Rotational Constraints Research Articles

Stress Relaxation for Granular Materials near Jamming under Cyclic Compression.

We have explored isotropically jammed states of semi-2D granular materials through cyclic compression. In each compression cycle, systems of either identical ellipses or bidisperse disks transition between jammed and unjammed states. We determine the evolution of the average pressure P and structure through consecutive jammed states. We observe a transition point ϕ_{m} above which P persists over many cycles; below ϕ_{m}, P relaxes slowly. The relaxation time scale associated with P increases with packing fraction, while the relaxation time scale for collective particle motion remains constant. The collective motion of the ellipses is hindered compared to disks because of the rotational constraints on elliptical particles.

Nonlinear normal modes of a shallow arch with elastic constraints for two-to-one internal resonances

The nonlinear normal modes (NNMs) of an elastically constrained (EC) shallow arch in the case of two-to-one internal resonance are constructed, and the effects of the vertical and rotational elastic boundary constraints are studied. The multiple scales method is directly applied to obtain the second-order uniform-expansion solution and the modulation equations from the dimensionless integral–partial–differential equation of motion. The elastic constraints have a corresponding relationship with the coefficients of modulation equations and influence the natural frequencies and modes, as demonstrated by solving the algebraic eigenvalue equation. The stability of the uncoupled single-mode and coupled-mode motions for the nonlinear system is investigated. Then the shape functions, activation conditions and space–time evolutions accounting for the two-to-one internally resonant NNMs for vertical and rotational elastic constraints are examined. The results show that the vertical and rotational elastic constraints play a fundamental role in the nonlinear dynamic phenomena of the EC shallow arch.

Inertial convection in a rotating narrow annulus: Asymptotic theory and numerical simulation

An important way of breaking the rotational constraint in rotating convection is to invoke fast oscillation through strong inertial effects which, referring to as inertial convection, is physically realizable when the Prandtl number Pr of rotating fluids is sufficiently small. We investigate, via both analytical and numerical methods, inertial convection in a Boussinesq fluid contained in a narrow annulus rotating rapidly about a vertical symmetry axis and uniformly heated from below, which can be approximately realizable in laboratory experiments [R. P. Davies-Jones and P. A. Gilman, “Convection in a rotating annulus uniformly heated from below,” J. Fluid Mech. 46, 65-81 (1971)]. On the basis of an assumption that inertial convection at leading order is represented by a thermal inertial wave propagating in either prograde or retrograde direction and that buoyancy forces appear at the next order to maintain the wave against the effect of viscous damping, we derive an analytical solution that describes the onset of inertial convection with the non-slip velocity boundary condition. It is found that there always exist two oppositely traveling thermal inertial waves, sustained by convection, that have the same azimuthal wavenumber, the same size of the frequency, and the same critical Rayleigh number but different spatial structure. Linear numerical analysis using a Galerkin spectral method is also carried out, showing a quantitative agreement between the analytical and numerical solutions when the Ekman number is sufficiently small. Nonlinear properties of inertial convection are investigated through direct three-dimensional numerical simulation using a finite-difference method with the Chorin-type projection scheme, concentrating on the liquid metal gallium with the Prandtl number Pr = 0.023. It is found that the interaction of the two counter-traveling thermal inertial waves leads to a time-dependent, spatially complicated, oscillatory convection even in the vicinity of the onset of inertial convection. The nonlinear properties are analyzed via making use of the mathematical completeness of inertial wave modes in a rotating narrow annulus, suggesting that the laminar to weakly turbulent transition is mainly caused by the nonlinear interaction of several inertial wave modes that are excited and maintained by thermal convection at moderately supercritical Rayleigh numbers.

Computational modelling of mobile bearing TKA anterior–posterior dislocation

Anterior–posterior stability in an unconstrained mobile-bearing total knee arthroplasty (TKA) and one with rotational constraints is compared in a computational model based on an ASTM test. Both TKA designs dislocate at loads greater than reported maximum in vivo forces. The posterior drawer forces (mean: 3027 N vs. 1817 N) needed to induce subluxation increase with a greater anterior jump distance (12 mm vs. 7 mm; refers to the vertical height of the anterior or posterior border of the tibial insert's articulating surface). The posterior jump distance for both tested TKA differed by 1.5 mm and had minimal effect on the magnitude of the anterior drawer forces at dislocation in mid-flexion (unconstrained vs. constrained: 445 N vs. 412 N). The unconstrained insert dislocated by means of spin-out whereas in the constrained TKA the femur dislocated from the bearing during posterior drawer and the bearing from the baseplate during anterior drawer. MCL function is an important consideration during ligament balancing since a ± 10% variation in MCL tension affects dislocation forces by ± 20%. The simulation platform provided the means to investigate TKA designs in terms of anterior–posterior stability as a function of knee flexion, collateral ligament function and mechanical morphology.

MERIDIONAL CIRCULATION IN SOLAR AND STELLAR CONVECTION ZONES

We present a series of 3-D nonlinear simulations of solar-like convection, carried out using the Anelastic Spherical Harmonic (ASH) code, that are designed to isolate those processes that drive and shape meridional circulations within stellar convection zones. These simulations have been constructed so as to span the transition between solar-like differential rotation (fast equator/slow poles) and ``anti-solar' differential rotation (slow equator/fast poles). Solar-like states of differential rotation, arising when convection is rotationally constrained, are characterized by a very different convective Reynolds stress than anti-solar regimes, wherein convection only weakly senses the Coriolis force. We find that the angular momentum transport by convective Reynolds stress plays a central role in establishing the meridional flow profiles in these simulations. We find that the transition from single-celled to multi-celled meridional circulation profiles in strong and weak regimes of rotational constraint is linked to a change in the convective Reynolds stress, a clear demonstration of gyroscopic pumping. Latitudinal thermal variations differ between these different regimes, with those in the solar-like regime conspiring to suppress a single cell of meridional circulation, whereas the cool poles and warm equator established in the anti-solar states tend to promote single-celled circulations. Though the convective angular momentum transport becomes radially inward at mid-latitudes in anti-solar regimes, it is the meridional circulation that is primarily responsible for establishing a rapidly-rotating pole. We conclude with a discussion of how these results relate to the Sun, and suggest that the Sun may lie near the transition between rapidly-rotating and slowly-rotating regimes.

Adaptive locomotion on slopes and stairs using pelvic rotation

In this paper, we introduce a new online motion retargeting technique to generate natural locomotion of walking on slopes and stairs using only a single captured reference motion. An inverse-kinematics solver is developed to generate poses satisfying smooth trajectories of positional and rotational constraints for feet and hands. By considering the rotations of the pelvis and upper body, our technique is able to produce natural poses without knee-popping artifacts.

Finger-position optimization by using caging qualities

Caging aims at constraining objects like a bird cage. It does not need force closure and contacts, and therefore is robust to perception noises. This paper considers these merits of caging and proposes an efficient approach to find the optimized finger positions for robust grasping under perception noises by measuring the quality of caging. It initially uses two quality models (the quality model of translational constraint and the quality model of rotational constraint) to combinatorically represent the quality of caging and finds the optimized finger positions (finger positions that have large robustness to perception noises) by maximizing the margins to caging breaking. Meanwhile, it employs Genetic Algorithm (GA) to accelerate the combinatorial optimization of the two quality models. The encoding rules, the initial procedure, and the stopping criterion of the GA are designed carefully towards the quality models to improve its computational efficiency. Experiments with various object shapes show that with the help of multi-model optimization and GA acceleration, the proposed approach is not only robustness to perception noises but also efficient in computation.

Stable estimation of horizontal velocity for planetary lander with motion constraints

The planetary lander usually selects image feature points and tracks them from frame to frame in order to determine its own position and velocity during landing. Aiming to keep features tracking in consecutive frames, this paper proposes an approach of calculating the field of view (FOV) overlapping area in a 2D plane. Then the rotational and translational motion constraints of the lander can be found. If the FOVs intersects each other, the horizontal velocity of the lander is quickly estimated based on the least square method after the ill-conditioned matrices are eliminated previously. The Monte Carlo simulation results show that the proposed approach is not only able to recover the ego-motion of planetary lander, but also improves the stabilization performance. The relationship of the estimation error, running time and number of points is shown in the simulation results as well.

Path Planning of Spatial Rigid Motion with Constrained Attitude

This paper presents a general quadratic optimization methodology for autonomous path planning of spatial rigid motion with constrained attitude. The motion to be planned has six degrees of freedom and is assumed under constant velocity in the body frame. The objective is to determine the motion orientation (or attitude), handled as control variables, along the planned paths. A procedure is discussed to transform the rotational constraints and attitude constraints as quadratic functions in terms of unit quaternions, and the path-planning problem is reformulated as a general, quadratically constrained, quadratic programming problem. A semidefinite relaxation method is then applied to obtain a bound on the global optimal value of the nonconvex, quadratically constrained, quadratic programming problem. Subsequently, an iterative rank minimization approach is proposed to find the optimal solution. Application examples of aircraft path-planning problems are presented using the proposed method and compared with those obtained from the other method.

Growing rod analysis for the fusionless correction of Early Onset Scoliosis (EOS)

Managing spinal deformities in young children is challenging, particularly early onset scoliosis (EOS). Surgical intervention is often required if EOS has been unresponsive to conservative treatment particularly with rapidly progressive curves. An emerging treatment option for EOS is fusionless scoliosis surgery. Similar to bracing, this surgical option potentially harnesses growth, motion and function of the spine along with correcting spinal deformity. Dual growing rods are one such fusionless treatment, which aims to modulate growth of the vertebrae. The aim of this study was to ascertain the extent to which semi-constrained growing rods (Medtronic) with a telescopic sleeve component, reduce rotational constraint on the spine compared with standard rigid rods and hence potentially provide a more physiological mechanical environment for the growing spine.

Eigenspace Stability Conditions in Mean-Field Replica Theories

I consider the eigenspace form of the saddle point conditions that apply for mean-field replica models that are characterized by a single overlap matrix order parameter. These allow for a characterization of the full set of saddle point solutions. Further, they motivate consideration of a particular class of solutions, which I call the principally-commuting set. These are the solutions that simultaneously satisfy the replica-space rotational stability constraints for all physical models. I show that this set satisfies the replica equivalence symmetry, as well as other more stringent conditions, and that it also contains the set of Parisi-type ultrametric solutions as a subset.

Drug-Enhanced Unclogging Motions of a Double Helical Magnetic Micromachine for Occlusive Vascular Diseases

We propose a novel double helical magnetic micromachine (DHMM) to achieve drug-enhanced unclogging abilities for occlusive vascular diseases (OVDs) in human blood vessels. The proposed DHMM can generate navigating and mechanical drilling motions actuated by an external rotating magnetic field (ERMF). It can also deliver a clot-busting drug to a target point (clogged area) and can precisely release the drug toward the clogged area. We derive rotational dynamic constraint equations for selective manipulation of the navigating, drug releasing, and mechanical drilling motions of the DHMM by controlling the ERMF. We then prototype the DHMM and demonstrate these motions to show the validity of the proposed DHMM and manipulation methods.

Thermomechanical behavior of NiTiPdPt high temperature shape memory alloy springs

Transformation strains in high temperature shape memory alloys (HTSMAs) are generally smaller than for conventional NiTi alloys and can be purposefully limited in cases where stability and repeatability at elevated temperatures are desired. Yet such alloys can still be used in actuator applications that require large strokes when used in the form of springs. Thus there is a need to understand the thermomechanical behavior of shape memory alloy spring actuators, particularly those consisting of alternative alloys. In this work, a modular test setup was assembled with the objective of acquiring stroke, stress, temperature, and moment data in real time during joule heating and forced convective cooling of Ni19.5Ti50.5Pd25Pt5 HTSMA springs. The spring actuators were subjected to both monotonic axial loading and thermomechanical cycling. The role of rotational constraints (i.e., by restricting rotation or allowing for free rotation at the ends of the springs) on stroke performance was also assessed. Finally, recognizing that evolution in the material microstructure can result in changes in HTSMA spring geometry, the effect of material microstructural evolution on spring performance was examined. This was done by taking into consideration the changes in geometry that occurred during thermomechanical cycling. This work thus provides insight into designing with HTSMA springs and predicting their thermomechanical performance.

Large-scale vortices in rapidly rotating Rayleigh–Bénard convection

AbstractUsing numerical simulations of rapidly rotating Boussinesq convection in a Cartesian box, we study the formation of long-lived, large-scale, depth-invariant coherent structures. These structures, which consist of concentrated cyclones, grow to the horizontal scale of the box, with velocities significantly larger than the convective motions. We vary the rotation rate, the thermal driving and the aspect ratio in order to determine the domain of existence of these large-scale vortices (LSV). We find that two conditions are required for their formation. First, the Rayleigh number, a measure of the thermal driving, must be several times its value at the linear onset of convection; this corresponds to Reynolds numbers, based on the convective velocity and the box depth, $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}{\gtrsim }100$. Second, the rotational constraint on the convective structures must be strong. This requires that the local Rossby number, based on the convective velocity and the horizontal convective scale, ${\lesssim }0.15$. Simulations in which certain wavenumbers are artificially suppressed in spectral space suggest that the LSV are produced by the interactions of small-scale, depth-dependent convective motions. The presence of LSV significantly reduces the efficiency of the convective heat transport.

Free vibration of moderately thick antisymmetric laminated annular sector plates with elastic edge constraints

Abstract This study presents, for the first time, free vibration results of laminated sector plates having elastic edges. Each layer is cylindrically orthotropic. A differential quadrature method (DQM) based formulation is used for studying the problem of shear-deformable laminated sector plates having translational as well as rotational edge constraints. By varying the edge stiffnesses, several combinations of simply supported and clamped edge conditions are simulated. The results are further validated by comparison with the results of laminated square plates (with elastic edges) and of laminated sector plates (without elastic edges) available in the literature.

Free Vibration Analysis of Moderately Thick Antisymmetric Angle-Ply Laminated Rectangular Plates with Elastic Edge Constraints

A simple formulation for studying the free vibration of shear-deformable antisymmetric angle-ply laminated rectangular plates having translational as well as rotational edge constraints is presented. The aim is to fill the void in the available literature. The spatial discretization of the resulting mathematical model in five field variables is carried out using the two-dimensional Differential Quadrature Method. Validation of the formulation is done with the help of convergence studies with respect to the number of nodes. The results are compared with those from past investigations available only for simpler problems. Effects of material, geometrical, and support parameters are studied.

Stability and free vibration analyses of cantilever shear buildings with semi-rigid support conditions and multiple masses

The stability and free vibration analyses of a cantilever shear building with generalized support conditions and with multiple masses (rotational and translational) rigidly attached at both ends and along its height are presented. The proposed model includes the simultaneous effects of: (1) lateral and rotational elastic restraints at the base support; (2) a uniform distributed mass and rotary inertia plus lumped rotary and translational masses rigidly attached at both extremes and along its height; (3) linearly distributed axial load plus the concentrated vertical axial loads caused by the lumped masses; and (4) shear deformations and shear forces induced by the applied axial forces. A parametric study is carried out that shows the importance of all variables included in this work on the stability and dynamic behavior of cantilever shear buildings, particularly the effects of the attached lumped masses and the rotational and translational constraints at the base support. A comparison with results presented by other researchers in previous studies shows that the proposed method and corresponding equations can be very useful in the assessment design of cantilever shear buildings. The main objective is to present readily solutions on the static stability and free vibration of cantilever shear buildings with generalized support conditions and multiple masses rigidly attached. The proposed method and corresponding expressions for the natural frequencies and modal shapes, buckling modes and axial critical loads are extensions of those presented recently by the senior author.

Unusual DNA packaging characteristics in endoreduplicated Caenorhabditis elegans oocytes defined by in vivo accessibility to an endogenous nuclease activity

BackgroundGerm cells in animals are highly specialized to preserve the genome. A distinct set of chromatin structures must be properly established in germ cells to maintain cell fate and genome integrity. We describe DNA-surface interactions in activated Caenorhabditis elegans oocytes that are revealed through the activity of an endogenous nuclease ('endocleavage’).ResultsOur analysis began with an unexpected observation that a majority (>50%) of DNA from ovulated but unfertilized C. elegans oocytes can be recovered in fragments of approximately 500 base pairs or shorter, cleaved at regular intervals (10 to 11 nt) along the DNA helix. In some areas of the genome, DNA cleavage patterns in these endoreduplicated oocytes appear consistent from cell-to-cell, indicating coherent rotational positioning of the DNA in chromatin. Particularly striking in this analysis are arrays of sensitive sites with a periodicity of approximately 10 bp that persist for several hundred base pairs of genomic DNA, longer than a single nucleosome core. Genomic regions with a strong bias toward a 10-nt periodic occurrence of A(n)/T(n) (so-called PATC regions) appear to exhibit a high degree of rotational constraint in endocleavage phasing, with a strong tendency for the periodic A(n)/T(n) sites to remain on the face of the helix protected from nuclease digestion.ConclusionThe present analysis provides evidence for an unusual structure in C. elegans oocytes in which genomic DNA and associated protein structures are coherently linked.

Jacobians and Hessians of mean value coordinates for closed triangular meshes

Mean value coordinates provide an efficient mechanism for the interpolation of scalar functions defined on orientable domains with a nonconvex boundary. They present several interesting features, including the simplicity and speed that yield from their closed-form expression. In several applications though, it is desirable to enforce additional constraints involving the partial derivatives of the interpolated function, as done in the case of the Green coordinates approximation scheme (Ben-Chen, Weber, Gotsman, ACM Trans. Graph.:1---11, 2009) for interactive 3D model deformation. In this paper, we introduce the analytic expressions of the Jacobian and the Hessian of functions interpolated through mean value coordinates. We provide these expressions both for the 2D and 3D case. We also provide a thorough analysis of their degenerate configurations along with accurate approximations of the partial derivatives in these configurations. Extensive numerical experiments show the accuracy of our derivation. In particular, we illustrate the improvements of our formulae over a variety of finite differences schemes in terms of precision and usability. We demonstrate the utility of this derivation in several applications, including cage-based implicit 3D model deformations (i.e., variational MVC deformations). This technique allows for easy and interactive model deformations with sparse positional, rotational, and smoothness constraints. Moreover, the cages produced by the algorithm can be directly reused for further manipulations, which makes our framework directly compatible with existing software supporting mean value coordinates based deformations.

The Vibration Characteristics Analysis of Miter Gate Based on ANSYS Workbench and Vibration Test

The 3d model of miter gate has been set up based on skeleton model of Pro/E, and it has been imported into ANSYS Workbench module for static structure analysis and modal analysis. In the process of finite element simulation, the rotational constraints has been imposed on the top and bottom pivot according to the actual operation situation of the miter gate, and obtain the first several order frequencies and corresponding modal vibration mode of the miter gate, which can show the hydrodynamic vibration stress and strain distribution. According to the results of the finite element simulation analysis, the prototype vibration test of the miter gate has been done. The test results show that the vibration amplitude and the stress and strain distribution of each part of the miter gate are corresponding to the vibration test.