Particle-wave duality: a dichotomy between symmetry and asymmetry

Symmetry plays a central role in many areas of modern physics. Here we show that it also underpins the dual particle and wave nature of quantum systems. We begin by noting that a classical point particle breaks translational symmetry whereas a wave with uniform amplitude does not. This provides a basis for associating particle nature with asymmetry and wave nature with symmetry. We derive expressions for the maximum amount of classical information we can have about the symmetry and asymmetry of a quantum system with respect to an arbitrary group. We find that the sum of the information about the symmetry (wave nature) and the asymmetry (particle nature) is bounded by log(D) where D is the dimension of the Hilbert space. The combination of multiple systems is shown to exhibit greater symmetry and thus more wavelike character. In particular, a class of entangled systems is shown to be capable of exhibiting wave-like symmetry as a whole while exhibiting particle-like asymmetry internally. We also show that superdense coding can be viewed as being essentially an interference phenomenon involving wave-like symmetry with respect to the group of Pauli operators.Comment: 20 pages, 3 figure

Schur Q-functions and degeneracy locus formulas for morphisms with symmetries

We give closed-form formulas for the fundamental classes of degeneracy loci associated with vector bundle maps given locally by (not necessary square) matrices which are symmetric (resp. skew-symmetric) w.r.t. the main diagonal. Our description uses essentially Schur Q-polynomials of a bundle, and is based on a certain push-forward formula for these polynomials in a Grassmann bundle.Comment: 22 pages, AMSTEX, misprints corrected, exposition improved. to appear in the Proceedings of Intersection Theory Conference in Bologna, "Progress in Mathematics", Birkhause

Inclusion-exclusion and Segre classes

We propose a variation of the notion of Segre class, by forcing a naive `inclusion-exclusion' principle to hold. The resulting class is computationally tractable, and is closely related to Chern-Schwartz-MacPherson classes. We deduce several general properties of the new class from this relation, and obtain an expression for the Milnor class of a scheme in terms of this class.Comment: 8 page

Stringy K-theory and the Chern character

For a finite group G acting on a smooth projective variety X, we construct two new G-equivariant rings: first the stringy K-theory of X, and second the stringy cohomology of X. For a smooth Deligne-Mumford stack Y we also construct a new ring called the full orbifold K-theory of Y. For a global quotient Y=[X/G], the ring of G-invariants of the stringy K-theory of X is a subalgebra of the full orbifold K-theory of the the stack Y and is linearly isomorphic to the ``orbifold K-theory'' of Adem-Ruan (and hence Atiyah-Segal), but carries a different, ``quantum,'' product, which respects the natural group grading. We prove there is a ring isomorphism, the stringy Chern character, from stringy K-theory to stringy cohomology, and a ring homomorphism from full orbifold K-theory to Chen-Ruan orbifold cohomology. These Chern characters satisfy Grothendieck-Riemann-Roch for etale maps. We prove that stringy cohomology is isomorphic to Fantechi and Goettsche's construction. Since our constructions do not use complex curves, stable maps, admissible covers, or moduli spaces, our results simplify the definitions of Fantechi-Goettsche's ring, of Chen-Ruan's orbifold cohomology, and of Abramovich-Graber-Vistoli's orbifold Chow. We conclude by showing that a K-theoretic version of Ruan's Hyper-Kaehler Resolution Conjecture holds for symmetric products. Our results hold both in the algebro-geometric category and in the topological category for equivariant almost complex manifolds.Comment: Exposition improved and additional details provided. To appear in Inventiones Mathematica

Calibration of <i>Herschel</i> SPIRE FTS observations at different spectral resolutions

The SPIRE Fourier Transform Spectrometer on-board the Herschel Space Observatory had two standard spectral resolution modes for science observations: high resolution (HR) and low resolution (LR), which could also be performed in sequence (H+LR). A comparison of the HR and LR resolution spectra taken in this sequential mode revealed a systematic discrepancy in the continuum level. Analysing the data at different stages during standard pipeline processing demonstrates that the telescope and instrument emission affect HR and H+LR observations in a systematically different way. The origin of this difference is found to lie in the variation of both the telescope and instrument response functions, while it is triggered by fast variation of the instrument temperatures. As it is not possible to trace the evolution of the response functions using housekeeping data from the instrument subsystems, the calibration cannot be corrected analytically. Therefore, an empirical correction for LR spectra has been developed, which removes the systematic noise introduced by the variation of the response functions

Performance of variable-orifice nozzles for liquid fertilizer applications

Citation: Sharda, A., Fulton, J. P., & Taylor, R. K. (2016). Performance of variable-orifice nozzles for liquid fertilizer applications. Applied Engineering in Agriculture, 32(3), 347-352. doi:10.13031/aea.32.11428Variable-rate application continues to gain interest among precision agriculture practitioners including the use of crop sensor technology for application of nitrogen in grain crops. For liquid fertilizers, variable-orifice nozzles are being implemented since they provide a much larger nozzle flow range compared to traditional fixed orifice nozzles. However, understanding the performance of variable-orifice nozzles under different field operating conditions has been limited. Therefore, the objective of this study was to evaluate the performance of variable orifice nozzles in support of variable-rate application. Two common variable-orifice nozzles offered by different companies were selected for this study. They were tested over three flow ranges (0.76 to 1.89 L/min) with all tests replicated three times. A commercially available 18.6-m, wet boom sprayer equipped with 37 nozzle bodies was used. Nozzles were numbered but then randomly assigned a position along the boom. To evaluate the performance of an individual nozzle, three random nozzle locations along the spray boom were established for both sets of nozzles. Therefore, 18 tests per replication were required to include the 3 flow rates, 3 different locations, and 2 nozzle types. Once the desired flow rate test was established, tip flow was measured using SpotOn Sprayer Calibrator technology. Tip flows were recorded and statistical analyses performed to evaluate flow uniformity (CV) across the boom but also detect off-rate errors by individual nozzles and locations across the boom. With the exception of a few nozzles, the uniformity across the spray boom, as defined by the CV, was acceptable for both nozzle types over approximately a 2:1 flow range. Both nozzle types were less uniform at the low flow rate. There were three nozzles of each type that resulted in unacceptable flow errors in multiple tests. © 2016 American Society of Agricultural and Biological Engineers

Ergodic directions for billiards in a strip with periodically located obstacles

We study the size of the set of ergodic directions for the directional billiard flows on the infinite band $\R\times [0,h]$ with periodically placed linear barriers of length $0<\lambda<h$. We prove that the set of ergodic directions is always uncountable. Moreover, if $\lambda/h\in(0,1)$ is rational the Hausdorff dimension of the set of ergodic directions is greater than 1/2. In both cases (rational and irrational) we construct explicitly some sets of ergodic directions.Comment: The article is complementary to arXiv:1109.458

Random walks and random fixed-point free involutions

A bijection is given between fixed point free involutions of $\{1,2,...,2N\}$ with maximum decreasing subsequence size $2p$ and two classes of vicious (non-intersecting) random walker configurations confined to the half line lattice points $l \ge 1$. In one class of walker configurations the maximum displacement of the right most walker is $p$. Because the scaled distribution of the maximum decreasing subsequence size is known to be in the soft edge GOE (random real symmetric matrices) universality class, the same holds true for the scaled distribution of the maximum displacement of the right most walker.Comment: 10 page

995-22 The Effect of Perioperative Storage Solutions on the Long Term Vein Graft Function and Morphology

It has been shown that suboptimal preparation of a vein graft prior to its insertion results in immediate morphological and functional damage to the endothelial cells but not to the underlying smooth muscle cells. However. little is known if such perioperative injury to the vein grafts may influence the subsequent development of intimal hyperplasia and smooth muscle cell contractility. This study examines the influence of storage in saline or Ringer's lactate on the development of intimal hyperplasia and vasomotor function in experimental vein grafts. Twenty-six NM rabbits had a carotid vein bypass graft performed after the veins had been immersed (15 minutes) in either heparinized saline (Sal; n=13) or Ringer's lactate (RL; n=13) and each group was harvested after 28 days for either histology (n=8) or functional studies (n=5; four 5 mm rings/graft). Saline storage of the vein graft resulted in a 38% increase in the thickness of the intimal hyperplasia (113±2 vs. 83±μm, Sal vs. RL; mean±SEM, p&lt;0.05) without a change in medial thickness (87±5 vs. 86±8μm, Sal vs. RL; p&gt;0.05). There was no difference in the sensitivity to norepinephrine, serotonin and bradykinin between the two sets of vein grafts. The maximal contractile forces to serotonin and bradykinin were increased in the saline compared to Ringer's lactate stored vein grafts.SalineRinger'sp-valueNorepinephrine0.88±0.121.57±020&lt;0.05Serotonin1.23±0.150.37±013&lt;0.01Bradykinin2.08±0.110.52±007&lt;0.01Values are the standardized maximal contractile force (maximal contraction/contraction to 60 mM KCI) expressed as mean±SEM.Saline storage of the vein graft results in the increased development of intimal hyperplasia with an overall enhanced contractility but without changes in agonist sensitivity. This study places further emphasis on the need for good perioperative care of the vein bypass graft because it results not only in the previously documented short term problems but also in long term structural and contractile changes which may contribute to decreased graft patency

Finite Element Modeling of the Bulk Magnetization of Railroad Wheels to Improve Test Conditions for Magnetoacoustic Residual Stress Measurements

The magnetoacoustic measurement technique has been used successfully for residual stress measurements in laboratory samples[l-4]. However, when used to field test samples with complex geometries, such as railroad wheels, the sensitivity of the method declines dramatically[5,6]. It has been suggested that the decrease in performance may be due, in part, to an insufficient or nonuniform magnetic induction in the test sample[6]. The purpose of this paper is to optimize the test conditions by using finite element modeling to predict the distribution of the induced bulk magnetization of railroad wheels. The results suggest that it is possible to obtain a sufficiently large and uniform bulk magnetization by altering the shape of the electromagnet used in the tests. Consequently, problems associated with bulk magnetization can be overcome, and should not prohibit the magnetoacoustic technique from being used to make residual stress measurements in railroad wheels