Maximum Gap Size Research Articles

Reinforcing membranes with subgaskets in proton exchange membrane water electrolysis: A model-based analysis

Ensuring the long-term mechanical durability of perfluorosulfonic acid membranes in proton exchange membrane water electrolysis (PEMWE) is essential for long lifetimes. This study investigates the potential of reinforcing the membrane by incorporating a subgasket layer outside the active area. Thus, experimental tensile measurements with the subgasket material and with the subgasket-membrane composite are conducted to characterize their mechanical properties. The obtained data are used to identify suitable material models and parameterize them by applying a tensile test simulation based on the finite element method. By integrating subgaskets in a structural mechanics PEMWE cell model, the impact of the reinforcement on the membrane stability was investigated. The results indicate that even thin layers of subgaskets stabilize the membrane at the gap interface between the cell frame and the porous transport layer. The level of stabilization is further enhanced when using thicker subgaskets that cover the entire gap. However, one-sided subgaskets exhibit reduced mechanical stabilization. Furthermore, membrane buckling due to an increased gap size can be prevented using a subgasket up to a maximum gap size of 0.45 mm.

Investigation of thermal damage in explosive bridgewire detonators via discrete element method simulations

AbstractExploding bridgewire (EBW) detonators are used to rapidly and reliably initiate energetic reactions by exploding a bridgewire via Joule heating. While the mechanisms of EBW detonators have been studied extensively in nominal conditions, comparatively few studies have addressed thermally damaged detonator operability. We present a mesoscale simulation study of thermal damage in a representative EBW detonator, using discrete element method (DEM) simulations that explicitly account for individual particles in the pressed explosive powder. We use a simplified model of melting, where solid spherical particles undergo uniform shrinking, and fluid dynamics are ignored. The subsequent settling of particles results in the formation of a gap between the solid powder and the bridgewire, which we study under different conditions. In particular, particle cohesion has a significant effect on gap formation and settling behavior, where sufficiently high cohesion leads to coalescence of particles into a free‐standing pellet. This behavior is qualitatively compared to experimental visualization data, and simulations are shown to capture several key changes in pellet shape. We derive a minimum and maximum limit on gap formation during melting using simple geometric arguments. In the absence of cohesion, results agree with the maximum gap size. With increasing cohesion, the gap size decreases, eventually saturating at the minimum limit. We present results for different combinations of interparticle cohesion and detonator orientations with respect to gravity, demonstrating the complex behavior of these systems and the potential for DEM simulations to capture a range of scenarios.

A structural optimization analysis of cable-driven soft manipulator

Cable-driven soft robots hold significant potential for surgical and industrial applications, yet their performance and maneuverability can be further enhanced through design optimization. By optimizing the design, factors such as bending angles, manipulator deformation, and overall functionality can be directly influenced, leading to improved interaction with the environment and more accurate task performance. This article presents a physics-based design optimization approach for cable-driven soft robotic manipulators, aiming to enhance bending performance through structural design enhancements. Four design criteria, namely, cross-sectional shape, material, gap shape, and gap size, are considered in the optimization process. Given the inherent nonlinearity of soft materials, finite element modeling techniques are employed to analyze the effects of modifying each design parameter on displacement and bending angle. The manipulator’s design is evaluated using ABAQUS/CAE, and an analysis of variance test is conducted to identify significant performance differences among the design parameters. The results reveal that material variation has the most substantial impact, followed by gap shape and gap size. Based on subsequent parameter optimization, Dragon Skin 10 is determined to be the optimal material for bending motion, while a trapezoidal gap shape is preferred. In addition, a genetic algorithm is utilized to select a maximum gap size of 8.87 mm. These findings provide valuable insights into key design principles for cable-driven soft manipulators, aiming to enhance flexibility and reduce actuation forces. By establishing a fundamental understanding of the relationship between morphology and motion capability, this methodology demonstrates an effective simulation-driven optimization approach that incorporates the nonlinear elastic behavior of materials to improve performance. Overall, this work establishes a framework for optimizing cable-driven architectures to suit various applications in the field of soft robotics.

Comparison of child and ATD belt fit and posture on belt-positioning boosters during self-selected, holding device, and nominal conditions

ObjectivePediatric anthropomorphic test devices (ATDs) are important tools for the assessment of child occupant protection and should represent realistic child belt fit and posture on belt-positioning boosters. Previous comparisons have been made to children in either self-selected or nominal postural conditions. This study compares belt fit and postural measurements between pediatric ATDs and a single cohort of children assuming different postures on boosters: self-selected, holding a portable electronic device, and nominal. MethodsA cohort of children (n = 25) were evaluated in a stationary vehicle on five boosters and in three postural conditions: nominal, self-selected, and a representative holding electronic device position. The Hybrid III 6- and 10-year-old and Q-Series 6- and 10-year-old ATDs were evaluated in the same five boosters and in two postural conditions: nominal and a representative holding electronic device position. A 3D coordinate measurement device was used to quantify belt fit (shoulder belt score, lap belt score, maximum gap size, and gap length) and anatomic landmark positions (head, suprasternale, ASIS, and patella). Landmark positions and belt fit were compared between ATDs and children for each booster and postural condition, and Pearson correlations (r) were assessed across boosters. ResultsATDs generally represented Nominal child postures across boosters. In the Device condition, ATDs were seldom able to be positioned to represent both the torso and head position of children, due to limited ATD spinal flexibility. When the torso position was matched, the ATD head was more rear by 63 mm. Correlations between Nominal child and ATD belt fit and belt gap metrics were generally weak and not significant, with the exception of lap belt score (all ATDs p < 0.07, r = 0.8549–0.9857). DiscussionATDs were generally able to represent realistic child postures and lap belt fit in Nominal and short duration Self-selected postures in a laboratory setting. However, these results display the potential difficulty of utilizing ATDs to represent more naturalistic child postures, especially the more forward head positions and flexed spinal posture associated with utilizing a portable electronic device.

The effect of abutment material stiffness on the mechanical behavior of dental implant assemblies: A 3D finite element study

PurposeThis study aimed to evaluate the stress distribution and microgap formation in implant assemblies with conical abutments made of different materials under an oblique load. Materials and methodsThe mechanical behavior of an implant assembly with a titanium abutment was analyzed and compared with that of an assembly with a Y-TZP abutment using finite element analysis (FEA). A torque of 20 Ncm was first applied to the abutment screw, followed by oblique loads of 10 N–280 N applied to the prosthesis placed on the implant. The maximum stress in the abutment screw, the microgap formation process, and the critical load for bridging the internal implant space were evaluated. ResultsNo significant difference in stress distribution between the two cases was observed, with the stresses being mainly concentrated at the top half of the screw (the predicted maximum von Mises stress was approximately 1200 MPa at 280 N). The area in contact at the implant-to-abutment interface decreased with increasing load for both abutments, with the critical load for bridging the internal implant space being roughly 140 N. The maximum gap size being was approximately 470 μm with either abutment. ConclusionThere was no significant difference in the stress distribution or microgap formed between implant assemblies with titanium and Y-TZP abutments having an internal conical connection.

Surgical Management of Submucous Cleft Palate by Radical Muscle Dissection Veloplasty: Speech Outcomes in Patients with 22q11.2 Deletion Syndrome.

To evaluate the benefit of anatomical muscle dissection repair for velopharyngeal insufficiency (VPI) in patients with submucous cleft palate (SMCP) with 22q11.2 deletion syndrome. Retrospective blinded randomised analysis of a surgeon's management over 10 years. The study was performed at a specialised Paediatric hospital in the United Kingdom. Children with SMCP and 22q11.2 deletion syndrome. All participants underwent radical muscle dissection veloplasty. Pre- and post- operative measurements included severity of anatomical defect, speech samples and lateral images which were digitised, randomised then externally and blindly analysed using validated techniques. Stata software was used to perform statistical analysis. 57 children with 22q11.2 deletion syndrome were included in this analysis. Intra-operatively, the majority of cases were identified as SMCP Grade I anomalies. Post-operatively, a statistically significant improvement in hypernasality, resting palate length, palate length at maximum closure, palate excursion and gap size at maximum closure was observed. Secondary surgery was performed for 59% of patients by ten years. Muscle dissection repair improves hypernasality, palate closure function and the closure gap in patients with 22q11.2 deletion syndrome. Although over 50% of patients may require further surgery, muscle dissection repair should be a first step due to its utility at a younger age, when invasive investigations are impossible, its lower morbidity, speech and language benefits or altering the plans for less obstructive secondary surgery when it lead to reduced velo-pharyngeal gap and improved palate mobility even when adequate velo-pharyngeal closure was not achieved.

Prediction of Gaps in Automated Tape Laying and Their Influence on Porosity in Consolidated Laminates

An efficient way to reduce direct operating costs in aerospace applications is to lower the overall weight. In this context, thermoplastic composites offer a high potential for weight reduction. However, their application requires time and cost-optimized process technologies. Thermoplastic tape laying with subsequent out-of-autoclave consolidation represents such a process technology. Typical process chains consist of several automated steps that can influence the component’s quality. Hence, a cross-process approach is applied to identify relevant process parameters. This paper focuses on minimizing the gaps between parallel-placed tapes and thereby reducing their influence on the laminate’s porosity. A geometrical model is developed and validated to predict the maximum gap sizes for a tape-laying process as a function of process accuracy, material accuracy, and process parameters. Based on this, a methodological approach is presented to minimize the influence of gaps on porosity. It is validated using automated tape laying and a novel low-pressure consolidation process. The findings make an important contribution to understanding the development of porosity along the process chain for the manufacture of thermoplastic composites for aerospace applications. It can be shown that the approach enables the prediction of gap sizes and allows to minimize their influence on porosity.

Optimization study of the electrode design of a 5 mm thick orthogonal-strip CdZnTe detector system

The geometry of electrodes is one of the most important factors in determining the performance of orthogonal-strip detectors. The aim of this work is to study the performance of a 5 mm thick cross-strip CdZnTe detector with different electrode widths. Our study consists of two main parts, simulations and experiments. We utilized four different anode sizes ranging from 0.1 mm to 0.6 mm. The anodes were interspersed with steering electrodes with varying sizes from 0.3 mm to 0.85 mm. The maximum gap size between the anodes and steering electrode strips was set to 0.3 mm, while the minimum gap size was 0.125 mm. The performance of the detector was investigated in terms of the steering electrode bias voltage, the energy resolution, and the charge sharing effect. For simulations, we developed a C++ based simulation program for charge transport inside the CdZnTe detector and charge collection at the electrodes. For photon interactions we used GEANT4 toolkit and for electric field and weighting potential simulations we used COMSOL software. The results demonstrated that -50 V is the optimal steering electrode bias for our detector when -500 V was applied to the cathodes and that the energy resolution performance drops with increasing steering electrode width. Also, the charge sharing effect becomes more dominant for larger steering electrode sizes. The experimental result are further compared with the simulations. The results are in a good agreement and the comparison validates our simulation model. Although, our simulation framework has need of better estimation for the intrinsic noise of CdZnTe. These results suggest that an optimization study between electrode widths and steering electrode bias is required to obtain the best performance in orthogonal-strip CdZnTe detectors.

Scheduling with gaps: new models and algorithms

We consider scheduling problems for unit jobs with release times, where the number or size of the gaps in the schedule is taken into consideration, either in the objective function or as a constraint. Except for several papers on minimum-energy scheduling, there is no work in the scheduling literature that uses performance metrics depending on the gap structure of a schedule. One of our objectives is to initiate the study of such scheduling problems. We focus on the model with unit-length jobs. First we examine scheduling problems with deadlines, where we consider two variants of minimum-gap scheduling: maximizing throughput with a budget for the number of gaps and minimizing the number of gaps with a throughput requirement. We then turn to other objective functions. For example, in some scenarios gaps in a schedule may be actually desirable, leading to the problem of maximizing the number of gaps. A related problem involves minimizing the maximum gap size. The second part of the paper examines the model without deadlines, where we focus on the tradeoff between the number of gaps and the total or maximum flow time. For all these problems we provide polynomial time algorithms, with running times ranging from O(nlog n) for some problems to O(n^7) for other. The solutions involve a spectrum of algorithmic techniques, including different dynamic programming formulations, speed-up techniques based on searching Monge arrays, searching X+Y matrices, or implicit binary search. Throughout the paper, we also draw a connection between gap scheduling problems and their continuous analogues, namely hitting set problems for intervals of real numbers. As it turns out, for some problems the continuous variants provide insights leading to efficient algorithms for the corresponding discrete versions, while for other problems completely new techniques are needed to solve the discrete version.

Effects of tightening torque on screw stress and formation of implant-abutment microgaps: A finite element analysis

Statement of problemThe mechanical behavior of the conical connection implant with different torque levels requires evaluation. PurposeThe purpose of this finite element analysis study was to investigate the impact of abutment screw torque on the formation of microgaps at the implant-to-abutment interface of a conical connection under oblique loading. This is important because it is thought that bacteria can invade the internal implant space through the abutment-implant microgaps, causing peri-implantitis. Material and methodsThree-dimensional finite element analyses of the conical implant-abutment connection were performed by using screw torques of 20 Ncm and 30 Ncm. Oblique loads from 10 N to 280 N were applied to the prosthesis placed on the implant. The maximum von Mises stress in the abutment screw, the microgap formation process, and the critical load for bridging the internal implant space were evaluated. ResultsThe stresses in the abutment screw under oblique loading had limited sensitivity to the screw torque. However, the residual stress in the screw with a 30-Ncm torque was 35% higher than that with a 20-Ncm torque in the absence of an external load. The area in contact at the implant-to-abutment interface decreased with increasing load for both torque values. The critical load for bridging the internal implant space was 160 N for a screw torque of 20 Ncm and 220 N for a screw torque of 30 Ncm. The maximum gap size was approximately 470 μm with all the loads. ConclusionsIncreasing the screw torque can reduce the formation of microgaps at the implant-to-abutment interface. However, this will result in higher mean stress in the abutment screw, which may reduce its fatigue life and consequently that of the prosthesis. Further research is needed to evaluate the relationship between the abutment screw torque and microleakage in implant-supported restorations.

Gap-filling snow-depth time-series with Kalman Filtering-Smoothing and Expectation Maximization: Proof of concept using spatially dense wireless-sensor-network data

We assessed the performance of Kalman Filtering-Smoothing and Expectation Maximization (EM-KF) in gap filling snow-depth sensor data. To this end, hourly snow-depth data from three spatially dense wireless-sensor networks were randomly removed and imputed using EM-KF. Maximum gap size was 40+ hours and differences between artificially removed and gap-filled data larger than 20 cm were removed before computing Root Mean Square Error and Bias. These differences are spurious over- and underestimations that can generally be identified through visual inspection, likely due to instability in the gap-filling process. The expected accuracy of EM-KF in this initial, controlled proof of concept is close to measurement uncertainty (1 to 2 cm for ultrasonic depth sensors). Compared to regressing missing data against nearby sensors, a frequently used strategy in the field, EM-KF tends to yield smaller errors in networks with a comparatively large number of co-located sensors (nine and eight as opposed to four in a third network). In these data-rich networks, maximum differences in daily Root Mean Square Errors between EM-KF and a regression are up to 6 to 8 cm at a daily time scale, with peaks in winter and in particular during snowfalls. EM-KF yields superior results particularly during snowfalls, likely because it exploits the temporal structure and uncertainty in the data through a state-space model. In the third network with fewer co-located sensors, differences in accuracy between EM-KF and a multilinear regression were inconsistent. This implies that the performance of EM-KF benefits from increasing the amount of available information and with increasing dependency of data across nodes. Temporally and spatially dense snow-depth data are being increasingly collected in operational contexts: EM-KF may support supervised filling of gaps in these data – particularly during snowfall events – and thus provide continuous-time information for avalanche or water-resources forecasting in snow-dominated regions. Automatic, unsupervised gap-filling using EM-KF will necessarily need more research to identify reasons of spurious over- and underestimations. Future work should also upscale this proof of concept to operational sensor networks spanning large water basins to bring conclusions closer to real-world applications.

Experimental Study of Composite Steel Plate Shear Wall with Flush End-Plate Connection

This paper presents an investigation on the structural performance of steel plate shear wall (SPSW) with flush end-plate beam–column connections and infill precast reinforced concrete (precast RC) panels. Two single-span two-story SPSW specimens, including unstiffened SPSW (NBRP) and precast RC panel restrained SPSW (Con-BRP), are first tested, followed with a parametric study by finite element method. Precast RC cover panels are installed on both sides of the infill steel plate and are disconnected from steel frame. Test results indicate that the use of precast RC cover panels increases the load carrying and energy dissipation capacities of the SPSW structure, but decreases its ductility. It is also effective in reducing the inward flexural deformation of columns. Moreover, the stiffening effect of the infill steel plate on the beam–column connections remains, which is a result of the precast RC cover panel’s resistance to the local buckling and the tears of the infill steel plates. The influence of the gap size between the precast RC cover plate and frame members on the failure mode of the specimen Con-BRP is also investigated, based on which a maximum gap size is recommended. Conclusions are drawn that SPSW structure with flush end-plate beam–column connections and precast RC cover panels fully exploits the strength of infill steel plates and exhibits excellent structural performance.

Computational investigation of laminar premixed hydrogen flame past a quenching mesh

PurposeThe purpose of this study is the computational analysis of atmospheric, laminar, stoichiometric and premixed hydrogen-air flames in the presence of a quenching mesh. The assessment of the predictive capability of different reaction mechanisms, the clarification of the relative importance of the thermal and chemical effects for mesh quenching and the investigation of the influence of the mesh geometry on the quenching effectiveness are the focal points of the investigation.Design/methodology/approachThe problem is posed as unsteady, two-dimensional. Differential governing equations are numerically solved by the finite volume method for the reacting hydrogen/air mixture, assuming an ideal gas behaviour. Thermal radiation and buoyancy are neglected. A coupled solver is used to treat the velocity-pressure coupling, along with a stiff-chemistry solver for the chemical kinetics. Second-order discretization schemes are used in space and time. A uniform grid resolution is used, where the grid independence in terms of the flame speed prediction is ensured in preliminary calculations for one-dimensional flames.FindingsIt is found that a detailed reaction mechanism is necessary for an accurate prediction. Meshes with round openings are found to be more effective that those with slit openings (SOs), by a factor of two in the maximum safe gap size. A perforated plate is observed to have a higher quenching potential compared to a wire mesh, for SOs. It is also found that the heat loss to the wall is the dominating quenching mechanism for the present problem, whereas adsorption of radicals plays a subordinate role.Originality/valueIn contrast to the previous studies in the field, a detailed reaction mechanism is applied instead of a single-step one, while still using the latter for comparison. The role of wall-radicals interaction for the quenching effectiveness of the mesh is addressed for the first time. Parametric studies are performed on the mesh geometry, which was not done before. Hydrogen is considered as fuel in contrast to the great majority of the previous work.

Influence of Material Selection on the Marginal Accuracy of CAD/CAM-Fabricated Metal- and All-Ceramic Single Crown Copings.

This study evaluated the marginal accuracy of CAD/CAM-fabricated crown copings from four different materials within the same processing route. Twenty stone replicas of a metallic master die (prepared upper premolar) were scanned and divided into two groups. Group 1 (n = 10) was used for a pilot test to determine the design parameters for best marginal accuracy. Group 2 (n = 10) was used to fabricate 10 specimens from the following materials with one identical CAD/CAM system (GAMMA 202, Wissner GmbH, Goettingen, Germany): A = commercially pure (cp) titanium, B = cobalt-chromium alloy, C = yttria-stabilized zirconia (YSZ), and D = leucite-reinforced glass-ceramics. Copings from group 2 were evaluated for the mean marginal gap size (MeanMG) and average maximum marginal gap size (AMaxMG) with a light microscope in the “as-machined” state. The effect of the material on the marginal accuracy was analyzed by multiple pairwise comparisons (Mann–Whitney, U-test, α = 0.05, adjusted by Bonferroni-Holmes method). MeanMG values were as follows: A: 46.92 ± 23.12 μm, B: 48.37 ± 29.72 μm, C: 68.25 ± 28.54 μm, and D: 58.73 ± 21.15 μm. The differences in the MeanMG values proved to be significant for groups A/C (p = 0.0024), A/D (p = 0.008), and B/C (p = 0.0332). AMaxMG values (A: 91.54 ± 23.39 μm, B: 96.86 ± 24.19 μm, C: 120.66 ± 32.75 μm, and D: 100.22 ± 10.83 μm) revealed no significant differences. The material had a significant impact on the marginal accuracy of CAD/CAM-fabricated copings.

Amplitude mode oscillations in pump-probe photoemission spectra from a d -wave superconductor

Recent developments in the techniques of ultrafast pump-probe photoemission have made possible the search for collective modes in strongly correlated systems out of equilibrium. Including inelastic scattering processes and a retarded interaction, we simulate time- and angle- resolved photoemission spectroscopy (trARPES) to study the amplitude mode of a d-wave superconductor, a collective mode excited through the nonlinear light-matter coupling to the pump pulse. We find that the amplitude mode oscillations of the d-wave order parameter occur in phase at a single frequency that is twice the quasi-steady-state maximum gap size after pumping. We comment on the necessary conditions for detecting the amplitude mode in trARPES experiments.

Microstructure of diffusion-brazing repaired IN738LC superalloy with uneven surface defect gap width

ABSTRACTSlots with uneven width were cut by femtosecond laser in small plates of IN738LC superalloy to imitate service cracks. The ‘cracks’ were repaired by diffusion brazing using BNi-1a or a mixed filler alloy at 1100°C. The joint region was composed of isothermal solidification zone (ISZ), diffusion affected zone (DAZ) and precipitate zone (PZ). The compositions were different between the upper and lower ISZ due to the variation of gap width. The sample, repaired with two kinds of filler metals, had similar DAZ microstructure. PZ of mixed filler alloy bonded sample had a similar microstructure with that of BNi-1a, but less borides. The maximum gap sizes of complete isothermal solidification were almost the same for different filler alloys, followed a square root relationship with time. However, PZ of BNi-1a bonded was larger, resulting from a more base metal dissolution. The relationship between the PZ, ISZ and crack width is discussed.

Maximum acceptable gap between urban-guided transport vehicles and platforms for persons with disabilities: the findings of an experimental study conducted to inform policy decisions

ABSTRACTThe French ministry responsible for transport has commissioned a study aimed at providing data to determine the maximum gap size between vehicle and platform for guided transport vehicles, which would become a legal requirement. Specific experimental conditions were created, with a physical mock-up simulating a tramway and a platform and providing several gap configurations (between 20 and 50 mm for the horizontal gap and between 20 and 75 mm for the vertical step), and an experimental design based on the negotiation of gaps by wheelchairs users (mainly manual or electric powered). The experiment was conducted with 46 participants with different functional abilities. Data were collected on performance and gap negotiation time. The results of this study indicate that despite the failures observed for the 50 × 50 mm gap size during the experiment, most wheelchair users who took part in the test have successfully negotiated this gap.

The role of bone void fillers in medial opening wedge high tibial osteotomy: a systematic review.

A variety of bone void filling materials and methods are available in opening medial wedge HTO (OWHTO). The pertinent question revolves around if and when bone void fillers are needed. The primary purpose of this study was to systematically review outcomes and complications after OWHTO with and without the use of bone void fillers. The EMBASE, PubMed\MEDLINE, Cochrane Library and Google Scholar databases were searched to identify articles that reported OWHTO results using different bone void fillers until March 2016. Only articles reporting the exact bone void filler type, the opening gap size and the fixation method were included. The extracted data included the study design, demographic data, the radiological and clinical results and complication rates. Outcomes were analysed with regard to bone void filler type, and comparison was made between the groups (allograft, autograft, synthetic bone void filler and OWHTO without bone void filling). Twenty-two articles reporting the results of 1421 OWHTO met the inclusion criteria. In total, 647 osteotomies were completed with allogeneic graft as bone void filler, 367 with synthetic materials, 199 with autograft and 208 without any bone void filling material. The maximum opening gap size was similar in all groups with mean of 9.8mm (range 4-17.5mm). Locking plate fixation was used in 90% of the osteotomies that were completed without bone void filler, while all allograft cases and more then 90% of the autograft cases were done with non-locking systems. The highest rates of non-union (1.1%) were seen in the synthetic group, compared to 0.5% in the all the other groups. This systematic review showed no definitive advantages for OWHTO with any bone void filler in terms of union rates and loss of correction. Moreover, the use of autografts or allografts showed more favourable outcomes than synthetic bone substitutes. OWHTO with gaps smaller then 10mm and rigid fixation might be successfully managed without bone grafting. However, when bone grafting is needed, autograft bone provides higher rates of clinical and radiographic union. The use of synthetic bone substitutes in OWHTO cannot be recommended. III.

Effect of data gaps: comparison of different spectral analysis methods

Abstract. In this paper we investigate quantitatively the effect of data gaps for four methods of estimating the amplitude spectrum of a time series: fast Fourier transform (FFT), discrete Fourier transform (DFT), Z transform (ZTR) and the Lomb–Scargle algorithm (LST). We devise two tests: the single-large-gap test, which can probe the effect of a single data gap of varying size and the multiple-small-gaps test, used to study the effect of numerous small gaps of variable size distributed within the time series. The tests are applied on two data sets: a synthetic data set composed of a superposition of four sinusoidal modes, and one component of the magnetic field measured by the Venus Express (VEX) spacecraft in orbit around the planet Venus. For single data gaps, FFT and DFT give an amplitude monotonically decreasing with gap size. However, the shape of their amplitude spectrum remains unmodified even for a large data gap. On the other hand, ZTR and LST preserve the absolute level of amplitude but lead to greatly increased spectral noise for increasing gap size. For multiple small data gaps, DFT, ZTR and LST can, unlike FFT, find the correct amplitude of sinusoidal modes even for large data gap percentage. However, for in-situ data collected in a turbulent plasma environment, these three methods overestimate the high frequency part of the amplitude spectrum above a threshold depending on the maximum gap size, while FFT slightly underestimates it.

Quartz c-axis orientation patterns in fracture cement as a measure of fracture opening rate and a validation tool for fracture pattern models

We evaluate a published model for crystal growth patterns in quartz cement in sandstone fractures by comparing crystal fracture-spanning predictions to quartz c-axis orientation distributions measured by electron backscatter diffraction (EBSD) of spanning quartz deposits. Samples from eight subvertical opening-mode fractures in four sandstone formations, the Jurassic–Cretaceous Nikanassin Formation, northwestern Alberta Foothills (Canada), Cretaceous Mesaverde Group (USA; Cozzette Sandstone Member of the Iles Formation), Piceance Basin, Colorado (USA), and upper Jurassic–lower Cretaceous Cotton Valley Group (Taylor sandstone) and overlying Travis Peak Formation, east Texas, have similar quartzose composition and grain size but contain fractures with different temperature histories and opening rates based on fluid inclusion assemblages and burial history. Spherical statistical analysis shows that, in agreement with model predictions, bridging crystals have a preferred orientation with c-axis orientations at a high angle to fracture walls. The second form of validation is for spanning potential that depends on the size of cut substrate grains. Using measured cut substrate grain sizes and c-axis orientations of spanning bridges, we calculated the required orientation for the smallest cut grain to span the maximum gap size and the required orientation of the crystal with the least spanning potential to form overgrowths that span across maximum measured gap sizes. We find that within a 10° error all spanning crystals conform to model predictions. Using crystals with the lowest spanning potential based on crystallographic orientation (c-axis parallel to fracture wall) and a temperature range for fracture opening measured from fluid inclusion assemblages, we calculate maximum fracture opening rates that allow crystals to span. These rates are comparable to those derived independently from fracture temperature histories based on burial history and multiple sequential fluid inclusion assemblages. Results support the R. Lander and S. Laubach model, which predicts that for quartz deposited synchronously with fracture opening, spanning potential, or likelihood of quartz deposits that are thick enough to span between fracture walls, depends on temperature history, fracture opening rate, size of opening increments, and size, mineralogy, and crystallographic orientation of substrates in the fracture wall (transected grains). Results suggest that EBSD maps, which can be more rapidly acquired than measurement of tens to hundreds of fluid inclusion assemblages, can provide a useful measure of relative opening rates within populations of quartz-filled fractures formed under sedimentary basin conditions. Such data are useful for evaluating fracture pattern development models.