New scaling laws for trapped-particle anomalous transport in tokamaks

An improved formula for anomalous transport caused by the dissipative trapped-ion instability (without shear effect) is derived numerically and by two independent analytical methods. The new shearless result is also used to derive the anomalous diffusion with shear effect by a general method already published.     

Studying anomalous scaling and heat transport of turbulent thermal convection using a dynamical model

Turbulent thermal convection is a well-studied problem with various issues of interest. In this paper, we review our work which shows the nature and origin of anomalous scaling and heat transport in the limit of very strong thermal forcing, can be gained by studying a dynamical model, known as shell model, of homogeneous turbulent thermal convection in which buoyancy acts directly at most scales. Specifically, we have obtained two results. The first result is that when buoyancy acts directly at most scales such that the dynamics are governed by a cascade of entropy, the scaling behavior is described by Bolgiano and Obukhov scaling plus corrections that are due to the variations of the local entropy transfer rate. This result indicates the validity of the extension of refined similarity hypothesis to turbulent thermal convection. The second result is that when buoyancy is acting directly at most scales, a damping term acting on the largest scale, which has to be added for the system to achieve stationarity, plays a crucial role in heat transport, and that the heat transport depends on the strength of thermal forcing in the same manner as that predicted for the ultimate state of very strong thermal forcing. With our interpretation of the damping term representing the effect of the boundaries, this result indicates that in the ultimate state of turbulent thermal convection, when buoyancy is acting at most scales, boundaries would play a significant role in heat transport.     

Growth dynamics of ZnPc and TiOPc thin films: Effect of crystallinity on anomalous scaling behavior

The surface morphology evolution and scaling behavior of zinc phthalocyanine (ZnPc) and titanyl phthalocyanine (TiOPc) thin films have been studied using atomic force microscopy, X-ray diffraction and height difference correlation function analysis. In contrast to the large growth exponent (β) values and anomalous scaling behavior previously reported for other crystalline molecular thin films, significantly small β and anomaly values were observed for amorphous TiOPc thin films. The relatively small anomaly value of ZnPc thin films, though larger than that of TiOPc thin films, is also rationalized by the lack of crystallographic ordering at the initial stage of growth.     

Ion-acoustic turbulence and anomalous transport

We present results for the dynamics of evolution of non-linear state plasmas in a d.c. electric field which causes ion-acoustic turbulence (IAT). We look at (1) the time variation of the drift electron velocity and of the effective collision frequency, (2) features of the redistribution and heating of resonance ions, (3) the evolution of the spectral and angular distribution of turbulent pulsations, (4) processes of heating of the bulk of the particles. The results of an analytical IAT theory are compared with computer simulations.Special attention is paid to the theory of inhomogeneous plasmas with IAT. A self-consistent theory of anomalous transport is presented. We discuss the anisotropy of anomalous transport and the influence of non-Maxwellian particle velocity distributions on the transport processes. The electromagnetic properties, self-organization and hydrodynamic instability of plasmas with IAT are discussed.     

A model of anomalous transport

A lattice model is used to derive a system of equations describing anomalous transport in the case of low tracer concentration. In the adopted model, anomalous transport is due to nonequilibrium distribution of tracer particles over sites in an inhomogeneous lattice. It is shown that a well-known time-fractional differential equation can be derived from the lattice equations under certain additional assumptions.     

Phonon-mediated anomalous dynamics of defects

Dynamics of an array of line defects interacting with a background elastic medium is studied in the linear regime. It is shown that the inertial coupling between the defects and the ambient phonons leads to an anomalous response behavior for the deformation modes of a defect-lattice, in the form of anisotropic and anomalous mass and elastic constants, resonant dissipation through excitation of phonons, and instabilities. The case of a single fluctuating line defect is also studied, and it is shown that it could lead to formation of shock waves in the elastic medium for sufficiently high frequency deformation modes.Received: 18 February 2003, Published online: 23 July 2003PACS: 63.20.Mt Phonon-defect interactions - 61.72.Bb Theories and models of crystal defects - 66.30.Lw Diffusion of other defects     

Local coupling of shell models leads to anomalous scaling

We consider cascade models of turbulence which are obtained by restricting the Navier-Stokes equation to local interactions. By combining the results of the method of extended self-similarity and a novel subgrid model, we investigate the inertial range fluctuations of the cascade. Significant corrections to the classical scaling exponents are found. The dynamics of our local Navier-Stokes models is described accurately by a simple set of Langevin equations proposed earlier as a model of turbulence [20]. This allows for a prediction of the intermittency exponents without adjustable parameters. Excellent agreement with numerical simulations is found.     

Warm cascades and anomalous scaling in a diffusion model of turbulence

A phenomenological turbulence model in which the energy spectrum obeys a nonlinear diffusion equation is analyzed. The general steady state contains a nonlinear mixture of the constant-flux Kolmogorov and fluxless thermodynamic components. Such "warm cascade" solutions describe a bottleneck phenomenon of spectrum stagnation near the dissipative scale. Transient self-similar solutions describing a finite-time formation of steady cascades are analyzed and found to exhibit nontrivial scaling behavior.     

Intrinsic anomalous scaling in a ferromagnetic thin film model

Recently, the interest on theoretical and experimental studies of dynamic properties of the magnetic domain wall (MDW) of ferromagnetic thin films with disorder placed in an external magnetic field has increased. In order to study global and local measurable observables, we consider the (1 + 1)-dimensional model introduced by Buceta and Muraca [Physica A 390, 4192 (2011)], based on rules of evolution that describe the MDW avalanches. From the values of the roughness exponents, global ζ, local ζ _loc, and spectral ζ _s , obtained from the global interface width, height-difference correlation function and structure function, respectively, recent works have concluded that the universality classes should be analyzed in the context of the anomalous scaling theory. We show that the model is included in the group of systems with intrinsic anomalous scaling (ζ ? 1.5, ζ _loc = ζ _s ? 0.5), and that the surface of the MDW is multi-affine. With these results, we hope to establish in short term the scaling relations that verify the critical exponents of the model, including the dynamic exponent z, the exponents of the distributions of avalanche-size τ and -duration α, among others.     

Finite size scaling and low mass glueballs

We propose finite lattice effects as a probe of the glueball mass spectrum, and give an analysis of the recent SU(2) Monte Carlo data of Brower, Nauenberg and Schalk in terms of a gas of free glueballs. For L⁴ lattices with L = 4, 5, 6 fits are made to ξ(m = 1/aξ) which indicate a rather large effective number of degrees of freedom (i.e. statistical degeneracy where a spin J counts as 2J + 1) from 5 to 15 states. As the degeneracy is increased, the central glueball mass increases from $\text{m = (1.3±0.2)}\text{κ}$ at degeneracy 5 to about $\text{m = (1.9±0.2)}\text{κ}$ at degeneracy 15, relative to the SU(2) string tension $\text{κ}$.     

Slow dynamics and anomalous nonlinear fast dynamics in diverse solids

Results are reported of the first systematic study of anomalous nonlinear fast dynamics and slow dynamics in a number of solids. Observations are presented from seven diverse materials showing that anomalous nonlinear fast dynamics (ANFD) and slow dynamics (SD) occur together, significantly expanding the nonlinear mesoscopic elasticity class. The materials include samples of gray iron, alumina ceramic, quartzite, cracked Pyrex, marble, sintered metal, and perovskite ceramic. In addition, it is shown that materials which exhibit ANFD have very similar ratios of amplitude-dependent internal-friction to the resonance-frequency shift with strain amplitude. The ratios range between 0.28 and 0.63, except for cracked Pyrex glass, which exhibits a ratio of 1.1, and the ratio appears to be a material characteristic. The ratio of internal friction to resonance frequency shift as a function of time during SD is time independent, ranging from 0.23 to 0.43 for the materials studied.     

Corrections to scaling and finite size effects

Numerical investigations of critical phenomena might lead to different leading correction-to-scaling terms, depending on the type of analysis. We discuss which leading correction-to-scaling behavior is expected for finite system sizes, using two-dimensional percolation as our main example. It turns out that a finite-size scaling from length L to L - 1 is less perturbed by correction-to-scaling terms.     

Relations between anomalous diffusion and fluctuation scaling: the case of ultraslow diffusion and time-scale-independent fluctuation scaling in language

The European Physical Journal B - This paper deals with spin deviation vs site number in an antiferromagnet with next nearest neighbour interactions along with bilinear, anisotropic, and...     

Berry-phase effect in anomalous thermoelectric transport

We develop a theory of the Berry-phase effect in anomalous transport in ferromagnets driven by statistical forces such as the gradient of temperature or chemical potential. Here a charge Hall current arises from the Berry-phase correction to the orbital magnetization rather than from the anomalous velocity, which does not exist in the absence of a mechanical force. A finite-temperature formula for the orbital magnetization is derived, which enables us to provide an explicit expression for the off-diagonal thermoelectric conductivity, to establish the Mott relation between the anomalous Nernst and Hall effects, and to reaffirm the Onsager relations between reciprocal thermoelectric conductivities. A first-principles evaluation of our expression is carried out for the material CuCr(2)Se(4-x)Br(x), obtaining quantitative agreement with a recent experiment.     

Interfacial three-phonon processes and anomalous interfacial energy transport

Interfacial three-phonon processes require only a moderately strong matrix element $\text{(～ 10}{}^5\text{erg}\text{cm}{}^2\text{)}$ to explain the anomalous energy transport observed at high phonon frequencies across the interface between ordinary and “quantum” materials. This mechanism is qualitatively consitent with a wide variety of experiments, and has a large number of symmetry-allowed couplings with which to explain the details of particular experiments. Near “onset”, this mechanism contributes anomalous reflection and transmission varying as the sixth power of the incident phonon frequency.