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differential
1
Book Chapter
Series: AIPP Books, Methods
Published: November 2022
10.1063/9780735422575_002
EISBN: 978-0-7354-2257-5
ISBN: 978-0-7354-2254-4
...Linear ODEs and Orthogonal Functions It has been recognized that the vast majority of the eigenvalue problems in physics lead to second-order differential equations with the general form ( Ince, 1927 ) (2.1) L ^ [ ϕ ] = R ( x ) , a ≤ x ≤ b , (2.2) L...
Book Chapter
Series: AIPP Books, Methods
Published: November 2022
10.1063/9780735422575_006
EISBN: 978-0-7354-2257-5
ISBN: 978-0-7354-2254-4
... and space), and we cannot easily add arbitrary real numbers because the computer’s number system is discrete. These inherent limitations of practical computations are essentially resolved by simply turning our problem into its discrete counterpart, in other words by discretizing the differential...
Images
in Strain Engineering of Metal Insulator Transition in VO2
> Strain Engineering in Functional Materials and Devices
Published: March 2023
FIG. 4.6 (a) XRD of thickness-dependent VO2 epitaxial film on rutile TiO2 substrate; (b) schematic shows the growth of rutile VO2 phase on rutile TiO2; (c) resistance–temperature plot; and (d) corresponding differential resistance plot showing occurrences of resistance drop at different temperatures for varied VO2 film thickness ( Fan et al., 2014 ). More about this image found in (a) XRD of thickness-dependent VO2 epitaxial film on rutile TiO...
Book Chapter
Series: AIPP Books, Professional
Published: March 2023
10.1063/9780735425477_009
EISBN: 978-0-7354-2547-7
ISBN: 978-0-7354-2544-6
... irradiation from contamination and radiation from radioactive material (that is, to help them attain the “differentiated view”). Like PPAR, the main goal of IiR is to help students acquire a “differentiated view.” Whereas the PLON-unit and PPAR discussed above originate in the Netherlands, Inquiry...
Book Chapter
Series: AIPP Books, Professional
Published: March 2023
10.1063/9780735425477_002
EISBN: 978-0-7354-2547-7
ISBN: 978-0-7354-2544-6
... undergraduate courses in calculus and differential equations and their applications to problems in fluid dynamics. The authors analyze the relationship between LE and FP representations of particles moving in a fluid due to Brownian motion in the presence of external fields. Although each description offers...
Book Chapter
Book: Toward Better Photovoltaic Systems: Design, Simulation, Optimization, Analysis, and Operations
Series: AIPP Books, Principles
Published: March 2023
0
EISBN: 978-0-7354-2561-3
ISBN: 978-0-7354-2560-6
... photovoltaic models by means of a hybrid differential evolution with whale optimization algorithm ,” Solar Energy 176 , 742 – 761 ( 2018 ). 10.1016/j.solener.2018.10.050 Yu , S. , Heidari , A. A. , Liang , G. , Chen , C. , Chen , H. , and Shao , Q. , “ Solar photovoltaic...
Book Chapter
Series: AIPP Books, Professional
Published: March 2023
10.1063/9780735425477_012
EISBN: 978-0-7354-2547-7
ISBN: 978-0-7354-2544-6
... relation or generate a causal prediction. This is also true for the differentiation between the three epistemic artifacts of sensemaking discussed in Sec. 12.2 (i.e., differentiating between explanations and arguments or between mechanistic models and explanations). Despite this limitation, we argue...
Book Chapter
Series: AIPP Books, Professional
Published: March 2023
10.1063/9780735425477_004
EISBN: 978-0-7354-2547-7
ISBN: 978-0-7354-2544-6
... [e.g., Nordine et al., 2011 ; Fig. 4.2(b )], and again others differentiate between forms of energy “in storage” and forms of energy “in transition” [e.g., Papadouris and Constantinou, 2016 ; Fig. 4.2(c )]. Research on the usefulness of the different energy flow diagrams is scarce...
Images
in High Breakdown Voltage β-Ga2O3 Schottky Diodes
> Ultrawide Bandgap β-Ga2O3 SemiconductorTheory and Applications
Published: February 2023
FIG. 8.13 (a) Schematic of a β-Ga2O3 SBD with a trench-filled SiO2 dielectric for edge termination. (b) Forward I–V characteristics and differential RON,sp of several representative devices. (c) Reverse breakdown characteristics of several representative devices. Reprinted with permission from Dong et al., IEEE Electron Device Lett. 43 (5), 765–768 (2022). Copyright 2022 IEEE. More about this image found in (a) Schematic of a β-Ga2O3 SBD with a trench-filled S...
Book Chapter
Series: AIPP Books, Professional
Published: March 2023
10.1063/9780735425477_008
EISBN: 978-0-7354-2547-7
ISBN: 978-0-7354-2544-6
... theory Measurement of eigenstate vs uncertainty results on superposition state Operator in quantum mechanics Wave-particle dualism in the SE solution Solution of a differential equation vs eigenfunction What is a potential well? Boundary condition and not divergence as physical...
Book Chapter
Series: AIPP Books, Professional
Published: March 2023
10.1063/9780735425514_002
EISBN: 978-0-7354-2551-4
ISBN: 978-0-7354-2548-4
... deficit model (i.e., the learning environment is not equitable and inclusive and is disadvantaging the underrepresented groups and leading to inequitable outcomes). In particular, these inequities are typically caused by differential opportunities for students based upon their privilege and societal...
Book Chapter
Series: AIPP Books, Professional
Published: March 2023
10.1063/9780735425477_005
EISBN: 978-0-7354-2547-7
ISBN: 978-0-7354-2544-6
...' law and Ampère's law in differential form. They found that students could typically write down correct expressions for divergence and curl, and realized that these operators are defined locally. However, some students appeared to interpret the latter as, e.g., the value of divergence being different...
Book Chapter
Series: AIPP Books, Professional
Published: March 2023
10.1063/9780735425514_011
EISBN: 978-0-7354-2551-4
ISBN: 978-0-7354-2548-4
... studies where functional/optimal performance is not differentiated provide little support—even when larger population sizes are employed 3 —whether the pre- and post-instruction results show a shift in the typical modes of functioning. Is it possible that many of the short-term...
Book Chapter
Series: AIPP Books, Professional
Published: March 2023
10.1063/9780735425712_002
EISBN: 978-0-7354-2571-2
ISBN: 978-0-7354-2568-2
.... Both virtual and physical environments incorporate specific features and affordances that implicitly or explicitly enact forms and structures of required laboratory activities, thus influencing and driving students' experimentation. Thus, research evidence revealed differential experimental strategies...
Book Chapter
Series: AIPP Books, Professional
Published: March 2023
EISBN: 978-0-7354-2547-7
ISBN: 978-0-7354-2544-6
...” and “uncertainty” and the probabilistic nature of quantum theory Measurement of eigenstate vs uncertainty results on superposition state Operator in quantum mechanics Wave-particle dualism in the SE solution Solution of a differential equation vs eigenfunction What is a potential well? Boundary...
Book Chapter
Series: AIPP Books, Professional
Published: March 2023
10.1063/9780735425477_024
EISBN: 978-0-7354-2547-7
ISBN: 978-0-7354-2544-6
.... This heterogeneity, which has sometimes been a source of difficulty for us in structuring the content of certain themes, appears to be a characteristic of the field. Beyond the themes, the selected studies are also differentiated according to the ways in which the different components of the practice are considered...
Book Chapter
Book: Toward Better Photovoltaic Systems: Design, Simulation, Optimization, Analysis, and Operations
Series: AIPP Books, Principles
Published: March 2023
10.1063/9780735425613_003
EISBN: 978-0-7354-2561-3
ISBN: 978-0-7354-2560-6
... and calculated intensity. The strategy used by Xiong et al. (2018) was integrating differential evolution with a whale optimization algorithm. Xiong et al. (2018) stated that parameter extraction of solar photovoltaic models is a complex non-linear multivariable optimization problem...
Book Chapter
Series: AIPP Books, Professional
Published: March 2023
10.1063/9780735425477_010
EISBN: 978-0-7354-2547-7
ISBN: 978-0-7354-2544-6
... of problem-solving assessments that measure insight and innovation. Though there have been proposals for such assessments ( Hull et al., 2013 and Kuo et al., 2020 ), more development and use of insight assessments is needed. Expertise is not a monolith; one differentiation is between...
Images
in High Breakdown Voltage β-Ga2O3 Schottky Diodes
> Ultrawide Bandgap β-Ga2O3 SemiconductorTheory and Applications
Published: February 2023
FIG. 8.10 Schematics of an unterminated β-Ga2O3 SBD, a β-Ga2O3 SBD with self-aligned fluorine plasma treatment (FPT), and a β-Ga2O3 SBD with self-aligned beveled fluorine plasma treatment (BFPT). (b) Forward I–V characteristics and differential RON,sp of the three different SBDs. (c) Reverse breakdown characteristics of the three different SBDs. Reprinted with permission from Hu et al., IEEE Electron Device Lett. 41 (3), 441–444 (2020a). Copyright 2020 IEEE. More about this image found in Schematics of an unterminated β-Ga2O3 SBD, a β-Ga
Book Chapter
Series: AIPP Books, Principles
Published: March 2023
10.1063/9780735425590_008
EISBN: 978-0-7354-2559-0
ISBN: 978-0-7354-2556-9
... j k l ∂ u k ( 0 ) ∂ x l n j + C i j k l ∑ P = 1 ∞ ε P ∂ u k ( P ) ∂ x l n j = 0. By differentiating this expression with respect to ε, and substituting ε = 0 (8.16) C i j k l ∂ u k...
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