibits Ising-type (as against classical, self-avoiding walk, XY, etc.) criticality. A general consideration of lattice discretization provides effective extrapolation of the intrinsically erratic zeta dependence, yielding (T*(c),rho*(c)) approximately equal to (0.0493(3),0.075) for the zeta=infinity RPM.     

Food chain chaos due to Shilnikov's orbit

Assume that the reproduction rate ratio zeta of the predator over the prey is sufficiently small in a basic tri-trophic food chain model. This assumption translates the model into a singularly perturbed system of two time scales. It is demonstrated, as a sequel to the earlier paper of Deng [Chaos 11, 514-525 (2001)], that at the singular limit zeta=0, a singular Shilnikov's saddle-focus homoclinic orbit can exist as the reproduction rate ratio epsilon of the top-predator over the predator is greater than a modest value epsilon(0). The additional conditions under which such a singular orbit may occur are also explicitly given. (c) 2002 American Institute of Physics.     

Numerical study of dynamo action at low magnetic Prandtl numbers

We present a three-pronged numerical approach to the dynamo problem at low magnetic Prandtl numbers P(M). The difficulty of resolving a large range of scales is circumvented by combining direct numerical simulations, a Lagrangian-averaged model and large-eddy simulations. The flow is generated by the Taylor-Green forcing; it combines a well defined structure at large scales and turbulent fluctuations at small scales. Our main findings are (i) dynamos are observed from P(M)=1 down to P(M)=10(-2), (ii) the critical magnetic Reynolds number increases sharply with P(M)(-1) as turbulence sets in and then it saturates, and (iii) in the linear growth phase, unstable magnetic modes move to smaller scales as P(M) is decreased. Then the dynamo grows at large scales and modifies the turbulent velocity fluctuations.     

Phenomenology of two-dimensional stably stratified turbulence under large-scale forcing

In this paper, we characterise the scaling of energy spectra, and the interscale transfer of energy and enstrophy, for strongly, moderately and weakly stably stratified two-dimensional (2D) turbulence, restricted in a vertical plane, under large-scale random forcing. In the strongly stratified case, a large-scale vertically sheared horizontal flow (VSHF) coexists with small scale turbulence. The VSHF consists of internal gravity waves and the turbulent flow has a kinetic energy (KE) spectrum that follows an approximate k^?3 scaling with zero KE flux and a robust positive enstrophy flux. The spectrum of the turbulent potential energy (PE) also approximately follows a k^?3 power-law and its flux is directed to small scales. For moderate stratification, there is no VSHF and the KE of the turbulent flow exhibits Bolgiano–Obukhov scaling that transitions from a shallow k^?11/5 form at large scales, to a steeper approximate k^?3 scaling at small scales. The entire range of scales shows a strong forward enstrophy flux, and interestingly, large (small) scales show an inverse (forward) KE flux. The PE flux in this regime is directed to small scales, and the PE spectrum is characterised by an approximate k^?1.64 scaling. Finally, for weak stratification, KE is transferred upscale and its spectrum closely follows a k^?2.5 scaling, while PE exhibits a forward transfer and its spectrum shows an approximate k^?1.6 power-law. For all stratification strengths, the total energy always flows from large to small scales and almost all the spectral indicies are well explained by accounting for the scale-dependent nature of the corresponding flux.     

Large deviations of extreme eigenvalues of random matrices

We calculate analytically the probability of large deviations from its mean of the largest (smallest) eigenvalue of random matrices belonging to the Gaussian orthogonal, unitary, and symplectic ensembles. In particular, we show that the probability that all the eigenvalues of an (N x N) random matrix are positive (negative) decreases for large N as approximately exp[-betatheta(0)N2] where the parameter beta characterizes the ensemble and the exponent theta(0)=(ln3)/4=0.274 653... is universal. We also calculate exactly the average density of states in matrices whose eigenvalues are restricted to be larger than a fixed number zeta, thus generalizing the celebrated Wigner semicircle law. The density of states generically exhibits an inverse square-root singularity at zeta.     

Scaling exponents for fracture surfaces in homogeneous glass and glassy ceramics

We investigate the scaling properties of postmortem fracture surfaces in silica glass and glassy ceramics. In both cases, the 2D height-height correlation function is found to obey Family-Viseck scaling properties, but with two sets of critical exponents, in particular, a roughness exponent zeta approximately 0.75 in homogeneous glass and zeta approximately 0.4 in glassy ceramics. The ranges of length scales over which these two scalings are observed are shown to be below and above the size of the process zone, respectively. A model derived from linear elastic fracture mechanics in the quasistatic approximation succeeds to reproduce the scaling exponents observed in glassy ceramics. The critical exponents observed in homogeneous glass are conjectured to reflect the damage screening occurring for length scales below the size of the process zone.     

Analysis of DNA elasticity

With a model that incorporates hydrodynamics directly, we show that flow experiments can be used for detecting some characteristics of the DNA elasticity which manifest themselves clearly at large length scales but cannot be observed by mechanical forcing experiments even at very small length scales. By systematic analysis, the conclusiveness of different experimental methods is evaluated. For the wormlike chain, confirmed as the correct model for DNA, we find an underlying scaling relation between its extension and flow velocity of the form L(p) approximately v(0.155), which emphasizes the significance of hydrodynamics.     

Random roughness enhances lift in supersonic flow

We study the scattering of shock waves by a rough wedge using second-order perturbation analysis and stochastic simulations employed synergistically to cover a large range in correlation length A and amplitude epsilon of the profile roughness (with length d). For small epsilon and A/d<1, the mean of the perturbed pressure scales alpha epsilon2 and alpha (A/d)(-2), while the corresponding variance scales alpha epsilon and alpha (A/d)(-1). However, for large epsilon, the mean pressure scales approximately alpha epsilon, while for A/d>1 it is independent of A. Our results are useful in evaluating the effects of roughness in high-speed flight but also in designing novel enhanced-lift aerodynamic surfaces using rough skin concepts.     

Structure of the magnetic reconnection diffusion region from four-spacecraft observations

Magnetic reconnection leads to energy conversion in large volumes in space but is initiated in small diffusion regions. Because of the small sizes of the diffusion regions, their crossings by spacecraft are rare. We report four-spacecraft observations of a diffusion region encounter at the Earth's magnetopause that allow us to reliably distinguish spatial from temporal features. We find that the diffusion region is stable on ion time and length scales in agreement with numerical simulations. The electric field normal to the current sheet is balanced by the Hall term in the generalized Ohm's law, E(n) approximately jxB/ne.n, thus establishing that Hall physics is dominating inside the diffusion region. The reconnection rate is fast, approximately 0.1. We show that strong parallel currents flow along the separatrices; they are correlated with observations of high-frequency Langmuir/upper hybrid waves.     

Scaling properties of three-dimensional magnetohydrodynamic turbulence

The scaling properties of three-dimensional magnetohydrodynamic turbulence with finite magnetic helicity are obtained from direct numerical simulations using 512(3) modes. The results indicate that the turbulence does not follow the Iroshnikov-Kraichnan phenomenology. The scaling exponents of the structure functions can be described by a modified She-Leveque model zeta(p) = p/9+1-(1/3)(p/3), corresponding to basic Kolmogorov scaling and sheetlike dissipative structures. In particular, we find zeta(2) approximately 0.7, consistent with the energy spectrum E(k) approximately k(-5/3) as observed in the solar wind, and zeta(3) approximately 1, confirming a recent analytical result.     

Modeling diffusion of adsorbed polymer with explicit solvent

Computer simulations of a polymer chain of length N strongly adsorbed at the solid-liquid interface in the presence of explicit solvent are used to delineate the factors affecting the N dependence of the polymer lateral diffusion coefficient, D(||). We find that surface roughness has a large influence, and D(||) scales as D(||) approximately N(-x), with x approximately 3/4 and x approximately 1 for ideal smooth and corrugated surfaces, respectively. The first result is consistent with the hydrodynamics of a "particle" of radius of gyration R(G) approximately N(nu) (nu=0.75) translating parallel to a planar interface, while the second implies that the friction of the adsorbed chains dominates. These results are discussed in the context of recent measurements.     

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.     

Mapping of the roughness exponent for the fuse model for fracture

The roughness exponent for fracture surfaces in the fuse model has been thought to be universal for narrow threshold distributions and has been important in the numerical studies of fracture roughness. We show that the fuse model gives a disorder dependent roughness exponent for narrow disorders when the lattice is influencing the fracture growth. When the influence of the lattice disappears, the local roughness exponent approaches zeta(local)=0.65+/-0.03 for distribution with a tail toward small thresholds, but with large jumps in the profiles giving corrections to scaling on small scales. For very broad disorders the distribution of jumps becomes a Lévy distribution and the Lévy characteristics contribute to the local roughness exponent.     

Activated escape of periodically modulated systems

The rate of noise-induced escape from a metastable state of a periodically modulated overdamped system is found for an arbitrary modulation amplitude A. The instantaneous escape rate displays peaks that vary with the modulation from Gaussian to strongly asymmetric. The prefactor nu in the period-averaged escape rate depends on A nonmonotonically. Near the bifurcation amplitude A(c) it scales as nu proportional, variant(A(c) - A)(zeta). We identify three scaling regimes, with zeta = 1/4, -1, and 1/2.     

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.