Kinetic roughening of ion-sputtered Pd(001) surface: beyond the Kuramoto-Sivashinsky model

We investigate the kinetic roughening of Ar+ ion-sputtered Pd(001) surface both experimentally and theoretically. In situ real-time x-ray reflectivity and in situ scanning tunneling microscopy show that nanoscale adatom islands form and grow with increasing sputter time t. Surface roughness W(t) and lateral correlation length xi(t) follow the scaling laws W(t) approximately t(beta) and xi(t) approximately t(1/z) with the exponents beta approximately 0.20 and 1/z approximately 0.20, for an ion beam energy epsilon=0.5 keV, which is inconsistent with the prediction of the Kuramoto-Sivashinsky (KS) model. We thereby extend the KS model by applying the coarse-grained continuum approach of the Sigmund theory to the order of O(inverted Delta(4),h(2)), where h is the surface height, and derive a new term of the form inverted Delta(2)(inverted Delta h)(2) which plays a decisive role in describing the observed morphological evolution of the sputtered surface.     

Crossover in the enstrophy decay in two-dimensional turbulence in a finite box

The numerical simulation of two-dimensional decaying turbulence in a large but finite box presented in this Letter uncovered two physically different regimes of enstrophy decay. During the initial stage, the enstrophy Omega, generated by a random Gaussian initial condition, decays as Omega(t) proportional variant t(-gamma) with gamma approximately 0.7-0.8. After that, the flow undergoes a transition to a gas or fluid composed of distinct vortices. Simultaneously, the magnitude of the decay exponent crosses over to gamma approximately 0.4. A theory predicting N(t) proportional variant t(-xi) and the magnitudes of exponents gamma=2/5 and xi=4/5 is presented.     

Dipole orientational order at liquid/vapor surfaces

We present ellipsometric observations of the orientational order alpha(2) of highly polar molecules at the noncritical liquid/vapor surface of critical polar+nonpolar mixtures. The dipoles, which are repelled from the interface via interactions with their image dipoles, are preferentially oriented with their axes parallel to the surface and possess an orientational order which is well described by alpha(2) approximately -t(2beta)D+(z/xi), where t=[T-T(c)]/T(c) is the reduced temperature, beta=0.328 is a critical exponent, and D+ is a universal function of the dimensionless depth z/xi with surface correlation length xi.     

Critical adsorption in the weak surface field limit

We study critical adsorption in the small surface field (h(1)) limit using a homologous series of critical liquid mixtures. The experiment data, in the one-phase regime, is accurately described by a universal surface scaling function G+(z/xi(+),z/l(h)) at distance z from the interface with correlation length xi(+) and surface field length l(h) approximately absolute value of (h(1))(-nu/Delta(1)), where h(1) approximately Deltasigma, the surface energy difference between the two components.     

Kinetic roughening in polymer film growth by vapor deposition

The growth front roughness of linear poly( p-xylylene) films grown by vapor deposition polymerization has been investigated using atomic force microscopy. The interface width w increases as a power law of film thickness d, w approximately d(beta), with beta = 0. 25+/-0.03, and the lateral correlation length xi grows as xi approximately d(1/z), with 1/z = 0.31+/-0.02. This novel scaling behavior is interpreted as the result of monomer bulk diffusion, and belongs to a new universality class that has not been discussed previously.     

Evolution of magnetic fields in freely decaying magnetohydrodynamic turbulence

We study the evolution of magnetic fields in freely decaying magnetohydrodynamic turbulence. By quasilinearizing the Navier-Stokes equation, we solve analytically the induction equation in the quasinormal approximation. We find that, if the magnetic field is not helical, the magnetic energy and correlation length evolve in time, respectively, as E(B) proportional to t(-2(1+p)/(3+p)) and xi(B) proportional to t(2/(3+p)), where p is the index of initial power-law spectrum. In the helical case, the magnetic helicity is an almost conserved quantity and forces the magnetic energy and correlation length to scale as E(B) proportional to (logt)(1/3)t(-2/3) and xi(B) proportional to (logt)(-1/3)t(2/3).     

Breakdown of dynamic scaling in surface growth under shadowing

Using Monte Carlo simulations and experimental results, we show that for common thin film deposition techniques, such as sputter deposition and chemical vapor deposition, a mound structure can be formed with a characteristic length scale, or "wavelength" lambda, that describes the separation of the mounds. We show that the temporal evolution of lambda is distinctly different from that of the mound size, or lateral correlation length xi. The formation of a mound structure is due to nonlocal growth effects, such as shadowing, that lead to the breakdown of the self-affinity of the morphology described by the well-established dynamic scaling theory. We show that the wavelength grows as a function of time in a power law form, lambda approximately t(p), where p approximately equals 0.5 for a wide range of growth conditions, while the mound size grows as xi approximately t(1-z), where 1/z varies depending on growth conditions.     

Universal dynamic exponent at the liquid-gas transition from molecular dynamics

The liquid-gas system is expected to exhibit distinct dynamic behavior in the fluid's critical region (model H). We present molecular dynamics simulations of a Lennard-Jones fluid model starting from specially designed, near-equilibrium, initial conditions. By following the fluid's relaxation towards equilibrium, we calculate the requisite transport coefficients in the critical region. The results yield the scaling behavior of the thermal diffusion coefficient D(T) approximately xi(-1.023+/-0.018) (xi is the correlation length) and a nonconventional divergent heat conductivity, all of which are in accord with mode-coupling and renormalization group predictions, as well as some experimental data.     

Autocorrelation exponent of conserved spin systems in the scaling regime following a critical quench

We study the autocorrelation function of a conserved spin system following a quench at the critical temperature. Defining the correlation length L(t) approximately t(1/z), we find that for times t' and t satisfying L(t')infinity limit, we show that lambda(')(c)=d+2 and phi=z/2. We give a heuristic argument suggesting that this result is, in fact, valid for any dimension d and spin vector dimension n. We present numerical simulations for the conserved Ising model in d=1 and d=2, which are fully consistent with the present theory.     

Stability of spikes in the shadow Gierer-Meinhardt system with Robin boundary conditions

We consider the shadow system of the Gierer-Meinhardt system in a smooth bounded domain Omega subset R(N),A(t)=epsilon(2)DeltaA-A+A(p)/xi(q),x is element of Omega, t>0, tau/Omega/xi(t)=-/Omega/xi+1/xi(s) integral(Omega)A(r)dx, t>0 with the Robin boundary condition epsilon partial differentialA/partial differentialnu+a(A)A=0, x is element of partial differentialOmega, where a(A)>0, the reaction rates (p,q,r,s) satisfy 10, r>0, s>or=0, 1or=0. We rigorously prove the following results on the stability of one-spike solutions: (i) If r=2 and 11 and tau sufficiently small the interior spike is stable. (ii) For N=1 if r=2 and 11 such that for a is element of (a(0),1) and mu=2q/(s+1)(p-1) is element of (1,mu(0)) the near-boundary spike solution is unstable. This instability is not present for the Neumann boundary condition but only arises for the Robin boundary condition. Furthermore, we show that the corresponding eigenvalue is of order O(1) as epsilon-->0.     

Correlations in ballistic processes

We investigate a class of reaction processes in which particles move ballistically and react upon colliding. We show that correlations between velocities of colliding particles play a crucial role in the long time behavior. In the reaction-controlled limit when particles undergo mostly elastic collisions and therefore are always near equilibrium, the correlations are accounted analytically. For ballistic aggregation, for instance, the density decays as n approximately t(-xi) with xi=2d/(d+3) in the reaction-controlled limit in d dimensions, in contrast with the well-known mean-field prediction xi=2d/(d+2).     

Formation and relaxation of two-dimensional vortex crystals in a magnetized pure-electron plasma

Systematic examinations are carried out experimentally about the contribution of background vorticity distributions (BGVD's) to the spontaneous formation and decay of ordered arrays (vortex crystals) composed of strong vortices (clumps) by using a pure-electron plasma. It is found that the BGVD level needs to be higher for an increasing number of clumps to form vortex crystals and that the number of the clumps constituting the crystal decreases in time as proportional to gamma lnt in contrast to proportional to t (-xi) with xi approximately 1 as accepted well in turbulence models. The decay rate gamma increases with the BGVD level. The observed configurations of the clumps cover the theoretically predicted catalogue of vortex arrays in superfluid helium, suggesting a possible relaxation path of the crystal states.     

Ensemble averages and nonextensivity at the edge of chaos of one-dimensional maps

Ensemble averages of the sensitivity to initial conditions xi(t) and the entropy production per unit of time of a new family of one-dimensional dissipative maps, x(t+1)=1-ae(-1/|x(t)|(z))(z>0), and of the known logisticlike maps, x(t+1)=1-a|x(t)|(z)(z>1), are numerically studied, both for strong (Lyapunov exponent lambda(1)>0) and weak (chaos threshold, i.e., lambda(1)=0) chaotic cases. In all cases we verify the following: (i) both [ln((q)x triple bond (x(1-q)-1)/(1-q); ln((1)x=ln(x] and [S(q) triple bond (1- sigma p(q)(i))/(q-1); S(1)=- sigma p(i)ln(p(i)] linearly increase with time for (and only for) a special value of q, q(av)(sen), and (ii) the slope of and that of coincide, thus interestingly extending the well known Pesin theorem. For strong chaos, q(av)(sen)=1, whereas at the edge of chaos q(av)(sen)(z)<1.     

Finite-size scaling and universality of the thermal resistivity of liquid 4He near Tlambda

We present measurements of the thermal resistivity rho(t,P,L) near the superfluid transition of 4He at saturated vapor pressure and confined in cylindrical geometries with radii L=0.5 and 1.0 microm [t identical with T/T(lambda)(P)-1]. For L=1.0 microm measurements at six pressures P are presented. At and above T(lambda) the data are consistent with a universal scaling function F(X)=(L/xi(0))(x/nu)(rho/rho(0)), X=(L/xi(0))(1/nu)t valid for all P (rho(0) and x are the pressure-dependent amplitude and effective exponent of the bulk resistivity rho, and xi=xi(0)t(-nu) is the correlation length). Indications of breakdown of scaling and universality are observed below T(lambda).     

Nuclear magnetic moment of the 57Cu ground state

The nuclear magnetic moment of the ground state of (57)Cu(Iota(pi) = 3/2(-), T(1/2) = 196.3 ms) has been measured to be /mu((57)Cu)/ = (2.00 +/- 0.05)mu(N) using the beta-NMR technique. Together with the known magnetic moment of the mirror partner (57)Ni, the spin expectation value was extracted as = -0.078 +/- 0.13. This is the heaviest isospin mirror T = 1/2 pair above the (40)Ca region for which both ground state magnetic moments have been determined. The discrepancy between the present results and shell-model calculations in the full f p shell giving mu((57)Cu) approximately 2.4mu(N) and approximately 0.5 implies significant shell breaking at (56)Ni with the neutron number N = 28.     

Coherent "metallic" resistance and medium localization in a disordered one-dimensional insulator

It is believed that a disordered one-dimensional (1D) wire with coherent electronic conduction is an insulator with the mean resistance approximately equal e(2L/xi) and resistance dispersion Delta(rho) approximately equal e(L/xi), where L is the wire length and xi is the electron localization length. Here we show that this 1D insulator undergoes at full coherence the crossover to a 1D "metal," caused by thermal smearing and resonant tunneling. As a result, Delta(rho) is smaller than unity and tends to be L/xi independent, while grows with L/xi first nearly linearly and then polynomially, manifesting the so-called medium localization.     

One-dimensional stochastic Levy-lorentz gas

We introduce a Levy-Lorentz gas in which a light particle is scattered by static point scatterers arranged on a line. We investigate the case where the intervals between scatterers xi(i) are independent random variables identically distributed according to the probability density function &mgr;(xi) approximately xi(-(1+gamma)). We show that under certain conditions the mean square displacement of the particle obeys /=Ct3-gamma for 1相似文献   

Critical spin dynamics of the 2D quantum Heisenberg antiferromagnets Sr2CuO2Cl2 and Sr2Cu3O4Cl2

We report a neutron scattering study of the long-wavelength dynamic spin correlations in the model two-dimensional S = 1/2 square lattice Heisenberg antiferromagnets Sr2CuO2Cl2 and Sr2Cu3O4Cl2. The characteristic energy scale, omega(0)(T/J), is determined by measuring the quasielastic peak width in the paramagnetic phase over a wide range of temperature ( 0.2 less similarT/J less similar0.7). The obtained values for omega(0)(T/J) agree quantitatively between the two compounds and also with values deduced from quantum Monte Carlo simulations. The combined data show scaling behavior, omega approximately xi(-z), over the entire temperature range with z = 1.0(1), in agreement with dynamic scaling theory.     

Universal sound absorption in low-temperature amorphous solids

A general elastohydrodynamic theory is developed based on the phenomenological assumption of a sharp decrease of shear relaxation time at large wave vectors k>k(xi), where k(xi) is of order of inverse of several interatomic distances a. This theory describes the low-energy excitations of glassy and amorphous solids, which contribute to anomalous linear-in-temperature specific heat and limit phonon thermal conductivity. The ratio of the wavelength of the phonon, lambda, to its mean free path, l, which is the universal property of sound absorption in glasses, is derived in this theory to be lambda/l=(2/3)(c(t)/c(l))(2)(k(xi)a)(3), where c(t) and c(l) are transverse and longitudinal sound velocities correspondingly.     

Oscillatory melting temperature of the vortex smectic phase in layered superconductors

We report on transport measurements of YBa 2Cu 3O (7-delta) single crystals with different oxygen contents in the geometry B, J ||ab (J perpendicularB). Our data show that the vortices become confined between the Cu-O planes below a well-defined temperature at which the effective size 2xi of the vortex core is approximately equal to the period of the Cu-O layers. This confinement strongly increases the vortex liquid freezing temperature. A new melting line is found separating a vortex liquid and a smectic phase, which shows an oscillatory field dependence reflecting differences between commensurate and incommensurate smectic states.