Student understanding of the Boltzmann factor

We present results of our investigation into student understanding of the physical significance and utility of the Boltzmann factor in several simple models. We identify various justifications, both correct and incorrect, that students use when answering written questions that require application of the Boltzmann factor. Results from written data as well as teaching interviews suggest that many students can neither recognize situations in which the Boltzmann factor is applicable, nor articulate the physical significance of the Boltzmann factor as an expression for multiplicity, a fundamental quantity of statistical mechanics. The specific student difficulties seen in the written data led us to develop a guided-inquiry tutorial activity, centered around the derivation of the Boltzmann factor, for use in undergraduate statistical mechanics courses. We report on the development process of our tutorial, including data from teaching interviews and classroom observations on student discussions about the Boltzmann factor and its derivation during the tutorial development process. This additional information informed modifications that improved students' abilities to complete the tutorial during the allowed class time without sacrificing the effectiveness as we have measured it. These data also show an increase in students' appreciation of the origin and significance of the Boltzmann factor during the student discussions. Our findings provide evidence that working in groups to better understand the physical origins of the canonical probability distribution helps students gain a better understanding of when the Boltzmann factor is applicable and how to use it appropriately in answering relevant questions

Rescue of splicing-mediated intron loss maximizes expression in lentiviral vectors containing the human ubiquitin C promoter.

Lentiviral vectors almost universally use heterologous internal promoters to express transgenes. One of the most commonly used promoter fragments is a 1.2-kb sequence from the human ubiquitin C (UBC) gene, encompassing the promoter, some enhancers, first exon, first intron and a small part of the second exon of UBC. Because splicing can occur after transcription of the vector genome during vector production, we investigated whether the intron within the UBC promoter fragment is faithfully transmitted to target cells. Genetic analysis revealed that more than 80% of proviral forms lack the intron of the UBC promoter. The human elongation factor 1 alpha (EEF1A1) promoter fragment intron was not lost during lentiviral packaging, and this difference between the UBC and EEF1A1 promoter introns was conferred by promoter exonic sequences. UBC promoter intron loss caused a 4-fold reduction in transgene expression. Movement of the expression cassette to the opposite strand prevented intron loss and restored full expression. This increase in expression was mostly due to non-classical enhancer activity within the intron, and movement of putative intronic enhancer sequences to multiple promoter-proximal sites actually repressed expression. Reversal of the UBC promoter also prevented intron loss and restored full expression in bidirectional lentiviral vectors

Thermodynamic and rheological properties of rhyolite and andesite melts

The heat capacities of a rhyolite and an andesite glass and liquid have been investigated from relative-enthalpy measurements made between 400 and 1800 K. For the glass phases, the experimental data agree with empirical models of calculation of the heat capacity. For the liquid phases, the agreement is less good owing to strong interactions between alkali metals and aluminum, which are not currently accounted for by empirical heat capacity models. The viscosity of both liquids has been measured from the glass transition to 1800 K. The temperature dependence of the viscosity is quantitatively related to the configurational heat capacity (determined calorimetrically) through the configurational entropy theory of relaxation processes. For both rhyolite and andesite melts, the heat capacity and viscosity do not differ markedly from those obtained by additive modeling from components with mineral compositions

Operator monotones, the reduction criterion and the relative entropy

We introduce the theory of operator monotone functions and employ it to derive a new inequality relating the quantum relative entropy and the quantum conditional entropy. We present applications of this new inequality and in particular we prove a new lower bound on the relative entropy of entanglement and other properties of entanglement measures.Comment: Final version accepted for publication, added references in reference [1] and [13

Microrheological Characterisation of Anisotropic Materials

We describe the measurement of anisotropic viscoelastic moduli in complex soft materials, such as biopolymer gels, via video particle tracking microrheology of colloid tracer particles. The use of a correlation tensor to find the axes of maximum anisotropy, and hence the mechanical director, is described. The moduli of an aligned DNA gel are reported, as a test of the technique; this may have implications for high DNA concentrations in vivo. We also discuss the errors in microrheological measurement, and describe the use of frequency space filtering to improve displacement resolution, and hence probe these typically high modulus materials.Comment: 5 pages, 5 figures. Replaced after refereeing/ improvement. Main results are the same. The final, published version of the paper is here http://link.aps.org/abstract/PRE/v73/e03190

Identifying Student Difficulties with Entropy, Heat Engines, and the Carnot Cycle

We report on several specific student difficulties regarding the Second Law of Thermodynamics in the context of heat engines within upper-division undergraduates thermal physics courses. Data come from ungraded written surveys, graded homework assignments, and videotaped classroom observations of tutorial activities. Written data show that students in these courses do not clearly articulate the connection between the Carnot cycle and the Second Law after lecture instruction. This result is consistent both within and across student populations. Observation data provide evidence for myriad difficulties related to entropy and heat engines, including students' struggles in reasoning about situations that are physically impossible and failures to differentiate between differential and net changes of state properties of a system. Results herein may be seen as the application of previously documented difficulties in the context of heat engines, but others are novel and emphasize the subtle and complex nature of cyclic processes and heat engines, which are central to the teaching and learning of thermodynamics and its applications. Moreover, the sophistication of these difficulties is indicative of the more advanced thinking required of students at the upper division, whose developing knowledge and understanding give rise to questions and struggles that are inaccessible to novices

Spin-lattice Interaction in Ruby Measured by ESR in Uniaxially Stressed Crystals

Spin-lattice Hamiltonian determined for chromium ions in ruby single crystal

Aircraft interior noise reduction by alternate resonance tuning

Model problem development and analysis continues with the Alternate Resonance Tuning (ART) concept. The various topics described are presently at different stages of completion: investigation of the effectiveness of the ART concept under an external propagating pressure field associated with propeller passage by the fuselage; analysis of ART performance with a double panel wall mounted in a flexible frame model; development of a data fitting scheme using a branch analysis with a Newton-Raphson scheme in multiple dimensions to determine values of critical parameters in the actual experimental apparatus; and investigation of the ART effect with real panels as opposed to the spring-mass-damper systems currently used in much of the theory