Random Fiber Research Articles

A Theoretical Investigation of an Ultrawide S-, C- and L-Band-Tunable Random Fiber Laser Based on the Combination of Tellurite Fiber and Erbium-Doped Fiber

In this paper, we present a new scheme to generate ultrawide tunable random fiber lasers (RFLs) covering the S-, C- and L-band by combining the broadband Raman gain in tellurite fibers and the active gain in erbium-doped fibers. A numerical simulation based on the power-balance model is conducted to verify the feasibility of the ultrawide tunable random fiber lasing generation. Pumped by a 1450 nm laser, the tunable random Raman fiber laser in the ranges of 1480–1560 nm and 1590–1640 nm can only be realized with a tellurite fiber. To further fill in the emission gap in the range of 1560–1590 nm, the erbium-doped fiber is incorporated in the cavity, which can provide efficient erbium-doped gain in the C- and L-band. By combining a 100 m long tellurite fiber and an 8 m long erbium-doped fiber, an ultrawide tunable RFL based on hybrid erbium–Raman gain can be realized with a wavelength tuning range (1480 nm–1640 nm) covering the S-, C- and L-band at 3.5 W pump power. Such a widely tunable RFL is of great importance in applications such as optical communication, sensing and imaging.

Unveiling optical rogue wave behavior with temporally localized structures in Brillouin random fiber laser comb

Unveiling optical rogue wave behavior with temporally localized structures in Brillouin random fiber laser comb

A materials informatics framework based on reduced‐order models for extracting structure–property linkages of additively manufactured continuous fiber‐reinforced polymer composites

AbstractThe innovative combination of additive manufacturing (AM) and continuous fiber‐reinforced polymer composites (CFRPCs) confers products with the dual advantages of integrated manufacturing and designability of properties, but lack an efficient and reliable method for property prediction. This study presents a materials informatics framework using reduced‐order models and machine learning (ML) to extract the structure–property (SP) linkages between microstructures and macroscopic elastic properties of AM‐CFRPCs. The initial step involves generating microstructural 2D cross‐sections and representative volume elements (RVEs) with random fiber and pore distributions based on the minimum potential method. Then, finite element (FE) calculations are performed on RVEs to obtain nine macroscopic elastic properties. Following that, the quantification and dimensionality reduction of the 2D cross‐sectional dataset are conducted separately using two‐point spatial correlations and principal component analysis (PCA). Finally, a Bayesian optimized composite kernel support vector regression (CK‐SVR) algorithm is used to effectively establish complex mapping relationships between the reduced‐order representations of the microstructures and the mechanical properties. Despite the reduced‐order dataset containing only 3–6 variables, the framework generates an interpretable model exhibiting excellent accuracy with all predicted R2 values surpassing 0.91. Therefore, this framework presents a prospective solution for expediting the design and optimization of AM‐CFRPCs.Highlights A materials informatics scheme is proposed to predict the 9 elastic properties of AM‐CFRPCs. Microstructures are quantified and dimensionally reduced by two‐point statistics and PCA. SP linkages are established between 2D cross‐sections and 3D macromechanical properties. Modified CK‐SVR exhibits higher prediction accuracy compared to conventional models.

High-order-mode Brillouin random fiber laser based on distributed Rayleigh scattering in all-few mode fiber half-open cavity

A high-order-mode (HOM) Brillouin random fiber laser (BRFL) based on distributed Rayleigh scattering in an all-few-mode fiber random cavity is proposed and experimentally demonstrated. Compared to traditional BRFLs oscillating in the single-mode-fiber cavity, the few-mode-fiber random cavity allows the high-order spatial mode Stokes beams to be activated and amplified via intra-mode stimulated Brillouin scattering for sufficient gain. Besides random feedback of distributed Rayleigh scattering along few-mode fibers, a few-mode fiber Bragg grating (FM-FBG) is employed to provide the one-end transverse mode-dependent reflection, which facilitates a high-purity oscillating random laser mode switchable between LP01 and LP11 mode by readily tunning the working wavelength of the Brillouin pump. Consequently, the all few-mode fiber-based BRFL emits a 600-Hz narrow-linewidth LP11 mode with a high mode purity of ∼91.3 %, which paves the way for spatial multiplexing coherent communication, high-resolution imaging, highly sensitive sensing, etc.

Implementation of Er-doped random fiber laser self-mixing sensor with ultra-limit sensitivity

This study first demonstrates that the random distributed feedback fiber laser (RDFL) can be implemented for sensing detection by using the self-mixing effect as a sensing mechanism. By constructing a compact self-mixing velocimeter based on Er-doped RDFL with the integration of a laser, sensing element, and transmission platform, we successfully measured the minimum detectable feedback intensity of 38.65 fW for the velocity signal, corresponding to 0.55 photons per Doppler cycle, exhibiting ultra-high sensitivity dynamics characteristics. In addition, the velocity measurement of a non-cooperative target at a single-channel distance of 100 km is accomplished because of the natural feature of long-distance transmission for the random distributed feedback fiber lasers, which greatly improves the ultra-long detection range in the field of self-mixing sensing. The proposed sensing scheme not only unveils a fresh perspective on the exploration of random fiber laser sensing but also showcases its diverse and wide-ranging applications within the realm of remote sensing measurements.

Aligned Nanofibers Promote Myoblast Polarization and Myogenesis through Activating Rac-Related Signaling Pathways.

The extracellular matrix (ECM) plays a crucial role in regulating cellular behaviors and functions. However, the impact of ECM topography on muscle cell adhesion and differentiation remains poorly understood from a mechanosensing perspective. In this study, we fabricated aligned and random electrospun polycaprolactone (PCL) nanofibers to mimic the structural characteristics of ECM. Mechanism investigations revealed that the orientation of nanofibers promoted C2C12 polarization and myogenesis through Rac-related signaling pathways. Conversely, cells cultured on random fibers exhibited spreading behavior mediated by RhoA/ROCK pathways, resulting in enhanced stress fiber formation but reduced capacity for myogenic differentiation. Our findings highlight the critical role of an ECM structure in muscle regeneration and damage repair, providing novel insights into mechanosensing mechanisms underlying muscle injury diseases.

Advanced Hollow Cathode Discharge Plasma Treatment of Unique Bilayered Fibrous Nerve Guidance Conduits for Enhanced/Oriented Neurite Outgrowth.

Despite all recent progresses in nerve tissue engineering, critical-sized nerve defects are still extremely challenging to repair. Therefore, this study targets the bridging of critical nerve defects and promoting an oriented neuronal outgrowth by engineering innovative nerve guidance conduits (NGCs) synergistically possessing exclusive topographical, chemical, and mechanical cues. To do so, a mechanically adequate mixture of polycaprolactone (PCL) and polylactic-co-glycolic acid (PLGA) was first carefully selected as base material to electrospin nanofibrous NGCs simulating the extracellular matrix. The electrospinning process was performed using a newly designed 2-pole air gap collector that leads to a one-step deposition of seamless NGCs having a bilayered architecture with an inner wall composed of highly aligned fibers and an outer wall consisting of randomly oriented fibers. This architecture is envisaged to afford guidance cues for the extension of long neurites on the underlying inner fiber alignment and to concurrently provide a sufficient nutrient supply through the pores of the outer random fibers. The surface chemistry of the NGCs was then modified making use of a hollow cathode discharge (HCD) plasma reactor purposely designed to allow an effective penetration of the reactive species into the NGCs to eventually treat their inner wall. X-ray photoelectron spectroscopy (XPS) results have indeed revealed a successful O2 plasma modification of the inner wall that exhibited a significantly increased oxygen content (24 → 28%), which led to an enhanced surface wettability. The treatment increased the surface nanoroughness of the fibers forming the NGCs as a result of an etching effect. This effect reduced the ultimate tensile strength of the NGCs while preserving their high flexibility. Finally, pheochromocytoma (PC12) cells were cultured on the NGCs to monitor their ability to extend neurites which is the base of a good nerve regeneration. In addition to remarkably improved cell adhesion and proliferation on the plasma-treated NGCs, an outstanding neural differentiation occurred. In fact, PC12 cells seeded on the treated samples extended numerous long neurites eventually establishing a neural network-like morphology with an overall neurite direction following the alignment of the underlying fibers. Overall, PCL/PLGA NGCs electrospun using the 2-pole air gap collector and O2 plasma-treated using an HCD reactor are promising candidates toward a full repair of critical nerve damage.

Experiment of droplet contact angle hysteresis on PTFE fibrous membrane in pore-scale

The present paper aims to study the influence of pore-scale fiber structure on the Cassie-Baxter contact angle of droplets on PTFE fibrous hydrophobic membranes. The fiber structure is obtained by the Confocal Laser Scanning Microscope (CLSM), and an optical test bench is built to measure the Cassie-Baxter contact angles of a droplet on a PTFE membrane. The free energy of the solid-liquid interface is measured by the surface tension integral on the droplet profile. An iterative algorithm for liquid-vapor interface shrinking is brought forward to analyze the liquid-vapor interface area between the droplet and the membrane, and the interface parameters of the Cassie-Baxter model are recognized. The experiment shows that the Cassie-Baxter contact angles and the contact line radii along the droplet circumference are in a normal distribution due to random fiber structures, and the variance of the normal distribution increases with the membrane pore diameter. The normal distribution of Cassie-Baxter’s contact angle indicates the constraint of the solid-liquid interface to the liquid-vapor interface. On the same normal contact pressure condition, the liquid-vapor area ratio of the droplet and membrane interface changes little, and Cassie-Baxter’s contact angle increases with the solid-liquid interface area ratio.

Random laser emission at 1064 and 1550 nm in a Er/Yb co-doped fiber-based dual-wavelength random fiber laser.

Dual-wavelength fiber lasers operating with a wide spectral separation are of considerable importance for many applications. In this study, we propose and experimentally explore an all-fiberized dual-wavelength random fiber laser with bi-directional laser output operating at 1064 and 1550 nm, respectively. A specially designed Er/Yb co-doped fiber, by optimizing the concentrations of the co-doped Er, Yb, Al and P, was developed for simultaneously providing Er ions gain and Yb ions gain for RFL. Two spans of single mode passive fibers are employed to providing random feedback for 1064 and 1550 nm random lasing, respectively. The RFL generates 5.35 W at 1064 nm and 6.61 W at 1550 nm random lasers. Two power amplifiers (PA) enhance the seed laser to 50 W at 1064 nm with a 3 dB bandwidth of 0.31 nm and 20 W at 1550 nm with a 3 dB bandwidth of 1.18 nm. Both the short- and long-term time domain stabilities are crucial for practical applications. The output lasers of 1064 and 1550 nm PAs are in the single transverse mode operating with a nearly Gaussian profile. To the best of our knowledge, this is the first demonstration of a dual-wavelength RFL, with a spectral separation as far as about 500 nm in an all-fiber configuration.

The model of ring-spun slub yarn based on random fiber arrangement and its application: Part 2 Prediction of morphology parameters for slub yarn and simulation of slub fabric

The morphology parameters of slub yarn include slub length, base length, the length of the transitional segment, slub multiple, slub linear density, base linear density, and average linear density of slub yarn. These parameters have an impact on the appearance of both slub yarn and its fabric. This paper aims to predict the morphology parameters of spun slub yarn by utilizing the model proposed in Part 1 for ring-spun slub yarns. Once the slub generation mode was known, slub yarn could be simulated with the morphology parameters. The simulated slub fabric was obtained by arranging the simulated slub yarn in the warp and weft directions. According to our study, the prediction accuracy of each morphology parameter was over 80% by comparing the simulated parameters with the measured ones of spun slub yarn. The CV (coefficient of variation) of the slub segment number per unit area was utilized to assess the distribution of slubs in the simulated fabric. This research can facilitate the development of slub yarn and its fabric, providing guidance for technicians to enhance production technology.

In Vitro Assessment of Bacterial Adhesion and Biofilm Formation on Novel Bioactive, Biodegradable Electrospun Fiber Meshes Intended to Support Tendon Rupture Repair.

The surgical repair of a ruptured tendon faces two major problems: specifically increased fibrous adhesion to the surrounding tissue and inferior mechanical properties of the scar tissue compared to the native tissue. Bacterial attachment to implant materials is an additional problem as it might lead to severe infections and impaired recovery. To counteract adhesion formation, two novel implant materials were fabricated by electrospinning, namely, a random fiber mesh containing hyaluronic acid (HA) and poly(ethylene oxide) (PEO) in a ratio of 1:1 (HA/PEO 1:1) and 1:4 (HA/PEO 1:4), respectively. Electrospun DegraPol (DP) treated with silver nanoparticles (DP-Ag) was developed to counteract the bacterial attachment. The three novel materials were compared to the previously described DP and DP with incorporated insulin-like growth factor-1 (DP-IGF-1), two implant materials that were also designed to improve tendon repair. To test whether the materials are prone to bacterial adhesion and biofilm formation, we assessed 10 strains of Staphylococcus aureus, Staphylococcus epidermidis, Pseudomonas aeruginosa, and Enterococcus faecalis, known for causing nosocomial infections. Fiber diameter, pore size, and water contact angle, reflecting different degrees of hydrophobicity, were used to characterize all materials. Generally, we observed higher biofilm formation on the more hydrophobic DP as compared to the more hydrophilic DP-IGF-1 and a trend toward reduced biofilm formation for DP treated with silver nanoparticles. For the two HA/PEO implants, a similar biofilm formation was observed. All tested materials were highly prone to bacterial adherence and biofilm formation, pointing toward the need of further material development, including the optimized incorporation of antibacterial agents such as silver nanoparticles or antibiotics.

Effective mechanisms responsible for increased strength and fracture strain of carbon fiber-reinforced plastic/steel hybrid laminates

The tensile properties of carbon fiber-reinforced plastic (CFRP)/steel laminates have been observed to exceed the expected values predicted by the rule of mixture. While the CFRP/steel laminate is expected to fail at the failure strain of the CFRP lamina, it was observed that hybridization with a steel lamina improves the failure strain. This study investigates numerically and analytically the roles of each influential mechanism responsible for this enhancement, including the thermal residual strain, bridging effect, effect of compressive transverse stress on CFRP layers, and effect of tensile transverse stress on steel layers. To assess these mechanisms, multiple finite-element and analytical models were developed. A mesoscale finite-element model was proposed, which uses novel random fiber distribution algorithm capable of reproducing random fibers with high fiber volume fractions exceeding 65%. Rather than the meso-scale model, macro finite-element models and analytical relationships were developed to assess each hybrid mechanism. Analysis showed 6% increase of the failure strain due to thermal effect and up to 11% increase of strength due to multiaxial stress in steel layer. The results of this study contribute to a deeper understanding of the role of each phenomenon that contributes to improved tensile properties in hybrid CFRP/metal laminates.

Mesoporous silica nanoparticles accommodating electrospun nanofibers as implantable local drug delivery system processed by cold atmospheric plasma and spin coating approaches

Nanofibers (NF) and nanoparticles are attractive for drug delivery to improve the drug bioavailability and administration. Easy manipulation of NF as macroscopic bulk material give rise to potential usages as implantable local drug delivery systems (LLDS) to overcome the failures of systemic drug delivery systems such as unmet personalized needs, side effects, suboptimal dosage. In this study, poly(ethylene glycol) polyethyleneimine (mPEG:PEI) copolymer blended poly ϵ-caprolactone NFs, NFblend accommodating mesoporous silica nanoparticles (MSN) as the implantable LLDS was achieved by employing spin coating and cold atmospheric plasma (CAP) as the post-process for accommodation on NFblend. The macroporous morphology, mechanical properties, wettability, and in vitro cytocompatibility of NFblend ensured their potential as an implantable LLDS and superior features compared to neat NF. The electron microscopy images affirmed of NFblend random fiber (average diameter 832 ± 321 nm) alignments and accessible macropores before and after MSN@Cur accommodation. The blending of polymers improved the elongation of NF and the tensile strength which is attributed as beneficial for implantable LLDS. CAP treatment could significantly improve the wettability of NF observed by the contact angle changes from ∼126° to ∼50° which is critical for the accommodation of curcumin-loaded MSN (MSN@Cur) and in vitro cytocompatibility of NF. The combined CAP and spin coating as the post-processes was employed for accommodating MSN@Cur on NFblend without interfering with the electrospinning process. The post-processing aided fine-tuning of curcumin dosing (∼3 µg to ∼15 µg) per dose unit and sustained zero-order drug release profile could be achieved. Introducing of MSN@Cur to cells via LLDS promoted the cell proliferation compared to MSN@Cur suspension treatments and assigned as the elimination of adverse effects by nanocarriers by the dosage form integration. All in all, NFblend-MSN@Cur was shown to have high potential to be employed as an implantable LLDS. To the best of our knowledge, this is the first study in which mPEG:PEI copolymer blend NF are united with CAP and spin coating for accommodating nano-drug carriers, which allows for NF both tissue engineering and drug delivery applications.

Wavelength injection locking actively Q-switched random fiber laser based on random phase-shifted fiber Bragg grating and electro-optic modulator

Wavelength injection locking actively Q-switched random fiber laser based on random phase-shifted fiber Bragg grating and electro-optic modulator

Tunable and switchable multi-wavelength random fiber laser based on random distributed feedback and improved Lyot filter

Tunable and switchable multi-wavelength random fiber laser based on random distributed feedback and improved Lyot filter

Hierarchical structure of poly(ε-caprolactone) crystals on its copolymer poly(l-lactide-co-ε-caprolactone) fibers

In crystallization, heterogeneous structures of copolymers are employed to establish a hierarchical architecture comprising two polymers, this typically occurs on the surface of block copolymers or blended polymers. While hierarchical structures in block copolymer fibers are well-established and widely utilized, achieving a regular hierarchical structure on random copolymer fibers is both meaningful and challenging. Here, we present a case of forming a hierarchical structure on the surface of the random copolymer poly(L-lactide-co-caprolactone) (PLCL)fibers. The (ε-caprolactone)(CL) polymer chain segments of the random copolymer are released on the surface of the modified copolymer fiber using sodium hydroxide. Subsequently, poly(ε-caprolactone)(PCL) forms a shish kebab-like crystalline structure under the guidance of the CL segments. The CL segments act as crystalline precursors to induce the formation of heterogeneous PLCL/PCL shish kebab structures. The variation of CL segments on the fiber changes with modification time, leading to the formation of crystalline lamellae of different sizes, which had been confirmed by characterization techniques such as scanning electron microscope (SEM), 1H NMR, X-ray photoelectron spectra (XPS), differential scanning calorimetry (DSC), etc. The implementation of this heterogeneous structure provides possibilities for the implementation of hierarchical structure in random copolymers.

Optimization of Electrospun Bilayer Vascular Grafts through Assessment of the Mechanical Properties of Monolayers.

Small-diameter vascular grafts must be obtained with the most appropriate materials and design selection to harmoniously display a variety of features, including adequate tensile strength, compliance, burst strength, biocompatibility, and biodegradability against challenging physiological and hemodynamic conditions. In this study, monolayer vascular grafts with randomly distributed or radially oriented fibers are produced using neat, blended, and copolymer forms of polycaprolactone (PCL) and poly(lactic acid) (PLA) via the electrospinning technique. The blending ratio is varied by increasing 10 in the range of 50-100%. Bilayer graft designs are realized by determining the layers with a random fiber distribution for the inner layer and radial fiber orientation for the outer layer. SEM analysis, wall thickness and fiber diameter measurements, tensile strength, elongation, burst strength, and compliance tests are done for both mono- and bilayer scaffolds. The findings revealed that the scaffolds made of neat PCL show more flexibility than the neat PLA samples, which possess higher tensile strength values than neat PCL scaffolds. Also, in blended samples, the tensile strength values do not show a significant improvement, whereas the elongation values are enhanced in tubular samples, depending on the blending ratio. Also, neat poly(l-lactide-co-caprolactone) (PLCL) samples have both higher elongation and strength values than neat and blended scaffolds, with some exceptions. The blended specimens comprising a combination of PCL and PLA, with blending ratios of 80/20 and 70/30, exhibited the most elevated burst pressures. Conversely, the PLCL scaffolds demonstrated superior compliance levels. These findings suggest that the blending approach and fiber orientation offer enhanced burst strength, while copolymer utilization in PLCL scaffolds without fiber alignment enhances their compliance properties. Thus, it is evident that using a copolymer instead of blending PCL and PLA and combining the PLCL layer with PCL and PLA monolayers in bilayer vascular graft design is promising in terms of mechanical and biological properties.

Simulation of fiber-induced melt pressure fluctuations within large scale polymer composite deposition beads

The process-structure-property relationship in Large Area Additive Manufacturing (LAAM) technology is an ongoing area of research as the inherent microstructural properties (chiefly fibers and voids) affect the performance of printed parts. Unfortunately, we currently lack adequate understanding of micro void nucleation and evolution during the LAAM and fused deposition modelling (FDM) processes. Modeling of the polymer melt flow during the extrusion process is important in understanding the underlying microstructural formation and associated properties of the print, that determines the part performance in service conditions. In this paper we compute fiber-induced local pressure fluctuations which may promote void formation in the bead’s microstructure. On a macro-scale, we determine flow fields of a purely viscous, Newtonian planar polymer deposition flow through a LAAM nozzle which are utilized on a micro-scale model where we simulate the evolution of a single ellipsoidal fiber along streamlines obtained from the macro-model. On the micro-scale, we determine instantaneous values of the translational and rotational velocities of the rigid ellipsoidal fiber that satisfies a balance of hydrodynamic forces and couples on the fiber’s surface based on a Newton Raphson algorithm and we track the fiber’s motion along the flow path via an explicit numerical iterative algorithm. Model verification is achieved by benchmarking results with solutions from well-known Jeffery’s equation of motion of a particle in homogeneous simple shear flow. We account for rotary diffusivity due to short-range fiber-fiber interaction in the FEA simulation by determining an effective fluid domain size representative of the interaction coefficient of the melt flow through a correlation analysis that yields an equivalent steady state orientation based on the Advani-Tucker equation. We also consider different possible motions of the fiber along individual LAAM flow paths from a given set of random initial fiber conditions to determine pressure bounds on the fiber surface along each streamline. For improved computational efficiency, calculations are carried out with respect to the fiber’s local coordinate axes to overcome the rigor of adaptive remeshing during the quasi-transient analysis. Results show low pressure extremes near the fiber’s surface which varies across the printed bead as well as through its thickness. Discussion is provided to gain insight into the effect of low-pressure extremes on micro void formation, particularly at the nozzle exit and during die swell/expansion.

Recycling and Reinforcing of Expanded Polystyrene by Woven Mat and Short E-Glass fibers

Expanded polystyrene (EPS) polymers are widely used in insulation and packaging applications. If their waste hasn’t been managed well and due to their long degradation time, they will cause severe environmental problems for human beings, plants, and animals. Therefore, recycling could be one of the acceptable solutions to overcome such problems in addition to reinforcing them to recover the decay in properties resulting from recycling. In this work two types of EPS have been recycled at different temperatures from 140 to 260°C, and then reinforced by E-glass fibers in mat form and as random short fibers with varied composition from 5 to 25 wt%. The samples have been prepared by homemade thermal press and the tensile properties such as strength, modulus, and ductility have been investigated showing an obvious enhancement of these properties upon an increase in temperature to certain level and with fiber content and length exceeding their critical lengths. Furthermore, interfacial adhesion has been stud-ied by estimating the strength and modulus efficiency factors. The results show that the E- glass fibers could im-prove the strength with more than 300%.

Magnetic Alignment of Micro Steel Fibers Embedded in Self-Compacting Concrete

Steel fiber reinforced cementitious composites (SFRCC) have emerged as one of the most efficient techniques to improve the flexural capacity and ductility performance of concrete. However, one of the most significant shortcomings is the randomness of steel fibers direction in the concrete matrix, which influences the extent of mechanical enhancement for a limited fiber content. An experimental approach to control the direction of steel fibers embedded in self-compacting concrete is presented in this study, which is based on generating a driving rotating force to overcome the viscous impeding forces acting onto the embedded fiber. The mechanical performance of micro steel fiber reinforced self-compacting concrete members was investigated. A uniform magnetic field of 9.8×10-3 Tesla generated by a cylindrical powered coil was capable of aligning micro steel fibers embedded in fresh self-compacting concrete along the desired direction. The testing program included seven beam specimens of size of 100 ×100 x 500 mm3. The micro steel fiber contents considered were 0.35%, 0.70%, and 1.05% by volume. Fiber volume fraction of 0.35% was the optimum dosage for magnetic alignment as it achieved the highest extents of mechanical enhancement. The concrete specimens reinforced with 0.35% of steel fiber content have exhibited enhancement rates of 5%, 28%, and 30% in four-point failure load, maximum mid-span deflection, and compressive strength, respectively. Based on the visual analysis of cross-sectional images, the highest orientation factor achieved was 0.91 when steel fiber dosage was 0.35%, whereas the random non-magnetized steel fiber reinforced beams achieved an orientation factor ranging from 0.30 to 0.50.