Kinematic Stage Research Articles

Locomotor Development of Zebrafish (Danio Rerio) Under Novel Hydrodynamic Conditions

The kinematics, neuromuscular control, and hydrodynamic aspects of normal locomotor activity in larval zebrafish have been extensively studied. Although locomotion depends heavily on the fluid properties of water, we have little knowledge of what sensory and developmental cues zebrafish larvae receive from their interaction with the fluid medium in which they grow. In this study, I manipulate the viscosity of water in which larvae grow until 5 and 7 days postfertilization (dpf) and record the kinematics of routine turns in their growth medium. Larvae are then transferred to a new medium of different viscosity and filmed again after short and long acclimation periods. Four hypotheses are tested: (1) larval kinematics are constrained by muscle activation patterns, (2) larval kinematics are guided by kinematic objectives, (3) routine turning control is independent of early locomotor experience, and (4) response to novel fluid environment is independent of developmental stage. The results indicate that a kinematic parameter, stage 1 angle, correlates with the kinematics of stage 1 while muscle activation patterns likely constrain stage 2. Development of this behavior is not dependent on locomotor experience both at 5 and 7 dpf, although the two age groups respond differently to increased viscosity.

The effect of convergence angle on the kinematic evolution of strain partitioning in transpressional brittle wedges: Insight from analog modeling and high‐resolution digital image analysis

Using analog modeling aided by digital image analysis (DPIV), we constrained the long‐term kinematic evolution of strain partitioning in transpressional brittle wedges as a function of convergence angle. We ran a series of dry quartz sand experiments representing highly oblique continent‐continent collision (convergence angles of 4° to 30°). The digital image analysis provided high‐resolution constraints on the long‐term kinematic evolution of these wedges, which could be subdivided in distinct kinematic stages, comprising (1) an initial “distributed strain” stage and (2) an “oblique wedge” stage before (3) the stage of strain partitioning is reached. Thus, we document the evolution of different deformation stages from a single plate tectonic boundary condition. In addition, the relationship between convergence angle, kinematic stages, and wedge geometry (including fault dips and fault hierarchy) was established. The modeling results show that smaller convergence angles lead to steeper faults. Besides, for a constant convergence angle, the proshears that evolved during the strain partitioning stage were less steep than those formed during the oblique wedge stage. The fault slip vector on individual fault segments was derived from the DPIV data set for each time increment, quantifying the magnitude and orientation of slip on fault segments during the different kinematic stages. In addition, in the 7.5° and 15° models, rotation of the slip vector by up to 40° was observed on a single proshear during the strain partitioning stage. These observations allow to some degree a validation of existing analytical models of strain partitioning, in particular the assumption of steady state.

Mantle flow and dynamic topography associated with slab window opening: Insights from laboratory models

We present dynamically self-consistent mantle-scale laboratory models that have been conducted to improve our understanding of the influence of slab window opening on subduction dynamics, mantle flow and associated dynamic topography over geological time scales. The adopted setup consists of a two-layer linearly viscous system simulating the subduction of a fixed plate of silicone (lithosphere) under negative buoyancy in a viscous layer of glucose syrup (mantle). Our experimental setting is also characterized by a constant-width rectangular window located at the center of a laterally confined slab, modeling the case of the interaction of a trench-parallel spreading ridge with a wide subduction zone. We found that the opening of a slab window does not produce consistent changes of the geometry and the kinematics of the slab. On the contrary, slab-induced mantle circulation, quantified both in the vertical and horizontal sections using the Feature Tracking image analysis technique, is strongly modified. In particular, rollback subduction and the opening of the slab window generate a complex mantle circulation pattern characterized by the presence of poloidal and toroidal components, with the importance of each evolving according to kinematic stages. Mantle coming from the oceanic domain floods through the slab window, indenting the supra-slab mantle zone and producing its deformation without any mixing between mantle portions. The opening of the slab window and the upwelling of sub-slab mantle produce a regional-scale non-isostatic topographic uplift of the overriding plate that would correspond to values ranging between ca. 1 and 5 km in nature. Assuming that our modeling results can be representative of the natural behavior of subduction zones, we compared them to the tectonics and volcanism of the Patagonian subduction zone. We found that the anomalous backarc volcanism that has been developing since the middle Miocene could result from the lateral flow of sub-slab mantle and that part of the Patagonian uplift could be dynamically supported.

Target block alignment error in XY stage metrology

This paper discusses a fundamental question in the characterization of XY stages: Is the orthogonality error of the stage distinguishable from a target block alignment error without explicitly measuring the target block misalignment? The conclusion reached here is that, for parallel kinematic stages this is not possible using any metrology setup or any number of measurements.

Complete Eulerian-mean tracer equation for coarse resolution OGCMs

McDougall and McIntosh showed that the adiabatic mesoscale mixing is represented incompletely in the tracer Eulerian-averaged equation (EAE) of coarse resolution OGCMs. We show that completing EAE requires an adequate decomposition of the mesoscale tracer flux which is achieved by means of transforming mesoscale fields to isopycnal coordinates (IC) where mesoscale dynamics has the simplest form. The transformation results in splitting F τ into two components and : the former is determined by buoyancy mesoscale dynamics only and has a trivial kinematic dependence on the mean tracer field, the latter is determined by mesoscale tracer dynamics. Thus, the problem of modelling (parameterizing) F τ in ZC is divided in two stages which can be termed kinematic and dynamic. The kinematic stage consists in adequate decomposing F τ, and the result is expressed in terms of mesoscale fields. The dynamic stage consists in applying a specific dynamic mesoscale model to parameterize the components of F τ. In this article, we show that some components of F τ are missing in ZC-OGCMs tracer equation and that their contribution is of the same order of magnitude as the mesoscale contribution itself. We also show that F τ has components across mean isopycnals and that their existence is consistent with the adiabatic approximation which requires vanishing all fluxes across isopycnal surfaces. As for practical results, we derive the complete equation for the large scale tracer in ZC-OGCMs and present the parameterization of the terms which have been missing thus far.

Stochastic analysis of subcritical amplification of magnetic energy in a turbulent dynamo

We present and analyze a simplified stochastic αΩ-dynamo model which is designed to assess the influence of additive and multiplicative noises, non-normality of dynamo equation, and nonlinearity of the α-effect and turbulent diffusivity, on the generation of a large-scale magnetic field in the subcritical case. Our model incorporates random fluctuations in the α-parameter and additive noise arising from the small-scale fluctuations of magnetic and turbulent velocity fields. We show that the noise effects along with non-normality can lead to the stochastic amplification of the magnetic field even in the subcritical case. The criteria for the stochastic instability during the early kinematic stage are established and the critical value for the intensity of multiplicative noise due to α-fluctuations is found. We obtain numerical solutions of nonlinear stochastic differential equations and find the series of phase transitions induced by random fluctuations in the α-parameter.

Magnetic-field generation in Kolmogorov turbulence.

We analyze the initial, kinematic stage of magnetic field evolution in an isotropic and homogeneous turbulent conducting fluid with a rough velocity field, v(l) approximately l(alpha), alpha<1. This regime is relevant to the problem of magnetic field generation in fluids with small magnetic Prandtl number, i.e., with Ohmic resistivity much larger than viscosity. We propose that the smaller the roughness exponent alpha, the larger the magnetic Reynolds number that is needed to excite magnetic fluctuations. This implies that numerical or experimental investigations of magnetohydrodynamic turbulence with small Prandtl numbers need to achieve extremely high resolution in order to describe magnetic phenomena adequately.

Deep structure and kinematics of the Northern Calcareous Alps (TRANSALP Profile)

The Northern Calcareous Alps (NCA) of southern Bavaria and northern Tyrol constitute a carbonate-dominated polyphase fold-thrust wedge; together with its Grauwacken Zone Basement, it is the northernmost part of the far-travelled Upper Austroalpine thrust complex of the Eastern Alps. The present geometry developed in several kinematic stages. Jurassic extensional faults that affected large parts of the NCA and their basement originated when the main part of the NCA was still located southeast of the Central Alpine Otztal-Silvretta complex. These faults and related facies transitions influenced the later style of detachment of the NCA thrust sheets. Mid to Late Cretaceous detachment, thrust-sheet stacking and motion over the Central Alpine complex are registered in clastic deposits of syntectonic basins. The latest Cretaceous to Cenozoic NNE- to N-directed motion of the NCA towards Europe in front of the Central Alpine complex created another set of significant contraction structures, which at depth overprinted all previous structures. During Cretaceous to Cenozoic deformation, the NCA experienced about 80 km of shortening, i.e., about 73% along the TRANSALP Profile. The European basement and autochthonous Mesozoic cover beneath the allochthonous NCA thrust sheets and flysch complexes seem to have remained relatively undeformed.

A model of nonlinear evolution and saturation of the turbulent MHD dynamo

The growth and saturation of magnetic field in conductingturbulent media with large magnetic Prandtl numbers areinvestigated. This regime is very common in low-density hotastrophysical plasmas. During the early (kinematic) stage, weakmagnetic fluctuations grow exponentially and concentrate at theresistive scale, which lies far below the hydrodynamic viscousscale. The evolution becomes nonlinear when the magnetic energyis comparable to the kinetic energy of the viscous-scale eddies. A physical picture of the ensuing nonlinear evolution of the MHD dynamo is proposed. Phenomenological considerations are supplemented with a simple Fokker-Planck model of thenonlinear evolution of the magnetic-energy spectrum. It isfound that, while the shift of the bulk of the magnetic energy from the subviscous scales to the velocity scales may bepossible, it occurs very slowly - at the resistive, ratherthan dynamical, timescale (for galaxies, this means thatthe generation of large-scale magnetic fields cannot be explainedby this mechanism). The role of Alfvénic motions and theimplications for the fully developed isotropic MHD turbulenceare discussed.

Author Index

An in-house-made alignment system for deep X-ray lithography is presented that features low costs, low weight and little demand in space. Synchrotron radiation illuminates alignment marks on mask and substrate. The radiation transmitted through these alignment marks is detected by X-ray-sensitive diodes. The mask is fixed to the vacuum chamber, whereas the substrate is mounted on a six-axis kinematic stage. The information about the degree of alignment is the obtained photocurrent, which reaches its maximum at the best alignment position. Variation of the photocurrent is an error signal in a feedback loop. A slit screen protects the resist in the pattern area from irradiation during the alignment procedure. The features of the alignment system offer guidelines for research groups interested in upgrading their system as well.

Pseudotachylytes in the southern border fault of the Cenozoic intracontinental Teletsk basin (Altai, Russia)

The Cenozoic intracontinental Teletsk basin in the Central Asian Altai Mountains is composed of a complexly structured northern and a more simple southern sub-basin. These sub-basins formed in two distinct kinematic stages when first the NNW-striking Teletsk- and then the NE-striking West-Sayan shear zones became reactivated in the Cenozoic under dominant NS-oriented horizontal compression. Although the entire Teletsk basin strikes roughly NS, the southern sub-basin is parallel to the NNW-trending, amphibolite facies Teletsk ductile shear zone, while the northern sub-basin is NS-striking and flanked by differently structured, greenschist facies basement. Basement reactivation closely controlled the southern sub-basin formation, but this is less clear for the northern sub-basin. Contrasts between northern and southern basement and the exclusive occurrence of pseudotachylytes along the margins of the southern basin are explored for their contribution to the formation of the Teletsk basin with two distinct sub-basins. In the ductile shear fabric of the basement flanking the southern sub-basin, concordantly interleaved pseudotachylytes and isolated breccia lenses reflect local brittle deformation along the ductile fabric. The genetic link between breccia lenses and pseudotachylyte occurrences was defined by microstructural investigation. It allows to explore their possible development in a dextral strike–slip zone. These rocks occur in a large fault-bounded segment of the basement. The geometry of the structures in the segment is comparable with a dextral strike–slip sidewall-ripout structure along the Teletsk shear zone. Seismic slip related to pseudotachylytes is attributed to the sudden stress release on the NNW-striking Teletsk shear zone, when the latter became unconstrained by reactivation of the NE-trending West-Sayan fault zone at its northern boundary. The boundary of the sidewall-ripout structure was reactivated as a large listric fault in a later stage. The northern sub-basins roughly develop along an NS strike and are assumed to reflect reactivation of the ductile shear zone underneath the variably structured greenschist facies basement outcropping along the flanks of the sub-basin.

Structural evolution of the Teletsk graben (Russian Altai)

Lake Teletskoye in the northeastern part of the Altai mountain range has attracted the attention of geo-scientists for a long time, because it fills an impressive tectonic depression. The lake is 77 km long and 4 km wide, and it has a maximum water depth of 325 m. The vertical offset of the basement surface is up to 3000 m. A multidisciplinary study of the Teletsk graben was carried out during the last few years, including satellite image and air photo analysis, bathymetric-, structural- and geomorphological mapping, high-resolution seismic profiling and seismic refraction. The structural study revealed that reactivation of preexisting weak basement zones is important in controlling the basin formation. These zones separate different tectonic terranes at the contact of which the Teletsk graben developed. This study identifies the significance of the basin in the regional neotectonic context. It shows that the major vertical movements are restricted to the basin itself, but do not characterize the whole region. Outside of the basin, recent tectonic structures have the same pattern as adjacent areas of Northeast Altai and West-Sayan. Quaternary glaciations have had no major influence on the basin formation. Two stages of faulting are identified. First, transpressive movements restricted to discrete (reactivated) fault zones controlled the opening of the basin. In the second stage, normal faulting is dominant and is responsible for the modern basin outline. An echo-sounding survey led to the recognition of several morphological characteristics of the lake bottom. In the southern part, the uppermost sediments seem slightly disturbed, whereas further north, transverse ridges and slope breaks are increasingly common. The deepest part of the lake is located in a highly disturbed zone of normal fault-bounded blocks. The structural difference between the southern and northern subbasins is supported by the interpretation of a deep seismic refraction profile which indicates a substantial increase of basement isochores in the area where the reactivated Teletsk (Paleozoic) shear zone crosses the lake. Correlation of high-resolution seismic profiles suggests that the Teletsk graben started to evolve during the Pleistocene, and that its present shape was formed in two stages. The first stage was responsible for the opening of the southern basin. It probably started in the Middle Pleistocene. A second kinematic stage induced by a sinistral reactivation of the NE striking West-Sayan fault initiated the opening of the different segments of the northern subbasin due to opposite movements between the reactivated Teletsk and West-Sayan faults. This second stage was active after the end of Late Pleistocene glaciations and during the Holocene. The recent lateral extension and the related N–S-trending normal faults result from a change in tectonic regime, with related extensional movements along the main reactivated fault zones. These recent movements result in the lateral escape of the lake borders and the collapse of the area between them.

Concept, construction and commissioning of an alignment system for deep X-ray lithography

An in-house-made alignment system for deep X-ray lithography is presented that features low costs, low weight and little demand in space. Synchrotron radiation illuminates alignment marks on mask and substrate. The radiation transmitted through these alignment marks is detected by X-ray-sensitive diodes. The mask is fixed to the vacuum chamber, whereas the substrate is mounted on a six-axis kinematic stage. The information about the degree of alignment is the obtained photocurrent, which reaches its maximum at the best alignment position. Variation of the photocurrent is an error signal in a feedback loop. A slit screen protects the resist in the pattern area from irradiation during the alignment procedure. The features of the alignment system offer guidelines for research groups interested in upgrading their system as well.

Effects of metamorphosis on the aquatic escape response of the two-lined salamander (Eurycea bislineata).

Although numerous studies have described the escape kinematics of fishes, little is known about the aquatic escape responses of salamanders. We compare the escape kinematics of larval and adult Eurycea bislineata, the two-lined salamander, to examine the effects of metamorphosis on aquatic escape performance. We hypothesize that shape changes associated with resorption of the larval tail fin at metamorphosis will affect aquatic locomotor performance. Escape responses were recorded using high-speed video, and the effects of life stage and total length on escape kinematics were analyzed statistically using analysis of covariance. Our results show that both larval and adult E. bislineata use a two-stage escape response (similar to the C-starts of fishes) that consists of a preparatory (stage 1) and a propulsive (stage 2) stroke. The duration of both kinematic stages and the distance traveled during stage 2 increased with total length. Both larval and adult E. bislineata had final escape trajectories that were directed away from the stimulus. The main kinematic difference between larvae and adults is that adults exhibit significantly greater maximum curvature during stage 1. Total escape duration and the distance traveled during stage 2 did not differ significantly between larvae and adults. Despite the significantly lower tail aspect ratio of adults, we found no significant decrease in the overall escape performance of adult E. bislineata. Our results suggest that adults may compensate for the decrease in tail aspect ratio by increasing their maximum curvature. These findings do not support the hypothesis that larvae exhibit better locomotor performance than adults as a result of stronger selective pressures on early life stages.

Numerical Analysis of Magnetic Field Amplification by Turbulence

We apply a Fourier spectral numerical method to the study of three-dimensional incompressible MHD turbulence with a magnetic Prandtl number Pr ≥ 1. We examine the processes by which an initially weak, large-scale seed magnetic field and an initially weak, small-scale, impulse-like seed magnetic field are amplified. We find that in both cases the magnetic energy spectrum grows at all scales. The growth rates at different amplification stages are analyzed. For a large-scale seed magnetic field, the magnetic energy density grows as ~t2 for the first few turbulence eddy turnover times, followed by a dynamic growth stage, where nonlinear interactions between different scales of the turbulence contribute to an exponential growth rate that is largely determined by the turbulence eddy turnover time. For a seed magnetic field that is initially set up at a small scale in the turbulence, during the kinematic development stage, the growth rate of magnetic energy is ∝1/τmax, where τmax is the eddy turnover time of the smallest eddies of the turbulence. The kinematic growth stage is followed by a dynamic growth stage, where nonlinearity plays important role. During such dynamic growth stage, the growth rate of total magnetic energy is determined by both the magnetic energy amplification within the turbulence inertial range and that within the turbulence dissipation range.

Study on Optimum Design of Linkage in Consideration of Geometry and Dynamics.

Inertia forces of high speed link mechanism depend on both the accelerations and the masses of moving links. Therefore, it is important for designing linkage to optimize the dimensions of links and to control the distributions of masses. In the present design method of planar linkage, the inertia forces do not be considered in the kinematic design stage. After deciding the dimensions, the inertia forces are balanced by using the method of redistributing masses, but it will be difficult for a link mechanism to improve dynamic characteristics greatly. This paper investigates the relationship between the geometric factors and dynamic characteristics for a planar link mechanism. A new graphical design method to improve dynamic characteristics in the geometric design of linkage is proposed. Two examples of mechanism are given, one is designed in considering the dynamic characteristics in the kinematic design stage, and the other is designed without considering it. Then the dynamic optimum design for two mechanisms are performed, and the shapes of coupler and lever of two mechanisms are given by using the small element method. It is known through comparing two mechanisms that the consideration of dynamics in the kinematic design stage is necessary to design a planar linkage with good dynamic characteristics.

Constraints on the kinematics of post-orogenic extension imposed by stretching lineations in the Aegean region

New kinematic data from shear zones of Tertiary age in the metamorphosed basement of the Aegean region, in combination with published kinematic, lithological and palaeomagnetic data, have enabled us to determine a detailed kinematic evolution of the region during post-orogenic extension in the Aegean. Three distinct stages are recognised. Firstly, extension of both the western and eastern Aegean started in the Late Oligocene–Early Miocene (∼36–25 Ma ago), initially in an ∼023° direction. Stage two started shortly after this with the division of the Aegean crust into the West Aegean Block (a coupled assemblage of small blocks) bound on its northwestern and southeastern margins by the Scutari–Pec Line and Mid-Cycladic Lineament (fracture zones), respectively. Between 25 Ma and ∼3 Ma the West Aegean Block underwent ∼30° clockwise rotation, whilst the eastern Aegean underwent, on average, ∼19° anticlockwise rotation. Rotation of the West Aegean Block as a semi-coherent block was aided by the relative `coolness' of the block compared to the `warmer' eastern Aegean region. As the crust thinned and rotated, the NW–SE-trending faults which characterise the West Aegean Block were cross-cut by E–W-trending faults. In the latest Miocene–Pliocene, the thermal front migrated westwards into the West Aegean Block and the Mid-Cycladic Lineament ceased activity. The final kinematic stage marked the start of the subdivision of the West Aegean Block into two portions in the Pliocene. The southeastern portion (NW Cycladic area) coupled with the SW Cycladic area to form a Central Aegean Block that started to translate southwest. The northern and western portion rotated a further ∼10–15° clockwise whilst the southeastern rim rotated anticlockwise. These data demonstrate that Aegean post-orogenic extension is not dominated by a single block rotation or radial spreading event, but is characterised by the sequential formation and reformation of lithospheric-scale blocks that have developed in response to large-scale partitioning of rotational strain.

Influence of spawning on swimming performance and muscle contractile properties in the short‐horn sculpin

The total distance travelled during the first two kinematic stages of the escape response of short‐horn sculpin was significantly greater in post spawning fish (0·41 L) than in gravid fish (0·23 L). The maximum velocity of the snout during the C‐bend was significantly higher (5·6 L s−1) in postspawning fish than in gravid fish (3·8 L s−1). To investigate some of the mechanisms underlying changes in swimming performance, the contractile properties of fast muscle fibres were determined in fish of similar body length. The rate of tetanic force relaxation (time from last stimulus to 50% peak force) was 34% faster in gr avid than in postspawning fish. Maximum contraction velocity, determined by the slack‐test method, was significantly higher in gravid than in postspawning fish (6·8 v. 5·9 muscle lengths s−1). In contrast, both maximum isometric stress and power output (determined from the force–velocity relationship) were &gt;50% higher in fibres from postspawning than from gravid fish, even though myofibrillar protein and water contents were similar (120 mg g−1 wet mass and 86% of body mass, respectively). The results show that swimming performance and the contractile properties of fast muscle fibres vary with the reproductive cycle in short‐horn sculpin acclimated to the same photoperiodic and temperature regime.

Multistage Multiobjective Optimization of Gearboxes

The problems of kinematic and strength designs of multispeed gearboxes are formulated as multiobjective optimization problems. In the kinematic design stage, the speeds of all the shafts, the number of teeth on various gears and the gear module are selected so as to minimize the deviation of output speeds from specified values and the overall center distance of the gearbox. In the strength design stage, the face widths of the various gear pairs are chosen so as to minimize the volume of the material of the gears and to maximize the power transmitted by the gearbox. A goal programming approach is suggested for the solution of the multiobjective nonlinear constrained optimization problem by treating the ideal feasible solutions as the goals for the corresponding objective functions. The utility of the resulting computer program is demonstrated through the design of six- and 18-speed gearboxes. The present methodology offers the feasibility of automating the design of gearboxes by incorporating all the (conflicting) design requirements and objectives.

Prolonged and burst swimming in anadromous and freshwater threespine stickleback, Gasterosteus aculeatus

Prolonged and burst, or "fast-start," swimming were measured in anadromous and resident freshwater sticklebacks. In prolonged swimming tests conducted at 5 body lengths/s, anadromous sticklebacks fatigued less easily than freshwater sticklebacks. Anadromous sticklebacks also had larger pectoral fins and less robust bodies than freshwater sticklebacks. At the start of a burst swimming sequence (kinematic stage 1), freshwater sticklebacks curved their bodies more than anadromous sticklebacks, but trailing-edge amplitudes were the same in both forms. During kinematic stage 2, freshwater sticklebacks had greater trailing-edge amplitudes than anadromous fish, but body curvature was the same in both forms. During burst swimming, freshwater sticklebacks attained both higher maximum and mean velocities than anadromous sticklebacks and also travelled a greater distance in the first 50 ms (2.67 vs. 1.98 cm). These results are discussed with respect to differences in habitat and life histories in the two forms of Gasterosteus.