scholarly journals TO THE THEORY OF n-DIMENSIONAL BRACHISTOCHRONE

2020 ◽  
pp. 53-60
Author(s):  
Gladkov S.O. ◽  
◽  
Bogdanova S.B. ◽  
Keyword(s):  
Three Dimensional ◽  
Plane Curve ◽  
Viscous Friction ◽  
Analytical Description ◽  
The Body ◽  
Viscous Drag ◽  
Friction Forces ◽  
Drag Forces ◽  
Moving Body ◽  
Plane Shape

In this paper, a solution to the problem of the motion of a brachistochrone in the ndimensional Euclidean space is firstly presented. The very first formulation of the problem in a two-dimensional case was proposed by J. Bernoulli in 1696. It represented an analytical description of the trajectory for the fastest rolling down under gravitational force only. Thereafter, a number of problems devoted to a brachistochrone were considered with account for gravitational forces, dry and viscous drag forces, and a possible variation in the mass of a moving body. Analytical solution to the formulated problem is presented in details by an example of the body moving along a brachistochrone in three-dimensional Cartesian coordinates. The obtained parametric solution is confirmed by a graphical interpretation of the calculated result. The formulated problem is solved for an ideal case when drag forces are neglected. If dry and viscous friction forces are taken into account, the plane shape of the brachistochrone remains the same,while the analysis of the solution becomes more complicated. When, for example, a side air flow is taken into account, the plane curve is replaced by a three-dimensional brachistochrone.

An Investigation of the Forces on Three Dimensional Bluff Bodies in Rough Wall Turbulent Boundary Layers

1977 ◽  
Vol 99 (3) ◽  
pp. 503-509 ◽  
Author(s):  
B. E. Lee ◽  
B. F. Soliman
Keyword(s):  
Three Dimensional ◽  
The Body ◽  
Bluff Bodies ◽  
Drag Forces ◽  
Pressure Distributions ◽  
Mean Pressure ◽  
Flow Phenomena ◽  
The Mean ◽  
Building Ventilation ◽  
Group Density

A study has been made of the influence of grouping parameters on the mean pressure distributions experienced by three dimensional bluff bodies immersed in a turbulent boundary layer. The range of variable parameters has included group density, group pattern and incident flow type and direction for a simple cuboid element form. The three flow regimes associated with increasing group density are reflected in both the mean drag forces acting on the body and their associated pressure distributions. A comparison of both pressure distributions and velocity profile parameters with established work on two dimensional bodies shows close agreement in identifying these flow regime changes. It is considered that the application of these results may enhance our understanding of some common flow phenomena, including turbulent flow over rough surfaces, building ventilation studies and environmental wind around buildings.

Effect of Viscoelasticity of PVA Brush on Friction during Post-CMP Cleaning: A Guideline for Nodule Configuration

2014 ◽  
Vol 219 ◽  
pp. 148-152 ◽  
Author(s):  
Y. Hara ◽  
T. Sanada ◽  
A. Fukunaga ◽  
H. Hiyama
Keyword(s):  
Direct Contact ◽  
Chemical Mechanical Planarization ◽  
Three Dimensional ◽  
Hydrodynamic Drag ◽  
Trial And Error ◽  
New Materials ◽  
Friction Forces ◽  
Drag Forces ◽  
Lubrication Characteristics

The application of new materials and three-dimensional structures are being used to achieve next-generation semiconductor devices. Hence, the role of the chemical-mechanical planarization (CMP) process has gained importance. Polyvinyl acetal (PVA) brushes are widely used as scrubbers during post-CMP cleaning. However, the mechanisms of brush scrubber cleaning are still a matter of debate because direct observation is difficult. Many researchers have proposed the removal mechanisms that operate during brush cleaning based on investigations of the forces acting on particles, friction, and the lubrication characteristics. Hydrodynamic drag forces and direct contact between the brush and the particles have been proposed as cleaning mechanisms [1–5]. Philipossian et al. [6] and Sun et al. [7] focused on the brush design and suggested that the existence of nodules or eccentricity of the roller brush had a significant effect on the friction. The friction system between the roller brush and the surface is complex because of the collision of nodules with the surface. Hence, the shapes of the nodules have been designed through trial and error. In this study, we focus on the friction of a single nodule to investigate the role of nodules in roller brush cleaning. The normal and friction forces are measured during brush sliding. In particular, we focus on the viscoelastic properties of a PVA brush and discuss its effects on friction.

Galerkin Boundary Elements for a Computation of the Surface Tractions in Exterior Stokes Flows

2014 ◽  
Vol 136 (11) ◽  
Author(s):  
Jorge D'Elía ◽  
Laura Battaglia ◽  
Alberto Cardona ◽  
Mario Storti ◽  
Gustavo Ríos Rodríguez
Keyword(s):  
Body Force ◽  
Three Dimensional ◽  
Boundary Integral ◽  
The Body ◽  
Creeping Flow ◽  
Viscous Drag ◽  
Singular Behavior ◽  
Fredholm Type ◽  
Total Body ◽  
Weighting Procedures

In the computation of a three–dimensional steady creeping flow around a rigid body, the total body force and torque are well predicted using a boundary integral equation (BIE) with a single concentrated pair Stokeslet- Rotlet located at an interior point of the body. However, the distribution of surface tractions are seldom considered. Then, a completed indirect velocity BIE of Fredholm type and second-kind is employed for the computation of the pointwise tractions, and it is numerically solved by using either collocation or Galerkin weighting procedures over flat triangles. In the Galerkin case, a full numerical quadrature is proposed in order to handle the weak singularity of the tensor kernels, which is an extension for fluid engineering of a general framework (Taylor, 2003, “Accurate and Efficient Numerical Integration of Weakly Singulars Integrals in Galerkin EFIE Solutions,” IEEE Trans. on Antennas and Propag., 51(7), pp. 1630–1637). Several numerical simulations of steady creeping flow around closed bodies are presented, where results compare well with semianalytical and finite-element solutions, showing the ability of the method for obtaining the viscous drag and capturing the singular behavior of the surface tractions close to edges and corners. Also, deliberately intricate geometries are considered.

Deterministic and Stochastic Prediction of the Hydrodynamics of a Three-Dimensional Body Falling Through Water

2008 ◽  
Author(s):  
Xuemei Zhu ◽  
Yuming Liu
Keyword(s):  
Deterministic Model ◽  
Three Dimensional ◽  
Field Measurements ◽  
The Body ◽  
Statistical Prediction ◽  
Viscous Drag ◽  
Physical Parameters ◽  
Practical Applications ◽  
Characteristic Features ◽  
Six Degree Of Freedom

We investigate the dynamics of a three-dimensional mine-shaped body falling through water deterministically and stochastically. A physics-based deterministic model, MINE6D, is developed for the prediction of the six degree-of-freedom motion of the body falling freely through water. In MINE6D, the hydrodynamic load due to the added inertia effect is obtained exactly by using a boundary-element method while the viscous drag associated with flow separation and vortex shedding is modeled using a quasi-steady approach. Since the mine motion is found to be highly sensitive to varying the physical parameters such as body geometry, mass distribution, and initial releasing conditions, we develop a stochastic model using Monte-Carlo MINE6D simulation for the statistical analysis of mine motions in practical applications. The statistical prediction is compared with available field measurements both qualitatively and quantitatively. The characteristic features and dependence on physical parameters of the statistical prediction of mine motions are investigated. The present study is of importance to the prediction of mine burial in seabed and the design of mines.

scholarly journals Sticking like sticky tape: tree frogs use friction forces to enhance attachment on overhanging surfaces

2013 ◽  
Vol 10 (80) ◽  
pp. 20120838 ◽  
Author(s):  
Thomas Endlein ◽  
Aihong Ji ◽  
Diana Samuel ◽  
Ning Yao ◽  
Zhongyuan Wang ◽  
...  
Keyword(s):  
Slope Angle ◽  
Three Dimensional ◽  
The Body ◽  
Adhesive Tape ◽  
Large Contribution ◽  
Lateral Direction ◽  
Friction Forces ◽  
Normal Forces ◽  
Adhesive Pads ◽  
Tree Frogs

To live and clamber about in an arboreal habitat, tree frogs have evolved adhesive pads on their toes. In addition, they often have long and slender legs to facilitate not only long jumps, but also to bridge gaps between leaves when climbing. Both adhesive pads and long limbs are used in conjunction, as we will show in this study. Previous research has shown that tree frogs change from a crouched posture (where the limbs are close to the body) to a sprawled posture with extended limbs when clinging on to steeper inclines such as vertical or overhanging slopes. We investigated this change in posture in White's tree frogs ( Litoria caerulea ) by challenging the frogs to cling onto a tiltable platform. The platform consisted of an array of 24 three-dimensional force transducers, which allowed us to measure the ground reaction forces of the frogs during a tilt. Starting from a crouched resting position, the normal forces on the forelimbs changed sign and became increasingly negative with increasing slope angle of the platform. At about 106°±12°, tilt of the platform the frogs reacted by extending one or two of their limbs outwards. At a steeper angle (131°±11°), the frogs spread out all their limbs sideways, with the hindlimbs stretched out to their maximum reach. Although the extension was strongest in the lateral direction, limbs were significantly extended in the fore–aft direction as well. With the extension of the limbs, the lateral forces increased relative to the normal forces. The large contribution of the in-plane forces helped to keep the angle between the force vector and the platform small. The Kendall theory for the peeling of adhesive tape predicts that smaller peel angles lead to higher attachment forces. We compare our data with the predictions of the Kendall model and discuss possible implications of the sliding of the pads on the surface. The forces were indeed much larger for smaller angles and thus can be explained by peeling theory.

scholarly journals An Accurate Cartesian Method for Incompressible Flows with Moving Boundaries

2014 ◽  
Vol 15 (5) ◽  
pp. 1266-1290 ◽  
Author(s):  
M. Bergmann ◽  
J. Hovnanian ◽  
A. Iollo
Keyword(s):  
Incompressible Flows ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Viscous Flows ◽  
The Body ◽  
Navier Stokes ◽  
Ghost Cell ◽  
Order Accuracy ◽  
Navier Stokes Equations ◽  
Moving Body

AbstractAn accurate cartesian method is devised to simulate incompressible viscous flows past an arbitrary moving body. The Navier-Stokes equations are spatially discretized onto a fixed Cartesian mesh. The body is taken into account via the ghost-cell method and the so-called penalty method, resulting in second-order accuracy in velocity. The accuracy and the efficiency of the solver are tested through two-dimensional reference simulations. To show the versatility of this scheme we simulate a three-dimensional self propelled jellyfish prototype.

Dynamics of a Moving Body With the Hole in Its Center and Characteristics of Fluid Flow in a Small Diameter Tube

2009 ◽  
Author(s):  
Toru Maeda ◽  
Akihiro Sato ◽  
Tatsuya Otsuka ◽  
Masatsugu Yoshizawa
Keyword(s):  
Rigid Body ◽  
Average Velocity ◽  
Small Diameter ◽  
Flow Characteristics ◽  
Viscous Friction ◽  
Terminal Velocity ◽  
The Body ◽  
Pressure Force ◽  
Viscous Friction Force ◽  
Moving Body

A rigid body moving with fluid in a narrow tube is expected to be developed for future engineering applications such as a capsule endoscopy, and it is also applied to some parts of industry. This paper deals with the flow characteristics around a single rigid body with a hole in its center and transient motion of the body when the body is influenced by pressure force from upstream. The model considered the width of the gap between the body and the wall is smaller than a diameter of a tube so that the force on the body can be numerically and analytically estimated as a viscous friction force. It was assumed that the flow is axisymmetric, laminar and taken to be Newtonian and incompressible. It was obtained that, with the hole in its center, the terminal velocity of the body becomes smaller than the average velocity at the inlet. Moreover, because there is a stagnation on the body, the pressure increases behind the body.

Magnetohydrodynamic wakes

1963 ◽  
Vol 15 (1) ◽  
pp. 1-12 ◽  
Author(s):  
M. B. Glauert
Keyword(s):  
Velocity Field ◽  
Electric Current ◽  
Degrees Of Freedom ◽  
Three Dimensional ◽  
Effective Diffusivity ◽  
The Body ◽  
Flow Perturbation ◽  
Drag Forces ◽  
Lift And Drag ◽  
Three Degrees Of Freedom

The most notable feature of the magnetohydrodynamic flow at large distances from a three-dimensional body is the formation of two wakes, within which vorticity and electric current are confined. In this paper results are obtained for the effective diffusivity and the relation between current and vorticity in each wake, for the balance between the strengths of the disturbances in the wakes and in the irrotational current-free flow outside, and for the lift and drag forces acting on the body. The final answers take the form of remarkably simple extensions of the corresponding formulae for non-conducting flow. In spite of the extra wake and the presence of a magnetic as well as a velocity field, the flow perturbation at large distances still has only three degrees of freedom.

An Approach to Determining the Kinematic Parameters of Biomechanical Systems with Applications to the Wrist

1992 ◽  
Vol 206 (4) ◽  
pp. 213-223 ◽  
Author(s):  
P Pittman ◽  
R Colbaugh ◽  
K Glass ◽  
B Rowen
Keyword(s):  
Three Dimensional ◽  
Spatial Location ◽  
The Body ◽  
Translation Vector ◽  
Computationally Efficient ◽  
Kinematic Parameters ◽  
Angular Rotation ◽  
Serial Link ◽  
Moving Body ◽  
Spatially Distributed

This paper presents an accurate and robust approach for determining the kinematic parameters of biomechanical systems. A computationally efficient algorithm is given for estimating the translation vector and rotation matrix of a moving body from measurements of the position of at least four spatially distributed points on the body. This algorithm provides an estimation of the spatial location and orientation of the body which is less sensitive to measurement error than other methods. It is indicated how the kinematic parameters can be used to determine the linear translation and angular rotation of the moving body in terms of an anatomically relevant coordinate system. The design, fabrication and calibration of an inexpensive, serial-link, three-dimensional mechanical digitizer for use in data acquisition is described. This device is kinematically optimized and is easy to use for accurate data collection. An implementation of this approach to quantifying certain aspects of the kinematics of the human wrist is discussed.

E. Coli Inspired Propulsion for Swimming Microrobots

2004 ◽  
Author(s):  
Bahareh Behkam ◽  
Metin Sitti
Keyword(s):  
Human Body ◽  
Silicone Oil ◽  
The Body ◽  
Viscous Drag ◽  
Smart Devices ◽  
Low Velocity ◽  
Drag Forces ◽  
Miniature Device ◽  
Pi Theorem ◽  
Localized Drug Delivery

Medical applications are among the most fascinating areas of microrobotics. For long, scientists have dreamed of miniature smart devices that can travel inside the human body and carry out a host of complex operations such as minimally invasive surgery (MIS), highly localized drug delivery, and screening for diseases that are in their very early stages. Still a distant dream, significant progress in micro and nanotechnology brings us closer to materializing it. For such a miniature device to be injected into the body, it has to be 800 μm or smaller in diameter. Miniature, safe and energy efficient propulsion systems hold the key to maturing this technology but they pose significant challenges. Scaling the macroscale natation mechanisms to micro/nano length scales is unfeasible. It has been estimated that a vibrating-fin driven swimming robot shorter than 6 mm can not overcome the viscous drag forces in water. In this paper, the authors propose a new type of propulsion inspired by the motility mechanism of bacteria with peritrichous flagellation, such as Escherichia coli, Salmonella typhimurium and Serratia marcescens. The perfomance of the propulsive mechanism is estimated by modeling the dynamics of the motion. The motion of the moving organelle is simulated and key parameters such as velocity, distribution of force and power requirments for different configurations of the tail are determined theoretically. In order to validate the theoretical result, a scaled up model of the swimming robot is fabricated and characterized in silicone oil using the Buckingham PI theorem for scaling. The results are compared with the theoretically computed values. These robots are intended to swim in stagnation/low velocity biofluid and reach currently inaccessible areas of the human body for disease inspection and possibly treatment. Potential target regions to use these robots include eyeball cavity, cerebrospinal fluid and the urinary system.

Sign in / Sign up

Export Citation Format

Share Document