Displacement Fluctuations Research Articles

The influence of peak-locking errors on turbulence statistics computed from PIV ensembles

The influence of peak-locking errors on turbulence statistics computed from ensembles of PIV data is considered. PIV measurements are made in the streamwise–wall-normal plane of turbulent channel flow. The PIV images are interrogated in three distinct ways, generating ensembles of velocity fields with absolute, moderate, and minimal peak locking. Turbulence statistics computed for all three ensembles of data indicate a general sensitivity to peak locking in the single-point statistics, except for the mean velocity profile. Peak-locking errors propagate into the fluctuations of velocity, rendering single-point statistics inaccurate when severe peak locking is present. Multi-point correlations of both streamwise and wall-normal velocity are also found to be influenced by severe levels of peak locking. The displacement range of the measurement, defined by the PIV time delay, appears to affect the influence of peak-locking errors on turbulence statistics. Smaller displacement ranges, particularly those that produce displacement fluctuations that are less than one pixel in magnitude, yield inaccurate turbulence statistics in the presence of peak locking.

Smectic layer displacement fluctuations in solid substrate supported smectic-A films.

In this paper we present results of calculations of static and dynamic characteristics of smectic layer displacement fluctuations in solid substrate supported smectic-A films with due regard for asymmetric profiles of the bending elastic constant K and the smectic layer compressibility B. We also take into account difference in properties of boundary surfaces of the film, namely, the surface tension of the free surface is taken to be finite whereas that of a film-substrate interface is assumed to be infinitely large. Profiles of the smectic layer displacement fluctuations and correlations between them are calculated for films formed of liquid crystalline compounds with the bulk smectic-A to nematic phase transition. The calculations are performed at temperatures much lower than that of the bulk phase transition and at maximum temperatures of existence of films of given thickness. The time dependent displacement-displacement correlation functions for thermal smectic layer displacement fluctuations and time dependent intensity-intensity correlation functions for diffuse x-ray scattering from the films are also calculated. It is shown that unlike free-standing smectic-A films, an effect of the temperature on dynamics of smectic layer displacement fluctuations in solid substrate supported smectic-A films can be observed in experiments on coherent x-ray dynamic scattering from not very thick films (N approximately 20) and at significantly smaller wave vector transfer component in the film plane.

Internal Displacement and Elastic Properties of the Silicon Tersoff Model

Martin's method, which is used to determine the internal displacement of atomic systems and elastic constants, is applied to the Tersoff potential. The potential is modified to provide an accurate description of the high-temperature elastic properties of silicon. The elastic constants of crystalline silicon were investigated at both low and high temperatures. Results were verified using the statistical thermodynamic method, i. e., ‘Fluctuation formula’. It was found that values of elastic constants and the influence of the internal displacement are valid. However, at high temperatures the gap becomes larger owing to the thermal fluctuation. Since the convergence of the Martin's method is faster by about two orders, it is the more effective method. It was also found that the fluctuation term includes the effects of the internal displacement and thermal fluctuation.

Effect of the inhomogeneous structure of freely suspended smectic-A films on the dynamics of fluctuations of smectic-layer displacements

The dynamics of fluctuations of smectic-layer displacements in freely suspended smectic-A films is studied theoretically with due regard for the dependence of the transverse-bending moduli K and extension (or compression) of smectic-B layers on the distance to the free surfaces of the films. The temperature dependences of the dynamic correlation functions are calculated for fluctuations of layer displacements in films of various thicknesses and then used to calculate the correlations between the X-ray intensities scattered by the film at different moments of time. The calculations were performed within a wide temperature range. It is shown that the influence of temperature on the X-ray dynamics of fluctuations of layer displacements in freely suspended smectic-A films can be detected in the experiments on the dynamical scattering by rather thick films (layer number N ≥ 100) at considerably high values of the recoil-momentum component in the film plane (≥106 cm−1).

Stochastic motion of 7 × 7 kinks at monoatomic step edges on the Si(1 1 1) surface

An offset of a straight step, called a kink, is occasionally formed on semiconductor surfaces. The motion of the kink on the Si(1 1 1) 7×7 surface in the [ 1 ̄ 1 ̄ 2 ] step was studied in detail by high-temperature scanning tunneling microscopy (STM), and thermal fluctuations of the kink displacement along the step edges was observed. The kink displacement did not diverge with time, suggesting that a restoring force acts on the kink. The displacement, however, could be clearly represented by the gaussian distribution and it was therefore considered to be a Brownian particle. The temperature dependence of the mean square displacement of the kink position showed that the displacement is a thermal activation process with an apparent activation energy of 1.54±0.1 eV. From the equation of motion on the kink displacement including an incoming and outgoing flux as a fluctuation source, the phenomenological Langevin equation was derived. The activation energy of the kink displacement is related to the diffusion coefficient of the two-dimensional adatom gas and the latent heat of the atoms from the kink site to the surface adatom.

Transverse pinning and vortex displacement fluctuations of moving vortex lattices interacting with periodic pinning

The dynamical behavior of driven vortex lattices commensurate with periodic pinning in a clean superconducting film is investigated theoretically. A mean-field model, previously introduced by us [Phys. Rev. B 66 (2002) 054514] and called dynamical cage model, is applied here to study transverse pinning and vortex displacement fluctuations. The critical force for transverse depinning and the mean-square fluctuations induced by the temperature and vortex motion are calculated as functions of the vortex lattice center of mass velocity (or driving force) and of the temperature. The critical force is found to be in good qualitative agreement with numerical simulation results. The displacement fluctuations induced by vortex motion are found to be anisotropic, with the largest ones occurring along the direction of motion. Application of the Lindemann criterion to these fluctuations suggests a transition from the commensurate vortex lattice to a smectic vortex phase, also in agreement with numerical results.

Strain‐driven homogenization of inelastic microstructures and composites based on an incremental variational formulation

AbstractThe paper investigates computational procedures for the treatment of a homogenized macro‐continuum with locally attached micro‐structures of inelastic constituents undergoing small strains. The point of departure is a general internal variable formulation that determines the inelastic response of the constituents of a typical micro‐structure as a generalized standard medium in terms of an energy storage and a dissipation function. Consistent with this type of inelasticity we develop a new incremental variational formulation of the local constitutive response where a quasi‐hyperelastic micro‐stress potential is obtained from a local minimization problem with respect to the internal variables. It is shown that this local minimization problem determines the internal state of the material for finite increments of time. We specify the local variational formulation for a setting of smooth single‐surface inelasticity and discuss its numerical solution based on a time discretization of the internal variables. The existence of the quasi‐hyperelastic stress potential allows the extension of homogenization approaches of elasticity to the incremental setting of inelasticity. Focusing on macro‐strain‐driven micro‐structures, we develop a new incremental variational formulation of the global homogenization problem where a quasi‐hyperelastic macro‐stress potential is obtained from a global minimization problem with respect to the fine‐scale displacement fluctuation field. It is shown that this global minimization problem determines the state of the micro‐structure for finite increments of time. We consider three different settings of the global variational problem for prescribed linear displacements, periodic fluctuations and constant stresses on the boundary of the micro‐structure and discuss their numerical solutions based on a spatial discretization of the fine‐scale displacement fluctuation field. The performance of the proposed methods is demonstrated for the model problem of von Mises‐type elasto‐visco‐plasticity of the constituents and applied to a comparative study of micro‐to‐macro transitions of inelastic composites. Copyright © 2002 John Wiley & Sons, Ltd.

Measurement of digital particle image velocimetryprecision using electro-optically created particle-imagedisplacements

The displacement (velocity) precision achieved withdigital particle image velocimetry (PIV) was measured. Thepurpose of this work was to determine the precision andsensitivity of digital PIV using real rather than theoretical images at 1 and 2 mm spatial resolution. The displacementmeasurement precision was determined by measuring the RMS noisefrom 60 identical displacement distributions. This work isunique in that it uses electro-optical image shifting to createa repeatable image displacement distribution of random particlefields. The displacement variance between images is caused bythe shot-to-shot variation in: (1) the particle-image fields,(2) the camera noise and (3) the variance in the correlationpeak detection. In addition to magnification variations, theparticle-number density, imaging-lens f-stop and image-planeposition errors were varied to determine the bestconfiguration. The results indicate that both the ensemble-meanand the RMS fluctuations of the image displacements are affected by these parameters and comparisons with results found in theliterature are presented. The extents of these variations arequantified. This variance does not, of course, include errors dueto random gradients and out-of-plane pairing losses, whichexist in real turbulent flows.

Homogenization of inelastic solid materials at finite strains based on incremental minimization principles. Application to the texture analysis of polycrystals

The paper presents new continuous and discrete variational formulations for the homogenization analysis of inelastic solid materials undergoing finite strains. The point of departure is a general internal variable formulation that determines the inelastic response of the constituents of a typical micro-structure as a generalized standard medium in terms of an energy storage and a dissipation function. Consistent with this type of finite inelasticity we develop a new incremental variational formulation of the local constitutive response, where a quasi-hyperelastic micro-stress potential is obtained from a local minimization problem with respect to the internal variables. It is shown that this local minimization problem determines the internal state of the material for finite increments of time. We specify the local variational formulation for a distinct setting of multi-surface inelasticity and develop a numerical solution technique based on a time discretization of the internal variables. The existence of the quasi-hyperelastic stress potential allows the extension of homogenization approaches of finite elasticity to the incremental setting of finite inelasticity. Focussing on macro-deformation-driven micro-structures, we develop a new incremental variational formulation of the global homogenization problem for generalized standard materials at finite strains, where a quasi-hyperelastic macro-stress potential is obtained from a global minimization problem with respect to the fine-scale displacement fluctuation field. It is shown that this global minimization problem determines the state of the micro-structure for finite increments of time. We consider three different settings of the global variational problem for prescribed displacements, non-trivial periodic displacements and prescribed stresses on the boundary of the micro-structure and develop numerical solution methods based on a spatial discretization of the fine-scale displacement fluctuation field. Representative applications of the proposed minimization principles are demonstrated for a constitutive model of crystal plasticity and the homogenization problem of texture analysis in polycrystalline aggregates.

Primary production on the continental shelf off Cape Hatteras, North Carolina

Abstract Distributions of primary production and chlorophyll size structure were examined in relationship to hydrographic properties during March and July 1996 in continental shelf waters off Cape Hatteras, North Carolina. Chlorophyll concentrations ranged highest (>10 mg m −3 ) during March. Peak values were associated with subsurface maxima near the shelf edge, which were dominated by larger (>8 μm) phytoplankton. In July, chlorophyll concentrations were generally lower with higher proportions associated with the 2.0 g C m −2 d −1 ) in association with the shelf–slope front. In contrast, highest values in July (>3.0 g C m −2 d −1 ) were associated with an intrusion of high-salinity, high-nutrient water into the southern portion of the study region. Average shelf-wide productivities were 1.3 g C m −2 d −1 in March and 2.1 g C m −2 d −1 in July. Contemporaneous Advanced Very High-Resolution Radiometer sea-surface temperature imagery revealed that regions of high productivity were proximal to Gulf Stream circulation features. In March, cross-shelf sections of hydrographic properties and nutrients provided evidence for onshore displacement of the shelf–slope front, apparently related to the combined effects of the strong winds prior to the cruise and the offshore presence of energetic Gulf Stream processes. We speculate that variable forcing, related to the dynamics of the Gulf Stream and wind, resulted in significant frontal displacement and frontal velocity fluctuations leading to enhanced mixing and injection of nutrients across the frontal boundary. In July, Gulf Stream circulation, in conjunction with upwelling favorable conditions, resulted in a subsurface intrusion of high-nutrient water onto the shelf analogous to similar phenomena observed in the South Atlantic Bight. Localized regions of enhanced productivity appear to be quantitatively important in the overall carbon/nitrogen budget of the southern Mid-Atlantic Bight shelf.

Interaction between shallow groundwater, saline surface water and nutrient discharge in a seasonal estuary: the Swan–Canning system

AbstractThe Swan and Canning Rivers converge to form an estuary that is seasonally forced by wet winter and dry summer conditions. The estuary is also tidally forced due to its contact with the Indian Ocean. The perception that the occurrence of nuisance algal blooms has increased in frequency and severity in recent years has prompted the present investigation into the interaction of the shallow groundwater system with the Swan–Canning Estuary. The extent to which this interaction contributes to nutrient delivery to the river is a focus of the work.Groundwater interaction with the upper reaches of the Swan River is shown to occur at three length scales: (i) the scale of the river‐bed sediments (i.e. <10 m); (ii) the scale over which tidal forcing of the river is transmitted into the adjacent aquifer (10 to 100 m); and (iii) the scale of the regional groundwater field (>1000 m). Two‐dimensional groundwater flow modelling in plan covering the regionally advected groundwater flow domain of the upper Swan River Estuary from the Causeway to Guildford shows that there is a net groundwater discharge to the Swan River of groundwater discharge of about 80 000 m3/day, or about 29 million m3/year. Between 1987 and 1996, the average surface tributary inflow to the Swan River was about 460 million m3/year. Thus groundwater discharge contributed approximately 6% of the total annual river flow. This percentage is clearly small in comparison to the total river flow. However, in the six months from November to April in summer, tributary flow into the Swan River declines sharply to an average total of approximately 12 million m3. Groundwater discharge during this six‐month period is approximately 14 million m3 or about 55% of the surface tributary flow, and thus groundwater is a significant component of the total inflow to the Swan–Canning Estuary during this period. Nutrient concentrations, particularly ammonium, within the sediment pore fluids underlying the river are very high relative to concentrations in the river, such that groundwater discharge rates of this magnitude are capable of introducing significant nutrient loadings to the river. The nitrogen load to the Swan River derived from regionally advected groundwater discharge is conservatively estimated at between 30 and 60 t/year. This ranks groundwater as one of the highest single inputs of nitrogen to the Swan–Canning Estuary when compared to surface water flows. It contributes about 10% of the total nitrogen load entering this reach of the river. Seasonal and tidal variations increase the complexity of the system and may act to increase the presence and availability of groundwater‐derived nutrients in the river and estuary system.Field observations and results from numerical groundwater flow modelling show that groundwater preferentially discharges into the Swan River along the outside of river meanders. Along the inside of meanders, groundwater discharge is either very low or at times the flow direction reverses such that saline river water recharges the aquifer during the late spring, summer and early autumn months. Short‐term, high‐frequency fluctuations such as wave‐induced displacement, seawater intrusion, hyporheic flux and tidal fluctuations may cause small spatial scale mixing and perturbation of the nutrient‐rich groundwater and sediment porewater with either the river water directly or with fresher groundwater as it discharges to the river. These short‐term fluctuations appear to cause nutrient release from the sediment pore fluids, particularly in summer low flow periods such that they are a significant contributing factor in triggering algal blooms. Copyright © 2001 John Wiley & Sons, Ltd.

Pinning of stripes in cuprate superconductors

We examine the effects of disorder on striped phases in high-temperature superconductors and related materials. In the presence of quenched disorder pinning, by the atomic lattice---which might give rise to commensuration effects---is irrelevant for two-dimensional stripe arrays on large length scales. As a consequence, the stripes have divergent displacement fluctuations and topological defects are present at all temperatures. Therefore, the positional order of the stripe array is short ranged with a finite correlation length even at zero temperature. Thus lock-in phenomena can exist only as crossovers but not as transitions. In addition, this implies the glassy nature of stripes observed in recent experiments.

Thermoelastic effects at low temperatures and quantum limits in displacement measurements

The displacement fluctuations of mirrors in optomechanical devices, induced via thermal expansion by temperature fluctuations due either to thermodynamic fluctuations or to fluctuations in the photon absorption, can be made smaller than quantum fluctuations, at the low temperatures, high reflectivities and high light powers needed to readout displacements at the standard quantum limit. The result is relevant for the design of quantum limited gravitational-wave detectors, both "interferometers" and "bars", and for experiments to study directly mechanical motion in the quantum regime.

Surface oscillations of smectic-A liquid crystals

A theoretical description of free surface motion is presented for a semi-infinite unbounded smectic-A (Sm-A) liquid crystal. The characteristic equation is analyzed in a wide range of frequencies and wave numbers. It is shown that at low frequencies the surface eigenmotion is a wave of the second sound type. The wave velocity is twice that of the maximum second sound velocity in the bulk phase. This Rayleigh mode may be excited and detected as surface transverse waves. At high frequencies the surface eigenmotion is a damping viscous mode. The spectral intensities of the surface displacement fluctuations are presented in rather simple form for separate areas of wave numbers and frequencies. These results may be used to describe light scattering experiments. It is shown that the surface tension is negligible when describing Sm-A surface eigenmotions, in contrast to ordinary liquids. At the same time the surface tension is sufficient for surface displacement fluctuations at low frequencies.

Electron parametric instabilities of relativistically intense laser light in under and overdense plasma

A unified treatment of electron parametric instabilities driven by ultraintense laser light in plasma is described. The method is valid for laser light of any polarization and intensity, for any plasma density both rarefied and classically overdense, and for any scattering geometry. A fully relativistic self-consistent three-dimensional (3D) analysis, based on the cold electron fluid and Maxwell’s equations without further assumption, is carried out in the laser pulse proper frame allowing a concise description in terms of a system of six ordinary differential equations. The approach is applied to linearly polarized laser light in underdense plasma, and overdense plasma accessible by self-induced transparency. Electron charge displacement and relativistic mass fluctuations give rise to hybrids of stimulated Raman scattering, the two plasmon decay, the relativistic modulational and filamentation instabilities, and to stimulated harmonic generation. There is vigorous growth over a wide range of wave numbers and harmonics.

Quantum n-vector anharmonic crystal II: Displacement fluctuations

Based on the 1/n-expansion derived in a previous paper, the displacement fluctuations are analyzed in a quantum n-vector model of anharmonic crystal in the large n regime. It is shown that in the ferroelectric phase the n→∞ limit of the local fluctuation field has faster large-distance correlation decay than its Hartree–Fock approximation. Also, the critical exponent of the global displacement fluctuation is strictly smaller there than the Hartree–Fock exponent. In particular, the displacement fluctuations may be normal in the ferroelectric phase in spite of the Hartree–Fock prediction.

Noise factors in detection of minute marks by domain wall displacement

Causes of data errors by DWDD and dominant noise factors which determine the density are discussed. Dropout of data mainly occurs during readout by domain wall displacement at mark length less than 110 nm. The bit shift causes serious data error when window width is shorter than 70 nm. A novel method has been introduced to analyze the jitter by reading the signal many times for the same area and by averaging the waveform. The space-dependent jitter obtained by averaging is 8.8 nm and is greater than the time-dependent jitter of 6.7 nm caused by the shot noise, the laser noise, and the system noise as well as caused by the fluctuation of the domain wall displacement. Comparison with the ordinary structured MO media has revealed that a bit length of 77 nm will be available when the space-dependent jitter is reduced to 3.8 nm which is the value for ordinary structured media.

Dynamics on Molecular Films. Ripplon Spectroscopy and Physics of Molecular Film.

Ripplon light scattering technique is introduced together with its application to the study on physical properties of molecular films formed on liquid surfaces. Ripplon is high frequency capillary waves generated by the thermal fluctuation of the liquid displacement, of which propagation constants yields information on the molecular dynamics in and near the surface. The ripplon frequency and damping constant is determined accurately by the light scattering system equipped by the optical beating spectroscopy techniques. The technique was successfully applied to the investigation of two dimensional gas-liquid phase transition of the Langmuir films. It reveals the critical behavior of the film, which is observed as the critical softening of the condensed phase with increasing temperature. Several other applications of ripplon light scattering for the observation of dynamic process of molecular adsorption/desorption process on to the surface are also presented.

Scalar Domination and Normal Fluctuations in N-Vector Quantum Anharmonic Crystals

A lattice model of N-dimensional quantum anharmonic oscillators with a polynomial anharmonicity and a ‘ferroelectric’ pair interaction is considered. For arbitrary N e $$\mathbb{N}$$ , correlation inequalities, showing that the temperature Green functions of this model are dominated by the corresponding Green functions of the scalar (N=1) model, are proven. These inequalities are then used to prove that the fluctuations of displacements of particles remain normal at all temperatures provided the model parameters obey a certain condition. In particular this means that the smallest distance between the energy levels of the corresponding one-dimensional isolated oscillator should be large enough or its mass should be small enough.

Quantum Effects in a Lattice Model of Anharmonic Vector Oscillators

A model of d-dimensional quantum anharmonic oscillators living on ℤv, with a polynomial anharmonicity and a ferroelectric pair interaction is considered. For all v, d ∈ ℕ, including the cases where such models undergo a structural phase transition, it is proved that the fluctuations of displacements of particles remain normal at all temperatures if the energy of zero-point oscillations of a given particle exceeds a certain value proportional to the energy of its interaction with the rest of oscillators. In particular, this occurs when the smallest distance between the energy levels of the corresponding one-dimensional isolated oscillator is large enough or its reduced mass is small enough. Therefore, in such systems strong zero-point oscillations may suppress abnormal fluctuations of any kind at all temperatures.