Transport models have successfully described many aspects of intermediate energy heavy-ion collision dynamics. As the energies increase in these models to the ultrarelativistic regime, Lorentz covariance and causality are not strictly respected. The standard argument is that such effects are not important to final results; but they have not been seriously considered at high energies. We point out how and why these happen, how serious of a problem they may be and suggest ways of reducing or eliminating the undesirable effects.PACS number(s): 25.75. +r, 24.85. +p
We discuss the development and functionality of the LON-CAPA system with a particular focus on its homework and examination functionality. We also describe its more general approach to course management and its infrastructure for course content sharing and reuse. We then focus on measures of student learning and the effectiveness of different content types.
Within QMD simulations we demonstrate the effect of virial corrections on heavy ion reactions. Unlike in standard codes, the binary collisions are treated as non-local so that the contribution of the collision flux to the reaction dynamics is covered. A comparison with standard QMD simulations shows that the virial corrections lead to a broader proton distribution bringing theoretical spectra closer towards experimental values. Complementary BUU simulations reveal that the non-locality enhances the collision rate in the early stage of the reaction. It suggests that the broader distribution appears due to an enhanced pre-equilibrium emission of particles.The Boltzmann equation including the Pauli blocking (the BUU equation [1]) and the closely related method of quantum molecular dynamics [2,3] (QMD) are extensively used to interpret experimental data from heavy ion reactions. Due to their quasi-classical character, they offer a transparent picture of the internal dynamics of reactions and allow one to link observed particle spectra with individual stages of reactions.An ambition to cover the heavy ion reactions within experimental errors has been recently cooled down by a failure of BUU simulations to describe the energy and angular distribution of neutrons and protons in low and mid energy domain [4][5][6]. Indeed, the Boltzmann equation is not the full story. As noticed in numerical studies of hard sphere cascade by Halbert [7] and more general by Malfliet [8], it is disturbing that all dynamical models rely more or less on the use of the space-and timelocal approximation of binary collisions inherited from the Boltzmann equation. This approximation neglects a contribution of the collision flux to the compressibility and the share viscosity which control the hydrodynamic motion during the reaction. To include the collision flux and other virial corrections, the non-local character of binary collisions has to be accounted for. Malfliet also demonstrated that non-local collisions can be easily incorporated into simulation BUU codes.In absence of a first principle theory, Malfliet in his pioneering study, and more recently Kortemeyer, Daffin and Bauer [9], had to use classical hard-sphere-like non-local collisions which naturally do not result in a full quantitative agreement with experimental data. This ad hoc approximation reflects a gap in former quasi-classical theories of quantum transport: authors either cared about non-local collisions leaving aside quasiparticle features or vice versa. Moreover, quantum theories of binary collisions treated non-local collisions via gradient contributions to the scattering integral [10,11] which are numerically inconvenient and thus have never been employed in demanding simulations of heavy ion reactions. Recent theoretical studies have filled this gap. Danielewicz and Pratt [12] pointed out that the collision delay can be used as a convenient tool to describe the virial corrections to the equation of state for the gas of quasiparticles. Although their discussion is limit...
The two genders make different use of being allowed multiple tries to solve online homework problems: male students frequently attempt to immediately solve the problem, while female students are more likely to first interact with peers and teaching assistants before entering answers. More male than female students state that they use the multiple allowed attempts to enter “random stuff,” while more female than male students state that the multiple attempts allow them to explore their own problem solving approaches without worrying or being stressed out by grades
An important result of physics education research is that students' learning and success in a course is correlated with their beliefs, attitudes, and expectations regarding physics. However, it is hard to assess these beliefs for individual students, and traditional survey instruments such as the Maryland Physics Expectations Survey ͑MPEX͒ are intended to evaluate the impact of one or more semesters of instruction on an overall class and improve teaching. In this study, we investigate the possibility of using the analysis of online student discussion behavior as an indicator of an individual student's approach to physics. These discussions are not tainted by the effects of self-reporting, and are gathered in authentic nonresearch settings, where students attempt to solve problems in the way that they believe is most efficient and appropriate. We calculate the correlation of both MPEX and student discussions with different measures of student learning, and find that on an individual base, student discussions are a stronger predictor of success than MPEX outcomes.
We investigate the stochastic Direct Simulation Monte Carlo method (DSMC) for numerically solving the collision-term in heavy-ion transport theories of the Boltzmann-Uehling-Uhlenbeck (BUU) type. The first major modification we consider is changes in the collision rates due to excluded volume and shadowing/screening effects (Enskog theory). The second effect studied by us is the inclusion of an additional advection term. These modifications ensure a non-vanishing second virial and change the equation of state for the scattering process from that of an ideal gas to that of a hard-sphere gas. We analyse the effect of these modifications on the calculated value of directed nuclear collective flow in heavy ion collisions, and find that the flow slightly increases.
When deploying online homework in physics courses, an important consideration is how many tries learners should be allowed to solve numerical free-response problems. While on the one hand, this number should be large enough to allow learners mastery of concepts and avoid copying, on the other hand, granting too many allowed tries encourages counter-productive behavior. We investigate data from an introductory calculus-based physics course that allowed different numbers of tries in different semesters. It turns out that the probabilities for successfully completing or abandoning problems during a particular try are independent of the number of tries already made, which indicates that students do not learn from their earlier tries. We also find that the probability for successfully completing a problem during a particular try decreases with the number of allowed tries, likely due to increased carelessness or guessing, while the probability to give up on a problem after a particular try is largely independent of the number of allowed tries. These findings lead to a mathematical model for learner usage of multiple tries, which predicts an optimum number of five allowed tries.
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