Initial Wavelength Research Articles

Initial instabilities of a granular bed sheared by a turbulent liquid flow: length-scale determination

The transport of granular matter by a fluid flow is frequently found in nature and in industry. When the shear stresses exerted by the fluid flow on a granular bed are bounded to some limits, a mobile granular layer known as bed-load takes place, in which the grainsstay in contact with the fixed part of the granular bed. Under these conditions, an initiallyflat granular bed may be unstable, generating ripples and dunes, such as those observed indeserts, but also in pipelines conveying sand. There are evidences that these forms have atypical length correlated to their initial wavelength. So, the length-scale of the initial linear instabilities is a key point to understand the typical structures observed. This paper presents a theoretical study of the initial instabilities on a granular bed sheared by aturbulent liquid flow without free-surface effects, when bed-load is present. This studyconsists of a linear stability analysis, taking into consideration fluid flow, relaxation and gravity effects, and it is compared to published experimental data. It is proposed here,differently from many previous studies, that the initial wavelength of bed-forms varies with flow conditions when the fluid is a liquid.

Optomechanics of liquid crystals for dynamical optical response of photonic structures

We show that the mechanical effect of light on the orientational ordering of the crystallineaxis of a mesophase can be used to control the dynamics of the optical response of liquidcrystal infiltrated photonic structures. The demonstration is made using a one-dimensionalperiodic structure whose periodicity is broken by the presence of a nematic liquid crystaldefect layer. In this study we report on output light polarization and/or intensity dynamicsthat depend on the initial molecular ordering and incident light wavelength and intensity.

Sand Dunes in Steady Flow at Low Froude Numbers: Dune Height Evolution and Flow Resistance

The development of sand dunes in an erodible bed exposed to flowing water is considered using a numerical flow model. The bed is initially given a small perturbation, which is followed in the time domain. Examples are given where a sinusoidal perturbation reaches the fully developed steady equilibrium shape. The flow modeling is based on a k-ω turbulence closure. The sediment transport is assumed to be bed-load only, with an avalanche-like movement on the steep dune front. The model is also found capable of predicting the growth in wavelength if the initially prescribed wavelength is sufficiently short. Results of the dune development are presented for different initial wavelengths. It is demonstrated that an equilibrium shape is developed for a range of wavelength-depth ratios as long as this ratio is sufficiently small.

Wavelength calibration by combining arc and night sky lines for LAMOST

A novel method is presented for the wavelength calibration of the Large Sky Area Multi-Object Fiber Spectroscopic Telescope (LAMOST). The proposed method combines the arc lines and night sky lines, and can achieve high performance. Firstly, the initial wavelength calibration is performed by employing arc lines. Afterwards, the centroids of sky lines are calculated by the initial calibration results and adjusted by the gravity method iteratively. Finally, the ultimate wavelength calibration is obtained by fitting the centroids of arc lines and sky lines with their corresponding wavelengths. Experiments are performed on the data observed by LAMOST, and the results of the proposed method are more accurate than that of the calibration only by arc lines or sky lines. The calibration sky lines are dense in the red channel (5,700–9,000 A) of LAMOST, but only a few ones are in the blue channel (3,700–5,900 A). The new method achieves excellent results in the red channel as the substantial sky lines are employed, and the calibration accuracy of the blue channel is also enhanced in some degree by the scare sky lines.

Experimental study of the individual differences in chromatic perception through blue‐yellow metameric matches of a white‐light continuum

A metameric colour matching test was designed to study inter-observer variability. Blue-yellow metameric matching to a white-light continuum was used to define the optimal wavelengths at which each of eight non-colour-defective observers achieved a match. The tests involved chromatic stimuli on a 2° bipartite field, with a white-light continuum presented on the left half, and a mixture of two monochromatic stimuli on the right half. The luminance of these chromatic stimuli was adjusted by the researcher using a staircase method, with the observer providing feedback about the similarity in luminance and chromaticity between the two halves of the field. Two series were performed for each observer, using different fixed yellow wavelengths. Since for each fixed yellow wavelength the match with the target white can be achieved by only one corresponding blue wavelength which is particular for each observer, the initial blue wavelengths were approximations based on the 2° CIE 1931 standard observer. Once the observers had attained an achromatic match, they modified the blue wavelength to achieve a perfect match of both halves. Generally, the observers found this modification of the blue wavelength necessary to achieve the metameric match. Each observer had a particular optimal blue wavelength which differed between the two series. The differences between the deviations from the standard observer for the two series were constant in value among the observers.

Measurements of the aeolian sand transport saturation length

The wavelength at which a dune pattern emerges from a flat sand bed is controlled by the sediment transport saturation length, which is the length needed for the sand flux to adapt to a change in wind strength. The influence of the wind shear velocity on this saturation length and on the subsequent dune initial wavelength has remained controversial. In this paper, we present direct measurements of the saturation length performed in a wind tunnel experiment. Complementary to this, initial dune wavelengths are measured under different wind conditions — in particular after storms. Using the linear stability analysis of dune formation, it is then possible to deduce the saturation length from field data. Both direct and indirect measurements agree that the saturation length is almost independent of the wind strength. This result supports the idea that grain inertia is the dominant dynamical mechanism limiting sediment transport saturation on dunes.

The Surface Expression of Semidiurnal Internal Tides near a Strong Source at Hawaii. Part II: Interactions with Mesoscale Currents*

Abstract Observations of semidiurnal surface currents in the Kauai Channel, Hawaii, are interpreted in the light of the interaction of internal tides with energetic surface-intensified mesoscale currents. The impacts on internal tide propagation of a cyclone of 55-km diameter and ∼100-m vertical decay scale, as well as of vorticity waves of ∼100-km wavelength and 100–200-m vertical decay scales, are investigated using 3D ray tracing. The Doppler-shifted intrinsic frequency is assumed to satisfy the classic hydrostatic internal wave dispersion relation, using the local buoyancy frequency associated with the background currents through thermal-wind or gradient-wind balance. The M2 internal tide rays with initial horizontal wavelength of 50 km and vertical wavelength of O(1000 m) are propagated from possible generation locations at critical topographic slopes through idealized mesoscale currents approximating the observed currents. Despite the lack of scale separation between the internal waves and background state, which is required by the ray-tracing approximation, the results are qualitatively consistent with observations: the cyclone causes the energy of internal tide rays propagating through its core to increase near the surface (up to a factor of 15), with surfacing time delayed by up to 5 h (∼150° phase lag), and the vorticity waves enhance or reduce the energy near the surface, depending on their phase. These examples illustrate the fact that, even close to their generation location, semidiurnal internal tides can become incoherent with astronomical forcing because of the presence of mesoscale variability. Internal tide energy is mainly affected by refraction through the inhomogeneous buoyancy frequency field, with Doppler shifting playing a secondary but not negligible role, inducing energy transfers between the internal tides and background currents. Furthermore, the vertical wavelength can be reduced by a factor of 6 near the surface in the presence of the cyclone, which, combined with the energy amplification, leads to increased vertical shear within the internal tide rays, with implications for internal wave-induced mixing in the ocean.

Dynamic and spatial behavior of a corrugated interface in the driven lattice gas model

The spatiotemporal behavior of an initially corrugated interface in the two-dimensional driven lattice gas (DLG) model with attractive nearest-neighbors interactions is investigated via Monte Carlo simulations. By setting the system in the ordered phase, with periodic boundary conditions along the external field axis. i.e. horizontal, and open along the vertical directions respectively, an initial interface was imposed, that consists in a series of sinusoidal profiles with amplitude A 0 and wavelength λ set parallel to the applied driving field axis. We studied the dynamic behavior of its statistical width or roughness W ( t ) , defined as the root mean square of the interface position. We found that W ( t ) decays exponentially for all λ and lattice longitudinal sizes L x , i.e., the lattice side that runs along the axis of the external field. We determined its relaxation time τ , and found that depends on λ as a power law τ ∝ λ p , where p depends on the temperature and L x . At low T ’s ( T ≪ T c ( E ) ) and large L x , p approaches to p = 3 / 2 . At intermediate T ’s ( T < T c ( E ) ), p decreases up to p ≈ 1 , and is free of finite effects. This indicates that the interface stabilizes faster than in the equilibrium model, i. e. the Ising lattice gas ( E = 0 ) where p = 3 . At higher T ’s p increases for T ≲ T c ( E ) , and the finite size dependence is recovered. Also, if T is fixed, p increases with L x until it saturates at large values of it, while this regime is vanishing at T ≲ T c ( E ) . In this way, the dynamic relaxation process of a sinusoidal interface is improved by the external driving field with respect to its equilibrium counterpart, if the system is set in an intermediate temperature stage far from T c ( E ) and in a lattice with a sufficiently large longitudinal side. The behavior of τ was also investigated as a function of E and in the intermediate stage T < T c ( E ) . It was found that τ decreases exponentially with E in the interval 0 < E ≲ 1 , while for higher fields it remains constant. The exponential decay depends on the wavelength of the initial profile. In order to study the spatial evolution of the profiles, we evaluated the structure factor of the interface, and the Fourier coefficients corresponding to the same wave vector of the initial profile. The obtained results allowed us to conclude that the spatial evolution of the profile maintains its initial wavelength, does not travel along the external field axis, and its shape is preserved over all the relaxation process.

Short wavelength seeding through compression for free electron lasers

In this paper, we propose a seeding scheme that compresses an initial laser modulation in the longitudinal phase space of an electron beam by using two opposite sign bunch compressors and two opposite sign energy chirpers. This scheme could potentially reduce the initial modulation wavelength by a factor of C and increase the energy modulation amplitude by a factor of C, where C is the compression factor of the first bunch compressor. Using two lasers as energy chirpers, such a modulation compression scheme can generate kilo-Amper short wavelength current modulation with significant bunching factor from an initial a few tens Amper current. This compression scheme can also be used to generate a prebunched single atto-second short wavelength current modulation and prebunched two color, two atto-second modulations.

Bedforms in a turbulent stream: formation of ripples by primary linear instability and of dunes by nonlinear pattern coarsening

It is widely accepted that both ripples and dunes form in rivers by primary linear instability; the wavelength of the former scaling on the grain size and that of the latter being controlled by the water depth. We revisit here this problem in a theoretical framework that allows to give a clear picture of the instability in terms of dynamical mechanisms. A multi-scale description of the problem is proposed, in which the details of the different mechanisms controlling sediment transport are encoded into three quantities: the saturated flux, the saturation length and the threshold shear stress. Hydrodynamics is linearized with respect to the bedform aspect ratio. We show that the phase shift of the basal shear stress with respect to the topography, responsible for the formation of bedforms, appears in an inner boundary layer where shear stress and pressure gradients balance. This phase shift is sensitive to the presence of the free surface, and the related effects can be interpreted in terms of standing gravity waves excited by topography. The basal shear stress is dominated by this finite depth effect in two ranges of wavelength: when the wavelength is large compared to the flow depth, so that the inner layer extends throughout the flow, and in the resonant conditions, when the downstream material velocity balances the upstream wave propagation. Performing the linear stability analysis of a flat sand bed, the relation between the wavelength at which ripples form and the flux saturation length is quantitatively derived. It explains the discrepancy between measured initial wavelengths and predictions that do not take this lag between flow velocity and sediment transport into account. Experimental data are used to determine the saturation length as a function of grain size and shear velocity. Taking the free surface into account, we show that the excitation of standing waves has a stabilizing effect, independent of the details of the flow and sediment transport models. Consequently, the shape of the dispersion relation obtained from the linear stability analysis of a flat sand bed is such that dunes cannot result from a primary linear instability. We present the results of field experiments performed in the natural sandy Leyre river, which show the formation of ripples by a linear instability and the formation of dunes by a nonlinear pattern coarsening limited by the free surface. Finally, we show that mega-dunes form when the sand bed presents heterogeneities such as a wide distribution of grain sizes.

Concentration distribution of elements and variation in phase composition during solid-solution decomposition in Fe-Cr-Co alloy

In the present work, we analyze the changes in chemical and phase composition in the decomposition of metastable supercooled hightemperature α solid solution in the alloy Fe + 31 wt % Cr + 23 wt % Co. Permanent magnets based on Fe-Cr-Co alloys are still widely used in industry, although they cannot match the properties of the latest alloys of rareearth metals with 3d metals. The explanation for their con� tinued use is that Fe-Cr-Co alloys combine satisfac� tory physicochemical and mechanical properties with low cost. In Fe-Cr-Co alloys, a highly coercive state arises as a result of the decomposition of the α solid solution into two amorphous phases: α1 and α2 (1). Moreover, some evidence suggests that Fe-Co-Cr alloys treated in the highly coercive state contain three magnetic phases: ferromagnetic, antiferromagnetic, and super� paramagnetic (2, 3). The coexistence of ferromagnetic and antiferromagnetic phases in magnetically ordered systems is the fundamental condition for the appear� ance of anomalies in most physical properties. Exam� ples include the anomalies of thermal expansion noted in Fe-Co-Cr alloys in (3). The contradictory data regarding the phase state of Fe-Co-Cr alloys prompts further study. The decomposition of the supersaturated solid solution is simulated by the Monte Carlo method, using the Metropolis criterion. The interaction energy is calculated by means of Material Studio 3.2 software, selected on the basis of the results in (4). The simula� tion of the isothermal decomposition of Fe-Cr-Co alloys was described in (5, 6). The alloy composition is chosen on the basis of detailed data regarding the for� mation of its phase state and microstructure (1, 7). The algorithm employed permits the construction of distributions of iron, chromium, and cobalt in the region considered. As an example, the chromium and cobalt distributions in the final microstructure after decomposition at 660°C are shown in Fig. 1. In contrast to the chaotic distribution of chromium and cobalt in the initial microstructure, the amplitude and wavelength of the concentration distribution are

Small-scale dissipation in binary-species, thermodynamically supercritical, transitional mixing layers

The irreversible entropy production (i.e. the dissipation) has three distinct modes due to viscous, heat and species-mass fluxes. Computations of the dissipation and its modes are conducted using transitional states obtained from Direct Numerical Simulations (DNS) of O2/H2 and C7H16/N2 temporal mixing layers at thermodynamically supercritical pressure. A non-dimensionalization of the mathematical expression for each dissipation mode is first performed and representative reference values computed using the DNS database are utilized to highlight the order of magnitude of each mode and their relative importance. For more quantitative results, the importance of each dissipative mode is assessed both at the DNS scale and at scales determined by filter sizes from four to sixteen times the DNS grid spacing. The subgrid-scale (SGS) dissipation is computed by subtracting the filtered-field dissipation from the DNS-field dissipation. For each species system, three layers are considered having different initial Reynolds number and perturbation wavelength. For all layers, it is found that the species-mass flux contribution dominates both the DNS and SGS dissipation due to high density-gradient-magnitude (HDGM) regions which are a distinctive physical aspect of these layers. Backscatter, indicated by regions of negative SGS dissipation, is found in a substantial portion (15–60%) of the domain, and decreases only slightly with increasing filter width. Regions of the most intense negative and positive SGS dissipation strongly correlate with the HDGM regions. On a domain-average basis, the proportional contribution of each dissipation mode to the total is similar at the DNS and SGS scales, indicating scale-similarity. The proportion of the species-mass dissipation mode to the total is remarkably similar in value across all simulations whether at the DNS or SGS scale. For each mode and the total, the SGS contribution to the DNS-field dissipation is only species-system and filter-size dependent but nearly independent of the initial Reynolds number and perturbation wavelength. The SGS contribution is smaller for O2/H2 layers than for C7H16/N2 ones, but increases more rapidly with increasing filter width. The implications of these results for Larger Eddy Simulation modeling are discussed.

Linear Stability Analysis of Double-Diffusive Convection in Porous Media, with Application to Geological Storage of CO2

Onset of double-diffusive buoyancy-driven flow resulted from vertical temperature and concentration gradients in a horizontal layer of a saturated and homogenous porous medium is investigated using amplification factor theory. After injection of CO2 into a deep saline aquifer, the density of the brine saturated with CO2 increases slightly. This increase in density induces natural convection. The effect of geothermal gradient is also considered in this work as a second incentive for convection and the double-diffusion convection was studied. Linear stability analysis is used to predict the inception of instabilities and initial wavelength of the convective instabilities. The analysis presented is applied to acid gas injection (as an analogue for CO2 storage) into saline aquifers in the Alberta basin. It is found that the geothermal gradient does not have significant effect on the onset of convection for these aquifers. It is shown that the geothermal effects on the onset of natural convection are negligible as compared to the solutal effects induced by dissolution and diffusion of CO2 in deep saline aquifers. Therefore, the linear stability analysis and the long-term numerical simulation of CO2 sequestration into such saline aquifers may be assumed to be isothermal in terms of natural convection occurrence.

Onset of initial planar instability with surface-tension anisotropy during directional solidification

A simple model is presented to describe the variation of the onset of the initial planar instability with surface tension anisotropy during directional solidification. The effect of surface-tension anisotropy on the incubation time and the initial average wavelength of planar instability are predicted by the simple model quantitatively, which are also verified by phase field simulation. Investigation results reveal that surface-tension anisotropy is one of important factors in the dynamic process of planar instability. The contribution of surface-tension anisotropy to the tilting modulation is also analyzed by comparing the results from the present simple model with those from phase field simulation.

Effect of the Laser Wavelength on the Saturated Level of Stimulated Brillouin Scattering

Equivalent stimulated Brillouin backscattering (SBS) saturation levels have been measured in the interaction with 0.527 and 0.351 microm laser beams demonstrating that the initial interaction wavelength is not influencing the final saturation levels. Experiments have been performed at the two wavelengths in similar interaction conditions obtained by preforming the plasma from a solid target with a creation beam converted at the same wavelength as the interaction beam. This produces an almost exponential density profile from vacuum to the critical density of the interaction beam in which large SBS gains are reached.

Controlling the Outcome of Electron Transfer Reactions in Ionic Liquids

In this article, we investigate the excited state intramolecular electron transfer (ET) reaction of crystal violet lactone (CVL) in the room temperature ionic liquid (RTIL) N-propyl-N-methylpyrrolidinium bis(trifluoromethylsulfonyl) imide [Pr(31)(+)][Tf(2)N(-)]. This system was chosen in light of recent experimental observations by Maroncelli and co-workers (J. Phys. Chem. B 2007, 111, 13473), in which the kinetics of electron transfer between S(1) (commonly referred as LE) and S(2) (commonly referred as CT) emission states and, therefore, the ratio of emitting populations were shown to be absorption-wavelength-dependent. Our computational studies indicate that the kinetics of the intramolecular ET between S(1) and S(2) states of CVL in [Pr(31)(+)][Tf(2)N(-)] is local solvent-environment-dependent. Because emission time scales are smaller than solvent relaxation time scales, this behavior is characteristic of RTILs but uncommon in conventional solvents. Therefore, RTILs open a window of opportunity for manipulating the outcome of chemical reactions simply by tunning the initial excitation wavelength. Our studies show that when acetonitrile is used as a solvent instead of [Pr(31)(+)][Tf(2)N(-)] the ratio of populations of emission states is independent of excitation wavelength, eliminating the opportunity for influencing the outcome of reactions.

A Unified Model for Remotely Estimating Chlorophyll a in Lake Taihu, China, Based on SVM andIn SituHyperspectral Data

Accurate estimation of chlorophyll a (Chla) in inland turbid lake waters by means of remote sensing is a challenging task due to their optical complexity. In order to explore the best solution, we observed water quality parameters and measured water reflectance spectra in Lake Taihu for 14 days in November 2007. After initial wavelength analysis and iterative optimization, the best three-wavelength factor (TWF) was determined as [R rs -1(661) - R rs -1(691)] R rs(727). Linear models and a support vector machine (SVM) model with TWFs as the inputs were established for retrieving Chla concentration level. It is found that linear models with a single TWF performed worse than the SVM model. The SVM model is highly accurate, whose R 2 and root-mean-square error are 0.8961 and 2.67 mg/m3, respectively. Validation of the SVM model using data sets obtained at another sampling time reveals small errors. Thus, this model can be used to extract Chla concentration levels in Lake Taihu waters but is not restricted by the sampling time. These findings underline the rationale of the TWF model and demonstrate the robustness of the SVM algorithm for remotely estimating Chla in Lake Taihu waters.

Onset of Convection in CO2 Sequestration in Deep Inclined Saline Aquifers

Abstract CO2 sequestration in deep geological formations has been suggested as an option to reduce greenhouse gas emissions. Saline aquifers are one of the most promising options for carbon dioxide storage. It has been shown that the dissolution of CO2 into brine causes the density of the mixture to increase. If the corresponding Rayleigh number of the porous medium is enough to initiate convection currents, the rate of dissolution will increase. Early time dissolution of CO2 in brine is mainly dominated by molecular diffusion, while late time dissolution is predominantly governed by a convective mixing mechanism. In this paper, linear stability analysis of density-driven miscible flow for carbon dioxide sequestration in deep inclined and homogeneous saline aquifers is presented. The effect of inclination and its influence on the pattern of convection cells has been investigated and the results are compared with the horizontal layer. The current analysis provides approximations for the initial wavelength of the convective instabilities and the onset of convection that helps in selecting suitable candidates for geological CO2 sequestration sites. Introduction Carbon dioxide sequestration is the capture and safe storage of carbon dioxide that would otherwise emit to the atmosphere. Sequestration refers to any storage scheme that can keep CO2 out of the atmosphere(1). In general, proposed storage sites of carbon dioxide can be divided into two categories: geological sites and marine sites. Carbon dioxide sequestration in deep geological formations has been suggested as a way of reducing greenhouse gas emissions. Geologic sequestration of CO2 is the capture of CO2 from major sources, transporting it usually by pipeline, and injecting it into underground formations such as oil and gas reservoirs, saline aquifers and unmineable coal seams for a significant period of time(2, 3). Unlike coalbed methane reserves and oil reservoirs, sequestration of CO2 in deep saline aquifers does not produce value-added by-products, but it has other advantages. While there are uncertainties regarding the scope, the world's total capacity to store CO2 deep underground is large(4). Underground formations are generally unused and are available in many parts of the world(5). It has been estimated that deep saline formations in the United States could potentially store up to 500 billion tonnes of CO2. Most existing large CO2 point sources are within easy access to a saline formation injection point and, therefore, sequestration in saline formations is compatible with a strategy of transforming large portions of the existing energy and industrial assets to near-zero carbon emissions via low-cost carbon sequestration retrofits(3). However, it is important to investigate the behaviour of CO2 injected into aquifers for effective and safe use of storage. Geological storage of CO2 as a greenhouse gas mitigation option was proposed in the 1970s(6), but little research was done until the early 1990s when the idea gained credibility through the work of individual research groups(7–10). When CO2 is injected into the formation above its critical temperature and pressure, the density of supercritical carbon dioxide is usually less than brine. This density difference causes CO2 to migrate upwards to the top of the formation under an impermeable caprock.

Spinodal decomposition in siloxane sol-gel systems in macroporous media

Spinodal decomposition in siloxane sol-gel systems has been investigated in a macroporous silica mould (pore diameter D = 2.74 µm) with a bicontinuous structure. Methyltrimethoxysilane (MTMS) and tetramethoxysilane (TMOS) have been employed as siloxane gel sources and as-sintered hydrophilic and octadecylsilylated hydrophobic macroporous silica were used as the confining moulds. In an MTMS-formamide system with a longer phase separation time and higher viscosity, the phase-separated gels in both moulds exhibited a similar morphology when the bulk correlation length Λ, i.e. spinodal wavelength in a free volume, was enough shorter than D. As Λ was made longer by altering the starting composition, a wetting transition occurred in both the hydrophilic and hydrophobic moulds. In an MTMS-methanol system with a shorter phase separation time and lower viscosity, the wetting transition unexpectedly occurred when Λ was much shorter than D in the hydrophobic mould. In TMOS-formamide system, fine and disordered structure has formed in the hydrophilic mould and never exhibited the wetting transition. A hydrodynamic wetting transition in each system was considered to occur when the ratio D/Λ becomes smaller than unity, whereas a diffusive wetting transition takes place in the early stage of spinodal decomposition in the case where the chemical affinity between siloxane gel and the mould is high. Additionally, when the initial wavelength of spinodal decomposition is shorter than D, spinodal decomposition is highly suppressed due to the presence of the random surfaces of macropores. These effects may interplay depending on the physical and chemical nature of the sol-gel systems and the moulds.

Soliton-number analysis of soliton-effect pulse compression to single-cycle pulse widths

We demonstrate that the soliton-effect compression to few- and single-cycle pulse widths in a highly nonlinear fiber can be optimized by properly choosing the input soliton number. Soliton compression to a $2\text{\ensuremath{-}}\mathrm{fs}$ pulse width with a compression ratio up to 50 is demonstrated for light pulses with an initial central wavelength of $1070\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$ by solving the generalized nonlinear Schr\odinger equation for a dispersion profile typical of a small-core photonic-crystal fiber.