6,449 research outputs found
BGG resolutions via configuration spaces
We study the blow-ups of configuration spaces. These spaces have a structure
of what we call an Orlik-Solomon manifold; it allows us to compute the
intersection cohomology of certain flat connections with logarithmic
singularities using some Aomoto type complexes of logarithmic forms. Using this
construction we realize geometrically the sl_2 Bernstein - Gelfand - Gelfand
resolution as an Aomoto complex.Comment: Latex, 19 page
Strain localization in a shear transformation zone model for amorphous solids
We model a sheared disordered solid using the theory of Shear Transformation
Zones (STZs). In this mean-field continuum model the density of zones is
governed by an effective temperature that approaches a steady state value as
energy is dissipated. We compare the STZ model to simulations by Shi, et
al.(Phys. Rev. Lett. 98 185505 2007), finding that the model generates
solutions that fit the data,exhibit strain localization, and capture important
features of the localization process. We show that perturbations to the
effective temperature grow due to an instability in the transient dynamics, but
unstable systems do not always develop shear bands. Nonlinear energy
dissipation processes interact with perturbation growth to determine whether a
material exhibits strain localization. By estimating the effects of these
interactions, we derive a criterion that determines which materials exhibit
shear bands based on the initial conditions alone. We also show that the shear
band width is not set by an inherent diffusion length scale but instead by a
dynamical scale that depends on the imposed strain rate.Comment: 8 figures, references added, typos correcte
Canister closing device Patent
Design and characteristics of device for closing canisters under high vacuum condition
UV Completions for Non-Critical Strings
Compactifications of the physical superstring to two dimensions provide a
general template for realizing 2D conformal field theories coupled to
worldsheet gravity, i.e. non-critical string theories. Motivated by this
observation, in this paper we determine the quasi-topological 8D theory which
governs the vacua of 2D N = (0,2) gauged linear sigma models (GLSMs) obtained
from compactifications of type I and heterotic strings on a Calabi-Yau
fourfold. We also determine the quasi-topological 6D theory governing the 2D
vacua of intersecting 7-branes in compactifications of F-theory on an
elliptically fibered Calabi-Yau fivefold, where matter fields and interaction
terms localize on lower-dimensional subspaces, i.e. defect operators. To cancel
anomalies / cancel tadpoles, these GLSMs must couple to additional chiral
sectors, which in some cases do not admit a known description in terms of a UV
GLSM. Additionally, we find that constructing an anomaly free spectrum can
sometimes break supersymmetry due to spacetime filling anti-branes. We also
study various canonical examples such as the standard embedding of heterotic
strings on a Calabi-Yau fourfold and F-theoretic "rigid clusters" with no local
deformation moduli of the elliptic fibration.Comment: v4: 102 pages, 2 figures, clarifications adde
Calculations of the thermodynamic and kinetic properties of LiV3O8
The phase behavior and kinetic pathways of Li1+xV3O8 are investigated by
means of density functional theory (DFT) and a cluster expansion (CE)
methodology that approximates the system Hamiltonian in order to identify the
lowest energy configurations. Although DFT calculations predict the correct
ground state for a given composition, both GGA and LDA fail to obtain phase
stability consistent with experiment due to strongly localized vanadium 3d
electrons. A DFT+U methodology recovers the correct phase stability for an
optimized U value of 3.0eV. GGA+U calculations with this value of U predict
electronic structures that qualitatively agree with experiment. The resulting
calculations indicate solid solution behavior from LiV3O8 to Li2.5V3O8 and
two-phase coexistence between Li2.5V3O8 and Li4V3O8. Analysis of the lithiation
sequence from LiV3O8 to Li2.5V3O8 reveals the mechanism by which lithium
intercalation proceeds in this material. Calculations of lithium migration
energies for different lithium concentrations and configurations provides
insight into the relevant diffusion pathways and their relationship to
structural properties
Reparameterisation Invariance Constraints on Heavy Particle Effective Field Theories
Since fields in the heavy quark effective theory are described by both a
velocity and a residual momentum, there is redundancy in the theory: small
shifts in velocity may be absorbed into a redefinition of the residual
momentum. We demonstrate that this trivial reparameterisation invariance has
non-trivial consequences: it relates coefficients of terms of different orders
in the expansion and requires linear combinations of these operators to
be multiplicatively renormalised. For example, the operator in the
effective lagrangian has zero anomalous dimension, coefficient one, and does
not receive any non-perturbative contributions from matching conditions. We
also demonstrate that this invariance severely restricts the forms of operators
which may appear in chiral lagrangians for heavy particles.Comment: (14 pages, 0 figures), UCSD/PTH 92-1
Spin Coherence During Optical Excitation of a Single NV Center in Diamond
We examine the quantum spin state of a single nitrogen-vacancy (NV) center in
diamond at room temperature as it makes a transition from the orbital
ground-state (GS) to the orbital excited-state (ES) during non-resonant optical
excitation. While the fluorescence read-out of NV-center spins relies on
conservation of the longitudinal spin projection during optical excitation, the
question of quantum phase preservation has not been examined. Using Ramsey
measurements and quantum process tomography, we establish limits on NV center
spin decoherence induced during optical excitation. Treating the optical
excitation and ES spin precession as a quantum process, we measure a process
fidelity of F=0.87\pm0.03, which includes ES spin dephasing during measurement.
Extrapolation to the moment of optical excitation yields F\approx0.95. This
result demonstrates that ES spin interactions may be used as a resource for
quantum control because the quantum spin state can survive incoherent orbital
transitions.Comment: 12 pages, 3 figure
Three-Dimensional Light Bullets in Arrays of Waveguides
We report the first experimental observation of 3D-LBs, excited by
femtosecond pulses in a system featuring quasi-instantaneous cubic nonlinearity
and a periodic, transversally-modulated refractive index. Stringent evidence of
the excitation of LBs is based on time-gated images and spectra which perfectly
match our numerical simulations. Furthermore, we reveal a novel evolution
mechanism forcing the LBs to follow varying dispersion/diffraction conditions,
until they leave their existence range and decay.Comment: 4 pages, 5 figures - Published by the American Physical Societ
Laplacian modes probing gauge fields
We show that low-lying eigenmodes of the Laplace operator are suitable to
represent properties of the underlying SU(2) lattice configurations. We study
this for the case of finite temperature background fields, yet in the
confinement phase. For calorons as classical solutions put on the lattice, the
lowest mode localizes one of the constituent monopoles by a maximum and the
other one by a minimum, respectively. We introduce adjustable phase boundary
conditions in the time direction, under which the role of the monopoles in the
mode localization is interchanged. Similar hopping phenomena are observed for
thermalized configurations. We also investigate periodic and antiperiodic modes
of the adjoint Laplacian for comparison.
In the second part we introduce a new Fourier-like low-pass filter method. It
provides link variables by truncating a sum involving the Laplacian eigenmodes.
The filter not only reproduces classical structures, but also preserves the
confining potential for thermalized ensembles. We give a first characterization
of the structures emerging from this procedure.Comment: 43 pages, 26 figure
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