1,891 research outputs found
Conceptually driven and visually rich tasks in texts and teaching practice: the case of infinite series
The study we report here examines parts of what Chevallard calls the institutional dimension of the students’ learning experience of a relatively under-researched, yet crucial, concept in Analysis, the concept of infinite series. In particular, we examine how the concept is introduced to students in texts and in teaching practice. To this purpose, we employ Duval's Theory of Registers of Semiotic Representation towards the analysis of 22 texts used in Canada and UK post-compulsory courses. We also draw on interviews with in-service teachers and university lecturers in order to discuss briefly teaching practice and some of their teaching suggestions. Our analysis of the texts highlights that the presentation of the concept is largely a-historical, with few graphical representations, few opportunities to work across different registers (algebraic, graphical, verbal), few applications or intra-mathematical references to the concept's significance and few conceptually driven tasks that go beyond practising with the application of convergence tests and prepare students for the complex topics in which the concept of series is implicated. Our preliminary analysis of the teacher interviews suggests that pedagogical practice often reflects the tendencies in the texts. Furthermore, the interviews with the university lecturers point at the pedagogical potential of: illustrative examples and evocative visual representations in teaching; and, student engagement with systematic guesswork and writing explanatory accounts of their choices and applications of convergence tests
A hybrid metal/semiconductor electron pump for quantum metrology
Electron pumps capable of delivering a current higher than 100pA with
sufficient accuracy are likely to become the direct mise en pratique of the
possible new quantum definition of the ampere. Furthermore, they are essential
for closing the quantum metrological triangle experiment which tests for
possible corrections to the quantum relations linking e and h, the electron
charge and the Planck constant, to voltage, resistance and current. We present
here single-island hybrid metal/semiconductor transistor pumps which combine
the simplicity and efficiency of Coulomb blockade in metals with the
unsurpassed performances of silicon switches. Robust and simple pumping at
650MHz and 0.5K is demonstrated. The pumped current obtained over a voltage
bias range of 1.4mV corresponds to a relative deviation of 5e-4 from the
calculated value, well within the 1.5e-3 uncertainty of the measurement setup.
Multi-charge pumping can be performed. The simple design fully integrated in an
industrial CMOS process makes it an ideal candidate for national measurement
institutes to realize and share a future quantum ampere
Ultrafast Molecular Imaging by Laser Induced Electron Diffraction
We address the feasibility of imaging geometric and orbital structure of a
polyatomic molecule on an attosecond time-scale using the laser induced
electron diffraction (LIED) technique. We present numerical results for the
highest molecular orbitals of the CO2 molecule excited by a near infrared
few-cycle laser pulse. The molecular geometry (bond-lengths) is determined
within 3% of accuracy from a diffraction pattern which also reflects the nodal
properties of the initial molecular orbital. Robustness of the structure
determination is discussed with respect to vibrational and rotational motions
with a complete interpretation of the laser-induced mechanisms
Effect of picosecond strain pulses on thin layers of the ferromagnetic semiconductor (Ga,Mn)(As,P)
The effect of picosecond acoustic strain pulses (ps-ASP) on a thin layer of
(Ga,Mn)As co-doped with phosphorus was probed using magneto-optical Kerr effect
(MOKE). A transient MOKE signal followed by low amplitude oscillations was
evidenced, with a strong dependence on applied magnetic field, temperature and
ps-ASP amplitude. Careful interferometric measurement of the layer's thickness
variation induced by the ps-ASP allowed us to model very accurately the
resulting signal, and interpret it as the strain modulated reflectivity
(differing for probe polarizations), independently from dynamic
magnetization effects.Comment: 6 pages, 5 figure
Laser induced electron diffraction: a tool for molecular orbital imaging
We explore the laser-induced ionization dynamics of N2 and CO2 molecules
subjected to a few-cycle, linearly polarized, 800\,nm laser pulse using
effective two-dimensional single active electron time-dependent quantum
simulations. We show that the electron recollision process taking place after
an initial tunnel ionization stage results in quantum interference patterns in
the energy resolved photo-electron signals. If the molecule is initially
aligned perpendicular to the field polarization, the position and relative
heights of the associated fringes can be related to the molecular geometrical
and orbital structure, using a simple inversion algorithm which takes into
account the symmetry of the initial molecular orbital from which the ionized
electron is produced. We show that it is possible to extract inter-atomic
distances in the molecule from an averaged photon-electron signal with an
accuracy of a few percents
Two-Color Coherent Photodissociation of Nitrogen Oxide in Intense Laser Fields
A simple one-dimensional semi-classical model with a Morse potential is used
to investigate the possibility of two-color infrared multi-photon dissociation
of vibrationally excited nitrogen oxide. The amplitude ratio effects and
adiabatic effects are investigated. Some initial states are found to have
thresholds smaller than expected from single-mode considerations and multiple
thresholds exist for initial states up to 32.
PACS: 42.50.HzComment: 3 pages, old papers, add source files to replace original postscrip
Bose-Einstein condensation in dark power-law laser traps
We investigate theoretically an original route to achieve Bose-Einstein
condensation using dark power-law laser traps. We propose to create such traps
with two crossing blue-detuned Laguerre-Gaussian optical beams. Controlling
their azimuthal order allows for the exploration of a multitude of
power-law trapping situations in one, two and three dimensions, ranging from
the usual harmonic trap to an almost square-well potential, in which a
quasi-homogeneous Bose gas can be formed. The usual cigar-shaped and
disk-shaped Bose-Einstein condensates obtained in a 1D or 2D harmonic trap take
the generic form of a "finger" or of a "hockey puck" in such Laguerre-Gaussian
traps. In addition, for a fixed atom number, higher transition temperatures are
obtained in such configurations when compared with a harmonic trap of same
volume. This effect, which results in a substantial acceleration of the
condensation dynamics, requires a better but still reasonable focusing of the
Laguerre-Gaussian beams
Iterative Approximate Consensus in the presence of Byzantine Link Failures
This paper explores the problem of reaching approximate consensus in
synchronous point-to-point networks, where each directed link of the underlying
communication graph represents a communication channel between a pair of nodes.
We adopt the transient Byzantine link failure model [15, 16], where an
omniscient adversary controls a subset of the directed communication links, but
the nodes are assumed to be fault-free.
Recent work has addressed the problem of reaching approximate consen- sus in
incomplete graphs with Byzantine nodes using a restricted class of iterative
algorithms that maintain only a small amount of memory across iterations [22,
21, 23, 12]. However, to the best of our knowledge, we are the first to
consider approximate consensus in the presence of Byzan- tine links. We extend
our past work that provided exact characterization of graphs in which the
iterative approximate consensus problem in the presence of Byzantine node
failures is solvable [22, 21]. In particular, we prove a tight necessary and
sufficient condition on the underlying com- munication graph for the existence
of iterative approximate consensus algorithms under transient Byzantine link
model. The condition answers (part of) the open problem stated in [16].Comment: arXiv admin note: text overlap with arXiv:1202.609
Monitoring Partially Synchronous Distributed Systems using SMT Solvers
In this paper, we discuss the feasibility of monitoring partially synchronous
distributed systems to detect latent bugs, i.e., errors caused by concurrency
and race conditions among concurrent processes. We present a monitoring
framework where we model both system constraints and latent bugs as
Satisfiability Modulo Theories (SMT) formulas, and we detect the presence of
latent bugs using an SMT solver. We demonstrate the feasibility of our
framework using both synthetic applications where latent bugs occur at any time
with random probability and an application involving exclusive access to a
shared resource with a subtle timing bug. We illustrate how the time required
for verification is affected by parameters such as communication frequency,
latency, and clock skew. Our results show that our framework can be used for
real-life applications, and because our framework uses SMT solvers, the range
of appropriate applications will increase as these solvers become more
efficient over time.Comment: Technical Report corresponding to the paper accepted at Runtime
Verification (RV) 201
The propensity of molecules to spatially align in intense light fields
The propensity of molecules to spatially align along the polarization vector
of intense, pulsed light fields is related to readily-accessible parameters
(molecular polarizabilities, moment of inertia, peak intensity of the light and
its pulse duration). Predictions can now be made of which molecules can be
spatially aligned, and under what circumstances, upon irradiation by intense
light. Accounting for both enhanced ionization and hyperpolarizability, it is
shown that {\it all} molecules can be aligned, even those with the smallest
static polarizability, when subjected to the shortest available laser pulses
(of sufficient intensity).Comment: 8 pages, 4 figures, to be submitted to PR
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