Search for the correction term to Fermi’s golden rule in positron annihilation

In the positron–electron annihilation process, finite deviations from the standard calculation based on Fermi’s golden rule are suggested in recent theoretical work. This paper describes an experimental test of the predictions of this theoretical work by searching for events with two photons from positron annihilation of energy larger than the electron rest mass ($511\,{\rm keV}$). The positrons came from a ${\rm {}^{22}Na}$ source, tagging the third photon from the spontaneous emission of ${\rm {}^{22}{Ne}^*}$ de-exitation to suppress backgrounds. Using the collected sample of $1.06\times 10^{7}$ positron–electron annihilations, triple coincidence photon events in the signal-enhanced energy regions are examined. The observed number of events in two signal regions, $N^{\rm SR1}_{\rm obs}=0$ and $N^{\rm SR2}_{\rm obs}=0$, are, within the current precision, consistent with the expected number of events, $N^{\rm SR1}_{\rm exp}=0.86\pm0.08({\rm stat.})^{+1.85}_{-0.81}({\rm syst.})$ and $N^{\rm SR2}_{\rm exp}=0.37\pm 0.05({\rm stat.})^{+0.80}_{-0.29}({\rm syst.})$ from Fermi’s golden rule, respectively. Based on the $P^{(d)}$ modeling, a 90% CL lower limit on the photon wave packet size is obtained.

Quadruple Flow and Acoustic Coincident Resonance of Rotating Bladed Disks Interacting With Stationary Elements

In recent years it has been discovered that besides non-uniform flow excitation such as from stator wakes; acoustic pressure pulsation can be a concern, especially for high pressure centrifugal compressor impellers. This has been termed “triple coincidence” and explains rare failures and likely a reason, at least partially, for some previous undocumented failures. Bladed disk interaction resonance discovered by the author in the mid 1970’s can be avoided such as for centrifugal impellers as needed, depending on vibratory mode involved, available damping, and potential excitation level. Especially for stages having vanes in the diffuser near impeller tips, concern for high cycle fatigue is very high as certain numbers of vanes combined with number of rotating blades can give correct phase to excite a highly responding mode. Intentional mistuning of disk-dominated modes has potential for reducing response. A similar but more complex interaction is with transverse acoustic modes having a specific number of nodal diameters. In this case acoustic gas modes in cavities at sides of impellers can match rotating acoustic pulsations at BPF (blade passing frequency) and/or harmonics, termed Tyler-Sofrin modes with increased noise. Also acoustic mode matching impeller structural mode can give the triple coincidence causing resonant response of the impeller. The concern for this coincidence is often difficult to evaluate. For some cases, calculations give enough evidence to modify number of vanes or blades to correct a possible cause of a fatigue failure. This coincidence can add to the direct response, e.g. from either upstream wakes or downstream diffuser vane interacting “potential flow” excitation, herein termed “quadruple coincidence resonance”. Dimensions of impeller side cavities are axisymmetric and are set by aerodynamics, so that outer and inner radii define transverse modes with small radial dimensional changes available. Often a minor aerodynamic performance compromise can be used to change designs to avoid serious resonances, e.g. revise numbers of vanes and/or blades, avoid the response of a matching diameter mode or have a different less responsive mode to alleviate concern. Besides turbomachinery e.g. compressors and pumps, some other methods as described could be utilized for any cavity that has diametrical mode shapes, or possibly other patterns for pressure pulsation frequencies. These modification(s), including patent-pending method, PCT/US2018/020880 described herein can alleviate if not eliminate concern for any mechanism having structural vibration excitation and/or environmental noise issues.

Review of Causes and Mitigation of Cavity Noise in Machinery and Other Mechanisms

Two significant causes of noise related to cavities are direct and indirect flow induced turbulence/vortex shedding mechanisms. Examples of induced noise can be found in many applications of both closed-flow and open-flow cavities — some with resonance of acoustic modes. An example is a flow valve with a cavity where flow along the cavity gives pulsations either trapped within the valve or exciting downstream piping acoustic modes. There are passive methods of mitigation besides detuning such as modification of the entrance to the cavity, blockage, and use of Helmholtz resonators. Natural frequencies of cavity acoustic modes can be irregular, but for many such as with circular, square, rectangular or axisymmetric shapes can give symmetry of modes. An example is a cavity at the sides of rotating disks, where transverse symmetrical modes having circular and diametric patterns are similar to structural vibratory modes for bladed disks. In the last decade it has been documented that for centrifugal compressors blade passing acoustic pressure pulsation due to Tyler-Sofrin spinning modes can add to alternating stress from non-uniform flow excitation, such as from stator wakes. Cavity acoustic mode excitation then has been termed “triple coincidence” or “triple crossing”, explaining rare documented impeller fatigue failures and likely a reason, at least partially, for some unexplained failures. A novel method described herein is to treat these and similar cavities as fluid-filled disks, then utilize or add blade-like elements within the cavities. The method described (patent application, PCT US1820880) to reduce response of these cavities is to intentionally mistune the elements as has been documented for bladed disk modes. Other applications of this method are possible for many other mechanisms. These modification(s) can alleviate concern for any mechanism having structural vibration excitation acoustically and/or for environmental noise issues.