Limit Of Displacement Research Articles

Limited utility of Birkhoff’s theorem in modified Newtonian dynamics: Nonzero accelerations inside a shell

We investigate the consequences of Birkhoff's theorem in general relativity (GR) and in Modified Newtonian dynamics (MOND). We study, in particular, the system of a finite-mass test particle inside a spherical shell. In both GR and MOND, we find non-vanishing acceleration for that test particle. The direction of the acceleration is such that it pushes the test particle toward the center of the shell. In GR, the acceleration is found analytically in the case of a small test mass with a small displacement from the center of the shell. In MOND, the acceleration is found analytically in the limit of large test mass and small displacement, and a comparison to numerical values is made. Numerical simulations are done for more general cases with parameters that mimic the system of a galaxy in a cluster. In GR, the acceleration is highly suppressed, and physically insignificant. In MOND, on the contrary, the acceleration of the point particle can be a significant fraction of the field just outside of the spherical shell.

ASYMPTOTIC BEHAVIOR OF STRUCTURES MADE OF CURVED RODS

In this paper, we study the asymptotic behavior of a structure made of curved rods of thickness 2δ when δ tends to 0. This study is carried on within the frame of linear elasticity by using the unfolding method. It is based on several decompositions of the structure displacements and on the passing to the limit in fixed domains. We show that any displacement of a structure is the sum of an elementary rods-structure displacement (e.r.s.d.) concerning the rods' cross sections and a residual one related to the deformation of the cross section. The e.r.s.d. coincides with rigid body displacements in the junctions. Any e.r.s.d. is given by two functions belonging to [Formula: see text] where [Formula: see text] is the skeleton structure (i.e. the set of rods with middle lines). One of this function [Formula: see text] is the skeleton displacement, the other [Formula: see text] gives the cross section rotation. We show that [Formula: see text] is the sum of an extensional displacement and an inextensional one. We establish a priori estimates and then, we characterize the unfolded limits of the rods-structure displacements. Eventually, we pass to the limit in the linearized elasticity system and using all results in [6], where on one hand, we obtain a variational problem that is satisfied by the limit extensional displacement, and on the other hand, a variational problem coupling the limit of inextensional displacement and the limit of the rod torsion angles.

Molecular diffusion in liquid crystals and chiral discrimination. I. Theory

The possibility of using cholesteric phases for discriminating enantiomers of a chiral solute on the basis of their different transport properties, motivates the investigation of the translational diffusion by taking fully into account the roto-translational coupling. In this article a detailed theoretical analysis is presented for the transport properties evaluated according to the asymptotic limit of the mean-squared displacement. A general relation is derived for the transport coefficients, having as main ingredients the mean-field potential due to the mesophase, and the diffusion tensor with its purely translational and rotational components, and with the blocks describing the roto-translational coupling. The application of the theory to nematic phases shows that the roto-translational coupling generates a dynamical contribution reducing the transport coefficients evaluated by taking into account only the translational diffusion components in the center of diffusion. The theory is also specialized to a cholesteric phase with a given helical pitch for the director arrangement, in a form which is suitable for calculations of model systems of chiral solutes to be presented in a forthcoming paper.

Dielectric function and localized diffusion in ion conducting glasses

We present the three coupled rate equations of the mismatch generated relaxation for the accommodation and transport of ions (MIGRATION) concept that describe the ion dynamics in, for example, ion-conducting glasses and simultaneously yield scaled conductivity and permittivity spectra. Here, model spectra are compared with the experimental spectra of xNa 2O·(1- x)GeO 2 glasses for x=0.0513, 0.0902, 0.213. This allows us to estimate the long-time limit of the localized rms displacement, lim t → ∞ { < R 2 ( t ) > − 6 ⁢ D ⁢ t } 0.5 , which may be roughly interpreted as the average size of the ion cage before the dynamics become diffusive. For the three compositions considered, we obtain an approximate x −1/3 dependence of this quantity, which implies that the ion dynamics are largely governed by the Coulomb interactions between the mobile ions.

Updip limit of the seismogenic zone beneath the accretionary prism of southwest Japan: An effect of diagenetic to low-grade metamorphic processes and increasing effective stress

Off southwest Japan the seaward limit of coseismic displacement (or updip limit of the seismogenic zone) of the 1946 Mw 8.3 thrust earthquake reaches to 4 km depth and ∼40 km landward of the trench. This limit coincides with the estimated location of the 150 °C isotherm, and has been linked to changes in physical properties associated with the smectite to illite clay-mineral transition. Here we show that this limit correlates with a suite of diagenetic to low-grade metamorphic processes characterized by (1) declining fluid production and decreasing fluid pressure ratio (λ*) and (2) active clay, carbonate, and zeolite cementation and the transition to pressure solution and quartz cementation. These diagenetic to low-grade metamorphic changes cause the onset of velocity weakening during thrust faulting, an increase in effective stress, and strengthening of the hanging wall, which together combine to produce recordable earthquakes.

Anterior tibial translation during eccentric, isokinetic quadriceps work in healthy subjects.

The effect of increasing isokinetic, eccentric quadriceps torques on sagittal translation of the tibia was examined in six healthy volunteers and compared to the translation at 20 degrees of knee flexion during a drawer test with 90 N force. The tibial translation increased in a linear fashion with a mean of 0.5 mm per 20% torque increase. In 20 degrees of knee flexion, 10% of eccentric quadriceps peak torque consumed 80% of the anterior tibial translation induced by the 90 N Lachman test while eccentric quadriceps peak torque utilized 100% of the translation at the same test. The in vivo relation between muscle force and tibial translation is of importance in the treatment of patients with injury to the cruciate ligaments. The results indicate that an already low eccentric quadriceps torque causes a tibial translation that reaches the limit of the passive knee joint displacement where strain is assumed to develop in the anterior cruciate ligament. Already low eccentric quadriceps torque levels may therefore be harmful during rehabilitation after anterior cruciate ligament surgery.

The Changes of Soil Structure in Shear Process.

There are problems to be studied on the changes of the soil structures in shear processes on the case of long creep. We studied these problems with a new trial direct shear apparatus and X-ray photographs.The characteristics of the apparatus are that one pair of an upper and a lower shear boxes about 600mm long is equipped, and the maximum limit of shear displacement of the lower box is 600mm.Each test was performed as below. X-ray contrast medium was injected in eight lines at a right angle to shear direction into soil sample compacted in the apparatus.Then shear test was performed by shear displacement prescribed for each sample within from 15mm to 300mm. After the test, the soil structures were observed with X-ray photographs of them.The soil structures developed through three stages in the shear processes as below. In the initial stage, the contineous deformation in the direction of the sample thickness appears. In the next stage (failure stage), many small and local shear failures appear everywhere in the sample. Then some of them connect to each other, and develop into a clear and thin shear layer as long as full length of the sample. In the last stage (creep stage), some thin soil masses only in the layer relatively slip with long distances, and the result of this phenomenon, the shear layer gradually changes into a creep layer.

Effect of columnar defects on the elastic behavior of vortices in YBa2Cu3O7- delta thin films.

A sensitive ac transport technique is used to determine the force displacement response in the elastic regime of vortices pinned in ${\mathrm{YBa}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{7\mathrm{\ensuremath{-}}\mathrm{\ensuremath{\delta}}}$ thin films both before and after irradiation with 2.7 GeV ${\mathrm{U}}^{238}$ ions. The restoring force that pinning defects exert on the vortices, and the elastic limit of displacement of the vortices before they depin are extracted from these data. The columnar defects which lie parallel to the c axis are seen both to increase the restoring force on the vortices for B\ensuremath{\parallel}c and also to reduce the elastic limit in this orientation to a value very close to the damage track diameter. Estimates of the pinning energies and correlation volume for collective pinning before and after irradiation are made and discussed.

The elastic regime of vortices in superconducting YBCO and multilayer YBCO/PrBCO films

A sensitive AC transport technique is used to determine the force-displacement response in the elastic regime of vortices pinned in YBCO and multilayer YBCO/PrBCO films. The dependences of the elastic limit of displacement and the Labusch parameter are presented as a function of temperature, magnetic-field amplitude and orientation. Results are presented for DC sputtered and laser-ablated epitaxial c-axis YBCO films as well as a DC sputtered multilayer YBCO/PrBCO film with a unit-cell ratio of 4:6. The elastic parameters enable the effective energy of the pinning wells to be determined, and comparisons of these values are made with activation energies extracted from thermally activated flux-flow analyses of magneto-resistance data. The force-displacement values show better agreement with magnetic-relaxation measurements than those from Arrhenius analyses.

Stability of R-FBI Bearings: Analysis and Experiment

The Resilient—Friction Base Isolator (R—FBI) is a device which can be incorporated into the foundations of new and existing structures to protect them from damaging earthquake ground motions. The device consists of a short column composed of a set of identical flat rings with an elastic core (reinforced rubber plug). The elastic core is positioned such that it carries no axial load and distributes the lateral displacement uniformly across the clear height of the column. In this paper, considering an R—FBI bearing as a short column, an approximate analytical model for the analysis of its stability is presented. Assuming no negative pressure at the interfaces of the flat rings, the values of the critical lateral displacement and the critical vertical load are defined and calculated in terms of the system's parameters. The upper limit of the safe lateral displacement, the lateral displacement beyond which the lateral load carrying capacity of the isolator deteriorates, is also defined. To validate the analysis method, a single bearing was fabricated and tested under various normal loads. The test results strongly confirm the analytical predictions.

Straightforward derivation of the long-time limit of the mean-square displacement in one-dimensional diffusion.

Considering one-dimensional diffusion as a sequence of exchange processes between occupied and vacant sites, the long-time limit of the mean-square displacement of the diffusants is shown to be easily calculable as the net effect of the random walk of the vacancies.

Contact placement errors for resistive and Hall measurements on cross-shaped samples

The calculation of lead-placement errors for resistivity and Hall signals is extended to the family of cross-shaped samples. Empirical expressions for errors [Δρ/ρ=− 1/2 (2d/D)2n and ΔRH/RH=− 1/2 (2d/D)n] are given in the limit of large contact displacement (d/D→ 1/2 ). For crosses, the exponent n was found to increase as n ∝ (l/D)−1.42 as the ratio of leg width to overall size, l/D, was reduced. For square and circular cloverleafs, n is less sensitive to the increase of the slit length, giving power laws with exponents of 0.8 and 0.6, respectively, in terms of the parameter λ=2r/D.

Horizontal optokinetic responses under stroboscopic illumination in cat, monkey and man

The horizontal optokinetic reflex (OKN) was studied in cat, monkey and man under conditions of steady or stroboscopic illumination. In all species, there was an abrupt decrease in OKN gain for a given spatial displacement of the stimulus between two consecutive stroboscopic flashes. The upper limit of spatial displacement which preserved optimal OKN gain was independent of stimulus velocity and flash frequency. The value of this limit differed in the three species studied. In the cat, OKN gain was affected when the spatial displacement between two stimuli exceeded 0.55 degrees of visual angle. In monkey and man, these limits were 1.48 degrees and 2.87 degrees, respectively. When human subjects were asked to volontary track the stimulus, the limit value reached 4.3 degrees. This result is discussed in the context of the evolution of the smooth pursuit system and its contribution to optokinetic response.

Measurement of contact placement errors in the van der Pauw technique

Van der Pauw resistivity measurements were performed on samples of six different shapes: circle, square, two circular cloverleafs, and two square cloverleafs, and the measurement error of the resistivity due to contact displacement was determined. Earlier predictions for this error were verified for the circle and square, and two circular cloverleafs, although significant higher-order corrections were found in all cases except the square. The three square shapes gave contact placement errors typically 10–100 times smaller than the errors in the corresponding circular shapes. All cloverleafs gave smaller errors than the corresponding nonclovered shapes, although this difference disappeared in the limit of large contact displacement.

A Study of Allowable Piping Loads on Double-suction Centrifugal Pumps : 2nd Report, Shaft Displacement Due to Pump Casing Deformation

Shaft displacement due to dump casing deformation which occurs when external piping forces and moments are applied was investigated. The test pump was an axially split, single-stage double suction volute type with foot support. An analysis by FEM(MSC/NASTRAN) was performed and considerable good agreement was obtained with actual measurement. It was found that shaft displacement due to pump casing deformation can not be neglected for pumps with foot support. In API 610-6th standard, limit of shaft displacement is 0.127 mm for pumps which have suction bores 300 mm or less. But according to this investigation, it is reasonable with pumps having suction bore diameters larger than 300 mm to enlarge this limitation. Effects of pump size and casing thickness on shaft displacement were investigated by FEM. The possibility of a galling of the casing wearing ring and a considerable leakage from mechanical seal caused by piping loads was also investigated.

足関節外側側副靭帯損傷に対するストレスＸ線撮影法の有用性について 主に計測値について

Utilizing a specially designed apparatus, the anterior drawer test was performed on 30 healthy adults, 7 amputated legs and 10 cadaver and 29 injured ankles. The varus stress test was performed manually on 100 healthy adults (200 ankles) and each of the above mentioned ankles.The results in the healthy adults showed that the upper limit of the anterior drawer displacement (ADD) range was 4mm (3.03±0.75) and that of the talar tilt angle was 5 degrees (3.68±0.33, P<0.05).In the amputated legs, cadaver ankles and injured ankles compared with healthy adults, each measurement increased significantly (p<0.05) and there were no remarkable differences between the groups.The cases of single ligamentous injury showed that anterior drawer displacements were from 4 to 6mm and talar tilt angles were from 5 to 10 degrees. The cases of double ligamentous injury showed that the former ranged above 6mm and the latter above 10 degrees.Each measurement increased according to the severity of the ligamentous injury. There was significant positive correlation (r=0.554) between ADD and TTA in the cadaver ankles.

Testing of Otolith Function

In order to investigate otolith function, horizontal eye displacement in total darkness during tilting laterally about body axis was examined in 23 normal subjects and 29 patients with vestibular lesions. The mean and standard deviation of this eye displacement in normal subjects were 18.9 + 6.1 degrees at 15 degrees of body-tilt. Thus, eye displacement below the lower tolerance limit of normal eye displacement at 15 degrees of body-tilt, that is, 8.8 degrees, was judged to be abnormal. Meanwhile, 12 cases or 41.4% of 29 patients with vestibular lesions showed abnormal eye displacement in this test. Especially in cases with positional vertigo and/or dizziness, the occurrence of abnormal results in this test (69%) was far higher compared with that of cases where vertigo and/or dizziness was not associated with postural changing (19%). Therefore, these abnormal results seem to be closely related to the disorder of otolith system.

A study of allowable piping loads on double-suction centrifugal pumps (2nd report, Shaft displacement due to pump casing deformation)

Shaft displacement due to pump casing deformation which occurs when external piping forces and moments are applied was investigated. The test pump was an axially split, single-stage double-suction volute type with foot support. An analysis by FEM (MSC/NASTRAN) and actual measurements were performed and considerable agreement was obtained. Ito was found that shaft displacement due to pump casing deformation can not be neglected in the case of pumps with foot support. In API 610-6th standard, limit of shaft displacement is 0.127 mm for pumps which have suction bores 300 mm or larger than 300 mm to enlarge this limitation. Effects of pump size and casing thickness on shaft displacement were investigated by FEM. The possibility of galling of casing wearing ring and considerable leakage from mechanical seal caused by piping loads also were investigated.

Random walks on bond percolation clusters: ac hopping conductivity below the threshold

The frequency dependence of the ac hopping conductivity in two and three dimensional lattices with random interruptions is calculated by Monte Carlo simulation of random walks on bond percolation clusters. At low frequencies the real and imaginary parts of the ac conductivity vanish linearly and quadratically with the frequency, respectively. The critical behaviour of the imaginary part of the ac conductivity below the percolation threshold is shown to depend on the long time limit of the mean square displacement of random walksR ∞ 2 , while the real part depends on the time constant of the system as well.R ∞ 2 is found to diverge with an exponentu=2ν-β according to the conjecture of Stauffer.

Homogenization in Stochastic Differential Geometry

It is well known that a diffusion process on Euclidean space can be rigorously considered as the limit of a sequence of transport processes. This idea, which dates at least to Rayleigh's problem of random flight [3] has now received a general treatment by modern probabilistic methods [2, 10]. In addition, we have shown that a suitable transport approximation remains valid for the Brownian motion of any complete Riemannian manifold [11]. In another direction several authors [1, 4, 5, 6, 7, 8] have considered parallel displacement, i.e. parallel displacement of vectors along Brownian motion curves in a manifold. The purpose of this paper is to show that the stochastic parallel displacement can be rigorously considered as the limit of parallel displacement along the paths of a transport process. The transport approximation introduces an extra velocity variable which disappears in the limit, hence the term homogenizatio7i. In addition to its elementary geometric appeal, our approach has the advantage of producing the following coordinate-free definition of the infinitesimal operator of the stochastic parallel displacement: