Separation in time

The last approximation is for finite At. When the equations of motions are solved exactly, the model provides the correct answer (cr = 0). When the time step is sufficiently large we argue below that equation (10) is still reasonable. The essential assumption is for the intermediate range of time steps for which the errors may maintain correlation. We do not consider instabilities of the numerical solution which are easy to detect, and in which the errors are clearly correlated even for large separation in time. Calculation of the correlation of the errors (as defined in equation (9)) can further test the assumption of no correlation of Q t)Q t )). 

Finite difference techniques are used to generate molecular dynamics trajectories with continuous potential models, which we will assume to be pairwise additive. The essential idea is that the integration is broken down into many small stages, each separated in time by a fixed time 6t. The total force on each particle in the configuration at a time t is calculated as the vector sum of its interactions with other particles. From the force we can determine the accelerations of the particles, which are then combined with the positions and velocities at a time t to calculate the positions and velocities at a time t + 6t. The force is assumed to be constant during the time step. The forces on the particles in their new positions are then determined, leading to new positions and velocities at time t - - 2St, and so on. 

In (a), a pulse of ions is formed but, for illustration purposes, all with the same m/z value. In (b), the ions have been accelerated but, because they were not all formed in the same space, they are separated in time and velocity, with some ions having more kinetic energy than others. In (c), the ions approach the ion mirror or reflectron, which they then penetrate to different depths, depending on their kinetic energies (d). The ones with greater kinetic energy penetrate furthest. In (e), the ions leave the reflectron and travel on to the detector (f), which they all reach at the same time. The path taken by the ions is indicated by the dotted line in (f). 

A fuller description of the microchannel plate is presented in Chapter 30. Briefly, ions traveling down the flight tube of a TOF instrument are separated in time. As each m/z collection of ions arrives at the collector, it may be spread over a small area of space (Figure 27.3). Therefore, so as not to lose ions, rather than have a single-point ion collector, the collector is composed of an array of miniature electron multipliers (microchannels), which are all connected to one electrified plate, so, no matter where an ion of any one m/z value hits the front of the array, its arrival is recorded. The microchannel plate collector could be crudely compared to a satellite TV dish receiver in that radio waves of the same frequency but spread over an area are all collected and recorded at the same time of course, the multichannel plate records the arrival of ions not radio waves. 

Diagram showing a flow of ions of m/z a, b, c, etc. traveling in bunches toward the front face of a microchannel array. After each ion strikes the inside of any one microchannel, a cascade of electrons is produced and moves toward the back end of the microchannel, where they are collected on a metal plate. This flow of electrons from the microchannel plate constitutes the current produced by the incoming ions (often called the ion current but actually a flow of electrons). The ion.s of m/z a, b, c, etc. are separated in time and reach the front of the microchannel collector array one set after another. The time at which the resulting electron current flows is proportional to V m/z). 

An assemblage (array) of single-point electron multipliers in a microchannel plate is designed to detect all ions of any single m/z value as they arrive separated in time. Thus, it is not necessary for each element of the array to be monitored individually for the arrival of ions. Instead, all of... 

Bands of ions of different m/z values and separated in time in a broad ion beam traveling from left to right toward the front face of a microchannel assembly. The ions produce showers of electrons, and these are detected at the collector plate, which joins all the elements as one assemblage. 

The times taken for ions of differing m/z values to reach the detector are of the order of a few microseconds, and the separation in times of arrival for ions of differing m/z value is less than this. Thus, if ions of different mass are to be separated adequately in a time domain (good resolution), they should all start from the ion source at exactly the same time or, more practically, within a few nanoseconds of each other. 

Unlike the array collector, with a microchannel plate all ions of only one m/z value are detected simultaneously, and instrument resolution does not depend on the number of elements in the micro-channel array or on the separation of one element from another. For a microchannel plate, resolution of m/z values in an ion beam depends on their being separated in time by the analyzer so that their times of arrival at the plate differ. 

In a beam of ions separated in time according to m/z value, the total time taken for ions of different m/z values to arrive at a microchannel plate is so short (about 30 psec) that the spectrum appears to have been obtained instantaneously. Thus, for practical purposes, the array and microchannel plate collectors produce an instantaneous mass spectrum, even though the first detects a spatially dispersed set of m/z values and the second detects a temporally dispersed set. 

If the three light pulses of the pulse sequence are only separated in time, and not separated in space (i.e. if the velocity of the atoms is parallel to the laser beams), the interferometer is in a gravimeter or accelerometer configuration. In a uniformly accelerating frame with the atoms, the frequency of the driving... 

Time-of-flight mass analyser A mass analyser in which ions are separated in time as they drift through a field-free flight tube. 

The concept of peak capacity is rather universal in instrumental analytical chemistry. For example, one can resolve components in time as in column chromatography or space, similar to the planar separation systems however, the concept transcends chromatography. Mass spectrometry, for example, a powerful detection method, which is often the detector of choice for complex samples after separation by chromatography, is a separation system itself. Mass spectrometry can separate samples in time when the mass filter is scanned, for example, when the mass-to-charge ratio is scanned in a quadrupole detector. The sample can also be separated in time with a time-of-flight (TOF) mass detector so that the arrival time is related to the mass-to-charge ratio. 

This approach uses a kinetic sequential principle to carry out multicomponent CL-based determinations. In fact, when the half-lives of the CL reactions involved in the determination of the analytes in mixture are appreciably different, the CL intensity-versus-time curve exhibits two peaks that are separate in time (in the case of a binary mixture) this allows both analytes to be directly determined from their corresponding calibration plots. In general, commercially available chemiluminometers have been used in these determinations, so the CL reaction was initially started by addition of one or two reaction ingredients. Thus, in the analysis of binary mixtures of cysteine and gluthatione, appropriate time-resolved response curves were obtained provided that equal volumes of peroxidase and luminol were mixed and saturated with oxygen and that copper(H) and aminothiol solutions were simultaneously injected [62, 63],... 

This energy difference may be interpreted in terms of two elliptical trajectories separated by Ae and with a phase lag between the leading and following edges of the element, ApAq that moves along the fuzzy trajectory. The two edges remain separated in time by a fixed amount A and define the elements A and B at -q0 and p respectively. 

The product of m and G, could be replaced by a new elasticity, which for convenience we could write as Gj. Equations (4.41) and (4.42) describe the relaxation of the stress in terms of a distribution of discrete processes. Some processes may be broadly separated in time to give two clearly separated relaxation processes. Other systems may show a distribution of elastic processes very closely separated in time. 

Keeping in view, this specific, rigid and stringent requirement, the separation-in-space method is found to be normally of lower precision and accuracy than the separation-in time-method. 

When the excitation light is polarized and/or if the emitted fluorescence is detected through a polarizer, rotational motion of a fluorophore causes fluctuations in fluorescence intensity. We will consider only the case where the fluorescence decay, the rotational motion and the translational diffusion are well separated in time. In other words, the relevant parameters are such that tc rp, where is the lifetime of the singlet excited state, zc is the rotational correlation time (defined as l/6Dr where Dr is the rotational diffusion coefficient see Chapter 5, Section 5.6.1), and td is the diffusion time defined above. Then, the normalized autocorrelation function can be written as (Rigler et al., 1993)... 

Redox processes also tend to be separated in time and space due to the relative sluggishness of solute transport. For example, molecular diffusion is the major mechanism by which solutes can be transported through the pore waters of sediments. In many cases this process is slower than the chemical reaction rates and, thus, prevents... 

It is evident that with the discrete cycles of the non-flame atomizers several reactions (desolvation, decomposition, etc.) which occur simultaneously" albeit over rather broad zones in a flame (due to droplet size distributions] are separated in time using a non-flame atomizer. This allows time and temperature optimization for each step and presumably improves atomization efficiencies. Unfortunately, the chemical composition and crystal size at the end of the dry cycle is matrix determined and only minimal control of the composition at the end of the ash cycle is possible, depending on the relative volatilities and reactivities of the matrix and analyte. These poorly controlled parameters can and do lead to changes in atomization efficiencies and hence to matrix interferences. 

The induction of PAL activity by the two growth factors can be separated in time so that they may act at different sites within the cell to bring about the response (40). Auxin added at the time of subculture of the tissue changes the pattern of protein synthesis of the cells by changing the transcription pattern of the mRNA after two hours (43). Kinetin does not have this effect (44). 

One of the more worrisome adverse effects of bupropion is seizures. At dosages of 450 mg/day or less, the rate of seizures is 0.4% for individuals without risk factors (Davidson, 1989). Because of this risk, a single dose of bupropion should not exceed 150 mg and a second dose should be separated in time by a minimum of 8 hours. Also, patients who are metabolically unstable (i.e., have bulimia) should be carefully assessed for the risk of seizures before initiating medication. Finally, bupropion is not associated with sexual side effects. 

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