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 $S:=\{x : \pi_0 \leq \pi^T x \leq \pi_0+1 \}$ 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 $S$ has max-facet-width equal to one in the sense that $\max\{\pi^T x : x \in S \}-\min\{\pi^T x : x \in S \} \leq 1$. 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 $w$ have width size $w$. A split cut of width size $w$ is then a valid inequality whose validity follows from a lattice point free rational polyhedron of width size $w$. The $w$-th split closure is the set obtained by adding all valid inequalities of width size at most $w$. 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 $w$-th split closure is a polyhedron. Given this result, a natural question is which width size $w^*$ is required to design a finite cutting plane proof for the validity of an inequality. Specifically, for this value $w^*$, a finite cutting plane proof exists that uses lattice point free rational polyhedra of width size at most $w^*$, but no finite cutting plane proof that only uses lattice point free rational polyhedra of width size smaller than $w^*$. We characterize $w^*$ 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$_3$, YTiO$_3$, V$_2$O$_3$, and Y$_2$Mo$_2$O$_7$. 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 $d$ 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 $t_{2g}$ 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