24,536 research outputs found
An analysis of mixed integer linear sets based on lattice point free convex sets
Split cuts are cutting planes for mixed integer programs whose validity is
derived from maximal lattice point free polyhedra of the form called split sets. The set obtained by adding all
split cuts is called the split closure, and the split closure is known to be a
polyhedron. A split set has max-facet-width equal to one in the sense that
. In this paper
we consider using general lattice point free rational polyhedra to derive valid
cuts for mixed integer linear sets. We say that lattice point free polyhedra
with max-facet-width equal to have width size . A split cut of width
size is then a valid inequality whose validity follows from a lattice point
free rational polyhedron of width size . The -th split closure is the set
obtained by adding all valid inequalities of width size at most . Our main
result is a sufficient condition for the addition of a family of rational
inequalities to result in a polyhedral relaxation. We then show that a
corollary is that the -th split closure is a polyhedron. Given this result,
a natural question is which width size is required to design a finite
cutting plane proof for the validity of an inequality. Specifically, for this
value , a finite cutting plane proof exists that uses lattice point free
rational polyhedra of width size at most , but no finite cutting plane
proof that only uses lattice point free rational polyhedra of width size
smaller than . We characterize based on the faces of the linear
relaxation
Linear response separation of a solid into atomic constituents: Li, Al, and their evolution under pressure
We present the first realization of the generalized pseudoatom concept
introduced by Ball, and adopt the name enatom to minimize confusion. This
enatom, which consists of a unique decomposition of the total charge density
(or potential) of any solid into a sum of overlapping atomiclike contributions
that move rigidly with the nuclei to first order, is calculated using
(numerical) linear response methods, and is analyzed for both fcc Li and Al at
pressures of 0, 35, and 50 GPa. These two simple fcc metals (Li is fcc and a
good superconductor in the 20-40 GPa range) show different physical behaviors
under pressure, which reflects the increasing covalency in Li and the lack of
it in Al. The nonrigid (deformation) parts of the enatom charge and potential
have opposite signs in Li and Al; they become larger under pressure only in Li.
These results establish a method of construction of the enatom, whose potential
can be used to obtain a real-space understanding of the vibrational properties
and electron-phonon interaction in solids.Comment: 13 pages, 9 figures, 1 table, V2: fixed problem with Fig. 7, V3:
minor correction
Experimental investigation of the Landau-Pomeranchuk-Migdal effect in low-Z targets
In the CERN NA63 collaboration we have addressed the question of the
potential inadequacy of the commonly used Migdal formulation of the
Landau-Pomeranchuk-Migdal (LPM) effect by measuring the photon emission by 20
and 178 GeV electrons in the range 100 MeV - 4 GeV, in targets of
LowDensityPolyEthylene (LDPE), C, Al, Ti, Fe, Cu, Mo and, as a reference
target, Ta. For each target and energy, a comparison between simulated values
based on the LPM suppression of incoherent bremsstrahlung is shown, taking
multi-photon effects into account. For these targets and energies, we find that
Migdal's theoretical formulation is adequate to a precision of better than
about 5%, irrespective of the target substance.Comment: 8 pages, 13 figure
The Stability Balloon for Two-dimensional Vortex Ripple Patterns
Patterns of vortex ripples form when a sand bed is subjected to an
oscillatory fluid flow. Here we describe experiments on the response of regular
vortex ripple patterns to sudden changes of the driving amplitude a or
frequency f. A sufficient decrease of f leads to a "freezing" of the pattern,
while a sufficient increase of f leads to a supercritical secondary "pearling"
instability. Sufficient changes in the amplitude a lead to subcritical
secondary "doubling" and "bulging" instabilities. Our findings are summarized
in a "stability balloon" for vortex ripple pattern formation.Comment: 4 pages, 5 figure
Construction of transferable spherically-averaged electron potentials
A new scheme for constructing approximate effective electron potentials
within density-functional theory is proposed. The scheme consists of
calculating the effective potential for a series of reference systems, and then
using these potentials to construct the potential of a general system. To make
contact to the reference system the neutral-sphere radius of each atom is used.
The scheme can simplify calculations with partial wave methods in the
atomic-sphere or muffin-tin approximation, since potential parameters can be
precalculated and then for a general system obtained through simple
interpolation formulas. We have applied the scheme to construct electron
potentials of phonons, surfaces, and different crystal structures of silicon
and aluminum atoms, and found excellent agreement with the self-consistent
effective potential. By using an approximate total electron density obtained
from a superposition of atom-based densities, the energy zero of the
corresponding effective potential can be found and the energy shifts in the
mean potential between inequivalent atoms can therefore be directly estimated.
This approach is shown to work well for surfaces and phonons of silicon.Comment: 8 pages (3 uuencoded Postscript figures appended), LaTeX,
CAMP-090594-
First-principle Wannier functions and effective lattice fermion models for narrow-band compounds
We propose a systematic procedure for constructing effective lattice fermion
models for narrow-band compounds on the basis of first-principles electronic
structure calculations. The method is illustrated for the series of
transition-metal (TM) oxides: SrVO, YTiO, VO, and
YMoO. It consists of three parts, starting from LDA. (i)
construction of the kinetic energy Hamiltonian using downfolding method. (ii)
solution of an inverse problem and construction of the Wannier functions (WFs)
for the given kinetic energy Hamiltonian. (iii) calculation of screened Coulomb
interactions in the basis of \textit{auxiliary} WFs, for which the
kinetic-energy term is set to be zero. The last step is necessary in order to
avoid the double counting of the kinetic-energy term, which is included
explicitly into the model. The screened Coulomb interactions are calculated in
a hybrid scheme. First, we evaluate the screening caused by the change of
occupation numbers and the relaxation of the LMTO basis functions, using the
conventional constraint-LDA approach, where all matrix elements of
hybridization involving the TM orbitals are set to be zero. Then, we switch
on the hybridization and evaluate the screening associated with the change of
this hybridization in RPA. The second channel of screening is very important,
and results in a relatively small value of the effective Coulomb interaction
for isolated bands. We discuss details of this screening and consider
its band-filling dependence, frequency dependence, influence of the lattice
distortion, proximity of other bands, and the dimensionality of the model
Hamiltonian.Comment: 35 pages, 25 figure
Pattern Dynamics of Vortex Ripples in Sand: Nonlinear Modeling and Experimental Validation
Vortex ripples in sand are studied experimentally in a one-dimensional setup
with periodic boundary conditions. The nonlinear evolution, far from the onset
of instability, is analyzed in the framework of a simple model developed for
homogeneous patterns. The interaction function describing the mass transport
between neighboring ripples is extracted from experimental runs using a
recently proposed method for data analysis, and the predictions of the model
are compared to the experiment. An analytic explanation of the wavelength
selection mechanism in the model is provided, and the width of the stable band
of ripples is measured.Comment: 4 page
Long-term high fat feeding of rats results in increased numbers of circulating microvesicles with pro-inflammatory effects on endothelial cells
Obesity and type 2 diabetes lead to dramatically increased risks of atherosclerosis and CHD. Multiple mechanisms converge to promote atherosclerosis by increasing endothelial oxidative stress and up-regulating expression of pro-inflammatory molecules. Microvesicles (MV) are small ( < 1 μm) circulating particles that transport proteins and genetic material, through which they are able to mediate cell–cell communication and influence gene expression. Since MV are increased in plasma of obese, insulin-resistant and diabetic individuals, who often exhibit chronic vascular inflammation, and long-term feeding of a high-fat diet (HFD) to rats is a well-described model of obesity and insulin resistance, we hypothesised that this may be a useful model to study the impact of MV on endothelial inflammation. The number and cellular origin of MV from HFD-fed obese rats were characterised by flow cytometry. Total MV were significantly increased after feeding HFD compared to feeding chow (P< 0·001), with significantly elevated numbers of MV derived from leucocyte, endothelial and platelet compartments (P< 0·01 for each cell type). MV were isolated from plasma and their ability to induce reactive oxygen species (ROS) formation and vascular cell adhesion molecule (VCAM)-1 expression was measured in primary rat cardiac endothelial cells in vitro. MV from HFD-fed rats induced significant ROS (P< 0·001) and VCAM-1 expression (P= 0·0275), indicative of a pro-inflammatory MV phenotype in this model of obesity. These findings confirm that this is a useful model to further study the mechanisms by which diet can influence MV release and subsequent effects on cardio-metabolic health
Electron-phonon interaction in the t-J model
We derive a t-J model with electron-phonon coupling from the three-band
model, considering modulation of both hopping and Coulomb integrals by phonons.
While the modulation of the hopping integrals dominates, the modulation of the
Coulomb integrals cannot be neglected. The model explains the experimentally
observed anomalous softening of the half-breathing mode upon doping and a
weaker softening of the breathing mode. It is shown that other phonons are not
strongly influenced, and, in particular, the coupling to a buckling mode is not
strong in this model.Comment: 4 pages, RevTeX, 3 eps figures; final version with minor correction
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