Propagation of causality

The causality resistor R / 2 clearly avoids the propagation of causality changes at the port of the ideal switch into the rest of the bond graph and captures the diode s high resistance Roft in reverse mode. The resistor R Ri represents the diode s small ON-resistance Ron-... 

In contrast, the output of a controlled source is algebraically related to its input. If the latter is not an output of an independent source or an energy store with integral causality, then it can be expressed by means of such outputs by back propagation of causal paths in the junction structure and by eliminating intermediate variables. 

If there were no causal paths between resistor ports then their outputs could be expressed by the two state variables mi, M2 and the input E by back propagation of causal paths. The result would be an ordered set of equations that could be computed in that order. Clearly, if state space matrices are needed, the outputs of the resistors could be inserted into the constitutive equations of the storage elements. 

J. P. Vigier, Superluminal propagation of the quantum potential in the causal interpretation of quantum mechanics, Lett. Nuovo Cimento 24(8) (Ser. 2), 258-264 (1979). 

Obviously, such interpetation led to disregard advanced solutions as nonphysical. For instance, Ritz [30] and Tetrode [31] considered that the mathematical existence of advanced solutions was a major weakness of Maxwell s equations. An attempt to provide a physical basis for advanced potentials is due to Lewis, who proposed focusing on the process of propagation from an emitter to an absorber far away from the emitter [32]. This concept also appears in the work of Wheeler and Feynman [33]. However, such model constitutes another form of causality violation. Lewis [32, p. 25] himself stated I shall not attempt to conceal the conflict between these views and common sense. ... 

In a strict sense, the time-evolution generated by the operator (2) is acausal A wavepacket that is initially strictly localized in a finite region of space instantaneously spreads over the whole space. Even for the Dirac equation there are some problems with causality and localization (see, e.g., [5]), but since the propagator of the Dirac equation (the time-evolution kernel) has support in the light-cone, distortions of wave functions and wave fronts can at most propagate with the velocity of light. 

Assign causality to one of the sources according to its type and propagate this causal information into the bond graph through its junction structure as far as possible by observing causality rules at element ports. 

The outputs of resistors depend algebraically on their inputs. By back propagation along causal paths through the junction structure, their outputs can be expressed by outputs of sources either independent, or controlled ones and outputs of energy stores. The outputs of dependent sources do not need to be eUminated, since they have already been determined in the previous step. 

Note, that if there are causal paths between resistor ports then impUcit, algebraic equations will result. This means, that the output of the resistor port at one end of the causal path cannot be computed without knowing the output of the resistive port at the other end of the causal path. In this case, intermediate variables cannot be eliminated and expressed by system inputs and state variables by back propagation along causal paths. The mathematical model will be of the form of a DAE system that can be transformed into an ODE system if the system of coupled algebraic equations can be solved symbolically. 

The common feature in both inductive and capacitive influences is that energies-per-entity are expressed in function of entity numbers. It should not be deduced that this means causality or irreversibility. Influence is a reversible phenomenon, based on a mutual adaptation of variables, without dedicated emitters and receivers, at least at the global level, without space-time consideration. When space-time plays a role, this adaptation may require propagation of a signal, but this is a subject that requires a better understanding of space-time. 

Along each power line chosen at step I propagate bicausality from the double source to the double detector and propagate causality through the junction structure taking into account the causality constraints ofO- and I-junctions, TF-and GY-elements. If at this step causal conflicts or non-solvable causal loops appear, repeat the previous steps with another set of disjoint I/O power lines. If none of them solves the problem of causal conflicts or non-solvable causal loop appearance then the model is not invertible (Criterion 3) and the procedure stops. 

Helping in trending data of how a hazard may propagate through a tightly coupled system, by sorting combinations of causal factors and potential effects... 

Figure 4 illustrates the relationship between the views SysFis and DysFis events are associated with different elements. T.inks between the elements of SysFis model can guide the analysis of the propagation of dysfunctions for causal links between events. 

The causality of accidents in modern transportation systems may be difficult to determine. Investigations of past accidents and incidents have led to the development of improved system defences, which have significantly reduced the incidence of fatal accidents. When accidents occur they tend to exhibit complex causalities. Reason [1] referred to such accidents in modern well-defended systems as organizational accidents. These accidents are typically multi-faceted, and they may involve unexpected interactions or unforeseen propagation of failures [2]. 

For X > 0 our integration contour in the upper-half -plane encloses only the pole at J. The scattered wave packet is proportional to e i as in the unscattered case (4.160). At times before the wave-packet centre reaches the scattering centre the wave packet is propagated without change of shape. Another name for this condition is causality. Disturbances due to the target appear after the centre of the wave packet has reached the target. Causality requires the scattering amplitude to be analytic in the upper-half -plane. 

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