Stochastic Vehicle Routing with Recourse

We study the classic Vehicle Routing Problem in the setting of stochastic optimization with recourse. StochVRP is a two-stage optimization problem, where demand is satisfied using two routes: fixed and recourse. The fixed route is computed using only a demand distribution. Then after observing the demand instantiations, a recourse route is computed -- but costs here become more expensive by a factor lambda. We present an O(log^2 n log(n lambda))-approximation algorithm for this stochastic routing problem, under arbitrary distributions. The main idea in this result is relating StochVRP to a special case of submodular orienteering, called knapsack rank-function orienteering. We also give a better approximation ratio for knapsack rank-function orienteering than what follows from prior work. Finally, we provide a Unique Games Conjecture based omega(1) hardness of approximation for StochVRP, even on star-like metrics on which our algorithm achieves a logarithmic approximation.Comment: 20 Pages, 1 figure Revision corrects the statement and proof of Theorem 1.

Oxygen impurities in NiAl: Relaxation effects

We have used a full-potential linear muffin-tin orbital method to calculate the effects of oxygen impurities on the electronic structure of NiAl. Using the supercell method with a 16-atom supercell we have investigated the cases where an oxygen atom is substitutionally placed at either a nickel or an aluminum site. Full relaxation of the atoms within the supercell was allowed. We found that oxygen prefers to occupy a nickel site over an aluminum site with a site selection energy of 138 mRy (21,370 K). An oxygen atom placed at an aluminum site is found to cause a substantial relaxation of its nickel neighbors away from it. In contrast, this steric repulsion is hardly present when the oxygen atom occupies the nickel site and is surrounded by aluminum neighbors. We comment on the possible relation of this effect to the pesting degradation phenomenon (essentially spontaneous disintegration in air) in nickel aluminides.Comment: To appear in Phys. Rev. B (Aug. 15, 2001

Two-soliton collisions in a near-integrable lattice system

We examine collisions between identical solitons in a weakly perturbed Ablowitz-Ladik (AL) model, augmented by either onsite cubic nonlinearity (which corresponds to the Salerno model, and may be realized as an array of strongly overlapping nonlinear optical waveguides), or a quintic perturbation, or both. Complex dependences of the outcomes of the collisions on the initial phase difference between the solitons and location of the collision point are observed. Large changes of amplitudes and velocities of the colliding solitons are generated by weak perturbations, showing that the elasticity of soliton collisions in the AL model is fragile (for instance, the Salerno's perturbation with the relative strength of 0.08 can give rise to a change of the solitons' amplitudes by a factor exceeding 2). Exact and approximate conservation laws in the perturbed system are examined, with a conclusion that the small perturbations very weakly affect the norm and energy conservation, but completely destroy the conservation of the lattice momentum, which is explained by the absence of the translational symmetry in generic nonintegrable lattice models. Data collected for a very large number of collisions correlate with this conclusion. Asymmetry of the collisions (which is explained by the dependence on the location of the central point of the collision relative to the lattice, and on the phase difference between the solitons) is investigated too, showing that the nonintegrability-induced effects grow almost linearly with the perturbation strength. Different perturbations (cubic and quintic ones) produce virtually identical collision-induced effects, which makes it possible to compensate them, thus finding a special perturbed system with almost elastic soliton collisions.Comment: Phys. Rev. E, in pres

Family Symmetries and Proton Decay

The proton decay modes $p\to K^0 e^+$ and $p\to K^0 \mu^+$ may be visible in certain supersymmetric theories, and if seen would provide evidence for new flavor physics at extremely short distances. These decay modes can arise from the dimension five operator $(Q_1Q_1Q_2L_{1,2})$, where $Q_i$ and $L_i$ are ${i^{th}}$ generation quark and lepton superfields respectively. Such an operator is not generated at observable levels due to gauge or Higgs boson exchange in a minimal GUT. However in theories that explain the fermion mass hierarchy, it may be generated at the Planck scale with a strength such that the decays $p\to K^0 \ell^+$ are both compatible with the proton lifetime and visible at Super-Kamiokande. Observable proton decay can even occur in theories without unification.Comment: NSF-ITP-94-69, LBL-35807, DOE/ER/40561-148-INT94-00-61, 13 pages, written with harvma

Laser ablation loading of a radiofrequency ion trap

The production of ions via laser ablation for the loading of radiofrequency (RF) ion traps is investigated using a nitrogen laser with a maximum pulse energy of 0.17 mJ and a peak intensity of about 250 MW/cm^2. A time-of-flight mass spectrometer is used to measure the ion yield and the distribution of the charge states. Singly charged ions of elements that are presently considered for the use in optical clocks or quantum logic applications could be produced from metallic samples at a rate of the order of magnitude 10^5 ions per pulse. A linear Paul trap was loaded with Th+ ions produced by laser ablation. An overall ion production and trapping efficiency of 10^-7 to 10^-6 was attained. For ions injected individually, a dependence of the capture probability on the phase of the RF field has been predicted. In the experiment this was not observed, presumably because of collective effects within the ablation plume.Comment: submitted to Appl. Phys. B., special issue on ion trappin

Towards a New Standard Model for Black Hole Accretion

We briefly review recent developments in black hole accretion disk theory, emphasizing the vital role played by magnetohydrodynamic (MHD) stresses in transporting angular momentum. The apparent universality of accretion-related outflow phenomena is a strong indicator that large-scale MHD torques facilitate vertical transport of angular momentum. This leads to an enhanced overall rate of angular momentum transport and allows accretion of matter to proceed at an interesting rate. Furthermore, we argue that when vertical transport is important, the radial structure of the accretion disk is modified at small radii and this affects the disk emission spectrum. We present a simple model demonstrating how energetic, magnetically-driven outflows modify the emergent disk emission spectrum with respect to that predicted by standard accretion disk theory. A comparison of the predicted spectra against observations of quasar spectral energy distributions suggests that mass accretion rates inferred using the standard disk model may severely underestimate their true values.Comment: To appear in the Fifth Stromlo Symposium Proceedings special issue of ApS

Understanding constraint expressions in large conceptual schemas by automatic filtering

Human understanding of constraint expressions (also called schema rules) in large conceptual schemas is very di cult. This is due to the fact that the elements (entity types, attributes, relationship types) involved in an expression are de ned in di fferent places in the schema, which may be very distant from each other and embedded in an intricate web of irrelevant elements. The problem is insignifi cant when the conceptual schema is small, but very signi cant when it is large. In this paper we describe a novel method that, given a set of constraint expressions and a large conceptual schema, automatically filters the conceptual schema, obtaining a smaller one that contains the elements of interest for the understanding of the expressions. We also show the application of the method to the important case of understanding the specication of event types, whose constraint expressions consists of a set of pre and postconditions. We have evaluated the method by means of its application to a set of large conceptual schemas. The results show that the method is eff ective and e cient. We deal with conceptual schemas in UML/OCL, but the method can be adapted to other languages.Peer ReviewedPreprin

Examining the Higgs boson potential at lepton and hadron colliders: a comparative analysis

We investigate inclusive Standard Model Higgs boson pair production at lepton and hadron colliders for Higgs boson masses in the range 120 GeV < m_H < 200 GeV. For m_H < 140 GeV we find that hadron colliders have a very limited capability to determine the Higgs boson self-coupling, \lambda, due to an overwhelming background. We also find that, in this mass range, supersymmetric Higgs boson pairs may be observable at the LHC, but a measurement of the self coupling will not be possible. For m_H > 140 GeV we examine ZHH and HH nu bar-nu production at a future e+e- linear collider with center of mass energy in the range of sqrt{s}=0.5 - 1 TeV, and find that this is likely to be equally difficult. Combining our results with those of previous literature, which has demonstrated the capability of hadron and lepton machines to determine \lambda in either the high or the low mass regions, we establish a very strong complementarity of these machines.Comment: Revtex, 25 pages, 2 tables, 10 figure

DKIST unveils the serpentine topology of quiet Sun magnetism in the photosphere

We present the first quiet Sun spectropolarimetric observations obtained with the Visible SpectroPolarimeter at the 4 m Daniel K. Inouye Solar Telescope. We recorded observations in a wavelength range that includes the magnetically sensitive Fe i 6301.5/6302.5 Å doublet. With an estimated spatial resolution of 0farcs08, this represents the highest spatial resolution full-vector spectropolarimetric observations ever obtained of the quiet Sun. We identified 53 small-scale magnetic elements, including 47 magnetic loops and four unipolar magnetic patches, with linear and circular polarization detected in all of them. Of particular interest is a magnetic element in which the polarity of the magnetic vector appears to change three times in only 400 km and which has linear polarization signals throughout. We find complex Stokes V profiles at the polarity inversion lines of magnetic loops and discover degenerate solutions, as we are unable to conclusively determine whether these arise due to gradients in the atmospheric parameters or smearing of opposite-polarity signals. We analyze a granule that notably has linear and circular polarization signals throughout, providing an opportunity to explore its magnetic properties. On this small scale, we see the magnetic field strength range from 25 G at the granular boundary to 2 kG in the intergranular lane (IGL) and sanity-check the values with the weak and strong field approximations. A value of 2 kG in the IGL is among the highest measurements ever recorded for the internetwork