We provide experiments that had been conducted to investigate the particle trajectory beneath a solitary water wave. Experimental results show that the surface drift is larger than the bottom drift. Meanwhile, the ratio of the net horizontal displacement to the total height of the trajectory at the free surface and subsurface will decrease with the initial vertical position and increase with th...

then so is the curve x(−t), as is easily verified by direct computation. (Note that d/dt(x(−t)) = ẍ(−t), since the two derivatives pull out two minus signs.) In terms of trajectories in phase space, we note that dx(−t)/dt = −ẋ(−t). This means that the momentum of the particle along the time-reversed trajectory is the negative of the momentum along the original trajectory. We may therefore formu...

The calculation of particle trajectories in the Earth’s magnetic field has been a subject of interest since the time of Störmer. The fundamental problem is that the trajectory-tracing process involves using mathematical equations that have ‘no solution in closed form’. This difficulty has forced researchers to use the ‘brute force’ technique of numerical integration of many individual trajector...

A ‘centrifugal force’ as experienced by particles in a centrifuge actually reflects the natural tendency of the particle to move in a straight line in the absence of external forces. If we view the experiment in the (fixed) reference frame of the laboratory, we observe that the particle is deflected from a linear trajectory by a centripetal force (directed toward the central axis of the rotor)....

In an earlier contribution we proposed a particle filter for underwater (UW) navigation, and applied it to an experimental trajectory. Here we focus on performance improvements and analysis. First, the Cramér Rao lower bound (CRLB) along the experimental trajectory is computed, which is only slightly lower than the particle filter estimate after initial transients. Simple rule of thumbs for how...

Any trajectory of a diffusing particle making a transition between two end points of an interval can be divided into two segments, which we call direct-transit and looping parts. The former is the final segment of the trajectory, when the particle goes from one end point of the interval to the opposite end point, without retouching the starting point. The rest of the trajectory is the looping p...

This paper describes a new system, dubbed Continuous Appearance-based Trajectory SLAM (CAT-SLAM), which augments sequential appearance-based place recognition with local metric pose filtering to improve the frequency and reliability of appearance based loop closure. As in other approaches to appearance-based mapping, loop closure is performed without calculating global feature geometry or perfo...

the southern coasts of caspian sea is subjected to synoptic/mesoscale weather systemsranging from locally enhanced sea breeze formation and small local front systems to synoptic scale cyclones.this study presents climatology of cyclones over the southern coasts of caspian sea covering a ten year period1996-2005. altogether 57 cyclones were formed during the ten year period. anoticeable seasonal...

A real-time, continuous optical particle separation method, termed cross-type optical particle separation, is investigated theoretically and experimentally. The trajectory of a particle subject to cross-type optical particle separation is predicted by solving the particle dynamic equation and compared with experimental data. For various flow velocities and particle sizes, the retention distance...

Recent developments concerning the unsteady dynamic forces on a spherical particle at finite Reynolds number are reviewed for solid particles and clean micro-bubble. A particle frequency response function and an energy transfer function are derived for a solid particle or a contaminated micro-bubble in gas or liquid flow. A simple, unified method for estimating the cut-off frequency, or cut-off...