Orthogonality relations for triple modes at dielectric boundary surfaces

We work out the orthogonality relations for the set of Carniglia-Mandel triple modes which provide a set of normal modes for the source-free electromagnetic field in a background consisting of a passive dielectric half-space and the vacuum, respectively. Due to the inherent computational complexity of the problem, an efficient strategy to accomplish this task is desirable, which is presented in the paper. Furthermore, we provide all main steps for the various proofs pertaining to different combinations of triple modes in the orthogonality integral.Comment: 15 page

Signatures of few-body resonances in finite volume

We study systems of bosons and fermions in finite periodic boxes and show how the existence and properties of few-body resonances can be extracted from studying the volume dependence of the calculated energy spectra. Using a plane-wave-based discrete variable representation to conveniently implement periodic boundary conditions, we establish that avoided level crossings occur in the spectra of up to four particles and can be linked to the existence of multi-body resonances. To benchmark our method we use two-body calculations, where resonance properties can be determined with other methods, as well as a three-boson model interaction known to generate a three-boson resonance state. Finding good agreement for these cases, we then predict three-body and four-body resonances for models using a shifted Gaussian potential. Our results establish few-body finite-volume calculations as a new tool to study few-body resonances. In particular, the approach can be used to study few-neutron systems, where such states have been conjectured to exist.Comment: 13 pages, 10 figures, 2 tables, published versio

Is a Trineutron Resonance Lower in Energy than a Tetraneutron Resonance?

We present quantum Monte Carlo calculations of few-neutron systems confined in external potentials based on local chiral interactions at next-to-next-to-leading order in chiral effective field theory. The energy and radial densities for these systems are calculated in different external Woods-Saxon potentials. We assume that their extrapolation to zero external-potential depth provides a quantitative estimate of three- and four-neutron resonances. The validity of this assumption is demonstrated by benchmarking with an exact diagonalization in the two-body case. We find that the extrapolated trineutron resonance, as well as the energy for shallow well depths, is lower than the tetraneutron resonance energy. This suggests that a three-neutron resonance exists below a four-neutron resonance in nature and is potentially measurable. To confirm that the relative ordering of three- and four-neutron resonances is not an artifact of the external confinement, we test that the odd-even staggering in the helium isotopic chain is reproduced within this approach. Finally, we discuss similarities between our results and ultracold Fermi gases.Comment: 6 pages, 5 figures, version compatible with published lette

Few-body physics in effective field theory

Effective Field Theory (EFT) provides a powerful framework that exploits a separation of scales in physical systems to perform systematically improvable, model-independent calculations. Particularly interesting are few-body systems with short-range interactions and large two-body scattering length. Such systems display remarkable universal features. In systems with more than two particles, a three-body force with limit cycle behavior is required for consistent renormalization already at leading order. We will review this EFT and some of its applications in the physics of cold atoms and nuclear physics. In particular, we will discuss the possibility of an infrared limit cycle in QCD. Recent extensions of the EFT approach to the four-body system and N-boson droplets in two spatial dimensions will also be addressed.Comment: 10 pages, 5 figures, Proceedings of the INT Workshop on "Nuclear Forces and the Quantum Many-Body Problem", Oct. 200

DEVELOPMENT OF A STOCHASTIC MODEL TO EVALUATE PLANT GROWERS' ENTERPRISE BUDGETS

Increased domestic concentration and international competition in the floricultural industry are forcing growers to improve resource management efficiency. Cost management and cost accounting methods are becoming key tools as growers attempt to reduce costs. These tools allow growers to allocate costs for each crop, increasing their greenhouse planning abilities. Growers have a relative high degree of risk due to potential crop and market failure. Individual growers have different tolerance for risk and risk bearing capacity. Growers need a cost accounting system that incorporates production and market risk, a system that allows them to make informed business decisions. The research reported in this paper developed a greenhouse budgeting model that incorporated risk to allow growers to compare production costs for flowers with different genetics and production technologies. This enables greenhouse growers to make production management decisions that incorporate production and market risk. The model gives growers the option of imputing their own production data to evaluate how various yield and price assumptions influence income and expense projections, and ultimately, profit. The model allows growers to compare total production cost and revenue varying grower type, production time, geographical location, operation size, and cost structure. The model evaluates budgets for growers who market to mass-market retail operations or wholesale intermediaries who sell to merchandisers or flower shops distribution channels. The model was demonstrated with sample data to illustrate how incorporating risk analysis into a grower's greenhouse budget model effects resource allocation and production decisions as compare to a budget model that does not incorporate risk. Deterministic and stochastic models were used to demonstrate differences in production decisions under various assumptions. The stochastic model introduced prices and flowering characteristics variability. The @Risk software was used to generate the random number simulation of the stochastic model, and stochastic dominance analysis was used to rank the alternatives. The result for both the deterministic and stochastic models identified the same cultivar as most profitable. However, there were differences in crop profits levels and rankings for subsequent cultivars that could influence growers' production choice decisions. The grower's risk aversion level influenced his/her choice of the most profitable cultivars in the stochastic model. The model summarizes the sources of variability that affect cost and revenue. The model enables the grower to measure effects that change in productivity might have on profit. Growers can identify items in their budget that have a greater effect on profitability, and make adjustments. The model can be used to allocate cost across activities, so the grower would be able to measure the economic impact of an item on the budget.Crop Production/Industries,

Galaxy disks do not need to survive in the L-CDM paradigm: the galaxy merger rate out to z~1.5 from morpho-kinematic data

About two-thirds of present-day, large galaxies are spirals such as the Milky Way or Andromeda, but the way their thin rotating disks formed remains uncertain. Observations have revealed that half of their progenitors, six billion years ago, had peculiar morphologies and/or kinematics, which exclude them from the Hubble sequence. Major mergers, i.e., fusions between galaxies of similar mass, are found to be the likeliest driver for such strong peculiarities. However, thin disks are fragile and easily destroyed by such violent collisions, which creates a critical tension between the observed fraction of thin disks and their survival within the L-CDM paradigm. Here we show that the observed high occurrence of mergers amongst their progenitors is only apparent and is resolved when using morpho-kinematic observations which are sensitive to all the phases of the merging process. This provides an original way of narrowing down observational estimates of the galaxy merger rate and leads to a perfect match with predictions by state-of-the-art L-CDM semi-empirical models with no particular fine-tuning needed. These results imply that half of local thin disks do not survive but are actually rebuilt after a gas-rich major merger occurring in the past nine billion years, i.e., two-thirds of the lifetime of the Universe. This emphasizes the need to study how thin disks can form in halos with a more active merger history than previously considered, and to investigate what is the origin of the gas reservoir from which local disks would reform.Comment: 19 pages, 7 figures, 2 tables. Accepted in ApJ. V2 to match proof corrections and added reference

Generalized Swiss-cheese cosmologies: Mass scales

We generalize the Swiss-cheese cosmologies so as to include nonzero linear momenta of the associated boundary surfaces. The evolution of mass scales in these generalized cosmologies is studied for a variety of models for the background without having to specify any details within the local inhomogeneities. We find that the final effective gravitational mass and size of the evolving inhomogeneities depends on their linear momenta but these properties are essentially unaffected by the details of the background model.Comment: 10 pages, 14 figures, 1 table, revtex4, Published form (with minor corrections

Symbolic Manipulators Affect Mathematical Mindsets

Symbolic calculators like Mathematica are becoming more commonplace among upper level physics students. The presence of such a powerful calculator can couple strongly to the type of mathematical reasoning students employ. It does not merely offer a convenient way to perform the computations students would have otherwise wanted to do by hand. This paper presents examples from the work of upper level physics majors where Mathematica plays an active role in focusing and sustaining their thought around calculation. These students still engage in powerful mathematical reasoning while they calculate but struggle because of the narrowed breadth of their thinking. Their reasoning is drawn into local attractors where they look to calculation schemes to resolve questions instead of, for example, mapping the mathematics to the physical system at hand. We model the influence of Mathematica as an integral part of the constant feedback that occurs in how students frame, and hence focus, their work

Beyond deficit-based models of learners' cognition: Interpreting engineering students' difficulties with sense-making in terms of fine-grained epistemological and conceptual dynamics

Researchers have argued against deficit-based explanations of students' troubles with mathematical sense-making, pointing instead to factors such as epistemology: students' beliefs about knowledge and learning can hinder them from activating and integrating productive knowledge they have. In this case study of an engineering major solving problems (about content from his introductory physics course) during a clinical interview, we show that "Jim" has all the mathematical and conceptual knowledge he would need to solve a hydrostatic pressure problem that we posed to him. But he reaches and sticks with an incorrect answer that violates common sense. We argue that his lack of mathematical sense-making-specifically, translating and reconciling between mathematical and everyday/common-sense reasoning-stems in part from his epistemological views, i.e., his views about the nature of knowledge and learning. He regards mathematical equations as much more trustworthy than everyday reasoning, and he does not view mathematical equations as expressing meaning that tractably connects to common sense. For these reasons, he does not view reconciling between common sense and mathematical formalism as either necessary or plausible to accomplish. We, however, avoid a potential "deficit trap"-substituting an epistemological deficit for a concepts/skills deficit-by incorporating multiple, context-dependent epistemological stances into Jim's cognitive dynamics. We argue that Jim's epistemological stance contains productive seeds that instructors could build upon to support Jim's mathematical sense-making: He does see common-sense as connected to formalism (though not always tractably so) and in some circumstances this connection is both salient and valued.Comment: Submitted to the Journal of Engineering Educatio

Adlayer core-level shifts of random metal overlayers on transition-metal substrates

We calculate the difference of the ionization energies of a core-electron of a surface alloy, i.e., a B-atom in a A_(1-x) B_x overlayer on a fcc-B(001)-substrate, and a core-electron of the clean fcc-B(001) surface using density-functional-theory. We analyze the initial-state contributions and the screening effects induced by the core hole, and study the influence of the alloy composition for a number of noble metal-transition metal systems. Data are presented for Cu_(1-x)Pd_x/Pd(001), Ag_(1-x) Pd_x/Pd(001), Pd_(1-x) Cu_x/Cu(001), and Pd_(1-x) Ag_x/Ag(001), changing x from 0 to 100 %. Our analysis clearly indicates the importance of final-state screening effects for the interpretation of measured core-level shifts. Calculated deviations from the initial-state trends are explained in terms of the change of inter- and intra-atomic screening upon alloying. A possible role of alloying on the chemical reactivity of metal surfaces is discussed.Comment: 4 pages, 2 figures, Phys. Rev. Letters, to appear in Feb. 199