Disk Pairs Research Articles

The Disk Orientations of Perseus Protostellar Multiples at ∼8 au Resolution

We present a statistical characterization of circumstellar disk orientations toward 12 protostellar multiple systems in the Perseus molecular cloud using the Atacama Large Millimeter/submillimeter Array at Band 6 (1.3 mm) with a resolution of ∼25 mas (∼8 au). This exquisite resolution enabled us to resolve the compact inner-disk structures surrounding the components of each multiple system and to determine the projected 3D orientation of the disks (position angle and inclination) to high precision. We performed a statistical analysis on the relative alignment of disk pairs to determine whether the disks are preferentially aligned or randomly distributed. We considered three subsamples of the observations selected by the companion separations a < 100 au, a > 500 au, and a < 10,000 au. We found for the compact (<100 au) subsample, the distribution of orientation angles is best described by an underlying distribution of preferentially aligned sources (within 30°) but does not rule out distributions with 40% misaligned sources. The wide companion (>500 au) subsample appears to be consistent with a distribution of 40%–80% preferentially aligned sources. Similarly, the full sample of systems with companions (a < 10,000 au) is most consistent with a fractional ratio of at most 80% preferentially aligned sources and rules out purely randomly aligned distributions. Thus, our results imply the compact sources (<100 au) and the wide companions (>500 au) are statistically different.

Cone-beam CT sampling incompleteness: analytical and empirical studies of emerging systems and source-detector orbits.

Motivated by emerging cone-beam computed tomography (CBCT) systems and scan orbits, we aim to quantitatively assess the completeness of data for 3D image reconstruction-in turn, related to "cone-beam artifacts." Fundamental principles of cone-beam sampling incompleteness are considered with respect to an analytical figure-of-merit [FOM, denoted ] and related to an empirical FOM (denoted ) for measurement of cone-beam artifact magnitude in a test phantom. A previously proposed analytical FOM [, defined as the minimum angle between a point in the 3D image reconstruction and the x-ray source over the scan orbit] was analyzed for a variety of CBCT geometries. A physical test phantom was configured with parallel disk pairs (perpendicular to the -axis) at various locations throughout the field of view, quantifying cone-beam artifact magnitude in terms of (the relative signal modulation between the disks). Two CBCT systems were considered: an interventional C-arm (Cios Spin 3D; Siemens Healthineers, Forcheim Germany) and a musculoskeletal extremity scanner; Onsight3D, Carestream Health, Rochester, United States)]. Simulations and physical experiments were conducted for various source-detector orbits: (a)a conventional 360deg circular orbit, (b)tilted and untilted semi-circular (196deg) orbits, (c)multi-source (three x-ray sources distributed along the axis) semi-circular orbits, and (d)a non-circular (sine-on-sphere, SoS) orbit. The incompleteness of sampling [] and magnitude of cone-beam artifacts () were evaluated for each system and orbit. The results show visually and quantitatively the effect of system geometry and scan orbit on cone-beam sampling effects, demonstrating the relationship between analytical and empirical . Advanced source-detector orbits (e.g., three-source and SoS orbits) exhibited superior sampling completeness as quantified by both the analytical and the empirical FOMs. The test phantom and metric were sensitive to variations in CBCT system geometry and scan orbit and provided a surrogate measure of underlying sampling completeness. For a given system geometry and source-detector orbit, cone-beam sampling completeness can be quantified analytically (in terms arising from Tuy's condition) and/or empirically (using a test phantom for quantification of cone-beam artifacts). Such analysis provides theoretical and practical insight on sampling effects and the completeness of data for emerging CBCT systems and scan trajectories.

A comparative study on the acetone sensing properties of ZnO disk pairs, flowers, and walnuts prepared by hydrothermal method

The synthesis of sensing materials in suitable morphology and microstructure is critical for fabricating fast, highly responsive, and reliable acetone sensing devices for human safety and health. Herein, ZnO disk pairs, flower-like, and walnut-like hierarchical architectures were prepared by varying the relative amount of citric acid and NaOH to Zinc acetate dihydrate during the hydrothermal process. At the lowest prime working temperature, the ZnO flowers exhibited the highest gas response, stability, and selectivity towards acetone due to the highest degree of (001) facet exposure and Schottky barrier height, the largest BET specific surface area and BJH average pore size. At the same temperature, the ZnO walnuts displayed the shortest response/recovery time and the lowest limit of detection due to the highest content of surface oxygen vacancy and the high reactivity of adsorbed O2– ions; the ZnO disk pairs showed unique selectivity towards ethylene glycol monomethyl ether due to the highest degree of (100) facet exposure and the smallest BJH average pore size. Replacing Zinc acetate dehydrate by Zinc nitrate hexahydrate improved the acetone sensing performance of the ZnO flowers in terms of response value, stability, and selectivity at the expense of a higher LOD and a slower recovery speed.

FlexLab and LevLab: A Portable Control and Mechatronics Educational System

This article describes a compact, low-cost, single-board FlexLab/LevLab electromechanical system for use in teaching modeling, dynamics, and control of mechatronic systems. The portable educational platform proposed in this article enables a flipped-lab approach where students can do experimental work outside a dedicated lab facility and so, achieve a better understanding through more extensive hands-on experiences. The system has actuators, sensors, and power electronics implemented on a 70 $\,\times \,$ 100 mm printed circuit board. Mechanical motion in up to three degrees of freedom (DoFs) is implemented using on-board spiral coils as Lorentz actuators to drive moving permanent magnets (PM) with Hall effect position sensing on each magnet. The maximum magnet motion range is 4 and 3 mm in the vertical direction for the FlexLab and LevLab, respectively, and the positioning noise of the Hall effect sensors with an oversampling filter is approximately 0.2 $\mu{\rm m}$ RMS. In the FlexLab configuration, up to three PM disk pairs can be mounted on a flexible cantilever beam in locations which interact with three spiral coils. This configuration allows modeling, measurement, and control of second-, fourth-, and sixth-order mass–spring system dynamics. In the LevLab configuration, the board can implement both single- and three-DoF magnetic suspension systems via Lorentz forces on either a spherical PM or three pairs of disk PMs on a triangular backbone.

Hydrodynamic Lubricant Film Separation During Codirectional and Counter-Directional Rotations of Disengaged Wet Clutch Packs

Abstract The parasitic drag losses incurred by wet clutches, used in transmission systems, can significantly affect vehicular powertrain efficiency. This paper presents a novel implicit solution for hydrodynamic parasitic drag losses of disengaged clutches. These are generated by conjunctional friction, taking into account lubricant film separation during codirectional and counter-directional disk pair rotations. Lubricant film rupture is considered through application of incipient reverse flow boundary condition, which is representative of lubricant film separation. The results point to the operating conditions at which significant power losses occur. In particular, the time efficient model is able to represent the small losses incurred during codirectional rotation of disk pairs.

Application of Suspended Nanoboric Acid as an Efficient Lubrication Additive in Engine Oil

Lubricants play a vital role in machine life and performance, reducing friction and wear and preventing component failure. Performance-enhancing additives are a vital part of today’s modern lubricants. In response to this need, this experimental work presents the development of the new suspended nanoboric acid (nBA) additive added in engine oil that can drastically lowered friction and wear.This is a new invention of nBA additive hold in suspension and added into 5W-40 fully synthetic commercial lubricating oil. This invention is confidential and realized by Tribor ARGE Co. in Teknopark of YILDIZ Technical University in Istanbul-TURKEY.The particle size of nBA is determined with (Transmission Electron Microscopy) (TEM). Turbiscan Tower Stability Analyzer results proved that nBA particles were in suspension in commercial engine oil. Suspended nBA in engine oil is applied between ball and disk system in order to investigate their effect on friction and wear under lubricated conditions. Simulation and measurement of friction and wear were conducted using a ball on disk reciprocating tribometer UMT-3. Surface analysis was performed using 3D digital optical microscope and surface roughness, Field Emission Scanning Electron Microscope (FESEM)/X-Ray and Atomic Force Microscopy (AFM). Boron (B) from nBA is well detected, mixed with other elements of additives and protected the surface under boundary lubrication conditions. The results indicate that nBA can considerably improve the tribological performance of a ball and disk pairs under lubricated conditions. It has found that the friction coefficient is reduced with nBA suspended engine oil and protected the surface on both ball and disk mixing with other additives.

Free-fall dynamics of a pair of rigidly linked disks

We investigate experimentally the free-fall motion of a pair of identical disks rigidly connected to each other. The three-dimensional coordinates of the pair of falling disks were constructed to quantitatively describe its trajectory, and the flow structure formed by the disk pair was identified by using dye visualization. The rigidly linked disk pair exhibits a novel falling pattern that creates a helical path with a conical configuration in which the lower disk rotates in a wider radius than the upper disk with respect to a vertical axis. The helical motion occurs consistently for the range of disk separation examined in this study. The dye visualization reveals that a strong, noticeable helical vortex core is generated from the outer tip of the lower disk during the helical motion. With an increasing length ratio, which is the ratio of the disk separation to the diameter of the disks, the nutation angle and the rate of change in the precession angle that characterize the combined helical and conical kinematics decrease linearly, whereas the pitch of the helical path increases linearly. Although all disk pairs undergo this helical motion, the horizontal-drift patterns of the disk pair depend on the length ratio.

Response of jammed packings to thermal fluctuations.

We focus on the response of mechanically stable (MS) packings of frictionless, bidisperse disks to thermal fluctuations, with the aim of quantifying how nonlinearities affect system properties at finite temperature. In contrast, numerous prior studies characterized the structural and mechanical properties of MS packings of frictionless spherical particles at zero temperature. Packings of disks with purely repulsive contact interactions possess two main types of nonlinearities, one from the form of the interaction potential (e.g., either linear or Hertzian spring interactions) and one from the breaking (or forming) of interparticle contacts. To identify the temperature regime at which the contact-breaking nonlinearities begin to contribute, we first calculated the minimum temperatures T_{cb} required to break a single contact in the MS packing for both single- and multiple-eigenmode perturbations of the T=0 MS packing. We find that the temperature required to break a single contact for equal velocity-amplitude perturbations involving all eigenmodes approaches the minimum value obtained for a perturbation in the direction connecting disk pairs with the smallest overlap. We then studied deviations in the constant volume specific heat C[over ¯]_{V} and deviations of the average disk positions Δr from their T=0 values in the temperature regime T_{C[over ¯]_{V}}<T<T_{r}, where T_{r} is the temperature beyond which the system samples the basin of a new MS packing. We find that the deviation in the specific heat per particle ΔC[over ¯]_{V}^{0}/C[over ¯]_{V}^{0} relative to the zero-temperature value C[over ¯]_{V}^{0} can grow rapidly above T_{cb}; however, the deviation ΔC[over ¯]_{V}^{0}/C[over ¯]_{V}^{0} decreases as N^{-1} with increasing system size. To characterize the relative strength of contact-breaking versus form nonlinearities, we measured the ratio of the average position deviations Δr^{ss}/Δr^{ds} for single- and double-sided linear and nonlinear spring interactions. We find that Δr^{ss}/Δr^{ds}>100 for linear spring interactions is independent of system size. This result emphasizes that contact-breaking nonlinearities are dominant over form nonlinearities in the low-temperature range T_{cb}<T<T_{r} for model jammed systems.

Localization of Radial Displacement in an Actual Isolated Transformer Winding—An Analytical Approach

In this paper, a novel analytical method is developed to locate and assess the severity of a true radial displacement (confined to 1 or 2 disk pairs) in an actual continuous-disk transformer winding. An analytical solution becomes possible mainly due to a simple manipulation of the system matrix, that is, to consider sum of the inverse squares of natural frequencies, instead of just the natural frequencies. This leads to an elegant expression that connects displacement location and its severity to changes in natural frequencies. For its implementation, short-circuit natural frequencies and variation of inductance as a function of winding length are the required inputs. Details of the derivation and experimental results are reported. In summary, it emerges that incipient and true radial displacements in an actual continuous-disk transformer winding can be localized with reasonable accuracy and a qualitative assessment of its severity is also possible.

Influence of shape and finishing on the corrosion of palladium-based dental alloys.

PURPOSEThe purpose of this study was to evaluate the effects of the surface treatment and shape of the dental alloy on the composition of the prosthetic work and its metallic ion release in a corrosive medium after casting.MATERIALS AND METHODSOrion Argos (Pd-Ag) and Orion Vesta (Pd-Cu) were used to cast two crowns and two disks. One of each was polished while the other was not. Two as-received alloys were also studied making a total of 5 specimens per alloy type. The specimens were submersed for 7 days in a lactic acid/sodium chloride solution (ISO standard 10271) and evaluated for surface structure characterization using SEM/EDAX. The solutions were quantitatively analysed for the presence of metal ions using ICP-MS and the results were statistically analysed with one-way ANOVA and a Tukey post-hoc test.RESULTSPalladium is released from all specimens studied (range 0.06-7.08 µg·cm-2·week-1), with the Pd-Cu alloy releasing the highest amounts. For both types of alloys, ion release of both disk and crown pairs were statistically different from the as-received alloy except for the Pd-Ag polished crown (P>.05). For both alloy type, disk-shaped pairs and unpolished specimens released the highest amounts of Pd ions (range 0.34-7.08 µg·cm-2·week-1). Interestingly, in solutions submerged with cast alloys trace amounts of unexpected elements were measured.CONCLUSIONShape and surface treatment influence ion release from dental alloys; polishing is a determinant factor. The release rate of cast and polished Pd alloys is between 0.06-0.69 µg·cm-2·week-1, which is close to or exceeding the EU Nickel Directive 94/27/EC compensated for the molecular mass of Pd (0.4 µg·cm-2·week-1). The composition of the alloy does not represent the element release, therefore we recommend manufacturers to report element release after ISO standard corrosion tests beside the original composition.

A single auditory tone alters the perception of multiple visual events.

We aimed to show that a single auditory tone crossmodally affects multiple visual events using a multiple stream/bounce display (SBD), consisting of two disk pairs moving toward each other at equal speeds, coinciding, and then moving apart in a two-dimensional (2-D) display. The temporal offsets were manipulated between the coincidences of the disk pairs (0 to ±240 ms) by staggering motion onset between the pairs. A tone was presented at the coincidence timing of one of the disk pairs on half of the trials. Participants judged whether the disks in each of two pairs appeared to stream through or bounce off each other. Results show that a tone presented at either of the disk pairs' coincidence points promoted bouncing percepts in both disk pairs compared to no-tone trials. Perceived bouncing persisted in the disk-pair whose coincidence was offset 60 ms before and up to more than 120 ms after the audiovisual coincidence timing of the other disk-pair. The temporal window of bounce promotion was comparable to that obtained with a conventional SBD. The interaction of a single auditory event and multiple visual events was also modulated by the kind of experimental task (the stream/bounce or simultaneity judgments). These findings suggest that, using a single auditory cue, the perceptual system resolves the ambiguity of the motion of multiple disk pairs presented within the conventional temporal window of crossmodal interaction.

Material-Selective Surface Chemistry for Nanoplasmonic Sensors: Optimizing Sensitivity and Controlling Binding to Local Hot Spots

Optical sensors utilizing the principle of localized surface plasmon resonance (LSPR) offer the advantage of a simple label-free mode of operation, but the sensitivity is typically limited to a very thin region close to the surface. In bioanalytical sensing applications, this can be a significant drawback, in particular since the surface needs to be coated with a recognition layer in order to ensure specific detection of target molecules. We show that the signal upon protein binding decreases dramatically with increasing thickness of the recognition layer, highlighting the need for thin high quality recognition layers compatible with LSPR sensors. The effect is particularly strong for structures that provide local hot spots with highly confined fields, such as in the gap between pairs of gold disks. While our results show a significant improvement in sensor response for pairs over single gold disks upon binding directly to the gold surface, disk pairs did not provide larger signal upon binding of proteins to a recognition layer (already for around 3 nm thin layers) located on the gold. Local plasmonic hot spots are however shown advantageous in combination with directed binding to the hot spots. This was demonstrated using a structure consisting of three surface materials (gold, titanium dioxide, and silicon dioxide) and a new protocol for material-selective surface chemistry of these three materials, which allows for controlled binding only in the gap between pairs of disks. Such a design increased the signal obtained per bound molecule by a factor of around four compared to binding to single disks.

Silver-Based Nanodisk Codes

We report a novel method for synthesizing silver-based nanodisk code (NDC) structures using on-wire lithography, where we employ milder synthetic and etching conditions than those used to synthesize the analogous gold structures. The silver structures exhibit stronger surface-enhanced Raman scattering signals than their Au counterparts at 633 and 532 nm excitation and, therefore, lead to lower limits of detection when used in the context of DNA-based detection assays. Finally, use of two enhancing nanostructured materials in one disk code dramatically increases the information storage density for encoding. For example, a disk code consisting of 5 gold disk pairs has 13 unique combinations of enhancing patterns, while one with 5 disk pairs that can be either gold or silver has 98.

Abrasive wear of steel against gravel with different rock–steel combinations

Wear testing equipment and tests used in research laboratories are often miniature or simplified versions of real applications. For example standardized ASTM dry sand rubber wheel abrasion test G 65 and pin abrasion test G 132 are widely used to study materials’ abrasion wear resistance. The test results, however, do not always correlate too well with the results obtained from real wear conditions. One reason for this is, for example, that in the crushing applications of mining industry the abrasive size is usually much larger than that used in the laboratory wear tests. To study the abrasive wear caused by larger size gravel, new three-body abrasion test equipment was therefore constructed. The equipment uses the pin-on-disk principle with free abrasive particles of sizes up to 10 mm. During the test the pin is repeatedly pressed against a fixed amount of abrasive that is rotating with the disk having confining walls. As the pin is prevented from touching the counterbody, only the abrasive acts as the wearing agent. Three steels of different hardnesses were cross-tested as pin–disk pairs and as pins against a rubber disk using three igneous rock gravels with different crushability properties as abrasives. The wear was measured as mass loss from both the pin and the disk, and the rock comminution was measured by sieving. The results indicate that the mechanism of wear is greatly affected by the hardness of the counterbody. When using large size abrasives, the rate of comminution is also a very important factor that can significantly affect the wear test results.

Effect of alumina air-abrasion on mechanical bonding between an acrylic resin and casting alloys

This study examined the effect of alumina air-abrasion with different pressure on bonding between an acrylic resin and casting alloys. Disk specimens (8 and 10 mm in diameter) were cast from a silver-palladium-copper-gold (Ag-Pd-Cu-Au, Castwell M.C.12) alloy and a titanium-aluminum-niobium alloy (Ti-6Al-7Nb, T-Alloy Tough). The disks were air-abraded with alumina particles (50-70 microm) under different air-pressures (0 unabraded, 0.1, and 0.6 MPa). The disk pairs were bonded together with a tri-n-butylborane (TBB)-initiated acrylic resin, and shear bond strengths were determined both before and after thermocycling. Bond strength varied from a maximum of 37.1 MPa to a minimum of 3.6 MPa for the Ag-Pd-Cu-Au alloy, whereas bond strength to Ti-6Al-7Nb alloy ranged from 34.7 MPa to 0.1 MPa. Specimens abraded with 0.6 MPa pressure recorded the greatest post-thermocycling bond strength (21.7 MPa and 17.9 MPa), and unabraded specimens showed the lowest strength (3.6 MPa and 0.1 MPa) for both alloys. Post-thermocycling bond strength to the Ag-Pd-Cu-Au alloy was higher than that to the Ti-6Al-7Nb alloy under identical air-abrading conditions. It can be concluded that alumina air-abrasion with an air-pressure of 0.6 MPa is effective in enhancing retentive characteristics of the TBB-initiated resin joined to the alloys.

Adhesive bonding of a lithium disilicate ceramic material with resin‐based luting agents

This study evaluates the bonding characteristics of a lithium disilicate-based ceramic material (IPS Empress 2). Two sizes of disk specimens of the material were made, and three groups of disk pairs were separately surface-prepared using three techniques; etching with phosphoric acid, etching with hydrofluoric acid, and air-abrasion with alumina. Each group was further divided into four sub-groups; group (i) was bonded with the Variolink II composite, (ii) was treated with the Monobond-S silane primer and bonded with the Variolink II composite, (iii) was bonded with the Super-Bond acrylic adhesive and (iv) was treated with the Porcelain Liner M silane primer and bonded with the Super-Bond acrylic adhesive. Shear bond strengths were determined before and after 100 000 thermocycles. Bond strength varied from 10.6 to 71.5 MPa before thermocycling, whereas post-thermocycling bond strength ranged from 0 to 61.2 MPa. Among the three surface preparations, hydrofluoric acid etching (HF) was most effective in enhancing bond strength of both luting materials, especially for unsilanized specimens. Application of the silane primer elevated bond strength of both luting agents regardless of surface preparation method. It can be concluded, for both luting agents, that durable bond to the Empress 2 ceramic material can be achieved through the combined application of HF and the proprietary silane primer.

Prediction of biomechanical properties of articular cartilage with quantitative magnetic resonance imaging

Quantitative magnetic resonance imaging (MRI) is the most potential non-invasive means for revealing the structure, composition and pathology of articular cartilage. Here we hypothesize that cartilage mechanical properties as determined by the macromolecular framework and their interactions can be accessed by quantitative MRI. To test this, adjacent cartilage disk pairs ( n=32) were prepared from bovine proximal humerus and patellofemoral surfaces. For one sample, the tissue Young's modulus, aggregate modulus, dynamic modulus and Poisson's ratio were determined in unconfined compression. The adjacent disk was studied at 9.4 T to determine the tissue T 2 relaxation time, sensitive to the integrity of the collagen network, and T 1 relaxation time in the presence of Gd-DTPA, a technique developed for the estimation of cartilage proteoglycan (PG) content. Quantitative MRI parameters were able to explain up to 87% of the variations in certain biomechanical parameters. Correlations were further improved when data from the proximal humerus was assessed separately. MRI parameters revealed a topographical variation similar to that of mechanical parameters. Linear regression analysis revealed that Young's modulus of cartilage may be characterized more completely by combining both collagen- and PG-sensitive MRI parameters. The present results suggest that quantitative MRI can provide important information on the mechanical properties of articular cartilage. The results are encouraging with respect to functional imaging of cartilage, although in vivo applicability may be limited by the inferior resolution of clinical MRI instruments.

Dynamic mechanical measurements on fresh-water ice during freezing and thawing: preliminary results

An automated measurement system for elastic (J' ) and viscous (J'' ) components of complex shear compliance, J* = J' – iJ'', and the elastic (G' ) and viscous (G'' ) components of complex shear modulus, G* = G' + iG'' = 1/J*, has been used to obtain these material parameters for fresh-water ice during freezing and thawing. The system is reviewed briefly and yields mechanical loss tangents, J''/J' = G''/G', the shear-wave velocity and attenuation, in addition to shear compliance and modulus, at sinusoidal vibration frequencies from 2 to 10 000 Hz at temperatures between –25 and 150°C. Results reported here are chiefly at temperatures from 10 to –10°C. The required sample disk pairs, which are clamped to a central drive plate, are prepared outside the apparatus for solids and gels. Liquids of known volume are inserted between the drive plate and surrounding clamps at a separation distance, h, by a syringe to form sample disks of area, A = Volume / h. Measurements at 58 frequencies between 2 and 10 000 Hz require 3.5 min; several measurements at each temperature were made to test for equilibrium. Results for both tap and distilled water above freezing revealed high values of elastic (J' ) compliance that decreased sharply at 100 Hz and higher frequencies. Tap-water samples with 4 to 6% by volume air bubbles were less compliant ("stiffer") above freezing than samples with 0 to 1% by volume air, but when frozen, the samples with the smaller volume of air bubbles were less compliant, that is, had higher modulus values than the samples with high air-bubble volumes. Dynamic mechanical property changes in the transition from water to ice are compared to changes previously found during phase transitions in other materials. Further investigation on the effects of air-bubble volumes on dynamic mechanical properties of both water and ice is planned. PACS Nos.: 62.30+d, 62.40+i

Tides and Markarian Activity in Karachentsev Disk Galaxy Pairs

Theories of nuclear activity mechanisms in disk galaxies range from internal (e.g., bars) to external (e.g., tidal perturbation by passing companions). The 1986–1987 simulation survey by Byrd and collaborators determined the tidal perturbation necessary to induce nuclear activity. We compare these simulations and theory with the observed Markarian activity in disk galaxy pairs in Karachentsev's 1983 list. For disk pairs, we derive the following tidal-hypothesis traits: (1) Compared with random association, there should be a numerical excess of pairs in which both galaxies are active, as well as a deficit of pairs with only one active member. There should be a small excess of pairs in which both are normal. (2) Nuclear activity will be preferentially excluded from pairs that are unequal and favorably distributed to pairs where the members are equal. (3) The product of velocity difference and separation in pairs where one or both members are active should be smaller than if both were normal. (4) The average size of pair members with one or both members active will be smaller than for pairs with both normal. A Monte Carlo match to the sample, assuming Keplerian orbits, reaches the same general conclusions as above. Observational surveys have raised doubts about the tidal explanation of Seyfert-type activity in galaxies, with some suggesting a weak or nonexistent correlation between nearby companions (tidal perturbation) and Seyfert activity as compared with a normal sample. The simulations show a several hundred million year delay in the appearance of activity after perturbation and a similar duration. Movement apart during delay and duration can explain these null results.

Cone Models for Embedded Foundation

The dynamic analysis of surface footings may be performed approximately, but quite accurately, by idealizing the soil as a truncated cone instead of an elastic half‐space. In this paper, cone models are extended to represent embedded foundations. To this end, a double‐cone model is introduced to represent a disk in the interior of a homogeneous full space. Symmetry considerations applied to a pair of double cones enable the simulation of a free surface midway between the two disks. By using a stack of such disk pairs, an embedded foundation is modeled. The subsequent calculation is conducted by conventional matrix methods familiar from elementary finite element analysis. The accuracy of both frequency‐domain and time‐domain formulations is just as good as for surface footings. This is confirmed by comparing the dynamic‐stiffness coefficients for cone models with rigorous solutions. In addition, cone models enable simple determination of the effective foundation input motion imposed by earthquakes upon structures with embedded foundations.