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Applications of Solid Freeform Fabrication at the Naval Research Laboratory
Solid Freeform Fabrication (SFF) and related techniques are used at the Naval Research
Laboratory (NRL) for a variety of materials related investigations. Research and applications
conducted over the past few years are described including: Helisys Laminated Object
Manufacturing System (LOMS) fabrication of: ceramic piezoelectric actuators, tooling for
multifunctional materials, and anatomical prototypes for surgical visualization; fabrication of
mesoscale electronic and sensor components using a laser forward transfer direct write
technique; and visualization of complex, 3-D microstructures using a Stratasys Fused-Deposition
Modeler. The paper closes with a brief overview of future SFF related work at the NRL.Support for this work from DARPA, Office of Naval Research, and the Naval Research
Laboratory Core Research Program is gratefully acknowledged.Mechanical Engineerin
Concerning the quark condensate
A continuum expression for the trace of the massive dressed-quark propagator
is used to explicate a connection between the infrared limit of the QCD Dirac
operator's spectrum and the quark condensate appearing in the operator product
expansion, and the connection is verified via comparison with a lattice-QCD
simulation. The pseudoscalar vacuum polarisation provides a good approximation
to the condensate over a larger range of current-quark masses.Comment: 7 pages, LaTeX2e, revtex
Nuclear Ground State Observables and QCD Scaling in a Refined Relativistic Point Coupling Model
We present results obtained in the calculation of nuclear ground state
properties in relativistic Hartree approximation using a Lagrangian whose
QCD-scaled coupling constants are all natural (dimensionless and of order 1).
Our model consists of four-, six-, and eight-fermion point couplings (contact
interactions) together with derivative terms representing, respectively, two-,
three-, and four-body forces and the finite ranges of the corresponding mesonic
interactions. The coupling constants have been determined in a self-consistent
procedure that solves the model equations for representative nuclei
simultaneously in a generalized nonlinear least-squares adjustment algorithm.
The extracted coupling constants allow us to predict ground state properties of
a much larger set of even-even nuclei to good accuracy. The fact that the
extracted coupling constants are all natural leads to the conclusion that QCD
scaling and chiral symmetry apply to finite nuclei.Comment: 44 pages, 13 figures, 9 tables, REVTEX, accepted for publication in
Phys. Rev.
The nuclear energy density functional formalism
The present document focuses on the theoretical foundations of the nuclear
energy density functional (EDF) method. As such, it does not aim at reviewing
the status of the field, at covering all possible ramifications of the approach
or at presenting recent achievements and applications. The objective is to
provide a modern account of the nuclear EDF formalism that is at variance with
traditional presentations that rely, at one point or another, on a {\it
Hamiltonian-based} picture. The latter is not general enough to encompass what
the nuclear EDF method represents as of today. Specifically, the traditional
Hamiltonian-based picture does not allow one to grasp the difficulties
associated with the fact that currently available parametrizations of the
energy kernel at play in the method do not derive from a genuine
Hamilton operator, would the latter be effective. The method is formulated from
the outset through the most general multi-reference, i.e. beyond mean-field,
implementation such that the single-reference, i.e. "mean-field", derives as a
particular case. As such, a key point of the presentation provided here is to
demonstrate that the multi-reference EDF method can indeed be formulated in a
{\it mathematically} meaningful fashion even if does {\it not} derive
from a genuine Hamilton operator. In particular, the restoration of symmetries
can be entirely formulated without making {\it any} reference to a projected
state, i.e. within a genuine EDF framework. However, and as is illustrated in
the present document, a mathematically meaningful formulation does not
guarantee that the formalism is sound from a {\it physical} standpoint. The
price at which the latter can be enforced as well in the future is eventually
alluded to.Comment: 64 pages, 8 figures, submitted to Euroschool Lecture Notes in Physics
Vol.IV, Christoph Scheidenberger and Marek Pfutzner editor
Properties of odd nuclei and the impact of time-odd mean fields: A systematic Skyrme-Hartree-Fock analysis
We present a systematic analysis of the description of odd nuclei by the
Skyrme-Hartree-Fock approach augmented with pairing in BCS approximation and
blocking of the odd nucleon. Current and spin densities in the Skyrme
functional produce time-odd mean fields (TOMF) for odd nuclei. Their effect on
basic properties (binding energies, odd-even staggering, separation energies
and spectra) is investigated for the three Skyrme parameterizations SkI3, SLy6,
and SV-bas. About 1300 spherical and axially-deformed odd nuclei with 16 < Z <
92 are considered. The calculations demonstrate that the TOMF effect is
generally small, although not fully negligible. The influence of the Skyrme
parameterization and the consistency of the calculations are much more
important. With a proper choice of the parameterization, a good description of
binding energies and their differences is obtained, comparable to that for even
nuclei. The description of low-energy excitation spectra of odd nuclei is of
varying quality depending on the nucleus
Analysis technique for exceptional points in open quantum systems and QPT analogy for the appearance of irreversibility
We propose an analysis technique for the exceptional points (EPs) occurring
in the discrete spectrum of open quantum systems (OQS), using a semi-infinite
chain coupled to an endpoint impurity as a prototype. We outline our method to
locate the EPs in OQS, further obtaining an eigenvalue expansion in the
vicinity of the EPs that gives rise to characteristic exponents. We also report
the precise number of EPs occurring in an OQS with a continuum described by a
quadratic dispersion curve. In particular, the number of EPs occurring in a
bare discrete Hamiltonian of dimension is given by ; if this discrete Hamiltonian is then coupled to continuum
(or continua) to form an OQS, the interaction with the continuum generally
produces an enlarged discrete solution space that includes a greater number of
EPs, specifically , in which
is the number of (non-degenerate) continua to which the discrete sector is
attached. Finally, we offer a heuristic quantum phase transition analogy for
the emergence of the resonance (giving rise to irreversibility via exponential
decay) in which the decay width plays the role of the order parameter; the
associated critical exponent is then determined by the above eigenvalue
expansion.Comment: 16 pages, 7 figure
Subgraphs in random networks
Understanding the subgraph distribution in random networks is important for
modelling complex systems. In classic Erdos networks, which exhibit a
Poissonian degree distribution, the number of appearances of a subgraph G with
n nodes and g edges scales with network size as \mean{G} ~ N^{n-g}. However,
many natural networks have a non-Poissonian degree distribution. Here we
present approximate equations for the average number of subgraphs in an
ensemble of random sparse directed networks, characterized by an arbitrary
degree sequence. We find new scaling rules for the commonly occurring case of
directed scale-free networks, in which the outgoing degree distribution scales
as P(k) ~ k^{-\gamma}. Considering the power exponent of the degree
distribution, \gamma, as a control parameter, we show that random networks
exhibit transitions between three regimes. In each regime the subgraph number
of appearances follows a different scaling law, \mean{G} ~ N^{\alpha}, where
\alpha=n-g+s-1 for \gamma<2, \alpha=n-g+s+1-\gamma for 2<\gamma<\gamma_c, and
\alpha=n-g for \gamma>\gamma_c, s is the maximal outdegree in the subgraph, and
\gamma_c=s+1. We find that certain subgraphs appear much more frequently than
in Erdos networks. These results are in very good agreement with numerical
simulations. This has implications for detecting network motifs, subgraphs that
occur in natural networks significantly more than in their randomized
counterparts.Comment: 8 pages, 5 figure
Two-loop corrections to the fermionic decay rates of the Higgs boson
We calculate the dominant two-loop
electroweak corrections to the fermi\-onic decay widths of a heavy Higgs boson
in the Standard Model. Use of the Goldstone-boson equivalence theorem reduces
the problem to one involving only the physical Higgs boson and the
Goldstone bosons and of the unbroken theory. The two-loop
corrections are opposite in sign to the one-loop electroweak corrections,
exceed the one-loop corrections in magnitude for , and
increase in relative magnitude as for larger values of . We
conclude that the perturbation expansion in powers of breaks down
for . We discuss briefly the QCD and the complete
one-loop electroweak corrections to , and
comment on the validity of the equivalence theorem. Finally we note how a very
heavy Higgs boson could be described in a phenomenological manner.Comment: 24 pages, RevTeX file, 4 figures in a separate compressed uuencoded
Postscript file or available by mail on request. Fig. 1 not included see
Figs. 1, 2 in Phys. Rev. D 48, 1061 (1993
Colossal dielectric constants in transition-metal oxides
Many transition-metal oxides show very large ("colossal") magnitudes of the
dielectric constant and thus have immense potential for applications in modern
microelectronics and for the development of new capacitance-based
energy-storage devices. In the present work, we thoroughly discuss the
mechanisms that can lead to colossal values of the dielectric constant,
especially emphasising effects generated by external and internal interfaces,
including electronic phase separation. In addition, we provide a detailed
overview and discussion of the dielectric properties of CaCu3Ti4O12 and related
systems, which is today's most investigated material with colossal dielectric
constant. Also a variety of further transition-metal oxides with large
dielectric constants are treated in detail, among them the system La2-xSrxNiO4
where electronic phase separation may play a role in the generation of a
colossal dielectric constant.Comment: 31 pages, 18 figures, submitted to Eur. Phys. J. for publication in
the Special Topics volume "Cooperative Phenomena in Solids: Metal-Insulator
Transitions and Ordering of Microscopic Degrees of Freedom
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