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Layered Fabrication of Branched Networks Using Lindenmayer Systems
A current challenge impeding the growth of bone tissue engineering is the lack of
functional scaffolds of geometric sizes greater than 10mm due to the inability of cells to
survive deep within the scaffold. It is hypothesized that these scaffolds must have an
inbuilt nutrient distribution network to sustain the uniform growth of cells. In this
paper, we seek to enhance the design and layered fabrication of scaffold internal
architecture through the development of Lindenmayer systems, a graphical language
based theory to create nutrient delivery networks. The scaffolds are fabricated using the
Texas Instruments DLP⢠system through UVâphotopolymerization to produce
polyethylene glycol hydrogels with internal branch structures. The paper will discuss
the Lindenmayer system, process planning algorithms, layered fabrication of samples,
challenges and future tasks.Mechanical Engineerin
Sowing Seeds of Tradition! Applying Traditional Family Values and Adaptive Reuse to Resurrect a Community.
There are problems in every community, including South Memphis, Tennessee. Issues that need to be addressed include teen pregnancies, school drop-outs, crime, childhood obesity, and lack of parental guidance. Traditional family characteristics such as spiritual life, caring and appreciation, commitment, flexibilty and openness to change were once guiding forces that have been lost in our current culture. The response has been to provide community centers, which have often failed because they do not teach the basic skills necessary for a productive life. One solution is to convert the Turner Dairy Warehouse on South Bellevue into a facility that will provide education, enrichment, and encouragement. The Family Educational Exchange & Development Center (F.E.E.D) will be an educational facility instilling family values, teaching integrated life skills, and giving back to the community. The skills taught will include horticulture, home-economics, parenting, and general education. This facility will bring life to a dying community
Diluted Networks of Nonlinear Resistors and Fractal Dimensions of Percolation Clusters
We study random networks of nonlinear resistors, which obey a generalized
Ohm's law, . Our renormalized field theory, which thrives on an
interpretation of the involved Feynman Diagrams as being resistor networks
themselves, is presented in detail. By considering distinct values of the
nonlinearity r, we calculate several fractal dimensions characterizing
percolation clusters. For the dimension associated with the red bonds we show
that at least to order {\sl O} (\epsilon^4),
with being the correlation length exponent, and , where d
denotes the spatial dimension. This result agrees with a rigorous one by
Coniglio. Our result for the chemical distance, d_{\scriptsize min} = 2 -
\epsilon /6 - [ 937/588 + 45/49 (\ln 2 -9/10 \ln 3)] (\epsilon /6)^2 + {\sl O}
(\epsilon^3) verifies a previous calculation by one of us. For the backbone
dimension we find D_B = 2 + \epsilon /21 - 172 \epsilon^2 /9261 + 2 (- 74639 +
22680 \zeta (3))\epsilon^3 /4084101 + {\sl O} (\epsilon^4), where , in agreement to second order in with a two-loop
calculation by Harris and Lubensky.Comment: 29 pages, 7 figure
Towards a Microscopic Model of Magnetoelectric Interactions in Ni3V2O8
We develop a microscopic magnetoelectric coupling in NiVO (NVO)
which gives rise to the trilinear phenomenological coupling used previously to
explain the phase transition in which magnetic and ferroelectric order
parameters appear simultaneously. Using combined neutron scattering
measurements and first-principles calculations of the phonons in NVO, we
determine eleven phonons which can induce the observed spontaneous
polarization. Among these eleven phonons, we find that a few of them can
actually induce a significant dipole moment. Using the calculated atomic
charges, we find that the required distortion to induce the observed dipole
moment is very small (~0.001 \AA) and therefore it would be very difficult to
observe the distortion by neutron-powder diffraction. Finally, we identify the
derivatives of the exchange tensor with respect to atomic displacements which
are needed for a microscopic model of a spin-phonon coupling in NVO and which
we hope will be obtained from a fundamental quantum calculation such as LDA+U.
We also analyze two toy models to illustrate that the Dzyaloskinskii-Moriya
interaction is very important for coexisting of magnetic and ferroelectric
order but it is not the only mechanism when the local site symmetry of the
system is low enough.Comment: 20 pages, 10 figure
Two-dimensional Site-Bond Percolation as an Example of Self-Averaging System
The Harris-Aharony criterion for a statistical model predicts, that if a
specific heat exponent , then this model does not exhibit
self-averaging. In two-dimensional percolation model the index .
It means that, in accordance with the Harris-Aharony criterion, the model can
exhibit self-averaging properties. We study numerically the relative variances
and for the probability of a site belongin to the
"infinite" (maximum) cluster and the mean finite cluster size . It was
shown, that two-dimensional site-bound percolation on the square lattice, where
the bonds play the role of impurity and the sites play the role of the
statistical ensemble, over which the averaging is performed, exhibits
self-averaging properties.Comment: 15 pages, 5 figure
Landau Expansion for the Kugel-Khomskii Hamiltonian
The Kugel-Khomskii (KK) Hamiltonian for the titanates describes spin and
orbital superexchange interactions between ions in an ideal perovskite
structure in which the three orbitals are degenerate in energy and
electron hopping is constrained by cubic site symmetry. In this paper we
implement a variational approach to mean-field theory in which each site, ,
has its own single-site density matrix \rhov(i), where , the
number of allowed single-particle states, is 6 (3 orbital times 2 spin states).
The variational free energy from this 35 parameter density matrix is shown to
exhibit the unusual symmetries noted previously which lead to a
wavevector-dependent susceptibility for spins in orbitals which is
dispersionless in the -direction. Thus, for the cubic KK model
itself, mean-field theory does not provide wavevector `selection', in agreement
with rigorous symmetry arguments. We consider the effect of including various
perturbations. When spin-orbit interactions are introduced, the susceptibility
has dispersion in all directions in -space, but the resulting
antiferromagnetic mean-field state is degenerate with respect to global
rotation of the staggered spin, implying that the spin-wave spectrum is
gapless. This possibly surprising conclusion is also consistent with rigorous
symmetry arguments. When next-nearest-neighbor hopping is included, staggered
moments of all orbitals appear, but the sum of these moments is zero, yielding
an exotic state with long-range order without long-range spin order. The effect
of a Hund's rule coupling of sufficient strength is to produce a state with
orbital order.Comment: 20 pages, 5 figures, submitted to Phys. Rev. B (2003
Globular Cluster Systems in Brightest Cluster Galaxies. III: Beyond Bimodality
We present new deep photometry of the rich globular cluster (GC) systems
around the Brightest Cluster Galaxies UGC 9799 (Abell 2052) and UGC 10143
(Abell 2147), obtained with the HST ACS and WFC3 cameras. For comparison, we
also present new reductions of similar HST/ACS data for the Coma supergiants
NGC 4874 and 4889. All four of these galaxies have huge cluster populations (to
the radial limits of our data, comprising from 12000 to 23000 clusters per
galaxy). The metallicity distribution functions (MDFs) of the GCs can still be
matched by a bimodal-Gaussian form where the metal-rich and metal-poor modes
are separated by ~0.8 dex, but the internal dispersions of each mode are so
large that the total MDF becomes very broad and nearly continuous from [Fe/H] =
-2.4 to Solar. There are, however, significant differences between galaxies in
the relative numbers of \emph{metal-rich} clusters, suggesting that they
underwent significantly different histories of mergers with massive, gas-rich
halos. Lastly, the proportion of metal-poor GCs rises especially rapidly
outside projected radii R > 4 R_eff, suggesting the importance of accreted
dwarf satellites in the outer halo. Comprehensive models for the formation of
GCs as part of the hierarchical formation of their parent galaxies will be
needed to trace the systematic change in structure of the MDF with galaxy mass,
from the distinctly bimodal form in smaller galaxies up to the broad continuum
that we see in the very largest systems.Comment: In press for Astrophysical Journa
Non Markovian persistence in the diluted Ising model at criticality
We investigate global persistence properties for the non-equilibrium critical
dynamics of the randomly diluted Ising model. The disorder averaged persistence
probability of the global magnetization is found to decay
algebraically with an exponent that we compute analytically in a
dimensional expansion in . Corrections to Markov process are
found to occur already at one loop order and is thus a novel
exponent characterizing this disordered critical point. Our result is
thoroughly compared with Monte Carlo simulations in , which also include a
measurement of the initial slip exponent. Taking carefully into account
corrections to scaling, is found to be a universal exponent,
independent of the dilution factor along the critical line at , and
in good agreement with our one loop calculation.Comment: 7 pages, 4 figure
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