209 research outputs found
Bayesian model averaging on hydraulic conductivity estimation and groundwater head prediction
Characterization of aquifer heterogeneity is inherently difficult because of the insufficiency of data, the inflexibility of parameterization methods, and non-uniqueness of parameterization methods. Groundwater predictions are greatly affected by multiple interpretations of aquifer properties and the uncertainties of model parameters. This study introduces a Bayesian model averaging (BMA) method along with multiple generalized parameterization (GP) methods to identify hydraulic conductivity and along with multiple simulation models to predict groundwater head and quantify the prediction uncertainty. Two major issues about BMA are discussed. The first problem is with using Occamâs window in usual BMA applications. Occamâs window only accepts models in a very narrow range, tending to single out the best method and discard other good methods. A variance window is proposed to replace Occamâs window to cope with this problem. The second problem is with using the Kashyap information criterion (KIC) in the approximation of posterior model probabilities, which tends to prefer highly uncertain model by considering the Fisher information matrix. The Bayesian information criterion (BIC) is recommended because it is able to avoid controversial results and it is computationally efficient. Numerical examples are designed to test the Bayesian model averaging method on hydraulic conductivity identification and groundwater head prediction. The proposed methodologies are then applied to the hydraulic conductivity identification of the Alamitos Gap area, and the hydraulic conductivity estimation and groundwater head prediction of the â1,500-footâ sand in East Baton Rouge Parish, Louisiana. The results show that the GP method provides great flexibility in parameterization with small conditional variance. The use of the variance window is necessary to avoid a dominant model when many models perform equally well. Compared to KIC, BIC is able to give an unbiased posterior model probability. It is also concluded that the uncertainty increases by including multiple models under the BMA framework, but risks are reduced by avoiding overconfidence in the solution from one model
Mechanical strain can switch the sign of quantum capacitance from positive to negative
Quantum capacitance is a fundamental quantity that can directly reveal many interactions among electrons and is expected to play a critical role in nanoelectronics. One of many tantalizing recent physical revelations about quantum capacitance is that it can posses a negative value, hence allowing for the possibility of enhancing the overall capacitance in some particular material systems beyond the scaling predicted by classical electrostatics. Using detailed quantum mechanical simulations, we find an intriguing result that mechanical strains can tune both signs and values of quantum capacitance. We use a small coaxially-gated carbon nanotube as a paradigmatical capacitor system and show that, for the range of mechanical strain considered, quantum capacitance can be adjusted from very large positive to very large negative values (in the order of plus/minus hundreds of at-to farads), compared with the corresponding classical geometric value (0.31035 aF). We elucidate the mechanisms underpinning the switching of the sign of quantum capacitance due to strain. This finding opens novel avenues in designing quantum capacitance for applications in nanosensors, energy storage, and nanoelectronics
Residue cross sections of Ti-induced fusion reactions based on the two-step model
Ti-induced fusion reactions to synthesize superheavy elements are
studied systematically with the two-step model developed recently, where fusion
process is divided into approaching phase and formation phase. Furthermore, the
residue cross sections for different neutron evaporation channels are evaluated
with the statistical evaporation model. In general, the calculated cross
sections are much smaller than that of Ca-induced fusion reactions, but
the results are within the detection capability of experimental facilities
nowadays. The maximum calculated residue cross section for producing superheavy
element is in the reaction Ti+Bk in channels with
pb at = 37.0 MeV.Comment: 6 pages, 7 figure
Cognitive analysis of students' errors and misconceptions in variables, equations, and functions
The fundamental goal of this study is to explore why so many students have
difficulty learning mathematics. To achieve this goal, this study focuses on why so many
students keep making the same errors over a long period of time. To explore such issues,
three basic algebra concepts - variable, equation, and function â are used to analyze
studentsâ errors, possible buggy algorithms, and the conceptual basis of these errors:
misconceptions. Through the research on these three basic concepts, it is expected that a
more general principle of understanding and the corresponding learning difficulties can
be illustrated by the case studies.
Although studentsâ errors varied to a great extent, certain types of errors related to
studentsâ misconceptions occurred frequently and repeatedly after one year of additional
instruction. Thus, it is possible to identify studentsâ misconceptions through working on
studentsâ systematic errors. The causes of studentsâ robust misconceptions were explored
by comparing high-achieving and low-achieving studentsâ understanding of these three
concepts at the object (structural) or process (operational) levels. In addition, high achieving students were found to prefer using object (structural) thinking to solve
problems even if the problems could be solved through both algebra and arithmetic
approaches. It was also found that the relationship between studentsâ misconception and
object-process thinking explained why some misconceptions were particularly difficult
to change. Studentsâ understanding of concepts at either of two stages (process and
object) interacted with either of two aspects (correct conception and misconception).
When students had understood a concept as a process with misconception, such
misconception was particularly hard to change.
In addition, other concerns, such as rethinking the misconception of the âequal
sign,â the influence of prior experience on studentsâ learning, misconceptions and
recycling curriculum, and developing teachersâ initial subject knowledge were also
discussed. The findings of this study demonstrated that the fundamental reason of
misconception of âequal signâ was the misunderstanding of either side of equation as a
process rather than as an object. Due to the existence of robust misconceptions as stated
in this study, the use of recycling curriculum may have negative effect on studentsâ
understanding of mathematics
Novel mesoporous TiO2(B) whisker-supported sulfated solid superacid with unique acid characteristics and catalytic performances
Mesoporous TiO2(B) whisker was firstly applied as a support for synthesizing the novel sulfated solid superacid (SO42â/TiO2(B)). According to NH3-TPD, TG and Py-IR characterization results, it was found that the similar amount of sulfate group on TiO2(B) and anatase showed significantly different acid characteristics and catalytic performances. The total acid amount of SO42â/TiO2(B) was about 1.8 times as anatase-supported sulfated solid superacid (SO42â/Anatase). Simultaneously, the SO42â/TiO2(B) possessed higher percentage of Brønsted acid and more weak-medium acid strength than SO42â/Anatase. These acidic properties endowed SO42â/TiO2(B) with the increased esterification reaction rate and decreased alkylation byproduct selectivity compared with that of SO42â/Anatase. Structure-performance analysis exhibited that there were more bridged bidentate sulfate groups coordinated to the TiO2(B) in SO42â/TiO2(B), which could induce more Ti cations than that of the chelating one. This was the key factor to be responsible for the unique acid characteristics of SO42â/TiO2(B). The present work provides a novel solid superacid and might open a strategy to mediate the acid characteristic for sulfated solid superacid
- âŚ