4,972 research outputs found
Mode summation approach to Casimir effect between two objects
In this paper, we explore the TGTG formula from the perspective of mode
summation approach. Both scalar fields and electromagnetic fields are
considered. In this approach, one has to first solve the equation of motion to
find a wave basis for each object. The two T's in the TGTG formula are
T-matrices representing the Lippmann-Schwinger T-operators, one for each of the
objects. The two G's in the TGTG formula are the translation matrices, relating
the wave basis of an object to the wave basis of the other object. After
discussing the general theory, we apply the prescription to derive the explicit
formulas for the Casimir energies for the sphere-sphere, sphere-plane,
cylinder-cylinder and cylinder-plane interactions. First the T-matrices for a
plane, a sphere and a cylinder are derived for the following cases: the object
is imposed with general Robin boundary conditions; the object is
semitransparent; and the object is magnetodielectric. Then the operator
approach is used to derive the translation matrices. From these, the explicit
TGTG formula for each of the scenarios can be written down. Besides summarizing
all the TGTG formulas that have been derived so far, we also provide the TGTG
formulas for some scenarios that have not been considered before.Comment: 42 page
Origins of ferromagnetism in transition-metal doped Si
We present results of the magnetic, structural and chemical characterizations of Mn<sup>+</sup>-implanted Si displaying <i>n</i>-type semiconducting behavior and ferromagnetic ordering with Curie temperature,T<sub>C</sub> well above room temperature. The temperature-dependent magnetization measured by superconducting quantum device interference (SQUID) from 5 K to 800 K was characterized by three different critical temperatures (T*<sub>C</sub>~45 K, T<sub>C1</sub>~630-650 K and T<sub>C2</sub>~805-825 K). Their origins were investigated using dynamic secondary mass ion spectroscopy (SIMS) and transmission electron microscopy (TEM) techniques, including electron energy loss spectroscopy (EELS), Z-contrast STEM (scanning TEM) imaging and electron diffraction. We provided direct evidences of the presence of a small amount of Fe and Cr impurities which were unintentionally doped into the samples together with the Mn<sup>+</sup> ions, as well as the formation of Mn-rich precipitates embedded in a Mn-poor matrix. The observed T*<sub>C</sub> is attributed to the Mn<sub>4</sub>Si<sub>7</sub> precipitates identified by electron diffraction. Possible origins of and are also discussed. Our findings raise questions regarding the origin of the high ferromagnetism reported in many material systems without a careful chemical analysis
On Measuring Fairness in Generative Models
Recently, there has been increased interest in fair generative models. In
this work, we conduct, for the first time, an in-depth study on fairness
measurement, a critical component in gauging progress on fair generative
models. We make three contributions. First, we conduct a study that reveals
that the existing fairness measurement framework has considerable measurement
errors, even when highly accurate sensitive attribute (SA) classifiers are
used. These findings cast doubts on previously reported fairness improvements.
Second, to address this issue, we propose CLassifier Error-Aware Measurement
(CLEAM), a new framework which uses a statistical model to account for
inaccuracies in SA classifiers. Our proposed CLEAM reduces measurement errors
significantly, e.g., 4.98% 0.62% for StyleGAN2 w.r.t. Gender.
Additionally, CLEAM achieves this with minimal additional overhead. Third, we
utilize CLEAM to measure fairness in important text-to-image generator and
GANs, revealing considerable biases in these models that raise concerns about
their applications. Code and more resources:
https://sutd-visual-computing-group.github.io/CLEAM/.Comment: Accepted in NeurIPS2
Casimir effect of electromagnetic field in Randall-Sundrum spacetime
We study the finite temperature Casimir effect on a pair of parallel
perfectly conducting plates in Randall-Sundrum model without using scalar field
analogy. Two different ways of interpreting perfectly conducting conditions are
discussed. The conventional way that uses perfectly conducting condition
induced from 5D leads to three discrete mode corrections. This is very
different from the result obtained from imposing 4D perfectly conducting
conditions on the 4D massless and massive vector fields obtained by decomposing
the 5D electromagnetic field. The latter only contains two discrete mode
corrections, but it has a continuum mode correction that depends on the
thicknesses of the plates. It is shown that under both boundary conditions, the
corrections to the Casimir force make the Casimir force more attractive. The
correction under 4D perfectly conducting condition is always smaller than the
correction under the 5D induced perfectly conducting condition. These
statements are true at any temperature.Comment: 20 pages, 4 figure
Impact of Online Renting on Software Piracy
Online rental of software is emerging as a new way of dissemination for several major software firms. Compared to outright selling, the renting scheme delivers the software as a service instead of a physical good. Hence, users cannot privately make copies for resale in the market. We investigate the impact of the renting mechanism on software piracy and pricing in a two-period model whereby a piracy market is present in the second period. We develop and compare models with or without renting. Our analysis shows that renting reduces social welfare but helps to increase a vendor’s profit under certain conditions. We also assess the difference in outcomes in the presence of network effect
Teachers' beliefs about knowledge and learning: A Singapore perspective
The purpose of this study is to explore the complex nature of Singapore teachers' beliefs about knowledge and learning and how these beliefs influence pedagogical practices in their classes. This paper presents findings from a large-scale survey study with 1806 teachers in Singapore. Data revealed that while teachers' beliefs about pedagogies, knowledge and learning were largely consistent, they also believed and practiced both teacher-centered and learner-centered pedagogies and assessment methods
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