Macroscopic Screening of Coulomb Potentials From UV/IR-Mixing

We compute the static potential in a non-commutative theory including a term due to UV/IR-mixing. As a result, the potential decays exponentially fast with distance rather than like a power law Coulomb type potential due to the exchange of massless particles. This shows that when quantum effects are taken into account the introduction of non-commutativity not only modifies physics at short distances but has dramatic macroscopic consequences as well. As a result, we give a lower bound on the scale of non-commutativity (if present at all) to be compatible with observations.Comment: 10 pages, V2 minor wording and reference

Household Food Expenditures, Parental Time Allocation, and Childhood Obesity

The increased prevalence of childhood obesity is a major concern for society. This study aims at exploring the influence of the parents (especially parental time allocation choices) on childrens obesity-related health outcomes and examining the potential differences between the fathers and the mothers marginal effects. A household with two parents and one child is modeled. The household production theory and the collective household modeling structure are combined. The model treats the mother, the father and the child as three separate agents with individual preferences. The two parents interaction is modeled within the collective model framework by assuming that they will reach Pareto efficient resource allocation between them. In order to capture the dynamics between parents and the child, parents-child interaction is modeled in a two-stage Stackleberg game structure where the child is allowed to have certain decision choices of his/her own. This game structure allows us to explore the parental influence on the childs health outcomes while allowing the child to have influencing power in the household decision-making process. Based on this theoretical model, a general triangular system with one childs health production equation and five health inputs demand equations is derived and estimated. The empirical estimation is performed for three systems: pooled model, the younger children model (of age 9 to 11), and the older children model (of age 13 to 15). The empirical results shows positive relationship between total household monthly food expenditure and the childs BMI outcome. Both parents time spent with the child are important and both show negatively significant impact on the childs BMI outcomes in all models and the pool model confirms the statistical difference between paternal and maternal time spent with the child. Other mother-related variables show more influence on the childrens BMI. There exists a complementary relationship between mothers income and fathers time allocation. Fathers have more significant influence on household food expenditure compared to mothers. In general, mothers show more significant influence on the parental time allocation compared to fathers. The main contribution of this study is that it develops a general theoretical framework to capture the dynamics in parents-child interaction. Based on this theoretical model, empirical analysis and future work can be conducted in a theoretically consistent way.Food Consumption/Nutrition/Food Safety, Health Economics and Policy,

The Case for Future Hadron Colliders From B→K(∗)μ+μ−B \to K^{(*)} \mu^+ \mu^- Decays

Recent measurements in $B \to K^{(*)} \mu^+ \mu^-$ decays are somewhat discrepant with Standard Model predictions. They may be harbingers of new physics at an energy scale potentially accessible to direct discovery. We estimate the sensitivity of future hadron colliders to the possible new particles that may be responsible for the anomalies: leptoquarks or $Z^\prime$s. We consider luminosity upgrades for a 14 TeV LHC, a 33 TeV LHC, and a 100 TeV $pp$ collider such as the FCC-hh. Coverage of $Z^\prime$ models is excellent: for narrow particles, with perturbative couplings that may explain the $b$-decay results for $Z^\prime$ masses up to 20 TeV, a 33 TeV 1 ab$^{-1}$ LHC is expected to cover most of the parameter space up to 8 TeV in mass, whereas the 100 TeV FCC-hh with 10 ab$^{-1}$ will cover all of it. A smaller portion of the leptoquark parameter space is covered by future colliders: for example, in a $\mu^+\mu^-jj$ di-leptoquark search, a 100 TeV 10 ab$^{-1}$ collider has a projected sensitivity up to leptoquark masses of 12 TeV (extendable to 21 TeV with a strong coupling for single leptoquark production), whereas leptoquark masses up to 41 TeV may in principle explain the anomalies.Comment: 24 pages, 10 figures. v2: Improved discussion and references added, version submitted to JHE

Primal robustness and semidefinite cones

This paper reformulates and streamlines the core tools of robust stability and performance for LTI systems using now-standard methods in convex optimization. In particular, robustness analysis can be formulated directly as a primal convex (semidefinite program or SDP) optimization problem using sets of gramians whose closure is a semidefinite cone. This allows various constraints such as structured uncertainty to be included directly, and worst-case disturbances and perturbations constructed directly from the primal variables. Well known results such as the KYP lemma and various scaled small gain tests can also be obtained directly through standard SDP duality. To readers familiar with robustness and SDPs, the framework should appear obvious, if only in retrospect. But this is also part of its appeal and should enhance pedagogy, and we hope suggest new research. There is a key lemma proving closure of a grammian that is also obvious but our current proof appears unnecessarily cumbersome, and a final aim of this paper is to enlist the help of experts in robust control and convex optimization in finding simpler alternatives.Comment: A shorter version submitted to CDC 1

Large enhancement of the effective second-order nonlinearity in graphene metasurfaces

Using a powerful homogenization technique, one- and two-dimensional graphene metasurfaces are homogenized both at the fundamental frequency (FF) and second harmonic (SH). In both cases, there is excellent agreement between the predictions of the homogenization method and those based on rigorous numerical solutions of Maxwell equations. The homogenization technique is then employed to demonstrate that, owing to a double-resonant plasmon excitation mechanism that leads to strong, simultaneous field enhancement at the FF and SH, the effective second-order susceptibility of graphene metasurfaces can be enhanced by more than three orders of magnitude as compared to the intrinsic second-order susceptibility of a graphene sheet placed on the same substrate. In addition, we explore the implications of our results on the development of new active nanodevices that incorporate nanopatterned graphene structures.Comment: 11 pages, 12 figure

Effective size of a trapped atomic Bose gas

We investigate the temperature-dependent effective size of a trapped interacting atomic Bose gas within a mean field theory approximation. The sudden shrinking of the average length, as observed in an earlier experiment by Wang {\it et al.} [Chin. Phys. Lett. {\bf 20}, 799 (2003)], is shown to be a good indication for Bose-Einstein condensation (BEC). Our study also supports the use of the average width of a trapped Bose gas for a nondestructive calibration of its temperature.Comment: RevTex4, 6 pages, 4 eps figures, to appear in Phys. Rev.

Near Infrared Microspectroscopy, Fluorescence Microspectroscopy, Infrared Chemical Imaging and High-Resolution Nuclear Magnetic Resonance Analysis of Soybean Seeds, Embryos and Single Cells

Chemical analysis of soybean seeds, somatic embryos and single cells were carried out by Fourier Transform Infrared (FT-IR), Fourier Transform Near Infrared (FT-NIR) Microspectroscopy, Fluorescence and High-Resolution NMR (HR-NMR). The first FT-NIR chemical images of biological systems approaching 1 micron (1μ) resolution are presented here. Chemical images obtained by FT-NIR and FT-IR Microspectroscopy are presented for oil in soybean seeds and somatic embryos under physiological conditions. FT-NIR spectra of oil and proteins were obtained for volumes as small as 2μ3. Related, HR-NMR analyses of oil contents in somatic embryos are also presented here with nanoliter precision. Such 400 MHz 1H NMR analyses allowed the selection of mutagenized embryos with higher oil content (e.g. ~20%) compared to non-mutagenized control embryos. Moreover, developmental changes in single soybean seeds and/or somatic embryos may be monitored by FT-NIR with a precision approaching the picogram level. Indeed, detailed chemical analyses of oils and phytochemicals are now becoming possible by FT-NIR Chemical Imaging/ Microspectroscopy of single cells. The cost, speed and analytical requirements of plant breeding and genetic selection programs are fully satisfied by FT-NIR spectroscopy and Microspectroscopy for soybeans and soybean embryos. FT-NIR Microspectroscopy and Chemical Imaging are also shown to be potentially important in functional Genomics and Proteomics research through the rapid and accurate detection of high-content microarrays (HCMA). Multi-photon (MP), pulsed femtosecond laser NIR Fluorescence Excitation techniques were shown to be capable of Single Molecule Detection (SMD). Therefore, such powerful techniques allow for the most sensitive and reliable quantitative analyses to be carried out both in vitro and in vivo. Thus, MP NIR excitation for Fluorescence Correlation Spectroscopy (FCS) allows not only single molecule detection, but also molecular dynamics and high resolution, submicron imaging of femtoliter volumes inside living cells and tissues. These novel, ultra-sensitive and rapid NIR/FCS analyses have numerous applications in important research areas, such as: agricultural biotechnology, food safety, pharmacology, medical research and clinical diagnosis of viral diseases and cancers