Maximum Net Force Research Articles

Propagation of solitary waves over a bottom-mounted barrier

The interactions between a solitary wave and a submerged, vertical, bottom-mounted barrier are investigated experimentally and numerically. Numerical results are calculated using the well-validated two-dimensional volume of fluid (VOF)-type model, named COBRAS (COrnell BReaking And Structure), based on the Reynolds-Averaged Navier–Stokes (RANS) equations and the non-linear k–ε turbulence closure model. Experiments are conducted to measure the free surface motion and velocity fields using a particle image velocimetry (PIV) system to provide data for model validation. Fairly good agreements at both the pre- and post-breaking stages are obtained. Then, the verified numerical results are employed to illustrate the free surface motion and the vortex evolution in detail. Wave breaking occurs in the direction opposite to that of the wave after a solitary wave propagates over the barrier. A local maximum value of turbulence intensity is observed for both experimental and numerical results at the impinging point of the breaking wave. An almost linear relationship between the maximum net force and the wave non-linearity is obtained. The effectiveness of the bottom-mounted barrier is estimated by evaluating the wave reflection, transmission, and dissipation coefficients using the energy integral method. Finally, the trajectories of marked fluid particles that are initially located around the barrier help understand the possible sediment transport.

The force–time profile of elite front crawl swimmers

In this study, we used recently developed technology to determine the force–time profile of elite swimmers, which enabled coaches to make informed decisions on technique modifications. Eight elite male swimmers with a FINA (Federation Internationale de Natation) rank of 900+ completed five passive (streamline tow) and five net force (arms and leg swimming) trials. Three 50-Hz cameras were used to video each trial and were synchronized to the kinetic data output from a force-platform, upon which a motorized towing device was mounted. Passive and net force trials were completed at the participant's maximal front crawl swimming velocity. For the constant tow velocity, the net force profile was presented as a force–time graph, and the limitation of a constant velocity assumption was acknowledged. This allowed minimum and maximum net forces and arm symmetry to be identified. At a mean velocity of 1.92 ± 0.06 m · s−1, the mean passive drag for the swimmers was 80.3 ± 4.0 N, and the mean net force was 262.4 ± 33.4 N. The mean location in the stroke cycle for minimum and maximum net force production was at 45% (insweep phase) and 75% (upsweep phase) of the stroke, respectively. This force–time profile also identified any stroke asymmetry.

Thermal gradient-induced forces on geodesic reference masses for LISA

The low frequency sensitivity of space-borne gravitational wave observatories will depend critically on the geodesic purity of the trajectories of orbiting test masses. Fluctuations in the temperature difference across the enclosure surrounding the free-falling test mass can produce noisy forces through several processes, including the radiometric effect, radiation pressure, and outgassing. We present here a detailed experimental investigation of thermal gradient-induced forces for the Laser Interferometer Space Antenna (LISA) gravitational wave mission and the LISA Pathfinder, employing high resolution torsion pendulum measurements of the torque on a LISA-like test mass suspended inside a prototype of the LISA gravitational reference sensor that will surround the test mass in orbit. The measurement campaign, accompanied by numerical simulations of the radiometric and radiation pressure effects, allows a more accurate and representative characterization of thermal-gradient forces in the specific geometry and environment relevant to LISA free-fall. The pressure dependence of the measured torques allows clear identification of the radiometric effect, in quantitative agreement with the model developed. In the limit of zero gas pressure, the measurements are most likely dominated by outgassing, but at a low level that does not threaten the current LISA noise estimate, which assumes a maximum net force per degreemore » of temperature difference of 100(pN/K) for the overall thermal gradient-induced effects.« less

Scaling of maximum net force output by motors used for locomotion

Biological and engineered motors are surprisingly similar in their adherence to two or possibly three fundamental regimes for the mass scaling of maximum force output (Fmax). One scaling regime (Group 1: myosin, kinesin, dynein and RNA polymerase molecules; muscle cells; whole muscles; winches; linear actuators) comprises motors that create slow translational motion with force outputs limited by the axial stress capacity of the motor, which results in Fmax scaling as motor mass0.67 (M0.67). Another scaling regime (Group 2: flying birds, bats and insects; swimming fish; running animals; piston engines; electric motors; jets) comprises motors that cycle rapidly, with significant internal and external accelerations, and for whom inertia and fatigue life appear to be important constraints. The scaling of inertial loads and fatigue life both appear to enforce Fmax scaling as M1.0 in these motors. Despite great differences in materials and mechanisms, the mass specific Fmax of Group 2 motors clusters tightly around a mean of 57 N kg(-1), a region of specific force loading where there appears to be a common transition from high- to low-cycle fatigue. For motors subject to multi-axial stresses, the steepness of the load-life curve in the neighborhood of 50-100 N kg(-1) may overwhelm other material and mechanistic factors, thereby homogenizing the mass specific Fmax of grossly dissimilar animals and machines. Rockets scale with Group 1 motors but for different mechanistic reasons; they are free from fatigue constraints and their thrust is determined by mass flow rates that depend on cross sectional area of the exit nozzle. There is possibly a third scaling regime of Fmax for small motors (bacterial and spermatazoan flagella; a protozoan spring) where viscosity dominates over inertia. Data for force output of viscous regime motors are scarce, but the few data available suggest a gradually increasing scaling slope that converges with the Group 2 scaling relationship at a Reynolds number of about 10(2). The Group 1 and Group 2 scaling relationships intersect at a motor mass of 4400 kg, which restricts the force output and design of Group 2 motors greater than this mass. Above 4400 kg, all motors are limited by stress and have Fmax that scales as M0.67; this results in a gradual decline in mass specific Fmax at motor mass greater than 4400 kg. Because of declining mass specific Fmax, there is little or no potential for biological or engineered motors or rockets larger than those already in use.

Molecules, muscles, and machines: universal performance characteristics of motors.

Animal- and human-made motors vary widely in size and shape, are constructed of vastly different materials, use different mechanisms, and produce an enormous range of mass-specific power. Despite these differences, there is remarkable consistency in the maximum net force produced by broad classes of animal- and human-made motors. Motors that use force production to accomplish steady translational motion of a load (myosin, kinesin, dynein, and RNA polymerase molecules, muscle cells, whole muscles, winches, linear actuators, and rockets) have maximal force outputs that scale as the two-thirds power of mass, i.e., with cross-sectional area. Motors that use cyclical motion to generate force and are more subject to multiaxial stress and vibration have maximal force outputs that scale as a single isometric function of motor mass with mass-specific net force output averaging 57 N x kg(-1) (SD = 14). Examples of this class of motors includes flying birds, bats, and insects, swimming fish, various taxa of running animals, piston engines, electric motors, and all types of jets. Dependence of force production and stress resistance on cross-sectional area is well known, but the isometric scaling and common upper limit of mass-specific force production by cyclical motion motors has not been recognized previously and is not explained by an existing body of theory. Remarkably, this finding indicates that most of the motors used by humans and animals for transportation have a common upper limit of mass-specific net force output that is independent of materials and mechanisms.

Discrete models for two- and three-dimensional fragmentation

We study an iterative stochastic process as a model for two- and three-dimensional discrete fragmentation. The model fulfills mass conservation and is defined on two- and three-dimensional lattices of linear size 2 n . At each step of the process the “most stressed” piece is broken in the direction of the maximum net force, which is a random variable. Despite their simplicity, reflected in deterministic fracture criteria and simple random forces acting on the materials, our models present complex features that reproduce some of the experimental results that have been obtained. For some regimes a log-normal and a power law behavior are obtained for the fragment size histogram. For this reason we propose them as basic models that can be substantially refined to describe the fragmentation process of more realistic models.

The principles and practice of molecular mechanics calculations

Abstract The major decisions affecting the construction of a general purpose molecular mechanics program are discussed, although care is taken to highlight techniques which may be useful in special cases. The choice of co-ordinate system, cartesian or internal, in which minimization is to be affected is largely a matter of personal preference as there is little to choose between the two options as far as speed or performance are concerned, although cartesians are probably slightly easier to program. Minimization algorithms based on the general Newton iteration, are the logical, and for practical purposes the only, choice of procedure. In order to obtain consistent and reliable results the maximum net force on any one atom at the local energy minimum should be less than 10−6 kcal mole−1 A−1 and this can only be achieved by means of a second derivative or quasi-Newton minimization algorithm. The latter techniques are rather sensitive to poor approximations to the minimum energy molecular conformation and may be profitably used in tandem with algorithms (pattern search, steepest descent, etc.) which have poorer convergence properties but are more tolerant of approximate trial structures. The choice of analytical or numerical derivatives to be used in conjunction with the (Newton iteration-based) minimization procedure is again something of an open question-analyticals are faster but numericals easier to program and more versatile. With care, numerical first and second derivatives can be calculated only marginally more slowly than analyticals and ways of achieving this are discussed. Calculation of transition states and a procedure midway between trial and error and least-squares generation of force fields are also discussed. Finally the program which resulted from the foregoing considerations is described and an indication of storage requirements and program performance is given. The program uses cartesian co-ordinates, a tandem quasi-Newton minimization procedure and numerical first and second derivatives.