Total Relative Motion Research Articles

Physical interpretation on development and validation of the reaction routes of complex chemical kinetic model

Simulating the complexity in its entirety proves highly challenging, to examine both the local and global stability of the model, as well as its positivity, recognizing the overall instability. To address this challenge, a strategy of splitting down the multi-route complex reactions into its independent sub-routes is employed. For the validation of sub-routes, the stability and positivity of each individual route were comprehensively analyzed. In addition, we employ techniques to simplify our models by considering factors such as reaction speed and thermodynamic properties, ensuring their accuracy. Furthermore, we integrate the Spectral Quasi-Equilibrium Manifold to obtain a deeper understanding of the sequential advancement of reactions, focusing on the slowest eigenvector. A comprehensive examination of the mathematical underpinnings of these reaction steps and diverse pathways is conducted. We also investigate the temporal behavior of these pathways, yielding fresh perspectives. Our findings suggest the feasibility of independently evaluating each pathway rather than treating the entire mechanism as a singular entity. To enhance our analysis, we conduct a local sensitivity assessment using the SimBiology toolbox in MATLAB of each route and compare calculation periods for TRM (Total Relative Motion). Furthermore, we employ the short-time Fourier transform graph to capture time–frequency information regarding the steady state of compounds in various routes, revealing spectral variations over time.

136. Relative vertebral motion after one- and two-level cervical disc arthroplasty

<h3>BACKGROUND CONTEXT</h3> While cervical disc arthroplasty has been studied for some time, few studies examined the relative motion between respective vertebral bodies. <h3>PURPOSE</h3> The purpose of this study was to examine the effects on the relative motion of the vertebral bodies above, below and at the surgical index level. <h3>STUDY DESIGN/SETTING</h3> Human cervical spines from C2-C7 were subjected to continuous loading cycles under flexion, extension, and lateral bending. Three-dimensional motion data were acquired using electromagnetic sensors at C4-C5, C5-C6 and C6-C7. <h3>PATIENT SAMPLE</h3> Eight planned cadaver cervical spines were subjected to each loading mode under intact, index (C5-C6) and inferior (C6-C7) artificial disc implantations. Specimens displayed degenerated discs with reduced intervertebral disc height. <h3>OUTCOME MEASURES</h3> The motion at C4-C5, C5-C6 and C6-C7 was computed to compare implantation vs intact conditions. Computations involved removal of induced motion by the testing apparatus and subsequently computing the relative motion between vertebral levels. <h3>METHODS</h3> Human cadaver specimens were loaded in extension, flexion and lateral bending under displacement control of 3 mm for 20 cycles at 0.1Hz. The testing configuration permitted orientation and loading of the specimen without removal from the testing apparatus. The loading modes were obtained by rotating the specimen into the loading axis of the testing apparatus. Motion data were collected continuously at 60 frames/second. Artificial discs were implanted by experienced spine surgeons for one- and two-level implantations at C5-C6 and C6-C7. Data were compared using a one-way ANOVA with Dunnett's post-hoc tests. Significance was set at P <0.05. <h3>RESULTS</h3> Based on half of the specimens analyzed, in flexion, a trend (P >0.05) toward increased motion was observed as the number of implanted levels increased. An increase in motion by 44.8% was observed with implantation at the index level relative to the intact condition. Implantation of a device inferiorly resulted in a 43% increase in motion relative to the intact level. In extension, no significant differences were seen regardless of the level of implantation. Lateral bending displayed a trend toward decreased motion though this was not statistically significant. The examination of total relative motion between vertebral bodies may be an improved consideration when evaluating the effects of disc arthroplasty. <h3>CONCLUSIONS</h3> Based on the number of specimens currently analyzed, a trend toward increased flexural motion was observed. Examination of isolated vertebral level motion may lead to unforeseen biomechanical conditions arising at adjacent levels from the index level. Further studies to include increased sample population could offer more insight toward ensuring that overall cervical motion is not unduly influenced. <h3>FDA DEVICE/DRUG STATUS</h3> prodisc C (Approved for this indication)

Late Quaternary slip rates for the southern Elsinore fault in the Coyote Mountains, southern California from analysis of alluvial fan landforms and clast provenance, soils, and U-series ages of pedogenic carbonate

Offset alluvial fans along the Elsinore fault in the south-central Coyote Mountains were studied to resolve an average late Quaternary slip rate for this major western strand of the San Andreas fault system in southern California. Alluvial fans and their offsets were mapped using high-resolution DEMs combined with field observations of fan-surface morphology and the character of the soils developed in each fan remnant. Clast assemblage data was used to determine the source of each alluvial fan upstream of the fault, and U-series dating of pedogenic carbonate was used to estimate minimum ages of the alluvial fan surfaces. Forty U-Th dates on pedogenic carbonate confirm the utility of the technique for dating late Pleistocene alluvium in arid regions and suggest that age variation among late Pleistocene fans grouped on the basis of soils and geomorphic criteria may be significant. Based on these data, the southernmost segment of the Elsinore fault has sustained a slip rate of 2.4 ± 0.4 mm/y for the past 60–70 ka and probably for the past 150 ka. Because displacement in the most recent surface rupture increases northwest of our slip rate sites, this rate is likely a minimum for the southern Elsinore fault, with the actual rate more likely close to 3 mm/y in the central part of the range. These new data confirm that slip gradients along individual fault segments must be considered when estimating pre-Holocene slip rates for seismic hazard estimates. These new results show that the southern Elsinore fault accounts for about 6% of the total relative motion between North America and the Pacific lithospheric plates in southernmost California. Assessment of previous estimates of slip in the most recent event suggests earthquakes of about Mw 6.8 and, when combined with the slip rate data, a recurrence of such events about every thousand years.

Large‐displacement, hydrothermal frictional properties of DFDP‐1 fault rocks, Alpine Fault, New Zealand: Implications for deep rupture propagation

The Alpine Fault, New Zealand, is a major plate‐bounding fault that accommodates 65–75% of the total relative motion between the Australian and Pacific plates. Here we present data on the hydrothermal frictional properties of Alpine Fault rocks that surround the principal slip zones (PSZ) of the Alpine Fault and those comprising the PSZ itself. The samples were retrieved from relatively shallow depths during phase 1 of the Deep Fault Drilling Project (DFDP‐1) at Gaunt Creek. Simulated fault gouges were sheared at temperatures of 25, 150, 300, 450, and 600°C in order to determine the friction coefficient as well as the velocity dependence of friction. Friction remains more or less constant with changes in temperature, but a transition from velocity‐strengthening behavior to velocity‐weakening behavior occurs at a temperature of T = 150°C. The transition depends on the absolute value of sliding velocity as well as temperature, with the velocity‐weakening region restricted to higher velocity for higher temperatures. Friction was substantially lower for low‐velocity shearing (V < 0.3 µm/s) at 600°C, but no transition to normal stress independence was observed. In the framework of rate‐and‐state friction, earthquake nucleation is most likely at an intermediate temperature of T = 300°C. The velocity‐strengthening nature of the Alpine Fault rocks at higher temperatures may pose a barrier for rupture propagation to deeper levels, limiting the possible depth extent of large earthquakes. Our results highlight the importance of strain rate in controlling frictional behavior under conditions spanning the classical brittle‐plastic transition for quartzofeldspathic compositions.

Slicing up the San Francisco Bay Area: Block kinematics and fault slip rates from GPS‐derived surface velocities

Observations of surface deformation allow us to determine the kinematics of faults in the San Francisco Bay Area. We present the Bay Area velocity unification (BV, “bay view”), a compilation of over 200 horizontal surface velocities computed from campaign‐style and continuous Global Positioning System (GPS) observations from 1993 to 2003. We interpret this interseismic velocity field using a three‐dimensional block model to determine the relative contributions of block motion, elastic strain accumulation, and shallow aseismic creep. The total relative motion between the Pacific plate and the rigid Sierra Nevada/Great Valley (SNGV) microplate is 37.9 ± 0.6 mm yr−1 directed toward N30.4°W ± 0.8° at San Francisco (±2σ). Fault slip rates from our preferred model are typically within the error bounds of geologic estimates but provide a better fit to geodetic data (notable right‐lateral slip rates in mm yr−1: San Gregorio fault, 2.4 ± 1.0; West Napa fault, 4.0 ± 3.0; zone of faulting along the eastern margin of the Coast Range, 5.4 ± 1.0; and Mount Diablo thrust, 3.9 ± 1.0 of reverse slip and 4.0 ± 0.2 of right‐lateral strike slip). Slip on the northern Calaveras is partitioned between both the West Napa and Concord/Green Valley fault systems. The total convergence across the Bay Area is negligible. Poles of rotation for Bay Area blocks progress systematically from the North America‐Pacific to North America‐SNGV poles. The resulting present‐day relative motion cannot explain the strike of most Bay Area faults, but fault strike does loosely correlate with inferred plate motions at the time each fault initiated.

Crustal deformation across the Imperial Fault: Results from kinematic GPS surveys and trilateration of a densely spaced, small‐aperture network

Kinematic Global Positioning System (GPS) surveys in 1991 and 1993 of a 66‐station, small‐aperture network across a 12‐km‐long segment of the Imperial Fault near El Centro, California, reveal a fairly uniform secular displacement field consistent with right‐lateral slip along a single, vertical dislocation surface. Total relative motion across the array equals 20±3 mm/yr at N49±7°W for sites 5–6 km away from the fault trace on opposite sides. These rates agree with simple dislocation models that assume 10 mm/yr of creep along the fault trace from the surface to a locking depth of 9 km and a plate boundary rate of 45 mm/yr oriented N40°W at depth. Model fit does not significantly improve if creep rates are permitted to vary along strike by several millimeters per year. A comparison of 1991/1993 GPS with 1987 high‐precision electronic distance measurements validates the dislocation models but suggests a smoother deformation field than that defined by the 1991/1993 velocities. The difference can be attributed to the poorer 1991 kinematic positioning accuracy rather than to temporal variations in strain. There is evidence for 20 mm of sympathetic coseismic slip from the 1987 Superstition Hills earthquake, although aseismic slip along both faults appears to be completely decoupled.

Microplate versus continuum descriptions of active tectonic deformation

Whether deformation of continents is more accurately described by the motions of a few small rigid plates or by quasi‐continuous flow has important implications for lithospheric dynamics, fault mechanics, and earthquake hazard assessment. Actively deforming regions of the western United States, central Asia, Japan, and New Zealand show features that argue for both styles of movement, but new observations are necessary to determine which is most appropriate and at what scale the description applies. Geologic, geodetic, seismic, and paleomagnetic measurements tend to sample complementary aspects of the deformation field, so an integrated observation program can utilize the strengths of each method and overcome their separate spatial or temporal biases. Provided the total relative motion across each region is known and the distribution of active faults is well mapped, determination of fault slip rates can provide potentially decisive constraints. Reconnaissance geological studies supply useful slip rate estimates, but precise values depend upon detailed intensive investigation of individual sites. Geodetic survey measurements can determine the spatial pattern of contemporary movements and extract slip rate information, but the sometimes elusive effects of cyclic elastic strain buildup and relief must be accounted for in relating current movements to the long‐term deformation pattern. Earthquake catalogs can be applied to determine seismic strain rates and relative velocities but must be averaged over large regions and are usually limited by the inadequate duration of historical or instrumental seismicity catalogs. Paleomagnetic determinations of vertical axis rotations provide estimates of block rotation rates but are often locally variable and averaged over many millions of years. Which of the two descriptions of continental tectonics is more nearly correct depends on the local rheological stratification of the lithosphere, especially the strength and thickness of the elastic crust relative to the ductile lithosphere, and dynamical models can provide contrasting forecasts of observable features with testable consequences.

Anatomy, structural evolution, and slip rate of a plate-boundary thrust: The Alpine fault at Gaunt Creek, Westland, New Zealand

Minimum slip rates calculated for plate-vector-parallel slickenside trends in cataclasite on the sole of the Alpine fault at Gaunt Creek, Westland, New Zealand, range from 18 to 24 mm/yr. Between half and two-thirds of the total relative motion between the Pacific and Australian plates is being accommodated by movement on a single structure, the Alpine fault. During the past 14 ka, the leading edge of the Alpine fault has changed from a moderately southeast-dipping, oblique reverse fault to a shallowly dipping thrust. The hanging wall (Pacific plate) is composed of a gradational sequence from basal gouge, through pseudotachylite-bearing cataclasite, to progressively more coherent schist-derived mylonite, which has been faulted against subhorizontally bedded, fluvio-glacial gravel in the footwall (Australian plate). During uplift the hanging-wall sequence has been internally sheared and imbricated, producing duplex structures, and retrogressively veined and altered by pervasive hydrothermal fluid flow. Erosion of the exhumed fault zone produced angular, cataclasite- and mylonite- derived, talus-fan breccias, building a west-dipping apron beneath the fault scarp. Wood fragments from near the base off the talus breccias have been 14 C dated at 12,650 ± 90 yr B.P. Progressive tectonic shortening resulted in 180 m of overthrusting of a schist-derived nappe across an irregular talus fan surface composed of its own erosional debris. The structural history of the Alpine fault at Gaunt Creek illustrates the importance of the interaction between fault-induced topography and erosion, and the control these processes exert on the continued tectonic, geometric, and geomorphic evolution of the fault zone.

Three-Dimensional Effects in Ship Relative-Motion Problems

The total relative motion between a ship and the sea surface, including the effects of the ship motions, the incident waves, the diffracted waves, and the radiated waves, is discussed. The radiated and diffracted wave components are calculated using the theory of Salvesen, Tuck, and Faltinsen (1970) with the zero-speed potentials determined by fully three-dimensional calculations. Comparisons with experiments and other theoretical calculations for a simple mathematical hull form are given. The proposed theory shows significant improvement over slender-body theory for the diffraction component and is equal to or better than strip theory for the radiation component.

Total motion knee goniometry

This paper treats the problems of total motion knee goniometry: goniometer design, attachment, data reduction and operating techniques to ensure accurate results. A new knee goniometer of the direct-attachment electromechanical type is described, and a computional technique for quantifying the total relative motion of the lower leg relative to the upper leg is developed. This entails six motion variables which must be reducible to three relative angular and three relative displacement variables, providing a more complete and precise quantification of knee motion than previously possible. Details of the spatial linkage and attachments are presented, along with operating experience demonstrating the importance of attachment technique. The goniometer is now in use as both a research and diagnostic tool. Typical results for normal and abnormal knees are presented to demonstrate the device and technique described.

Increasing rate of movement with time between California and the Pacific Plate: From Delgada Submarine Fan source areas

Changes in the percentages of clay minerals and coarse fraction minerals with depth in Deep Sea Drilling Project cores from Delgada submarine fan suggest that the rate of motion between California and the Pacific plate has increased with time during the past 15 m.y. The major changes in mineralogy indicate changes in provenance. The times of these changes found in fan sediment and palcogeographic lithologic reconstructions of California demon- strate an increase in rate of motion from about 3.0 cm/yr 15 m.y. ago to 6.5 cmfyr at preent. During the time interval of 4-9 m.y. ago the data suggest a rate of motion of 4.5 cm/yr. Rates of motion between lithospheric plates are of major concern in determining the quan- titative nature of the dynamic earth system. Spreading centers as plate boundaries have been emphasized in the study of rates of motion. Rates of movement in these areas are usually calculated from the apparent age of basement rock, as deduced from the geomagnetic time scale of Heirtzler et al. (1968), and the dis- tance between rocks of different deduced ages. Studies of the SaN Andreas fault, a transform fault plate boundary, have considered move- ment between the Pacific and the American plates primarly in terms of a constant rate of motion with time (Dickinson and Grantz, 1968; Atwater, 1970; Hayes and Pitman, 1970). Such an extrapolation of a constant rate of motion with time was necessary because of poorly understood dynamics of a transform fault plate boundary and magnetic anomalies representing only the last 4 m.y. of history between these two plates (Anderson, 1971; Larson et al., 1968). Possibilities of variable rates of motion with time are discussed by Atwater (1970), Dickinson et al. (1972), and Hein (1973). Hu.f)- man (1972), working within the San Andreas fault zone and therefore not necessarily mea- suring total relative motion between the Pacific and the American plates, suggests a change in the rate of motion of the San Andreas fault sometime in the last 22 m.y. Larson (1972), from a study of the Gulf of California and from the results of previous studies, suggests a signifi- cant change in motion of these two plates 10 m.y. ago. Frerichs and Shive (1971) speculate about episodic movement on spreading centers with an increase in spreading rate 10 m.y. ago, although they are not concerned specifically with the American and Pacific plates. Talwani et al. (1971) provide concrete evidence, from distribution of sediment, of an increase in spreading rate at 10 m.y.B.P. in the North Atlantic. This paper concerns a method by which the history of relative movement can be determined between California and the Pacific

Deep-sea Sediment Source Areas: Implications of Variable Rates of Movement between California and the Pacific Plate

RECENT work has indicated acceleration of motion on the San Andreas Fault1, but previous studies have not delineated variable rates of motion with time between the Pacific and American plates. Offsets on the San Andreas and associated fault systems yield a mean rate of motion for a given period of time and deal with motion within the area of a wide plate boundary; therefore, these do not show total relative motion or variations in velocity between the two plates2. Magnetic anomalies can be used to measure the total relative motion and variations in velocity between the two plates. But magnetic anomalies at the mouth of the Gulf of California represent only the past few million years of movement which has been going on for at least 25 m.y. (ref. 3). Here I describe a method by which the amount and rates of motion between California and the Pacific plate with time can be determined.