18,890 research outputs found
Developing Mathematics Enrichment Workshops for Middle School Students: Philosophy and Sample Workshops
This paper describes our approach to organizing enrichment activities using advanced mathematics topics for diverse audiences of middle school students. We discuss our philosophy and approaches for the structure of these workshops, and then provide sample schedules and resource materials. The workshops cover activities on the following topics: Graphing Calculators; The Chaos Game; Statistical Sampling; CT Scans–the reconstruction problem; The Platonic and Archimedean solids; The Shape of Space; Symmetry; The Binary Number System and the game of NIM; Graph Theory: Proof by Counterexample
Specific Nature of Hydrolysis of Insulin and Tobacco Mosaic Virus Protein by Thermolysin
Oxidized bovine insulin and tobacco mosaic virus protein used to determine hydrolysis specificity of thermolysi
Nanotrapping and the thermodynamics of optical tweezers
Particles that can be trapped in optical tweezers range from tens of microns
down to tens of nanometres in size. Interestingly, this size range includes
large macromolecules. We show experimentally, in agreement with theoretical
expectations, that optical tweezers can be used to manipulate single molecules
of polyethylene oxide suspended in water. The trapped molecules accumulate
without aggregating, so this provides optical control of the concentration of
macromolecules in solution. Apart from possible applications such as the
micromanipulation of nanoparticles, nanoassembly, microchemistry, and the study
of biological macromolecules, our results also provide insight into the
thermodynamics of optical tweezers.Comment: 5 pages, 3 figures, presented at 17th AIP Congress, Brisbane, 200
A statistical study of the global structure of the ring current
[1] In this paper we derive the average configuration of the ring current as a function of the state of the magnetosphere as indicated by the Dst index. We sort magnetic field data from the Combined Release and Radiation Effects Satellite (CRRES) by spatial location and by the Dst index in order to produce magnetic field maps. From these maps we calculate local current systems by taking the curl of the magnetic field. We find both the westward (outer) and the eastward (inner) components of the ring current. We find that the ring current intensity varies linearly with Dst as expected and that the ring current is asymmetric for all Dst values. The azimuthal peak of the ring current is located in the afternoon sector for quiet conditions and near midnight for disturbed conditions. The ring current also moves closer to the Earth during disturbed conditions. We attempt to recreate the Dst index by integrating the magnetic perturbations caused by the ring current. We find that we need to multiply our computed disturbance by a factor of 1.88 ± 0.27 and add an offset of 3.84 ± 4.33 nT in order to get optimal agreement with Dst. When taking into account a tail current contribution of roughly 25%, this agrees well with our expectation of a factor of 1.3 to 1.5 based on a partially conducting Earth. The offset that we have to add does not agree well with an expected offset of approximately 20 nT based on solar wind pressure
Analytic approximations to the phase diagram of the Jaynes-Cummings-Hubbard model with application to ion chains
We discuss analytic approximations to the ground state phase diagram of the
homogeneous Jaynes-Cummings-Hubbard (JCH) Hamiltonian with general short-range
hopping. The JCH model describes e.g. radial phonon excitations of a linear
chain of ions coupled to an external laser field tuned to the red motional
sideband with Coulomb mediated hopping or an array of high- coupled cavities
containing a two-level atom and photons. Specifically we consider the cases of
a linear array of coupled cavities and a linear ion chain. We derive
approximate analytic expressions for the boundaries between Mott-insulating and
superfluid phases and give explicit expressions for the critical value of the
hopping amplitude within the different approximation schemes. In the case of an
array of cavities, which is represented by the standard JCH model we compare
both approximations to numerical data from density-matrix renormalization group
(DMRG) calculations.Comment: 9 pages, 5 figures, extended and corrected second versio
A quantitative assessment of empirical magnetic field models at geosynchronous orbit during magnetic storms
[1] We evaluate the performance of recent empirical magnetic field models (Tsyganenko, 1996, 2002a, 2002b; Tsyganenko and Sitnov, 2005, hereafter referred to as T96, T02 and TS05, respectively) during magnetic storm times including both pre- and post-storm intervals. The model outputs are compared with GOES observations of the magnetic field at geosynchronous orbit. In the case of a major magnetic storm, the T96 and T02 models predict anomalously strong negative Bz at geostationary orbit on the nightside due to input values exceeding the model limits, whereas a comprehensive magnetic field data survey using GOES does not support that prediction. On the basis of additional comparisons using 52 storm events, we discuss the strengths and limitations of each model. Furthermore, we quantify the performance of individual models at predicting geostationary magnetic fields as a function of local time, Dst, and storm phase. Compared to the earlier models (T96 and T02), the most recent storm-time model (TS05) has the best overall performance across the entire range of local times, storm levels, and storm phases at geostationary orbit. The field residuals between TS05 and GOES are small (≤3 nT) compared to the intrinsic short time-scale magnetic variability of the geostationary environment even during non-storm conditions (∼24 nT). Finally, we demonstrate how field model errors may affect radiation belt studies when estimating electron phase space density
Intensity interferometry of single x-ray pulses from a synchrotron storage ring
We report on measurements of second-order intensity correlations at the high
brilliance storage ring PETRA III using a prototype of the newly developed
Adaptive Gain Integrating Pixel Detector (AGIPD). The detector recorded
individual synchrotron radiation pulses with an x-ray photon energy of 14.4 keV
and repetition rate of about 5 MHz. The second-order intensity correlation
function was measured simultaneously at different spatial separations that
allowed to determine the transverse coherence length at these x-ray energies.
The measured values are in a good agreement with theoretical simulations based
on the Gaussian Schell-model.Comment: 16 pages, 6 figures, 42 reference
Collecting single molecules with conventional optical tweezers
The size of particles which can be trapped in optical tweezers ranges from
tens of nanometres to tens of micrometres. This size regime also includes large
single molecules. Here we present experiments demonstrating that optical
tweezers can be used to collect polyethylene oxide (PEO) molecules suspended in
water. The molecules that accumulate in the focal volume do not aggregate and
therefore represent a region of increased molecule concentration, which can be
controlled by the trapping potential. We also present a model which relates the
change in concentration to the trapping potential. Since many protein molecules
have molecular weights for which this method is applicable the effect may be
useful in assisting nucleation of protein crystals.Comment: 5 pages, 4 figure
Feedback control of unstable cellular solidification fronts
We present a numerical and experimental study of feedback control of unstable
cellular patterns in directional solidification (DS). The sample, a dilute
binary alloy, solidifies in a 2D geometry under a control scheme which applies
local heating close to the cell tips which protrude ahead of the other. For the
experiments, we use a real-time image processing algorithm to track cell tips,
coupled with a movable laser spot array device, to heat locally. We show,
numerically and experimentally, that spacings well below the threshold for a
period-doubling instability can be stabilized. As predicted by the numerical
calculations, cellular arrays become stable, and the spacing becomes uniform
through feedback control which is maintained with minimal heating.Comment: 4 pages, 4 figures, 1 tabl
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