Static errors

How can we apply molecular dynamics simulations practically. This section gives a brief outline of a typical MD scenario. Imagine that you are interested in the response of a protein to changes in the amino add sequence, i.e., to point mutations. In this case, it is appropriate to divide the analysis into a static and a dynamic part. What we need first is a reference system, because it is advisable to base the interpretation of the calculated data on changes compared with other simulations. By taking this relative point of view, one hopes that possible errors introduced due to the assumptions and simplifications within the potential energy function may cancel out. All kinds of simulations, analyses, etc., should always be carried out for the reference and the model systems, applying the same simulation protocols. 

Static reliability models are used in preliminary analyses to determine necessary reliability levels for subsystems and components. A subsystem is a particular low level grouping of components. Some trial and error is usually necessary to obtain reasonable groupings for any particular system. Early identification of potential system weaknesses facilitates corrective action. 

This ranking implies that human errors are more likely to occur than active equipment failures (functioning equipment, such as a mnning pump) and that active equipment failures are more likely to occur than passive equipment failures (static, nonfunctioning equipment, such as a storage tank). 

For information on prediction of static-hole error, see Shaw, J. Fluid Mech., 7, 550-564 (I960) Livesey, Jackson, and Southern, Airci Eng., 34, 43-47 (February 1962). 

There are certain limitations on the range of usefulness of pitot tubes. With gases, the differential is very small at low velocities e.g., at 4.6 m/s (15.1 ft/s) the differential is only about 1.30 mm (0.051 in) of water (20°C) for air at 1 atm (20°C), which represents a lower hmit for 1 percent error even when one uses a micromanometer with a precision of 0.0254 mm (0.001 in) of water. Equation does not apply for Mach numbers greater than 0.7 because of the interference of shock waves. For supersonic flow, local Mac-h numbers can be calculated from a knowledge of the dynamic and true static pressures. The free stream Mach number (MJ) is defined as the ratio of the speed of the stream (V ) to the speed of sound in the free stream ... 

The pitot-static tube is also sensitive to yaw or angle of attack than is the simple pitot tube because of the sensitivity ofthe static taps to orientation. The error involved is strongly dependent upon the exac-t probe dimensions. In general, angles greater than 10° should be avoided if the velocity error is to be 1 percent or less. 

Disturbances upstream of the probe can cause large errors, in part because of the turbulence generated and its effect on the static-pressure measurement. A calming section of at least 50 pipe diameters is desirable. If this is not possible, the use of straightening vanes or a honeycomb is advisable. 

With nonnewtouiau fluids the pressure measured at the wall with non-flush-mounted pressure gauges may be in error (see subsection Static Pressure ). 

Shortly after this time, it was discovered that Bridgman s static high-pressure scale was in error due to calibration problems, and the shock-induced 13 GPa transition became the new calibration standard. 

Statistical errors of dynamic properties could be expressed by breaking a simulation up into multiple blocks, taking the average from each block, and using those values for statistical analysis. In principle, a block analysis of dynamic properties could be carried out in much the same way as that applied to a static average. However, the block lengths would have to be substantial to make a reasonably accurate estimate of the errors. This approach is based on the assumption that each block is an independent sample. 

Flow Low mass flow indicated. Mass flow error. Transmitter zero shift. Measurement is high. Measurement error. Liquid droplets in gas. Static pressure change in gas. Free water in fluid. Pulsation in flow. Non-standard pipe runs. Install demister upstream heat gas upstream of sensor. Add pressure recording pen. Mount transmitter above taps. Add process pulsation damper. Estimate limits of error. 

I he origins of the above two errors are chfferent in cause and nature. A sim ple example is, when the mass of a weight is less than its nominal value, a systematic error occurs, which is constant in absolute value and sign. This is a pure systematic error. A ventilation-related example is, when the instrument faaor of a Pitot-static tube, which defines the relationship between the measured pressure difference and the velocity, is incorrect, a systematic error occurs. On the other hand, if a Pitot-static tube is positioned manually in a duct in such a way that the tube tip is randomly on either side of the intended measurement point, a random error occurs. This way, different phenomena create different ty pes of error. I he (total) error of measurement usually is a combination of the above two types. 

As well as measurement errors due to the pressure measurement instrument itself, other errors related to pressure measurements must be considered. In ventilation applications a frequently measured quantity is the duct static pressure. This is determined by drilling in the duct a hole or holes in which a metal tube is secured. The rubber tube of the manometer is attached to the metal tube, and the pressure difference between the hole and the environment or some other pressure is measured. 

When the axis of the Pitot-static tube is not aligned to the main flow direction, an error of inclination occurs known as yaw. It is not more than 1% for the measured pressure difference if standard tubes are used and the devia tion from the flow direction is less than 11-13°. 44 (hg further... 

In measuring the local velocity in ducts, the sensor will obstruct a part of the duct cross-section. This results in accelerated flow by the sensor and an error occurs. In a Pitot-static tube, this is called stem blockage. If the ratio of the tube diameter to the duct diameter is smaller than 0.02, stem blockage can be neglected. Otherwise a correction has to be applied. 

There will be strong emphasis on the collection of data on possible causal factors that could have contributed to an accident. The specific data that are collected may be based on an error model such as that shown in Figure 6.2. However, this model will usually be modified depending upon the extent to which it fits the data collected over a period of time. The systems approach is therefore dynamic rather than static. 

When the static pressure in a moving fluid is to be determined, the measuring surface must be parallel to the direction of flow so that no kinetic energy is converted into pressure energy at the surface. If the fluid is flowing in a circular pipe the measuring surface must be perpendicular to the radial direction at any point. The pressure connection, which is known as a piezometer tube, should terminate flush with the wall of the pipe so that the flow is not disturbed the pressure is then measured near the walls where the velocity is a minimum and the reading would be subject only to a small error if the surface were not quite parallel to the direction of flow. A piezometer tube of narrow diameter is used for accurate measurements. 

These two disturbances cause errors in opposite directions, and the static pressure should therefore be measured at the point where the effects are equal and opposite. 

If the head and stem are situated at a distance of 14 diameters from each other as on the standard instrument,<4) the two disturbances are equal and opposite at a section 6 diameters from the head and 8 from the stem. This is, therefore, the position at which the static pressure orifices should be located. If the distance between the head and the stem is too great, the instrument will be unwieldy if it is too short, the magnitude of each of the disturbances will be relatively great, and a small error in the location of the static-pressure orifices will appreciably affect the reading. 

The main error sources are noise in the wavefront sensor measurement, imperfect wavefront correction due to the finite number of actuators and bandwidth error due to the finite time required to measure and correct the wavefront error. Other errors include errors in the telescope optics which are not corrected by the AO system (e.g. high frequency vibrations, high spatial frequency errors), scintillation and non-common path errors. The latter are wavefront errors introduced in the corrected beam after light has been extracted to the wavefront sensor. Since the wavefront sensor does not sense these errors they will not be corrected. Since the non-common path errors are usually static, they can be measured off-line and taken into account in the wavefront correction. 

From a basis set study at the CCSD level for the static hyperpolarizability we concluded in Ref. [45] that the d-aug-cc-pVQZ results for 7o is converged within 1 - 2% to the CCSD basis set limit. The small variations for the A, B and B coefficients between the two triple zeta basis sets and the d-aug-cc-pVQZ basis, listed in Table 4, indicate that also for the first dispersion coefficients the remaining basis set error in d-aug-cc-pVQZ basis is only of the order of 1 - 2%. This corroborates that the results for the frequency-dependent hyperpolarizabilities obtained in Ref. [45] by a combination of the static d-aug-cc-pVQZ hyperpolarizability with dispersion curves calculated using the smaller t-aug-cc-pVTZ basis set are close to the CCSD basis set limit. 

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