Integrating a system

Thus for Hamiltonians of finite dimension the effective action functional can be found by immediately integrating a system of ordinary differential equations. The simplest yet very important case is a bath of two-level systems. 

This chapter deals with the problem of integrating a system of N ordinary differential equations ... 

The problem of integrating a system of differential or algebraic-differential equations with boundary conditions is indicated with the acronym BVP. 

Integrating a system under fault-free conditions, then assessing the fault tolerance or failure management following installation. 

These expressions, Eqs. 5.20 and 5.23, are easily extended to higher-order RKI. It will now be relatively straight-forward to apply the Cq adjustment steps to all the boundary value cases discussed in Chapt. 4 in all cases, g is somehow evaluated and finally leads to an expression (or expressions) for Cq, which must in all cases be adjusted stepwise as above. This is left to the reader. There are other, more efficient methods of integrating a system such as 5.14 Runge-Kutta integration however, has the advantage of being very easy to use. 

Kakhu, A. L, and Flower, J. R., Synthesi ng Heat-Integrated Distillation Systems Using Mixed Integer Programming, Trans. IChemE ChERD, 66 241, 1988. 

In integrated photoelasticity it is impossible to achieve a complete reconstruction of stresses in samples by only illuminating a system of parallel planes and using equilibrium equations of the elasticity theory. Theory of the fictitious temperature field allows one to formulate a boundary-value problem which permits to determine all components of the stress tensor field in some cases. If the stress gradient in the axial direction is smooth enough, then perturbation method can be used for the solution of the inverse problem. As an example, distribution of stresses in a bow tie type fiber preforms is shown in Fig. 2 [2]. 

If the impulse response function g(x) of a system is known, the output signal y(x) of the system is given for any input signal u(x). The integral equation, which is called superposition integral. 

Therefore it is reasonable to prepare already the data acquisition for a three dimensional evaluation in cone-beam-technique by means of two-dimensional detectors. The system is already prepared to integrate a second detector- system for this purpose. An array of up to four flat panel detectors is foreseen. The detector- elements are based on amorphous silicon. Because of the high photon energy and the high dose rates special attention was necessary to protect the read-out electronics. Details of the detector arrangement and the software for reconstruction, visualisation and comparison between the CT results and CAD data are part of a separate paper during this conference [2]. 

In order to prepare the system for 3D-CT, it is not enough to integrate a second detector array. Besides this special attention has to be paid to the computer hardware, the synchronisation between object movement and the data read out as well as to the collimator of the LINAC. The collimator has been built with 4 tungsten blocks which can be moved individually m order to shape different sht sizes for 2D-CT as well as different cone angles for 3D-CT or digital radiography. 

If improvements should be achieved by an automation of the inspection process this requires a control of the process parameters of the whole equipment by an integrated "intelligent" system and not by displays still being controlled by the human inspector. This integrated control-system ensures that the inspection conditions are at the highest reproduction level. 

This expression assumes a system with a discrete level structure for systems with both a discrete and a continuous portion to their spectrum the expression consists of a sum over the discrete states and an integral over the continuous states.) Flere, ifi (v) is a solution of the time-independent Sclirodinger equation,... 

First, a few definitions a system is any region of space, any amount of material for which the boundaries are clearly specified. At least for thennodynamic purposes it must be of macroscopic size and have a topological integrity. It may not be only part of the matter in a given region, e.g. all the sucrose in an aqueous solution. A system could consist of two non-contiguous parts, but such a specification would rarely be usefLil. 

A system is mixing if, for every pair of fimctioiis/and g whose squares are integrable on. S, ... 

When quantum effects are large, the PF can be evaluated by path integral methods [H], Our exposition follows a review article by Gillan [12], Starting with the canonical PF for a system of particles... 

I k/X. For a system with a large number of scattering elements, the suimnation in equation (B1.9.28) may be replaced by an integral... 

This is better understood with a picture see figure B3.3.11. The discretized path-integral is isomorphic to the classical partition fiinction of a system of ring polymers each having P atoms. Each atom in a given ring corresponds to a different imaginary tune point p =. . . P. represents tire interatomic interactions... 

Ryckaert J-P, Ciccotti G and Berendsen H J C 1977 Numerical integration of the Cartesian equations of motion of a system with constraints molecular dynamics of n-alkanes J. Comput. Phys. 23 327-41... 

Consider a system of N particles in d dimensions. Using the standard procedure of integrating over the momenta in Cartesian coordinates, we can write the average of a mechanical property A(r ) as... 

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