Continuous-time systems

If there is particle—particle interaction, as is the case for flocculated systems, the viscosity is higher than in the absence of flocculation. Furthermore, a flocculated dispersion is shear thinning and possibly thixotropic because the floccules break down to the individual particles when shear stress is appHed. Considered in terms of the Mooney equation, at low shear rates in a flocculated system some continuous phase is trapped between the particles in the floccules. This effectively increases the internal phase volume and hence the viscosity of the system. Under sufficiently high stress, the floccules break up, reducing the effective internal phase volume and the viscosity. If, as is commonly the case, the extent of floccule separation increases with shearing time, the system is thixotropic as well as shear thinning. 

All processes may be classified as batch, continuous, or semibatch depending on how materials are transferred into and out of the system. Also, the process operation may be characterized as unsteady state (i.e., transient) or steady state, depending on whether the process variables (e.g., pressure, temperature, compositions, flowrate, etc.) are changing with time or not, respectively. In a batch process, the entire feed material (i.e., charge) is added instantaneously to the system marking the beginning of the process, and all the contents of the system including the products are removed at a later time, at the end of the process. In a continuous process, the materials enter and leave the system as continuous streams, but not necessarily at the same rate. In a semibalch process, the feed may be added at once but the products removed continuously, or vice versa. It is evident that batch and semibatch processes are inherently unsteady state, whereas continuous processes may be operated in a steady or unsteady-state mode. Start-up and shut-down procedures of a steady continuous production process are examples of transient operation. 

Reliability.23 —Let a mechanical or an electronic system be divided into n components that can fail independently. In addition, let the failure of a component be independent of the duration and frequency of its period of use. The probability that a component not in use at time t will be used at or before time t + r is independent of when it was last used. Assume that the system operates continuously except for interruptions caused by failure. A component that fails is replaced by a new component having identical statistics as the original had when new. Let Ft(t) be the probability that an type component,... 

As a consequence, good, safe, steam-sampling points are required, and automatic, real-time continuous analyzer systems for monitoring of steam and condensate quality are very useful. These requirements usually are not a problem in larger power and process HP boiler plants. Here, each facility tends to have a unique combination of operating conditions and waterside chemistry circumstances that necessitate the provision of a steady stream of reliable operational data, and this can be obtained realistically only from continuous, real-time analysis. 

The dynamic viewpoint of chemical kinetics may be contrasted with the essentially static viewpoint of thermodynamics. A kinetic system is a system in unidirectional movement toward a condition of thermodynamic equilibrium. The chemical composition of the system changes continuously with time. A system that is in thermodynamic equilibrium, on the other hand, undergoes no net change with time. The thermo-dynamicist is interested only in the initial and final states of the system and is not concerned with the time required for the transition or the molecular processes involved therein the chemical kineticist is concerned primarily with these issues. 

Reliability and availability Does the running system reliably continue to perform correctly over extended periods of time What proportion of time is the system up and running In the presence of failure, does it degrade gracefully rather than shut down completely Reliability is measured as the mean time to system failure availability is the proportion of time the system is functioning. Both qualities are typically dealt with by making the architecture fault-tolerant using duplicated hardware and software resources. 

The next level beyond the step-and-shoot method is the helical-scan approach. The conveyor belt of a heftcal-scan system moves continuously at a uniform speed and is synchronized with the rotating disk that holds the X-ray source and detectors. The synchronization ensures that by the time a bag has advanced by... 

In the example we have been using (see Section 3.1), the response from the system was measured nine times. The resulting data is a sample of the conceptually infinite number of results that might be obtained if the system were continuously measured. This conceptually infinite number of responses constitutes what is called the... 

The control is a set of real parameters/ , which have been combined to a vector /. These can be timings, amplitudes, and/or phases of a given number of discrete pulses, or describe a time-continuous modulation of the system. Here, we focus on time-dependent control, where the/(r) parameterize the system Hamiltonian as Hg = Hglfit)], or the unitary evolution operator 6/(t) = =... 

As far as the controls are concerned, we here consider time-continuous modulation of the system Hamiltonian, which allows for vastly more freedom compared to control that is restricted to stroboscopic pulses as in DD [42, 55, 91]. We do not rely on rapidly changing control fields that are required to approximate stroboscopic a -pulses. These features allow efficient optimization under energy constraint. On the other hand, the generation of a sequence of well-defined pulses may be preferable experimentally. We may choose the pulse timings and/or areas as continuous control parameters and optimize them with respect to a given bath spectrum. Hence, our approach encompasses both pulsed and continuous modulation as special cases. The same approach can also be applied to map out the bath spectrum by measuring the coherence decay rate for a narrow-band modulation centered at different frequencies [117]. 

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