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Fig. 10 in Mode of life and hydrostatic stability of orthoconic ectocochleate cephalopods: Hydrodynamic analyses of restoring moments from 3D printed, neutrally buoyant models

Fig. 10. Hydrodynamic restoration of the Baculites compressus 3D printed model following overdamped harmonic motion. Apertural angle (θa) measured in degrees as a function of time after rotating approximately 38° from the equilibrium orientation. An angle of -90° represents a condition where the aperture is directed downwards. The function of decay in θa with time is represented by the grey dashed curve. Note that this model restores more quickly and does not oscillate about the equilibrium orientation.

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Fig. 7 in Mode of life and hydrostatic stability of orthoconic ectocochleate cephalopods: Hydrodynamic analyses of restoring moments from 3D printed, neutrally buoyant models

Fig. 7. Virtual and physical hydrostatic models of Nautilus pompilius with computed percentage of the phragmocone emptied for neutral buoyancy (Φ) and hydrostatic stability (St). The tip of the up-side-down pyramid = center of buoyancy. The tip of the right-side-up pyramid = total center of mass. A. External view of the virtual model. B. Medial section of the virtual model with each component of unique density (green, soft body; red, cameral gas; blue, cameral liquid; grey, shell). C. Modified virtual model with simplified internal geometry and bismuth counterweight (yellow, PLA plastic; red, air; blue, liquid; purple, bismuth counterweight). D. Neutrally-buoyant, 3D printed model. The differences in Φ and the apertural angle (θa) are a result of the mass discrepancy (Table 5) and irregular geometry of the balloon. The error in St was computed assuming that the total mass discrepancy was distributed in the positive or negative z-directions.

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Fig. 9 in Mode of life and hydrostatic stability of orthoconic ectocochleate cephalopods: Hydrodynamic analyses of restoring moments from 3D printed, neutrally buoyant models

Fig. 9. Virtual and physical hydrostatic models of Baculites compressus with computed percentage of the phragmocone emptied for neutral buoyancy (Φ) and hydrostatic stability (St). Green, soft body; grey, shell; red, gas; blue, liquid; yellow, PLA plastic; purple, bismuth counterweight; B, center of buoyancy; M, center of mass. A. Virtual model with an even distribution of cameral liquid and gas in the phragmocone (center of mass of cameral liquid and gas = center of volume of the phragmocone; cameral liquid and gas not shown). B. Modified virtual model with simplified internal geometry ("Modified 1" in Table 3). C. Neutrally-buoyant, 3D printed model. D. Modified virtual model with simplified internal geometry and axel hole through pivot point of rotation ("Modified 2" in Table 3). E. Neutrally-buoyant, 3D printed model fixed to an axel and silicone tubing used to supply thrust in the ventral direction. For this model, the mass discrepancy (Table 5) resulted in a slightly lower of 97.3%, but was held constant at 100%. All computed errors in St were computed assuming that the total mass discrepancy was distributed in the positive or negative z-directions.

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Fig. 6 in Mode of life and hydrostatic stability of orthoconic ectocochleate cephalopods: Hydrodynamic analyses of restoring moments from 3D printed, neutrally buoyant models

Fig. 6. Hydrostatic models of Baculites compressus with computed percentage of the phragmocone emptied for neutral buoyancy (Φ) and hydrostatic stability (St). All models are oriented dorsum-left. The centers of buoyancy are marked by the tip of the higher pyramid. The total centers of mass are marked by the tip of the lower pyramid. Each material of unique density is designated a color (green, soft body; red, cameral gas; blue, cameral liquid; transparent grey, shell). A. Virtual model with 40% body chamber length to total length (BCL/L). B. Virtual model with 33% BCL/L and adorally distributed cameral liquid. C. Virtual model with 33% BCL/L and adapically distributed cameral liquid. D, E. B. compressus model modified with a concave dorsum similar to B. grandis and 33% BCL/L. Adorally (D) and adapically (E) distributed cameral liquid.

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Fig. 3. Full 3D in Mode of life and hydrostatic stability of orthoconic ectocochleate cephalopods: Hydrodynamic analyses of restoring moments from 3D printed, neutrally buoyant models

Fig. 3. Full 3D model of Baculites compressus with model components. A. Complete, digitally-reconstructed shell rendered in X-ray view to show internal structure. B. Three-dimensional model the soft body. C. Three-dimensional model of the cameral volumes within the phragmocone.

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Fig. 4 in Mode of life and hydrostatic stability of orthoconic ectocochleate cephalopods: Hydrodynamic analyses of restoring moments from 3D printed, neutrally buoyant models

Fig. 4. Generation of a 3D printed model of Nautilus pompilius with theoretically equal physical properties to the virtual counterparts. A. Original virtual model from Peterman et al. (2019: fig. 2.5). B. Modified virtual model with simplified internal geometry. The center of buoyancy remains the same because external geometry does not change. The total center of mass, however, is corrected by a bismuth counterweight of known volume, density, and mass. C. 3D printed posterior half of the physical model with bismuth counterweight in the computed position. D. Anterior half of the physical model showing the one-way valve for liquid to exit upon displacement by an air-filled balloon. E. Neutrally buoyant physical model with the required volume to liquid ratio for neutral buoyancy. This computed volume of air is inserted through a one-way entrance valve into the internal balloon. Tracking points are placed parallel to the aperture in order to analyze movement in a hydrodynamic setting.

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Fig. 5 in Mode of life and hydrostatic stability of orthoconic ectocochleate cephalopods: Hydrodynamic analyses of restoring moments from 3D printed, neutrally buoyant models

Fig. 5. Position of the ventral tracking point (V) and umbilical tracking point (U) as a function of time measured with the physics modeling software (Tracker 4.11.0; Brown 2017). Note that the rotation of the aperture is coupled with translational motion, resulting in complex movement.

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Fig. 11 in Mode of life and hydrostatic stability of orthoconic ectocochleate cephalopods: Hydrodynamic analyses of restoring moments from 3D printed, neutrally buoyant models

Fig. 11. Thrust required to change the Baculites compressus model orientation (θa). A. Thrust Scenario 1: A continuous thrust supplied to the venter with a similar thrust ratio to Nautilus (Table 1). The average change from a vertical resting orientation (Δ θpeak) is 22.7°. B. Thrust Scenario 2: Periodic pulses from a pump with a simulated mantle cavity of 20% soft body volume of B. compressus (Table 1). The average change from a vertical resting orientation ( Δ θpeak) is 25.6°. C. Thrust Scenario 3: Periodic pulses from a pump with a thrust ratio between Sepia officinalis and Loligo vulgaris (Table 1). The average change from a vertical resting orientation (Δ θpeak) is 72.2°. Average peak thrust (Fpeak) error bars represent one standard deviation calibrated from 30 second intervals of pumping.

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Fig. 8 in Mode of life and hydrostatic stability of orthoconic ectocochleate cephalopods: Hydrodynamic analyses of restoring moments from 3D printed, neutrally buoyant models

Fig. 8. Hydrodynamic restoration of the Nautilus pompilius 3D printed model following underdamped harmonic oscillation. Apertural angle (θa) measured in degrees as a function of time after rotating approximately 38° from the equilibrium orientation. An angle of zero represents a condition where the aperture is horizontally oriented. Open dots represent the peaks used to calculate decay in amplitude with time (grey dashed curves).

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Fig. 2 in Mode of life and hydrostatic stability of orthoconic ectocochleate cephalopods: Hydrodynamic analyses of restoring moments from 3D printed, neutrally buoyant models

Fig. 2. Shell and septum thickness measured from three specimens of Baculites compressus (WSU-1400, WSU-1401, and WSU-1405). Exponential curves were fit to these points to define thickness for the full 3D model as a function of whorl height.

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Fig. 1 in Mode of life and hydrostatic stability of orthoconic ectocochleate cephalopods: Hydrodynamic analyses of restoring moments from 3D printed, neutrally buoyant models

Fig. 1. Three-dimensional reconstruction of a fragmentary baculite Baculites compressus Say, 1820 (WSU-1400) from the late Campanian Pierre Shale of Meade County, South Dakota. A. Model of a fragmentary specimen generated by photogrammetry with the software (3DF Zephyr). B. Broken septum isolated from the photogrammetry model. C. Suture pattern. D. Complete septum created by reconstructing the higher-order frilling with the suture pattern as a template.

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Fig. 3. The lecanocrinid species Ammonicrinus doliiformis Wolburg, 1938a in Revision of the flexible crinoid genus Ammonicrinus and a new hypothesis on its life mode

Fig. 3. The lecanocrinid species Ammonicrinus doliiformis Wolburg, 1938a (for 1937) from the Selscheid Formation of Ohle, Sauerland (Wolburg 1938a: 230). A. Casts of nearly complete specimen. Specimen attached to a brachiopod valve (right arrow) (A1), showing the characteristic triangular connection between mesi− and dististele (left arrow) and slightly compressed mesistele (from Wolburg 1938a: pl. 17: 1); detail view of the attachment disc (arrow) (A2), encrusting the brachiopod (from Wolburg 1938a: pl. 18: 8); detail view of the triangular connection between mesi− and dististele (arrow) (A3) (from Wolburg 1938a: pl. 17: 6a); detail view of the coiled, slightly compressed mesistele (A4) (from Wolburg 1938a: pl. 17: 4). B. Former assumed reconstruction of life mode, figured with a crown that protrudes toward the lateral−exterior (arrow) (from Wolburg 1938a: 240, fig. 5). C. Former assumed reconstruction of the crown (1938a: 233, fig. 4). Not to scale.

opencc-by-4.0Nov 2010View details →
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Fig. 4 in Revision of the flexible crinoid genus Ammonicrinus and a new hypothesis on its life mode

Fig. 4. First illustration of the actual plate diagram and definition of genus Ammonicrinus as a lecanocrinid Flexibilia by Ubaghs (1952). A. Ammonicrinus doliiformis Wolburg, 1938a (for 1937), SMF−XXIII−165a from the "Rommersheim Formation" of the Auburg, Gerolstein, Eifel, Germany (Ubaghs 1952: 220). View of coiled mesistele (A1); view of exposed proxistele (A2) (taken from Ubaghs 1952: pl. 3: 1, 3). B. Anomalous crown of "Ammonicrinus wanneri" from the "Rommersheim Formation" of the Steineberg, N of Kerpen, Eifel, Germany (Ubaghs 1952: 220) (= holotype of A. jankei sp. nov., no. SMF−XXIII−167a) coiled by the mesistele. View of the coiled mesistele (B1) (Ubaghs 1952: pl. 1: 3); partly excavated crown (B2), showing radiating ridges on radials and one slightly lobe−like enlarged appendage that possibly could support the lateral water respectively faecal−ejection (arrow) (Ubaghs 1952: pl. 1: 4); excavated crown in lateral view (B3, B4), the second "radianal plate" respectively "supplementary plate" (see arrows) is based on an anomaly (Ubaghs 1952: pl. 2: 3, 2); plate diagram (B5), showing the two anomalous plates (arrows) (slightly modified after Ubaghs 1952: 205, fig. 1); schematic drawing of the coiled specimen (B6); reconstruction of the assumed living feeding position (B7) (Ubaghs 1952: 110, fig. 2; p. 223, fig. 5). Not to scale.

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Fig. 14. A in Revision of the flexible crinoid genus Ammonicrinus and a new hypothesis on its life mode

Fig. 14. A. Schematic reconstruction of Ammonicrinus (strongly modified after Piotrowski 1977: 209, fig. 3) of a feeding Ammonicrinus within low−intensity current water. Alternating water pressure was possibly generated in the interior of the enrolled proximal stem by slow, bellow−like partial opening and closing (red arrows) of the base of the central mass; due to the synarthrial (bifacial) articulation of the ammonicrinid mesistele that developed two huge ligamentary facets (orange), separated by the fulcrum, bellow−like partial opening could possibly enabled by stiffening of the outer ligaments (see orange bars in A1); closing could be controlled by stiffening of the inner ligaments (see orange bars in A2). A1, suction during opening may result from low−pressure (P−) and create an ingesting water flow (blue arrow); A, ejection during closure (red arrow) resulted from overpressure (P+); to minimise faecal recycling, 2 the water ejection may have occurred laterally (blue arrows), feasibly at both lateral centres, which have "openings". B. Lobe−like enlarged appendages (framed in red) could possibly support the lateral water faecal−ejection (modified from Ubaghs 1952: pl. 1: 4). C. Reconstruction of a feeding "encased runner−type" of A. leunisseni sp. nov., attached to a tabulate coral (model); the spined specimen dwelled enrolled on the muddy seafloor; alternating water pressure was obviously generated in the interior of the enrolled proximal stem globe by non−muscular, probably MCT−controlled, slow, bellow−like partial opening and closing of the oblate sphere at its bottom (dashed arrow); suction during opening created an ingesting water flow (see arrow on the left), which was funnelled in a "canal", formed by the unspined interior of the columnals of the mesistele, whose U−shaped LCEE additionally formed a protection against immersive sediment; ejection during closure resulted from overpressure; to minimise faecal recycling, the water ejection occurred supposably laterally, feasibly at both lateral centres, which accordingly show "openings" (see arrows on the right). Not to scale.

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Fig. 9. Lecanocrinid Ammonicrinus species. A–J. Ammonicrinus wanneri Springer, 1926. A–I in Revision of the flexible crinoid genus Ammonicrinus and a new hypothesis on its life mode

Fig. 9. Lecanocrinid Ammonicrinus species. A–J. Ammonicrinus wanneri Springer, 1926. A–I. From the Eifel (locality 3, Appendix 1), Germany, Lower Givetian (Middle Devonian). J. From the Eifel (locality 7, Appendix 1), Germany, Lower Givetian (Middle Devonian). A. Lateral view of a partly preserved specimen (GIK−2133) with coiled mesistele. B. Lateral view, respectively view of external columnal flanks of the coiled mesistele of a partly preserved specimen (GIK−2134) with one preserved, postulated cup ossicle (arrow). C. View of external columnal flanks of the mesistele of a partly preserved specimen (GIK−2135). D. Lateral view, respectively view of external columnal flanks of the coiled mesistele of a partly preserved specimen (GIK−2136), +

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Fig. 8 in Revision of the flexible crinoid genus Ammonicrinus and a new hypothesis on its life mode

Fig. 8. Reconstruction of a spined "settler−type" of Ammonicrinus leunisseni sp. nov., attached to a brachiopod brachial valve (Schizophoria sp.); the original (GIK−2103) from locality 6 is figured in Fig. 12L. Not to scale.

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Fig. 13 in Revision of the flexible crinoid genus Ammonicrinus and a new hypothesis on its life mode

Fig. 13. Postmortem epizoan encrusting on disarticulated columnals of the lecanocrinid crinoid species Ammonicrinus sulcatus Kongiel, 1958. A–G. From the Eifel (locality 1, Appendix 1), Germany, upper Eifelian (Middle Devonian). H, I. From the Eifel (locality 2, Appendix 1), Germany, upper Eifelian (Middle Dvonian). A. View of external flanks of a pluricolumnal of the mesistele (GIK−2147), encrusted by a trepostomate bryozoan (Leptrotrypella(?) sp.) (arrows). B. Internal view of a pluricolumnal of the distal−most mesistele (GIK−2148), encrusted by a cystoporate bryozoan (Eridopora(?) sp.) (arrows). C. Facet view of an isolated, distal−most columnal of the mesistele (GIK−2149), encrusted by a trepostomate bryozoan [Leptrotrypella(?) sp.] (arrows). D. External flanks of a pluricolumnal of the mesistele (GIK−2150), encrusted by a trepostomate bryozoan (Eostenopora(?) sp.) (see arrows below); the bryozoan is infested by a crinoid attachment disc (arrows in D2); general view (D1), detail view (D2). E. View of external flanks of a pluricolumnal of the mesistele (GIK−2151), encrusted by a crinoid holdfast (arrow). F. Facet view of an isolated columnal of the mesistele (GIK−2152), encrusted by a cystoporate bryozoan (Cyclotrypa(?) sp.) (arrows). G. Facet view of a pluricolumnal of the mesistele (GIK−2153), encrusted by a cystoporate bryozoan (Cyclotrypa(?) sp.) (arrows). H. Facet view of an isolated columnal of the mesistele (GIK−2154) (H1), encrusted by microconchid valves (see arrows in detail view (H2). I. Facet view of an isolated columnal of the mesistele (GIK−2155), encrusted by a holdfast of a fenestrate bryozoan (arrow). Scale bars 10 mm.

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Fig. 2 in Revision of the flexible crinoid genus Ammonicrinus and a new hypothesis on its life mode

Fig. 2. The first figures of Ammonicrinus from Springer (1926) and Krause (1927). A. Ammonicrinus wanneri Springer, 1926 (from Springer 1926: pl. 6: 4a, b). A1, view of the extetrnal flanks of the coiled mesistele; A2, coiled mesistele in lateral view. B. Ammonicrinus leunisseni sp. nov. (= "A. wanneri" in Springer 1926: pl. 6: 5, 5b). B1, view of the extetrnal flanks of the coiled mesistele; B2, coiled mesistele in lateral view. C. Photograph of the holotype of Ammonicrinus wanneri Springer, 1926, USNM−S2115; lateral view of coiled mesistele; connection between mesi− and dististele, dististele and attachment missing (see fracture surface at distal mesistele). D. Photograph of USNM−S2115, the Springer (1926) original of "Ammonicrinus wanneri" (= A. leunisseni sp. nov. herein); lateral view of coiled mesistele; connection between mesi− and dististele, dististele and attachment missing (see fracture surface at distal mesistele). E. Ammonicrinus doliiformis Wolburg, 1938a (for 1937) (= "A. wanneri" in Krause 1927: pl. 8: 4, 2). E1, view of the extetrnal flanks of the coiled mesistele; E2, coiled mesistele in lateral view. A–D from the Middle Devonian, Eifel Limestone; Prüm, Eifel, Germany (Springer 1926: 25); E from the Middle Devonian of Sötenich, Eifel (Krause 1927: 456). A, B, E not to scale; C, D scale bars 10 mm.

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Fig. 1. A in Revision of the flexible crinoid genus Ammonicrinus and a new hypothesis on its life mode

Fig. 1. A. Reconstruction of the Ammonicrinus life time position (modified after Piotrowski 1977: 208, fig. 2). B. Ammonicrinus plate diagram (not to scale).

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Fig. 7 in Revision of the flexible crinoid genus Ammonicrinus and a new hypothesis on its life mode

Fig. 7. Ammonicrinus leunisseni sp. nov. A. Reconstruction of a "encased runner−type" of A. leunisseni sp. nov. attached to a tabulate coral (model); the spined specimen dwelled enrolled on the muddy seafloor. B. The original (GIK−2102) from the Eifel (locality 6, Appendix 1), Germany, Lower Givetian (Middle Devonian); showing slightly compressed proximal mesistele. A not to scale, B scale bar 10 mm.

opencc-by-4.0Nov 2010View details →

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Last verified 2026-04-29Open record