Theory of viscous and thermal attenuation of sound by small spheres

The problem is to calculate the attenuation of plane sound waves passing through a viscous, heat-conducting fluid containing small spherical inhomogeneities. The attenuation is calculated by evaluating the rate of increase of entropy caused by two irreversible processes: (1) the mechanical work done by the viscous stresses in the presence of velocity gradients, and (2) the flow of heat down the thermal gradients. The method is first applied to a homogeneous fluid with no spheres and shown to give the classical Stokes-Kirchhoff expressions. The method is then used to calculate the additional viscous and thermal attenuation when small spheres are present. The viscous attenuation agrees with Epstein's result obtained in 1941 for a non-heat-conducting fluid. The thermal attenuation is found to be similar in form to the viscous attenuation and, for gases, of comparable magnitude. The general results are applied to the case of water drops in air and air bubbles in water.

For water drops in air the viscous and thermal attenuations are camparable; the thermal losses occur almost entirely in the air, the thermal dissipation in the water being negligible. The theoretical values are compared with Knudsen's experimental data for fogs and found to agree in order of magnitude and dependence on frequency. For air bubbles in water the viscous losses are negligible and the calculated attenuation is almost completely due to thermal losses occurring in the air inside the bubbles, the thermal dissipation in the water being relatively small. (These results apply only to non-resonant bubbles whose radius changes but slightly during the acoustic cycle.)

I. The attenuation and dispersion of sound in a condensing medium. II. The flow of a gas-particle mixture downstream of a normal shock in a nozzle

I. The attenuation of sound due to particles suspended in a gas was first calculated by Sewell and later by Epstein in their classical works on the propagation of sound in a two-phase medium. In their work, and in more recent works which include calculations of sound dispersion, the calculations were made for systems in which there was no mass transfer between the two phases. In the present work, mass transfer between phases is included in the calculations.

The attenuation and dispersion of sound in a two-phase condensing medium are calculated as functions of frequency. The medium in which the sound propagates consists of a gaseous phase, a mixture of inert gas and condensable vapor, which contains condensable liquid droplets. The droplets, which interact with the gaseous phase through the interchange of momentum, energy, and mass (through evaporation and condensation), are treated from the continuum viewpoint. Limiting cases, for flow either frozen or in equilibrium with respect to the various exchange processes, help demonstrate the effects of mass transfer between phases. Included in the calculation is the effect of thermal relaxation within droplets. Pressure relaxation between the two phases is examined, but is not included as a contributing factor because it is of interest only at much higher frequencies than the other relaxation processes. The results for a system typical of sodium droplets in sodium vapor are compared to calculations in which there is no mass exchange between phases. It is found that the maximum attenuation is about 25 per cent greater and occurs at about one-half the frequency for the case which includes mass transfer, and that the dispersion at low frequencies is about 35 per cent greater. Results for different values of latent heat are compared.

II. In the flow of a gas-particle mixture through a nozzle, a normal shock may exist in the diverging section of the nozzle. In Marble’s calculation for a shock in a constant area duct, the shock was described as a usual gas-dynamic shock followed by a relaxation zone in which the gas and particles return to equilibrium. The thickness of this zone, which is the total shock thickness in the gas-particle mixture, is of the order of the relaxation distance for a particle in the gas. In a nozzle, the area may change significantly over this relaxation zone so that the solution for a constant area duct is no longer adequate to describe the flow. In the present work, an asymptotic solution, which accounts for the area change, is obtained for the flow of a gas-particle mixture downstream of the shock in a nozzle, under the assumption of small slip between the particles and gas. This amounts to the assumption that the shock thickness is small compared with the length of the nozzle. The shock solution, valid in the region near the shock, is matched to the well known small-slip solution, which is valid in the flow downstream of the shock, to obtain a composite solution valid for the entire flow region. The solution is applied to a conical nozzle. A discussion of methods of finding the location of a shock in a nozzle is included.

Attenuation of inflammatory events in human intervertebral disc cells with a tumor necrosis factor antagonist.

STUDY DESIGN: The inflammatory responses of primary human intervertebral disc (IVD) cells to tumor necrosis factor α (TNF-α) and an antagonist were evaluated in vitro. OBJECTIVE: To investigate an ability for soluble TNF receptor type II (sTNFRII) to antagonize TNF-α-induced inflammatory events in primary human IVD cells in vitro. SUMMARY OF BACKGROUND DATA: TNF-α is a known mediator of inflammation and pain associated with radiculopathy and IVD degeneration. sTNFRs and their analogues are of interest for the clinical treatment of these IVD pathologies, although information on the effects of sTNFR on human IVD cells remains unknown. METHODS: IVD cells were isolated from surgical tissues procured from 15 patients and cultured with or without 1.4 nmol/L TNF-α (25 ng/mL). Treatment groups were coincubated with varying doses of sTNFRII (12.5-100 nmol/L). Nitric oxide (NO), prostaglandin E₂ (PGE₂), and interleukin-6 (IL6) levels in media were quantified to characterize the inflammatory phenotype of the IVD cells. RESULTS: Across all patients, TNF-α induced large, statistically significant increases in NO, PGE₂, and IL6 secretion from IVD cells compared with controls (60-, 112-, and 4-fold increases, respectively; P < 0.0001). Coincubation of TNF-α with nanomolar doses of sTNFRII significantly attenuated the secretion of NO and PGE₂ in a dose-dependent manner, whereas IL6 levels were unchanged. Mean IC₅₀ values for NO and PGE₂ were found to be 35.1 and 20.5 nmol/L, respectively. CONCLUSION: Nanomolar concentrations of sTNFRII were able to significantly attenuate the effects of TNF-α on primary human IVD cells in vitro. These results suggest this sTNFR to be a potent TNF antagonist with potential to attenuate inflammation in IVD pathology.

An efficient method of radiation attenuation through aircraft cooling vents

Some critical avionic systems require cooling air via vents on the side of the aircraft, thus creating leakage points for high-intensity electromagnetic radiation. This paper presents a novel application of high-intensity radiated field (HIRF) shielding using a rectangular waveguide array, while maintaining cooling airflow requirements. Signal attenuation versus frequency and depth of the array has been calculated using closed-form equations. The simulation and measurement results are in good agreement with the calculated values. (C) 2004 Wiley Periodicals, Inc.

Effect of dissolved NaCl, MgCl2, and Na2SO4 in seawater on the optical attenuation in the region from 430 to 630 nm

The split-pulse laser method is used to reinvestigate the optical attenuation of distilled water in the region from 430 to 630 nm. The studies are then extended to ionic solutions of NaCl, MgCl2, and Na2SO4, these salts forming the major constituents of seawater. The effect of the concentration of these constituents on optical attenuation is investigated. Further, optical attenuation studies are carried out for the region from 430 to 630 nm for an aqueous solution prepared with all the major constituents in the same proportions as in natural seawater. These values are then compared with values obtained for natural seawater. The relative role of dissolved salts and suspended particles on optical attenuation in seawater is discussed. The lowest attenuation is observed at ~450 nm for all solutions and is found to coincide with that for distilled water.

Unusually high differential attenuation at C band: Results from a two-year analysis of the French Trappes polarimetric radar data

The differential phase (ΦDP) measured by polarimetric radars is recognized to be a very good indicator of the path integrated by rain. Moreover, if a linear relationship is assumed between the specific differential phase (KDP) and the specific attenuation (AH) and specific differential attenuation (ADP), then attenuation can easily be corrected. The coefficients of proportionality, γH and γDP, are, however, known to be dependent in rain upon drop temperature, drop shapes, drop size distribution, and the presence of large drops causing Mie scattering. In this paper, the authors extensively apply a physically based method, often referred to as the “Smyth and Illingworth constraint,” which uses the constraint that the value of the differential reflectivity ZDR on the far side of the storm should be low to retrieve the γDP coefficient. More than 30 convective episodes observed by the French operational C-band polarimetric Trappes radar during two summers (2005 and 2006) are used to document the variability of γDP with respect to the intrinsic three-dimensional characteristics of the attenuating cells. The Smyth and Illingworth constraint could be applied to only 20% of all attenuated rays of the 2-yr dataset so it cannot be considered the unique solution for attenuation correction in an operational setting but is useful for characterizing the properties of the strongly attenuating cells. The range of variation of γDP is shown to be extremely large, with minimal, maximal, and mean values being, respectively, equal to 0.01, 0.11, and 0.025 dB °−1. Coefficient γDP appears to be almost linearly correlated with the horizontal reflectivity (ZH), differential reflectivity (ZDR), and specific differential phase (KDP) and correlation coefficient (ρHV) of the attenuating cells. The temperature effect is negligible with respect to that of the microphysical properties of the attenuating cells. Unusually large values of γDP, above 0.06 dB °−1, often referred to as “hot spots,” are reported for 15%—a nonnegligible figure—of the rays presenting a significant total differential phase shift (ΔϕDP > 30°). The corresponding strongly attenuating cells are shown to have extremely high ZDR (above 4 dB) and ZH (above 55 dBZ), very low ρHV (below 0.94), and high KDP (above 4° km−1). Analysis of 4 yr of observed raindrop spectra does not reproduce such low values of ρHV, suggesting that (wet) ice is likely to be present in the precipitation medium and responsible for the attenuation and high phase shifts. Furthermore, if melting ice is responsible for the high phase shifts, this suggests that KDP may not be uniquely related to rainfall rate but can result from the presence of wet ice. This hypothesis is supported by the analysis of the vertical profiles of horizontal reflectivity and the values of conventional probability of hail indexes.

Coda wave attenuation in the Parecis Basin, Amazon Craton, Brazil: sensitivity to basement depth

Small local earthquakes from two aftershock sequences in Porto dos GaA(0)chos, Amazon craton-Brazil, were used to estimate the coda wave attenuation in the frequency band of 1 to 24 Hz. The time-domain coda-decay method of a single backscattering model is employed to estimate frequency dependence of the quality factor (Q (c)) of coda waves modeled usingwhere Q (0) is the coda quality factor at frequency of 1 Hz and eta is the frequency parameter. We also used the independent frequency model approach (Morozov, Geophys J Int, 175:239-252, 2008), based in the temporal attenuation coefficient, chi(f) instead of Q(f), given by the equation for the calculation of the geometrical attenuation (gamma) and effective attenuation Q (c) values have been computed at central frequencies (and band) of 1.5 (1-2), 3.0 (2-4), 6.0 (4-8), 9.0 (6-12), 12 (8-16), and 18 (12-24) Hz for five different datasets selected according to the geotectonic environment as well as the ability to sample shallow or deeper structures, particularly the sediments of the Parecis basin and the crystalline basement of the Amazon craton. For the Parecis basin for the surrounding shield and for the whole region of Porto dos GaA(0)chos Using the independent frequency model, we found: for the cratonic zone, gamma = 0.014 s (-aEuro parts per thousand 1), nu a parts per thousand 1.12; for the basin zone with sediments of similar to 500 m, gamma = 0.031 s (-aEuro parts per thousand 1), nu a parts per thousand 1.27; and for the Parecis basin with sediments of similar to 1,000 m, gamma = 0.047 s (-aEuro parts per thousand 1), nu a parts per thousand 1.42. Analysis of the attenuation factor (Q (c)) for different values of the geometrical spreading parameter (nu) indicated that an increase of nu generally causes an increase in Q (c), both in the basin as well as in the craton. But the differences in the attenuation between different geological environments are maintained for different models of geometrical spreading. It was shown that the energy of coda waves is attenuated more strongly in the sediments, (in the deepest part of the basin), than in the basement, (in the craton). Thus, the coda wave analysis can contribute to studies of geological structures in the upper crust, as the average coda quality factor is dependent on the thickness of sedimentary layer.

DOC and UVA attenuation with soil aquifer treatment in the saturated zone of an artificial coastal sandfill

Results from a direct recharge experiment conducted in the field to investigate DOC and UVA(254) attenuation rates during the direct injection of UF treated wastewater into a artificial coastal sandfill are presented in this paper. Approximately 500 m(3) of ultra-filtered wastewater was injected into the saturated zone, over a period of 9 days. The movement of the plume was tracked over 80 days, during which time samples were obtained from multilevel samplers installed in transects across the drift axis of the plume. An analysis of fluorescein in the samples obtained during the drift of the UF plume showed that DOC and UVA were attenuated beyond rates predicted by conservative mixing, by up to a maximum of 45%. A degradation coefficient of 0.0175 day(-1) was found to be applicable for DOC degradation. After a drift period of 80 days, DOC and UVA reduced to approximately 4.5 mg/l and 0.100 cm(-1), respectively, from initial values of 8.06 mg/l and 0.199 cm(-1).

A note on the attenuation of the sommerfeld effect of a non-ideal system taking into account a MR damper and the complete model of a DC motor

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Effect of α-tocopherol, taurine and selenium on the attenuation of ischemia/reperfusion injury of splanchnic organs

Background: Splanchnic artery occlusion shock is caused by increased capillary permeability and cellular injury precipitated by oxygen derived free radicals following ischemia and reperfusion of splanchnic organs. The purpose of this study was to assess the role of several well-known oxygen- derived free radical scavengers in ameliorating or preventing this syndrome. Study design: Anesthetized rats were subjected to periods of occlusion of the visceral arteries and reperfusion. Tocopherol, taurine, selenium or a 'cocktail' of these three agents was injected subcutaneously for 4 consecutive days prior to operation. Mean arterial blood pressure was measured throughout the experimental period. Fluorometry and technetium-99m pyrophosphate counting of the visceral organs were performed as well as a histologic grading system for intestinal viability. Results: Final mean arterial blood pressure associated with the 'cocktail' and selenium groups was 79.1 ± 27.4 mmHg and 83.6 ± 17.8 mmHg, respectively. These values were significantly higher than the control group, 40.8 ± 11.4 mmHg (P < 0.05). Similar patterns of the benefit of selenium in contrast with the other groups were obtained with fluorescein perfusion, radioisotopic activity and histologic analysis. Conclusion: Pretreatment with selenium of splanchnic ischemia and reperfusion in the rat improves mean arterial blood pressure and microcirculatory visceral perfusion. Further analysis of the precise protective mechanism of selenium for reperfusion injury will enable visceral organs to withstand the consequences of increased capillary leakage and oxidant injury.

LED light attenuation through human dentin: A first step toward pulp photobiomodulation after cavity preparation

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Analysis of hourly global, direct and diffuse solar radiations attenuation as a function of optical air mass

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Polarimetric X-band weather radar measurements in the tropics: radome and rain attenuation correction

A polarimetric X-band radar has been deployed during one month (April 2011) for a field campaign in Fortaleza, Brazil, together with three additional laser disdrometers. The disdrometers are capable of measuring the raindrop size distributions (DSDs), hence making it possible to forward-model theoretical polarimetric X-band radar observables at the point where the instruments are located. This setup allows to thoroughly test the accuracy of the X-band radar measurements as well as the algorithms that are used to correct the radar data for radome and rain attenuation. For the campaign in Fortaleza it was found that radome attenuation dominantly affects the measurements. With an algorithm that is based on the self-consistency of the polarimetric observables, the radome induced reflectivity offset was estimated. Offset corrected measurements were then further corrected for rain attenuation with two different schemes. The performance of the post-processing steps was analyzed by comparing the data with disdrometer-inferred polarimetric variables that were measured at a distance of 20 km from the radar. Radome attenuation reached values up to 14 dB which was found to be consistent with an empirical radome attenuation vs. rain intensity relation that was previously developed for the same radar type. In contrast to previous work, our results suggest that radome attenuation should be estimated individually for every view direction of the radar in order to obtain homogenous reflectivity fields.

Towards the 3D attenuation imaging of active volcanoes: methods and tests on real and simulated data

The purpose of my PhD thesis has been to face the issue of retrieving a three dimensional attenuation model in volcanic areas. To this purpose, I first elaborated a robust strategy for the analysis of seismic data. This was done by performing several synthetic tests to assess the applicability of spectral ratio method to our purposes. The results of the tests allowed us to conclude that: 1) spectral ratio method gives reliable differential attenuation (dt*) measurements in smooth velocity models; 2) short signal time window has to be chosen to perform spectral analysis; 3) the frequency range over which to compute spectral ratios greatly affects dt* measurements. Furthermore, a refined approach for the application of spectral ratio method has been developed and tested. Through this procedure, the effects caused by heterogeneities of propagation medium on the seismic signals may be removed. The tested data analysis technique was applied to the real active seismic SERAPIS database. It provided a dataset of dt* measurements which was used to obtain a three dimensional attenuation model of the shallowest part of Campi Flegrei caldera. Then, a linearized, iterative, damped attenuation tomography technique has been tested and applied to the selected dataset. The tomography, with a resolution of 0.5 km in the horizontal directions and 0.25 km in the vertical direction, allowed to image important features in the off-shore part of Campi Flegrei caldera. High QP bodies are immersed in a high attenuation body (Qp=30). The latter is well correlated with low Vp and high Vp/Vs values and it is interpreted as a saturated marine and volcanic sediments layer. High Qp anomalies, instead, are interpreted as the effects either of cooled lava bodies or of a CO2 reservoir. A pseudo-circular high Qp anomaly was detected and interpreted as the buried rim of NYT caldera.

Modeling Englacial Radar Attenuation at Siple Dome, West Antarctica, Using Ice Chemistry and Temperature Data

The radar reflectivity of an ice-sheet bed is a primary measurement for discriminating between thawed and frozen beds. Uncertainty in englacial radar attenuation and its spatial variation introduces corresponding uncertainty in estimates of basal reflectivity. Radar attenuation is proportional to ice conductivity, which depends on the concentrations of acid and sea-salt chloride and the temperature of the ice. We synthesize published conductivity measurements to specify an ice-conductivity model and find that some of the dielectric properties of ice at radar frequencies are not yet well constrained. Using depth profiles of ice-core chemistry and borehole temperature and an average of the experimental values for the dielectric properties, we calculate an attenuation rate profile for Siple Dome, West Antarctica. The depth-averaged modeled attenuation rate at Siple Dome (20.0 +/- 5.7 dB km(-1)) is somewhat lower than the value derived from radar profiles (25.3 +/- 1.1 dB km(-1)). Pending more experimental data on the dielectric properties of ice, we can match the modeled and radar-derived attenuation rates by an adjustment to the value for the pure ice conductivity that is within the range of reported values. Alternatively, using the pure ice dielectric properties derived from the most extensive single data set, the modeled depth-averaged attenuation rate is 24.0 +/- 2.2 dB km(-1). This work shows how to calculate englacial radar attenuation using ice chemistry and temperature data and establishes a basis for mapping spatial variations in radar attenuation across an ice sheet.