2,329 research outputs found
Una Destinatio, Viae Diversae – One Destination, Many Paths: An Invitation to Design Curriculum
One goal of early childhood teacher educators is to teach in ways that model teaching young children. What better way to study curriculum than to design it? This article describes a graduate early childhood curriculum course in which the students participate in the process of designing the syllabus. They receive a syllabus empty of topics, schedule, and readings. Together, we design the course according to their interests and needs. By semester’s end there is a full reading list and schedule. The invitation to co-design curriculum provides opportunities for investigation, representation and reflection as does constructivist teaching for children, and demonstrates concretely that curricular goals can be addressed in multiple and varied ways
Distribution of label spacings for genome mapping in nanochannels
In genome mapping experiments, long DNA molecules are stretched by confining
them to very narrow channels, so that the locations of sequence-specific
fluorescent labels along the channel axis provide large-scale genomic
information. It is difficult, however, to make the channels narrow enough so
that the DNA molecule is fully stretched. In practice its conformations may
form hairpins that change the spacings between internal segments of the DNA
molecule, and thus the label locations along the channel axis. Here we describe
a theory for the distribution of label spacings that explains the heavy tails
observed in distributions of label spacings in genome mapping experiments.Comment: 18 pages, 4 figures, 1 tabl
One-parameter scaling theory for DNA extension in a nanochannel
Experiments measuring DNA extension in nanochannels are at odds with even the
most basic predictions of current scaling arguments for the conformations of
confined semiflexible polymers such as DNA. We show that a theory based on a
weakly self-avoiding, one-dimensional "telegraph" process collapses
experimental data and simulation results onto a single master curve throughout
the experimentally relevant region of parameter space and explains the
mechanisms at play.Comment: Revised version. 5 pages, 4 figures, revised version, supplementary
informatio
Shuttle/spacelab MMAP/electromagnetic environment experiment phase B definition study
Progress made during the first five months of the Phase B definition study for the MMAP/Electromagnetic Environment Experiment (EEE) was described. An antenna/receiver assembly has been defined and sized for stowing in a three pallet bay area in the shuttle. Six scanning modes for the assembly are analyzed and footprints for various antenna sizes are plotted. Mission profiles have been outlined for a 400 km height, 57 deg inclination angle, circular orbit. Viewing time over 7 geographical areas are listed. Shuttle interfaces have been studied to determine what configuration the antenna assembly must have to be shared with other experiments of the Microwave Multi-Applications Payload (MMAP) and to be stowed in the shuttle bay. Other results reported include a frequency plan, a proposed antenna subsystem design, a proposed receiver design, preliminary outlines of the experiment controls and an analysis of on-board and ground data processing schemes
Lie conformal algebra cohomology and the variational complex
We find an interpretation of the complex of variational calculus in terms of
the Lie conformal algebra cohomology theory. This leads to a better
understanding of both theories. In particular, we give an explicit construction
of the Lie conformal algebra cohomology complex, and endow it with a structure
of a g-complex. On the other hand, we give an explicit construction of the
complex of variational calculus in terms of skew-symmetric poly-differential
operators.Comment: 56 page
Stable Frank-Kasper phases of self-assembled, soft matter spheres
Single molecular species can self-assemble into Frank Kasper (FK) phases,
finite approximants of dodecagonal quasicrystals, defying intuitive notions
that thermodynamic ground states are maximally symmetric. FK phases are
speculated to emerge as the minimal-distortional packings of space-filling
spherical domains, but a precise quantitation of this distortion and how it
affects assembly thermodynamics remains ambiguous. We use two complementary
approaches to demonstrate that the principles driving FK lattice formation in
diblock copolymers emerge directly from the strong-stretching theory of
spherical domains, in which minimal inter-block area competes with minimal
stretching of space-filling chains. The relative stability of FK lattices is
studied first using a diblock foam model with unconstrained particle volumes
and shapes, which correctly predicts not only the equilibrium {\sigma} lattice,
but also the unequal volumes of the equilibrium domains. We then provide a
molecular interpretation for these results via self-consistent field theory,
illuminating how molecular stiffness regulates the coupling between
intra-domain chain configurations and the asymmetry of local packing. These
findings shed new light on the role of volume exchange on the formation of
distinct FK phases in copolymers, and suggest a paradigm for formation of FK
phases in soft matter systems in which unequal domain volumes are selected by
the thermodynamic competition between distinct measures of shape asymmetry.Comment: 40 pages, 22 figure
Chaotic Properties of Dilute Two and Three Dimensional Random Lorentz Gases II: Open Systems
We calculate the spectrum of Lyapunov exponents for a point particle moving
in a random array of fixed hard disk or hard sphere scatterers, i.e. the
disordered Lorentz gas, in a generic nonequilibrium situation. In a large
system which is finite in at least some directions, and with absorbing boundary
conditions, the moving particle escapes the system with probability one.
However, there is a set of zero Lebesgue measure of initial phase points for
the moving particle, such that escape never occurs. Typically, this set of
points forms a fractal repeller, and the Lyapunov spectrum is calculated here
for trajectories on this repeller. For this calculation, we need the solution
of the recently introduced extended Boltzmann equation for the nonequilibrium
distribution of the radius of curvature matrix and the solution of the standard
Boltzmann equation. The escape-rate formalism then gives an explicit result for
the Kolmogorov Sinai entropy on the repeller.Comment: submitted to Phys Rev
Rational Approximate Symmetries of KdV Equation
We construct one-parameter deformation of the Dorfman Hamiltonian operator
for the Riemann hierarchy using the quasi-Miura transformation from topological
field theory. In this way, one can get the approximately rational symmetries of
KdV equation and then investigate its bi-Hamiltonian structure.Comment: 14 pages, no figure
Understanding deterministic diffusion by correlated random walks
Low-dimensional periodic arrays of scatterers with a moving point particle
are ideal models for studying deterministic diffusion. For such systems the
diffusion coefficient is typically an irregular function under variation of a
control parameter. Here we propose a systematic scheme of how to approximate
deterministic diffusion coefficients of this kind in terms of correlated random
walks. We apply this approach to two simple examples which are a
one-dimensional map on the line and the periodic Lorentz gas. Starting from
suitable Green-Kubo formulas we evaluate hierarchies of approximations for
their parameter-dependent diffusion coefficients. These approximations converge
exactly yielding a straightforward interpretation of the structure of these
irregular diffusion coeficients in terms of dynamical correlations.Comment: 13 pages (revtex) with 5 figures (postscript
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