Sedimentation of two spheres in a square tube

In this study, we simulated the sedimentation of two identical spheres having the same density in a square tube. Compared with the center-line and the diagonal planes (including the reverse diagonal plane), the sedimentation of spheres on other planes is more complicated. Results show that at relatively low and high Reynolds number, the spheres will deflect and eventually move to the diagonal plane of the square tube. At the medium Reynolds number, the spheres settle near the initial plane. The possible mechanisms underlying these behaviors are examined. Finally, it is shown that the distance between the spheres increases with an increase in the Reynolds number, which is applicable to all the initial settlement planes studied.

Leg Dominance Effects on Postural Control When Performing Challenging Balance Exercises

Leg dominance reflects the preferential use of one leg over another and is typically attributed to asymmetries in the neural circuitry. Detecting leg dominance effects on motor behavior, particularly during balancing exercises, has proven difficult. The current study applied a principal component analysis (PCA) on kinematic data, to assess bilateral asymmetry on the coordinative structure (hypothesis H1) or on the control characteristics of specific movement components (hypothesis H2). Marker-based motion tracking was performed on 26 healthy adults (aged 25.3 ± 4.1 years), who stood unipedally on a multiaxial unstable board, in a randomized order, on their dominant and non-dominant leg. Leg dominance was defined as the kicking leg. PCA was performed to determine patterns of correlated segment movements (“principal movements” PMks). The control of each PMk was characterized by assessing its acceleration (second-time derivative). Results were inconclusive regarding a leg-dominance effect on the coordinative structure of balancing movements (H1 inconclusive); however, different control (p = 0.005) was observed in PM3, representing a diagonal plane movement component (H2 was supported). These findings supported that leg dominance effects should be considered when assessing or training lower-limb neuromuscular control and suggest that specific attention should be given to diagonal plane movements.

Constructions of copulas with given diagonal (and opposite diagonal) sections and some generalizations

We review various methods for constructing bivariate copulas with given diagonal sections from seminal work to the most recent research on copulas with given diagonal and opposite diagonal sections. A survey on a generalization of copulas with given diagonal plane sections in higher dimensions and other sections that generalize the diagonal and opposite diagonal sections is of particular interest.

The Motion of a Neutrally Buoyant Ellipsoid Inside Square Tube Flows

The motion and rotation of an ellipsoidal particle inside square tubes and rectangular tubes with the confinement ratio R/a∈(1.0,4.0) are studied by the lattice Boltzmann method (LBM), where R and a are the radius of the tube and the semi-major axis length of the ellipsoid, respectively. The Reynolds numbers (Re) up to 50 are considered. For the prolate ellipsoid inside square and rectangular tubes, three typical stable motion modes which depend on R/a are identified, namely, the kayaking mode, the tumbling mode, and the log-rolling mode are identified for the prolate spheroid. The diagonal plane strongly attracts the particle in square tubes with 1.2≤R/a<3.0. To explore the mechanism, some constrained cases are simulated. It is found that the tumbling mode in the diagonal plane is stable because the fluid force acting on the particle tends to diminish the small displacement and will bring it back to the plane. Inside rectangular tubes the particle will migrate to a middle plane between short walls instead of the diagonal plane. Through the comparisons between the initial unstable equilibrium motion state and terminal stable mode, it is seems that the particle tend to adopt the mode with smaller kinetic energy.

A Slim Sector Model for the Analysis of Fatigue Life of Fine Pitch Flip Chip Packages

In the near future, it is likely that the interconnection pitch of flip chips will fall below 100 microns. For a flip chip of 20mm × 20mm at this pitch, there will be 40,000 interconnections on the chip. Even after taking advantage of symmetry whereby only a one-eighth model need be analyzed, there will be 5,000 interconnections. If solder were used to form the interconnection, plasticity and creep effects would need to be taken into account. Despite the great advances in computer technology, the computer memory and computation time required for a full 3D finite element analysis (FEA) of such a fine-pitch IC package is prohibitive. This paper presents a slim sector model which could be used to overcome this problem. Essentially, a slim sector of the package adjacent to the diagonal is analyzed rather than a 1/8 model. The appropriate boundary condition to be applied to the slim sector model is a critical issue. With the large number of interconnections, it is reasonable to expect that the displacement of points close to the diagonal plane of the package will tend to be directed radially outwards from the neutral point at the centre of the package. The validity of this assumption was investigated by performing a full 3D FEA of the 1/8 model of two flip chip packages of dimensions 4mm square and 6mm square. A few slim sector models have been developed and their accuracy and computational efficiency studied. The fatigue life of the critical solder joint was determined by performing a temperature cycling simulation between −40C and 150C. The elastoplastic and creep properties of solder were taken into account. As the 1/8 model is the most accurate model, its results were taken as reference. It was found that the accuracy of the best slim sector model ranged between 12% and 27%. A comparison was also made between the slim sector model and the popular strip model. It was found that the slim sector model was much more accurate than the strip model which gives error of 61–248%.

Local, Near-Field Mixing Augmentation Using Square Coaxial Jets

Results from un-forced experiments in flows ensuing from circular and equivalent square coaxial nozzles with parallel sides are presented in this paper. The nozzles are contoured and are designed so that the hydraulic diameters of the internal flow passages are identical for both geometries. The flow experiments were conducted at a co-flow-jet Reynolds number of Re = 16,000 and inner-to-outer jet nominal velocity ratios of λ = 0, 0.5, 1.5. Axis switching, a phenomenon readily observed in single non-axisymmetric nozzles, is shown for the first time to occur in the square coaxial nozzles as well. Comparisons of the mixing regions of the flows from both geometries are made to examine mixing advantages when using square nozzle configurations. Comparisons of stream wise mean velocity fields measured on a center plane parallel to the square nozzle sides, on a diagonal plane of the square nozzle and the center plane of the corresponding circular nozzle, are presented and discussed. Axis switching is shown to be evident in the near-field shear regions for all velocity ratios, resulting in considerable mixing advantages. The spreading rates (and therefore mixing rates) of the outer mixing region of the square nozzles clearly exceed the spreading rate observed in the circular case on the central plane. Axis switching and improved mixing is also observed in the inner mixing region of the square nozzle. This work is relevant to coaxial nozzles for gas turbine combustor applications, although the study has been carried out in a scaled up geometry with respect to this application.