Time, another dimension

HAZOP studies may be made on batch as well as continuous processes. For a continuous process, the working document is usually a set of flow sheets or piping and instrument diagrams (P IDs). Batch processes have another dimension time. Time is usually not significant with a continuous process that is operating smoothly, although start-up and shutdown must also be considered, when the continuous process will resemble a batch process. For batch processes, the working documents consist not only of the flow sheets or P IDs but also... 

The application of force to a stationary or moving system can be described in static, kinematic, or dynamic terms that define the mechanical similarity of processing equipment and the solids or liquids within their confines. Static similarity relates the deformation under constant stress of one body or structure to that of another it exists when geometric similarity is maintained even as elastic or plastic deformation of stressed structural components occurs [53], In contrast, kinematic similarity encompasses the additional dimension of time, while dynamic similarity involves the forces (e.g., pressure, gravitational, centrifugal) that accelerate or retard moving masses in dynamic systems. The inclusion of tune as another dimension necessitates the consideration of corresponding times, t and t, for which the time scale ratio t, defined as t = t It, is a constant. 

We note that the term dipole implies the existence of another charge, —q, that remains fixed at the origin all the time. If the charge q is accelerating, it will emit radiation according to Eq. 2.61, where we replace the product qjr by the second derivative of p with respect to time, p. Dimensions of the displacement of charge will be of the order of the size of atoms or molecules, usually assumed to be small with regard to both... 

However, my findings and parapsychological findings on precognition in general have forced me to theorize further that there is another dimension of time (and probably of space as well) that some aspect of our awareness can sometimes make contact with. This second dimension acts as the channel for psi information. I theorize that one property of this second dimension of time is that the experienced present of awareness is wider than the experienced present of ordinary consciousness. In my theory of states of consciousness [173], ordinary consciousness is seen as basic awareness modulated by brain mechanisms and thus tied to ordinary time. 

Browning the beef before braising adds another dimension of flavor, but isn t absolutely necessary. Try it both ways skipping the browning step saves time and mess. 

Time worked even more extravagant magic when it sent him into another dimension, where 1 would be aware of a pervasive bright pure light, like a kind of invisible sunlit snow ... 

It was Schrodinger s intention to associate Zitterbewegung with electron spin, but such an assumption would serve simply to clarify one mystery in terms of another. Instead, one could try first to understand the nature of Zitterbewegung within the region identified as the electron. The only substance available to support the periodic motion is space itself and there seems to be two possibilities either space consists of continuous stuff or of compacted particles. Winterberg [68] explored the latter possibility. Wave motion in a continuous aether is probably easier to visualize and needs fewer assumptions. The only postulate is that ponderable matter and its properties represent special configurations of space. Hence flat Euclidean space (-time) in dimensions of any number, is featureless and empty. 

Patterns can be collected with meaningful statistics within fractions of seconds, if strong scatterers are studied, or they can be built up in repetitive measurements if reversible changes are studied. As a consequence, complete one-dimensional or two-dimensional image patterns can be collected in consecutive time intervals or time frames. The image information of each consecutive time frame has to be accumulated in separate memory segments. Thus time is added as another dimension to the one-or two- dimensional position information. 

The frequency dependence of the spin density is exploited in spectroscopic imaging (cf. Section 6.2.4) to derive spectroscopic NMR parameter contrast from another dimension attached to the imaging experiment. Yet when measuring time is at a premium, a spectroscopic dimension cannot be acquired. The frequency dependence will then lead to a degradation of the spatial resolution. If, however, time-independent gradients are applied, and if the spectrum does not vary over the sample, that is, if s(t, r) = s(t), then the Fourier transform of the FID (5.4.8) is given by the convolution (cf. eqn (4.2.1)) of the spin density with the NMR spectrum S co),... 

The material presented earlier was confined to steady-state flows over simply shaped bodies such as flat plates, with and without pressure gradients in the streamwise direction, or stagnation regions on blunt bodies. The simplicity of these flow configurations allows reduction of the problems to the solution of steady-state ordinary differential equations. The evaluation of convective heat transfer to more complex three-dimensional configurations, characteristic of real aerodynamic vehicles, involves the solution of partial differential equations. Even when the latter are confined to steady-state problems, they require extensive use of computers in the solution of finite difference or finite element formulations Nonsteady flows further complicate the problems by introducing another dimension, namely, time. 

Another dimension of feasibility, projected schedule feasibility, relates to project duration. The purpose of this assessment is to determine whether the timelines and due dates can be met and that meeting those dates will be sufficient to meet the objectives of the organization. For example, it could be that the system must be developed in time to meet a regulatory deadline or must be completed at a certain point in a business cycle, such as a holiday or a point in the year when new products are typically introduced to market. 

One problem of shifting the sampling rate of a PCM sound is the intrinsic link between pitch and time. Pitch shifting upward by one octave yields a sound which plays at twice as high a pitch, and for half the time. Another problem is the so-called munchkinification ect. This relates to the apparent shift in the perceived sound-producing obj ect when the pitch and time is shifted. For example, the octave-up pitch shift also yields the perception of a talker whose head sounds half the size of a normal person. This other dimension, which has to do with the quality of sounds rather than pitch, loudness, or time, is called timbre. Once we ve learned more about the frequency domain, we ll have better tools to explain munchkimfication and timbre, and we ll also have a lot more tools to avoid (or control independently) all of these dimensions. 

The turnover time of a substance denotes that time when the substance in the volume regarded becomes practically zero. Only in the case of the zero-order removal process, i. e. the removal rate is constant over time and depends not on the concentration and x, marks exactly the time when c = 0. The basic equation (4.337) changes into (note that the removal coefficient k becomes identical to the removal flux and gets another dimension) ... 

The main advantage of ion mobility analyzers is the addition of another dimension of separation to mass spectrometry. FAIMS improves signal-to-noise ratios by removing isobaric ions that have three-dimensional shapes that are different from those of the analyte. IMS enables the measurement of the cross-sectional areas of ions in addition to the dimensions of retention time, mass and intensity provided by the chromatograph and mass spectrometer, respectively. IMS can also improve the quality of spectra by separating species that overlap chromatographically and would otherwise give mixed spectra. 

---