Finite element simulation of the liquid-liquid transition to metallic hydrogen

Hydrogen at high temperature and pressure undergoes a phase transition from a liquid molecular phase to a conductive atomic state, or liquid metallic hydrogen, sometimes referred to as the plasma phase transition (PPT). The PPT phase line was observed in a recent experiment studying laser-pulse heated hydrogen in a diamond anvil cell in the pressure range $\sim 100 - 170 \text{GPa}$ for temperatures up to $\sim 2000 \text{K}$. The experimental signatures of the transition are (i) a negative pressure-temperature slope, (ii) a plateau in the heating curve, assumed to be related to the latent heat of transformation, and (iii) an abrupt increase in the reflectance of the sample. We present a finite element simulation that accurately takes into account the position and time dependence of the heat deposited by the laser pulse. We calculate the heating curves and the sample reflectance and transmittance. This simulation confirms that the observed plateaus are related to the phase transition, however we find that large values of latent heat are needed and may indicate that dynamics at the transition are more complex than considered in current models. Finally, experiments are proposed that can distinguish between a change in optical properties due to a transition to a metallic state or due to closure of the bandgap in molecular hydrogen.Comment: 23 pages, 4 figure

Mindset, Attitudes, and Success in Statistics

Students in many disciplines are required to take an introductory statistics course while pursuing a college education. Despite the utility of statistical methods in future research and career pursuits, many students have negative views of statistics. We are interested in how students’ mindsets and attitudes towards statistics impacts their performance in an undergraduate statistics course. We administered a survey to students in several undergraduate statistics courses at Utah State University. This survey included questions addressing mathematics experience, attitudes towards statistics, mindset, and course performance. We describe the results and conclusions from the survey

A Bayesian Markov Chain Monte Carlo Approach to Uncertainty Quantification

Uncertainty quantification (UQ) is a framework used frequently in engineering analyses to understand how uncertainty in system inputs lead to uncertainty in the system output. An instability is observed in a UQ method proposed by Roy and Oberkampf and a Bayesian Markov Chain Monte Carlo approach to UQ is offered as an alternative. The Bayesian approach allows analysts to incorporate information from various available sources including observed measurements and expert opinion and to update the analysis and results as more information becomes available. An illustrative engineering example is provided as a platform to demonstrate the Bayesian UQ approach and to compare it with the Roy and Oberkampf method. Methods for visualizing and interpreting the results from the Bayesian UQ approach are explored. This research is expected to produce a new approach to UQ that will be useful to engineers and other practitioners as they quantify the uncertainty in a system, visualize the uncertainty, and interpret the results to inform decisions

Does Dewey have an “epistemic argument” for democracy?

The analysis and defence of democracy on the grounds of its epistemic powers is now a well-established, if contentious, area of theoretical and empirical research. This article reconstructs a distinctive and systematic epistemic account of democracy from Dewey's writings. Running like a thread through this account is a critical analysis of the distortion of hierarchy and class division on social knowledge, which Dewey believes democracy can counteract. The article goes on to argue that Dewey’s account has the resources to defuse at least some important forms of the broader charges of instrumentalism and depoliticization that are directed at the epistemic project. The gloomy conviction of the stratified character of capitalist societies and the conflictual character of their politics shapes Dewey’s view of political agency, and this article outlines how this epistemic conception of democracy is deployed as a critical standard for judging and transforming existing political forms but also serves as a line of defence for democratic political forms against violent and authoritarian alternatives

The Normative and the Transformative in Ferrara's Exemplary Politics

In The Democratic Horizon and other works, Alessandro Ferrara offers an original theory of political judgment, exemplarity and political liberalism. This article examines two distinctive features of this theory, his accounts of the normativity of a Rawlsian form of political liberalism and of democratic openness or transformative politics. It is suggested that there are some tensions between his commitment to a judgment-centred epistemology and political liberalism

Performance and Complexity Co-Evaluations of MPEG4-ALS Compression Standard for Low-Latency Music Compression

In this thesis compression ratio and latency of different classical audio music tracks are analyzed with various encoder options of MPEG4ALS. Different tracks of audio music tracks are tested with MPEG4-ALS coder with different options to find the optimum values for various parameters to obtain maximum compression ratio with minimum CPU time (encoder and decoder time). Optimum frame length for which the compression ratio saturates for music audio is found out by analyzing the results when different classical music tracks are experimented with various frame lengths. Also music tracks with varying sampling rate are tested and the compression ratio and latency relationship with sampling rate are analyzed and plotted. It is found that the compression gain rate was higher when the codec complexity is less, and joint channel correlation and long term correlations are not significant and latency trade off make the more complex codec options unsuitable for applications where latency is critical. When the two entropy coding options, Rice code and BGMC (Block Gilbert-Moore Codes) are applied on various classical music tracks, it was obvious that the Rice code is more suitable for low-latency applications compared to the more complex BGMC coding, as BGMC improved compression performance with the expense of latency, making it unsuitable in real-time applications