Two-dimensional tracking

Watson, R.W, Jones, R.D., and Sharman, N.B. 1997. Two-dimensional tracking tasks for quantification of sensory-motor dysfunction and their application to Parkinson s disease. Med. Biol. Eng. Comput. 35 141-145. 

Direct observation of molecular diffusion is the most powerful approach to evaluate the bilayer fluidity and molecular diffusivity. Recent advances in optics and CCD devices enable us to detect and track the diffusive motion of a single molecule with an optical microscope. Usually, a fluorescent dye, gold nanoparticle, or fluorescent microsphere is used to label the target molecule in order to visualize it in the microscope [31-33]. By tracking the diffusive motion of the labeled-molecule in an artificial lipid bilayer, random Brownian motion was clearly observed (Figure 13.3) [31]. As already mentioned, the artificial lipid bilayer can be treated as a two-dimensional fluid. Thus, an analysis for a two-dimensional random walk can be applied. Each trajectory observed on the microscope is then numerically analyzed by a simple relationship between the displacement, r, and time interval, T,... 

These two-dimensional, formula-like diagrams help you count and keep track of valence electrons, and communicate essential information about the placement and bonding of atoms or ions in a molecule. Chemists often draw Lewis structures in a way that suggests the shape of a molecule. However, this is not their function. It is important to remember that Lewis structures do not communicate any information about a molecule s shape. To represent the shapes of real molecules, you need a model that depicts them in three-dimensions. 

Two-Dimensional NMR—Basically, the two-dimensional NMR techniques of nuclear Overhauser effect spectroscopy (NOESY) and correlation spectroscopy (COSY) depend on the observation that spins on different protons interact with one another. Protons that are attached to adjacent atoms can be directly spin-coupled and thus can be studied using the COSY method. This technique allows assignment of certain NMR frequencies by tracking from one atom to another. The NOESY approach is based on the observation that two protons closer than about 0.5 nm perturb one another s spins even if they are not closely coupled in the primary structure. This allows spacial geometry to be determined for certain molecules. 

Monte Carlo methods, direct tracking methods, and vertex models, where the evolution of the two-dimensional grain structure is described in terms of the motion of the vertices. After initial transients, all of these simulations exhibit statistical self-similarity during growth and an average grain area that increases linearly with time according to Eq. 15.35. 

Qian H, Sheetz MP, Elson EL (1991) Single particle tracking. Analysis of diffusion and flow in two-dimensional systems. Biophys J 60 910-921... 

Thus, in the gravitational-crossflow zone particle separation is a two-dimensional process, where their trajectories are in fact ballistic tracks. Unlike the counterflow zone, the cut size depends not only on the particle s terminal velocity, but mainly on the chamber length and height. These parameters are chosen in such a way that particles with the cut size land at the farthest point A of the bottom (Fig. lb). 

Prior to tracking particles, the groundwater flow equation must be solved in order to determine the hydraulic head distribution within the aquifer. The two-dimensional, steady-state groundwater flow equation is... 

P 7] The topic has only been treated theoretically so far [28], A mathematical model was set up slip boundary conditions were used and the Navier-Stokes equation was solved to obtain two-dimensional electroosmotic flows for various distributions of the C, potential. The flow field was determined analytically using a Fourier series to allow one tracking of passive tracer particles for flow visualization. It was chosen to study the asymptotic behavior of the series components to overcome the limits of Fourier series with regard to slow convergence. In this way, with only a few terms highly accurate solutions are yielded. Then, alternation between two flow fields is used to induce chaotic advection. This is achieved by periodic alteration of the electrodes potentials. 

In the last decades, the modeling of both compacted particulates and flowing particle assemblies under loads and under flow conditions has been advanced by DEM, first developed by Cundall (46) for two-dimensional compacted-disk assemblies in 1971. The origins of DEM are in the field of molecular dynamics (MD), where the motions of individual molecules are tracked under the influence of an external force (e.g., electrostatic) field (47). Experimental results such as those with model photo-elastic assemblies just discussed have also assisted the development of the DEM simulation models. 

Nd glass laser. The two crucial features of this apparatus are an optical configuration designed specifically to optimize the spectrometric range and accuracy, and an advanced two dimensional optical multichannel analyzer system which acquires and processes two full spectral data tracks for each laser shot. In the following sections we present details of the system s design followed by examples of its high accuracy and wide utility in scientific applications. 

The previous example involved a two-dimensional system (involving two independent dynamic species). Thus the CME followed from the two-dimensional reaction diagram. For systems with more species, the dimension of the problem grows accordingly. For a system with three species, say A, B, and C, the CME tracks the three-dimensional probability of A molecules, m B molecules, and n C molecules present at time t. In general, the mathematical description of an A-dimensional system is the joint probability distribution... 

The analysis of the chemical composition of the sample was conducted by coupled SEC-FTIR using the LC Transform. After separating the sample with respect to molecular size, the fractions were deposited on the germanium disc and FTIR spectra were recorded continuously along the sample track. In total, a set of about 80 spectra was obtained which was presented in a three-dimensional plot (Fig. 29). The projection of the 3D plot on the retention time-IR frequency coordinate system yielded a two-dimensional representation, where the intensities of the absorption peaks were given by a color code. Such a contour plot readily provides information on the chemical composition of each chromato-... 

To show the relative roles of various two-dimensional modes at all frequencies, the real and imaginary part of the wave numbers (a jCKj) are plotted in Fig. 2.25 as a function of non-dimensional circular frequency for Re = 1000. The three downstream propagating modes that are present at this Reynolds number for moderate frequencies are marked by numerals and are tracked in Fig. 2.25 for their variation with circular frequency. All these two-dimensional modes disappear abruptly one by one, as the frequency is decreased- as noted in Fig. 2.25. Values of circular frequencies at which... 

TLC Analysis. Small sample requirements, minimal sample preparation, high sensitivity, and low cost make TLC an attractive method for organic archaeometry. Its suitability for the detection of resin acids in complex mixtures was tested by subjecting the Carthaginian samples to a two-dimensional technique. Ether solutions of the organic material were spotted onto the plate and first freed from nonpolar components by elution in one direction with heptane. The residual carboxylic acids were then developed, with reference standards in adjacent tracks, in the second direction with heptane-toluene-ether (1 1 1). Under these conditions, 7-ketodehydro-abietic acid remains at or very near the origin (maximum retardation factor [Rf] = 0.04), but abietic acid and dehydroabietic acid are readily identified. 

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