Maximum Sound Speed Research Articles

A General, Scale-independent Description of the Sound Speed in Neutron Stars

Using more than a million randomly generated equations of state that satisfy theoretical and observational constraints, we construct a novel, scale-independent description of the sound speed in neutron stars, where the latter is expressed in a unit cube spanning the normalized radius, r/R, and the mass normalized to the maximum one, M/M TOV. From this generic representation, a number of interesting and surprising results can be deduced. In particular, we find that light (heavy) stars have stiff (soft) cores and soft (stiff) outer layers, or that the maximum of the sound speed is located at the center of light stars but moves to the outer layers for stars with M/M TOV ≳ 0.7, reaching a constant value of as M → M TOV. We also show that the sound speed decreases below the conformal limit at the center of stars with M = M TOV. Finally, we construct an analytic expression that accurately describes the radial dependence of the sound speed as a function of the neutron-star mass, thus providing an estimate of the maximum sound speed expected in a neutron star.

Sound Speed in Glassy AsxSe1−x (x = 0.4, 0.5, and 0.6) by Inelastic X‐Ray Scattering

Inelastic X‐ray scattering (IXS) measurements are carried out for glassy , , and to investigate atomic dynamics in the glasses. Momentum transfer (Q) dependence of the acoustic excitation energy in each glass follows the ultrasonic sound speed. No positive dispersion is observed in these glasses although liquid near the melting point shows it. The stoichiometric glass shows a maximum sound speed and the speed decreases with increasing As concentration. The results seem to be correlated with a prediction by rigidity theory that glassy is most stable.

Evidence for a maximum mass cut-off in the neutron star mass distribution and constraints on the equation of state

We infer the mass distribution of neutron stars in binary systems using a flexible Gaussian mixture model and use Bayesian model selection to explore evidence for multi-modality and a sharp cut-off in the mass distribution. We find overwhelming evidence for a bimodal distribution, in agreement with previous literature, and report for the first time positive evidence for a sharp cut-off at a maximum neutron star mass. We measure the maximum mass to be $2.0M_\odot < m_\mathrm{max} < 2.2M_\odot$ (68\%), $2.0M_\odot < m_\mathrm{max}< 2.6M_\odot$ (90\%), and evidence for a cut-off is robust against the choice of model for the mass distribution and to removing the most extreme (highest mass) neutron stars from the dataset. If this sharp cut-off is interpreted as the maximum stable neutron star mass allowed by the equation of state of dense matter, our measurement puts constraints on the equation of state. For a set of realistic equations of state that support $>2M_\odot$ neutron stars, our inference of $m_\mathrm{max}$ is able to distinguish between models at odds ratios of up to $12:1$, whilst under a flexible piecewise polytropic equation of state model our maximum mass measurement improves constraints on the pressure at $3-7\times$ the nuclear saturation density by $\sim 30-50\%$ compared to simply requiring $m_\mathrm{max}> 2M_\odot$. We obtain a lower bound on the maximum sound speed attained inside the neutron star of $c_s^\mathrm{max} > 0.63c$ (99.8\%), ruling out $c_s^\mathrm{max} < c/\sqrt{3}$ at high significance. Our constraints on the maximum neutron star mass strengthen the case for neutron star-neutron star mergers as the primary source of short gamma-ray bursts.

Error analysis of speed of sound reconstruction in ultrasound limited angle transmission tomography

We have investigated limited angle transmission tomography to estimate speed of sound (SOS) distributions for breast cancer detection. That requires both accurate delineations of major tissues, in this case by segmentation of prior B-mode images, and calibration of the relative positions of the opposed transducers. Experimental sensitivity evaluation of the reconstructions with respect to segmentation and calibration errors is difficult with our current system. Therefore, parametric studies of SOS errors in our bent-ray reconstructions were simulated. They included mis-segmentation of an object of interest or a nearby object, and miscalibration of relative transducer positions in 3D. Close correspondence of reconstruction accuracy was verified in the simplest case, a cylindrical object in homogeneous background with induced segmentation and calibration inaccuracies. Simulated mis-segmentation in object size and lateral location produced maximum SOS errors of 6.3% within 10 mm diameter change and 9.1% within 5 mm shift, respectively. Modest errors in assumed transducer separation produced the maximum SOS error from miscalibrations (57.3% within 5 mm shift), still, correction of this type of error can easily be achieved in the clinic. This study should aid in designing adequate transducer mounts and calibration procedures, and in specification of B-mode image quality and segmentation algorithms for limited angle transmission tomography relying on ray tracing algorithms.

EXTENSION OF THE MURAM RADIATIVE MHD CODE FOR CORONAL SIMULATIONS

ABSTRACT We present a new version of the MURaM radiative magnetohydrodynamics (MHD) code that allows for simulations spanning from the upper convection zone into the solar corona. We implement the relevant coronal physics in terms of optically thin radiative loss, field aligned heat conduction, and an equilibrium ionization equation of state. We artificially limit the coronal Alfvén and heat conduction speeds to computationally manageable values using an approximation to semi-relativistic MHD with an artificially reduced speed of light (Boris correction). We present example solutions ranging from quiet to active Sun in order to verify the validity of our approach. We quantify the role of numerical diffusivity for the effective coronal heating. We find that the (numerical) magnetic Prandtl number determines the ratio of resistive to viscous heating and that owing to the very large magnetic Prandtl number of the solar corona, heating is expected to happen predominantly through viscous dissipation. We find that reasonable solutions can be obtained with values of the reduced speed of light just marginally larger than the maximum sound speed. Overall this leads to a fully explicit code that can compute the time evolution of the solar corona in response to photospheric driving using numerical time steps not much smaller than 0.1 s. Numerical simulations of the coronal response to flux emergence covering a time span of a few days are well within reach using this approach.

Development of a nonlinear model for the pressure dependent attenuation and sound speed in a bubbly liquid and its experimental validation

Presence of the MBs in the sound field increases the attenuation of the medium and changes the sound speed. A detailed knowledge about the attenuation of the medium is critical for controlling and optimizing the behavior of the MBs in applications. However, existing models of ultrasound attenuation in bubbly mediums are based on linear approximations (low amplitude MB oscillations) and thus are not valid in many regimes used in applications. A model to calculate the nonlinear attenuation and sound speed is developed by deriving the complex and real part of the wave number from the Calfish model. The predictions of the model were validated by measuring the attenuation and sound speed of dilute monodisperse MB solutions (5000 microbubbles/ml) with median diameter of 5.2 and 9.8 µm using acoustic pressure range of 10–130 kPa. The attenuation of the medium was calculated by numerically solving the radial oscillations of the MB and incorporating it in the attenuation model. Predictions of the model were in good agreement with the experimental results. As the acoustic pressure increased, the attenuation and maximum sound speed of the medium increased from 5 dB/cm to 12 dB/cm and 1500 to ~1530 m/s, respectively.

Evaluating the sonic layer depth relative to the mixed layer depth

Using a global set of in situ temperature and salinity profile observations, the sonic layer depth (SLD) and the mixed layer depth (MLD) are analyzed and compared over the annual cycle. The SLD characterizes the potential of the upper ocean to trap acoustic energy in a surface duct while MLD characterizes upper ocean mixing. The SLD is computed from temperature and salinity profile pairs using a new tunable method while MLD is computed using recently developed methods and either temperature only profiles or temperature and salinity profile pairs. Both SLD and MLD estimates provide information on different and important aspects of the upper ocean. The SLD and MLD often coincide because sound speed increases with depth down to the MLD, where (typically) a decrease in temperature occurs, resulting in a local maximum sound speed. The depth of this maximum sound speed is the SLD. The SLD and MLD are not always the same because sound speed is substantially more sensitive to temperature than to salinity compared to density. Since MLD is a commonly known and studied parameter, MLD is often used as a proxy for SLD in scientific and operational applications. In the boreal spring when fresh restratification events occur, the SLD is 10 m deeper (shallower) than the MLD in 39% (7%) of the observed profiles. A parabolic equation acoustic transmission model is used to evaluate the relative skill of the SLD and MLD estimates to predict surface acoustic trapping as measured by a simple metric.

Coincidence of rotational energy of H2O ortho-para molecules and translation energy near specific temperatures in water and ice

A hypothesis of the quantum nature of the specific temperatures T s of water and ice, whose values is not random, was formulated. It was found that the quantum energy hΩ mn of closely located rotational transitions in the ortho and para spin isomers of H2O molecules coincides with the translation energy kT near the well-known specific temperatures T s in ice and water. On the basis of this fact it was suggested that ortho-para conversion occurs at temperatures close to T s upon inelastic collisions and resonance energy exchange kT s ↔ hΩ mn in the rotation-translation-rotation (RTR) processes. Such conversion can induce rearrangement of the H-bond set structure and repacking of H2O molecules. The coincidence kT s ≈ hΩ mn was checked for ice and water at 12 known T s, as well as for heavy water D2O near T s = 11.2°C (maximum density) and −140°C (glassy transition). The previously observe strong deformation of the OH Raman band near T s = 4, 19, 36, and 76°C (maximum density, maximum surface tension, minimum heat capacity, and maximum speed of sound, respectively) was interpreted as a manifestation of the water structure rearrangement induced by H2O ortho-para conversion.

TH-C-I-609-09: Quantifying Breast Density for Improved Evaluation of Breast Cancer Risk

Purpose: To quantify a preliminary relationship between breast density and acoustic velocity using ultrasoundcomputed tomography. The existence of such a relationship may provide quantitative prognostic information that can be used to determine breast cancer risk. Method and Materials: A sample of female patients was imaged using the CURE, or Computerized Ultrasound Risk Evaluation, device. The mammographic densities of each patient were assigned by a certified radiologist on a 1 (fatty) to 4 (dense) scale. Regions of interest (160 mm2) were selected contralateral to present anomalies in multiple adjacent slices centrally located on the breast, away from the chest wall and nipple regions. The minimum, maximum, mean, and standard deviation of the acoustic velocity were recorded for each slice. Results: This statistical information was then correlated against breast density to investigate the presence of meaningful relationships. Initial assessment of this sample suggests that the maximum sound speed values increase with increasing mammographic density, while the minimum values appear to decrease with increasing density. The mean sound speed shows a weak but steady trend with increasing density. The behavior of these correlations suggests that the intrinsic scatter of sound speeds within the breast tissue is a strong function of the mammographic breast density. However, these relationships are statistically weak due to a small sample size, and further investigation will be required to strengthen this association. Conclusion: This preliminary examination suggests that a quantifiable relationship between breast density and sound speed may exist. If these results are further validated in larger studies, then it may be possible to utilize CURE measurements to assess breast cancer risk with a quantitative score. Results will be available for forty additional patients in July, and a more definitive conclusion regarding these findings can then be provided.

Comparison of sound-speed computation methods.

The computation of sound speeds in nitrogen, oxygen, and methane was performed with two methods. Results from the traditional method that relied on virial coefficients B and their temperature derivatives T dB/dT, T2 d2B/dT2, were compared with those given by a simplified method. At a pressure of 101.325 kPa, and at a temperature of −10 °C, the maximum sound speed deviations between the two methods are within 0.2% and −0.4% for nitrogen and oxygen, respectively. For methane, at the above pressure, and over the temperature range from zero to 450 °C, the maximum deviation is 1.2%. For the above gases, the sound-speed deviations between the methods are largest at low temperatures. It can be shown that by modifying the numerical values of the virial coefficients and their temperature derivatives, the sound-speed deviations between the two methods can be reduced substantially. For nitrogen, when B, T dB/dT, and T2 d2B/dT2 are modified by multiplication factors of −0.1, 0.55, and 0.7, respectively, the difference between the sound speeds obtained with the two methods decreases to less than ±0.05%. It is noted that the sign of the numerical value of B is reversed. Uncertainties of the results obtained with both methods were examined.

Design limitations on ultra-high velocity projectile launchers

The maximum velocity attainable in a gasdynamic gun is limited by the maximum sound speed in the driver gas. For a conventional 2-stage light gas gun, the limit is ∼ 10 km/s. Higher velocities are possible, but probably not without the destruction of the gun barrel. As long as this occurs on a time scale longer than the residence time of the projectile, a useful system may still result. Using a newly developed computer code called IGUN, we have evaluated the performance of several multistage designs capable of achieving ultra-high projectile velocities. The main problem is in maintaining the integrity of the projectile. Our calculations indicate that 20 km/s should be achievable without fracturing the projectile. If it is only required to retain near original areal density, velocities in excess of 30 km/s appear feasible.

Speed of Sound in Distilled Water as a Function of Temperature and Pressure

An ultrasonic pulse type apparatus was used to measure the speed of sound in distilled water over the pressure range 14.7 to 14 000 psia and the temperature range 0.9 to 91.2°C. The temperature where the maximum sound speed occurs shifts to a higher temperature when the pressure is increased. At atmospheric pressure the computed maximum speed was 1555.36 m/sec and occurred at a temperature of 74.164°C. The isotherms of sound speed, plotted as a function of pressure, are concave upward below 20°C, concave downward above 20°C, and are approximately linear near 20°C for the pressure range of 14.7 to 14 000 psia. These curvatures have a maximum value of 1 part in 300 compared to the estimated accuracy of measurement which is 1 part in 10 000. The results are presented in tables and also in the form of a fourth degree equation fitted to the experimental data by the method of least squares.