Existence of Dirac resonances in the semi-classical limit

We study the existence of quantum resonances of the three-dimensional semiclassical Dirac operator perturbed by smooth, bounded and real-valued scalar potentials V decaying like ⟨x⟩−δ at infinity for some δ>0. By studying analytic singularities of a certain distribution related to V and by combining two trace formulas, we prove that the perturbed Dirac operators possess resonances near supV+1 and infV−1. We also provide a lower bound for the number of resonances near these points expressed in terms of the semiclassical parameter

ESR Process Instabilities while Melting Pipe Electrodes

With the demonstration of the viability of using the electroslag remelting process for the decontamination of radionuclides, interest has increased in examining the unique aspects associated with melting steel pipe electrodes. These electrodes consist of several nested pipes, welded concentrically to atop plate. Since these electrodes can be half as dense as a solid electrode, they present unique challenges to the standard algorithms used in controlling the melting process. Naturally the electrode must be driven down at a dramatically increased speed. However, since the heat transfer is greatly influenced and enhanced with the increased area to volume ratio, considerable variation in the melting rate of the pipes has been found. Standard control methods can become unstable as a result of the variation at increased speeds, particularly at shallow immersion depths. The key to good control lies in the understanding of the melting process. Several experiments were conducted to observe the characteristics of the melting using two different control modes. By using a pressure transducer to monitor the pressure inside the pipes, the venting of the air trapped inside the electrode was observed. The measurements reveal that for a considerable amount of time. the pipes are not completely immersed in the slag, allowing the gas inside to escape without the formation of bubbles. This result has implications for the voltage swing as well as for the decontamination reactions

Maximum ionization in restricted and unrestricted Hartree-Fock theory

In this paper, we investigate the maximum number of electrons that can be bound to a system of nuclei modelled by Hartree-Fock theory. We consider both the Restricted and Unrestricted Hartree-Fock models. We are taking a non-existence approach (necessary but not sufficient), in other words we are finding an upper bound on the maximum number of electrons. In giving a detailed account of the proof of Lieb’s bound [Theorem 1, Phys. Rev. A 29 (1984), 3018] for the Hartree-Fock models we establish several new auxiliary results, furthermore we propose a condition that, if satisfied, will give an improved upper bound on the maximum number of electrons within the Restricted Hartree-Fock model. For two-electron atoms we show that the latter condition holds

Pathways, Contexts, and Voices of Shame and Compassion: A Grounded Theory of the Evolution of Perinatal Suicidality

There is an urgent need to generate deeper understandings of how suicidality manifests and evolves during pregnancy and the following year. Several perinatal studies have examined the incidence of suicidal thoughts and behaviours and associated social and obstetric risk factors; however, there is very limited research offering insights into women’s experiences of suicidality at this time in their lives. This study aimed to generate a theory to explain how suicidality evolves in the perinatal period. A grounded theory design was used with data generated using anonymous online surveys (119 participants) and in-depth interviews (20 participants) with women who received pregnancy care in the past 5 years in Australia. The developed theory holds shame as a core concept. Origins and contexts of shame reflect current epidemiological understandings of risk for perinatal suicide, including experiences of gender-based violence, adverse childhood experiences, and a history of mental health difficulties. When women feel that they are defective, are unworthy of love and belonging, and do not possess what it takes to be a good mother, they can conclude that their family is better off without them. Pathways beyond shame were facilitated by compassionate and rehumanising care from family, friends, and care providers. Findings demonstrate that perinatal suicidality is a complex multidimensional phenomenon, influenced by socio-cultural expectations of motherhood and interpersonal, systemic, and intergenerational experiences of trauma. Increasing the prominence of perinatal suicide prevention within health professional education and practice, and addressing systemic barriers to compassionate health care are critical first steps to addressing perinatal suicide

Multiple Input Electrode Gap Control During Vacuum Arc Remelting

Accurate control of the electrode gap in a vacuum arc remelting (VAR) furnace has been a goal of melters for many years. The size of the electrode gap has a direct influence on ingot solidification structure. At the high melting currents (30 to 40 kA) typically used for VAR of segregation insensitive Ti and Zr alloys, process voltage is used as an indicator of electrode gap, whereas drip-short frequency (or period) is usually used at the lower currents (5 to 8 kA) employed during VAR of superalloys. Modem controllers adjust electrode position or drive velocity to maintain a voltage or drip-short frequency (or period) set-point. Because these responses are non-linear functions of electrode gap and melting current, these controllers have a limited range for which the feedback gains are valid. Models are available that relate process voltage and drip-short frequency to electrode gap. These relationships may be used to linearize the controller feedback signal. An estimate of electrode gap may then be obtained by forming a weighted sum of the independent gap estimates obtained from the voltage and drip-short signals. By using multiple independent measures to estimate the gap, a controller that is less susceptible to process disturbances can be developed. Such a controller was designed, built and tested. The tests were carried out at Allvac Corporation during VAR of 12Cr steel at intermediate current levels

Application specific compression : final report.

With the continuing development of more capable data gathering sensors, comes an increased demand on the bandwidth for transmitting larger quantities of data. To help counteract that trend, a study was undertaken to determine appropriate lossy data compression strategies for minimizing their impact on target detection and characterization. The survey of current compression techniques led us to the conclusion that wavelet compression was well suited for this purpose. Wavelet analysis essentially applies a low-pass and high-pass filter to the data, converting the data into the related coefficients that maintain spatial information as well as frequency information. Wavelet compression is achieved by zeroing the coefficients that pertain to the noise in the signal, i.e. the high frequency, low amplitude portion. This approach is well suited for our goal because it reduces the noise in the signal with only minimal impact on the larger, lower frequency target signatures. The resulting coefficients can then be encoded using lossless techniques with higher compression levels because of the lower entropy and significant number of zeros. No significant signal degradation or difficulties in target characterization or detection were observed or measured when wavelet compression was applied to simulated and real data, even when over 80% of the coefficients were zeroed. While the exact level of compression will be data set dependent, for the data sets we studied, compression factors over 10 were found to be satisfactory where conventional lossless techniques achieved levels of less than 3