Dispersion Integral Research Articles

Explicit formulation of second and third order optical nonlinearity in the FDTD framework

The finite-difference time-domain (FDTD) method is a flexible and powerful technique for rigorously solving Maxwell’s equations. However, three-dimensional optical nonlinearity in current commercial and research FDTD softwares requires solving iteratively an implicit form of Maxwell’s equations over the entire numerical space and at each time step. Reaching numerical convergence demands significant computational resources and practical implementation often requires major modifications to the core FDTD engine. In this paper, we present an explicit method to include second and third order optical nonlinearity in the FDTD framework based on a nonlinear generalization of the Lorentz dispersion model. A formal derivation of the nonlinear Lorentz dispersion equation is equally provided, starting from the quantum mechanical equations describing nonlinear optics in the two-level approximation. With the proposed approach, numerical integration of optical nonlinearity and dispersion in FDTD is intuitive, transparent, and fully explicit. A strong-field formulation is also proposed, which opens an interesting avenue for FDTD-based modelling of the extreme nonlinear optics phenomena involved in laser filamentation and femtosecond micromachining of dielectrics.

Non-random dispersal mediates invader impacts on the invertebrate community.

Dispersers are often not a random draw from a population, dispersal propensity being conditional on individual phenotypic traits and local contexts. This non-randomness consequently results in phenotypic differences between dispersers and non-dispersers and, in the context of biological invasions, in an invasion front made of individuals with a biased phenotype. This bias of phenotypes at the front may subsequently modulate the strength of ecological effects of an invasive species on invaded communities. We recently demonstrated that more asocial mosquitofish (Gambusia affinis), one of the 100 worst invasive species, disperse further, suggesting a sociability-biased invasion front. As behavioural types are related to the strength of interspecific interactions, an invasion by a biased subset of individuals should have important ecological implications for native communities. Here, we tested the impact of phenotypic biases in dispersing individuals (relative to non-dispersers) on prey communities in experimental mesocosms. We show that dispersers reduce prey abundance more than do non-dispersers during the first 4weeks after introduction, and that the disperser's social types are likely drivers of these differences. These differences in prey communities disappeared after 8weeks suggesting prey community resilience against predation in these mesocosm ecosystems. Consequently, we call for the integration of non-random dispersal, dispersal syndromes and more generally intraspecific variation into studies predicting the impacts of invasions.

Extended chiral Khuri\u2013Treiman formalism for eta rightarrow 3pi and the role of the a_0(980), f_0(980) resonances

Recent experiments on eta rightarrow 3pi decays have provided an extremely precise knowledge of the amplitudes across the Dalitz region which represent stringent constraints on theoretical descriptions. We reconsider an approach in which the low-energy chiral expansion is assumed to be optimally convergent in an unphysical region surrounding the Adler zero, and the amplitude in the physical region is uniquely deduced by an analyticity-based extrapolation using the Khuri–Treiman dispersive formalism. We present an extension of the usual formalism which implements the leading inelastic effects from the Kbar{K} channel in the final-state pi pi interaction as well as in the initial-state eta pi interaction. The constructed amplitude has an enlarged region of validity and accounts in a realistic way for the influence of the two light scalar resonances f_0(980) and a_0(980) in the dispersive integrals. It is shown that the effect of these resonances in the low-energy region of the eta rightarrow 3pi decay is not negligible, in particular for the 3pi ^0 mode, and improves the description of the energy variation across the Dalitz plot. Some remarks are made on the scale dependence and the value of the double quark mass ratio Q.

Negative phenotypic and genetic correlation between natal dispersal propensity and nest-defence behaviour in a wild bird

Natural selection is expected to favour the integration of dispersal and phenotypic traits allowing individuals to reduce dispersal costs. Accordingly, associations have been found between dispersal and personality traits such as aggressiveness and exploration, which may facilitate settlement in a novel environment. However, the determinism of these associations has only rarely been explored. Here, we highlight the functional integration of individual personality in nest-defence behaviour and natal dispersal propensity in a long-lived colonial bird, the Alpine swift (Apus melba), providing insights into genetic constraints shaping the coevolution of these two traits. We report a negative association between natal dispersal and nest-defence (i.e. risk taking) behaviour at both the phenotypic and genetic level. This negative association may result from direct selection if risk-averseness benefits natal dispersers by reducing the costs of settlement in an unfamiliar environment, or from indirect selection if individuals with lower levels of nest defence also show lower levels of aggressiveness, reducing costs of settlement among unfamiliar neighbours in a colony. In both cases, these results highlight that risk taking is an important behavioural trait to consider in the study of dispersal evolution.

Peripheral transverse densities of the baryon octet from chiral effective field theory and dispersion analysis

The baryon electromagnetic form factors are expressed in terms of two-dimensional densities describing the distribution of charge and magnetization in transverse space at fixed light-front time. We calculate the transverse densities of the spin-1/2 flavor-octet baryons at peripheral distances b=O(Mπ−1) using methods of relativistic chiral effective field theory (χEFT) and dispersion analysis. The densities are represented as dispersive integrals over the imaginary parts of the form factors in the timelike region (spectral functions). The isovector spectral functions on the two-pion cut t>4Mπ2 are calculated using relativistic χEFT including octet and decuplet baryons. The χEFT calculations are extended into the ρ meson mass region using an N/D method that incorporates the pion electromagnetic form factor data. The isoscalar spectral functions are modeled by vector meson poles. We compute the peripheral charge and magnetization densities in the octet baryon states, estimate the uncertainties, and determine the quark flavor decomposition. The approach can be extended to baryon form factors of other operators and the moments of generalized parton distributions.

Transverse Densities of Octet Baryons from Chiral Effective Field Theory

Transverse densities describe the distribution of charge and current at fixed light-front time and provide a frame-independent spatial representation of hadrons as relativistic systems. We calculate the transverse densities of the octet baryons at peripheral distances b = O(M_pi^{-1}) in an approach combining chiral effective field theory (ChEFT) and dispersion analysis. The densities are represented as dispersive integrals of the imaginary parts of the baryon electromagnetic form factors in the timelike region (spectral functions). The spectral functions on the two-pion cut at t > 4 M_pi^2 are computed using relativistic ChEFT with octet and decuplet baryons in the EOMS renormalization scheme. The calculations are extended into the rho-meson mass region, using a dispersive method that incorporates the timelike pion form-factor data. The approach allows us to construct densities at distances b > 1 fm with controlled uncertainties. Our results provide insight into the peripheral structure of nucleons and hyperons and can be compared with empirical densities and lattice-QCD calculations.

η−η′ mixing and the derivative of the topological susceptibility at zero momentum transfer

The couplings of the isosinglet axial-vector currents to the Eta and Eta' mesons are evaluated in a stable, model independent way by use of polynomial kernels in dispersion integrals. The corrections to the Gell-Mann-Oakes-Renner relation in the isoscalar channel are deduced. The derivative of the topological susceptibility at the origin is calculated taking into account instantons and instanton screening.

Two-photon exchange correction to2S−2Psplitting in muonicHe3ions

We calculate the two-photon exchange correction to the Lamb shift in muonic helium-3 ions within the dispersion relations framework. Part of the effort entailed making analytic fits to the electron-$^3$He quasielastic scattering data set, for purposes of doing the dispersion integrals. Our result is that the energy of the 2$S$ state is shifted downwards by two-photon exchange effects by 15.14(49) meV, in good accord with the result obtained from a potential model and effective field theory calculation.

Dispersal: a central and independent trait in life history

The study of tradeoffs among major life history components (age at maturity, lifespan and reproduction) allowed the development of a quantitative framework to understand how environmental variation shapes patterns of biodiversity among and within species.Because every environment is inherently spatially structured, and in most cases temporally variable, individuals need to move within and among habitats to maximize fitness. Dispersal is often assumed to be tightly integrated into life histories through genetic correlations with other vital traits. This assumption is particularly strong within the context of a fast‐slow continuum of life‐history variation. Such a framework is to date used to explain many aspects of population and community dynamics. Evidence for a consistent and context‐independent integration of dispersal in life histories is, however, weak. We therefore advocate the explicit integration of dispersal into life history theory as a principal axis of variation influencing fitness, that is free to evolve, independently of other life history traits.We synthesize theoretical and empirical evidence on the central role of dispersal and its evolutionary dynamics on the spatial distribution of ecological strategies and its impact on population spread, invasions and coexistence. By applying an optimality framework we show that the inclusion of dispersal as an independent dimension of life histories might substantially change our view on evolutionary trajectories in spatially structured environments.Because changes in the spatial configuration of habitats affect the costs of movement and dispersal, adaptations to reduce these costs will increase phenotypic divergence among and within populations. We outline how this phenotypic heterogeneity is anticipated to further impact population and community dynamics.

Higgs boson decay to two photons and dispersion relations

We discuss the computation of the Higgs boson decay amplitude to two photons through the W-loop using dispersion relations. The imaginary part of the form factor F_W(s) that parametrizes this decay is unambiguous in four dimensions. When it is used to calculate the unsubtracted dispersion integral, the finite result for the form factor F_W(s) is obtained. However, the F_W(s) obtained in this way differs by a constant term from the result of a diagrammatic computation, based on dimensional regularization. It is easy to accommodate the missing constant by writing a once-subtracted dispersion relation for F_W(s) but it is unclear why the subtraction needs to be done. The goal of this paper is to investigate this question in detail. We show that the correct constant can be recovered within a dispersive approach in a number of ways that, however, either require an introduction of an ultraviolet regulator or unphysical degrees of freedom; unregulated and unsubtracted computations in the unitary gauge are insufficient, in spite of the fact that such computations give a finite result.

One-pot synthesis of Pt/SnO2/GNs and its electro-photo-synergistic catalysis for methanol oxidation

In this work, a simple one-pot strategy was used to synthesize an anodic electrocatalyst Pt/SnO2/GNs (EDTA) for direct methanol fuel cells (DMFCs). Under hydrothermal conditions, the reduction of H2PtCl6 and graphene oxide (GO), the oxidation of SnCl2 and the formation of SnO2 were occurred synchronously without additional reducing or oxidizing agent. The introduction of EDTA results in good dispersion and full integration of Pt and SnO2 nanoparticles, due to the complexation between Pt4+ (Sn2+) and EDTA. Electrochemical experiments show Pt/SnO2/GNs (EDTA) has much higher catalytic activity and better stability for MOR compared with the commercial Pt/C catalyst and Pt/GNs (EDTA). Furthermore, it is interesting to find that catalytic properties of Pt/SnO2/GNs (EDTA) toward MOR are significantly enhanced under external light irradiation. Especially, after UV irradiation for 30 min, Pt/SnO2/GNs (EDTA) composite shows an ultrahigh forward peak current density of 1103 mA mg−1. The remarkably improved performances under external light irradiation mainly derives from the synergistic effects between the electro-catalytic and photo-catalytic properties, which provides a novel strategy to effectively enhance the catalytic activities of Pt catalyst in DMFCs by coupling with photoresponsive metal oxides.

Characteristics of the surface plasma wave in a self-gravitating magnetized dusty plasma slab

The dispersion properties of surface dust ion-acoustic waves in a self-gravitating magnetized dusty plasma slab are investigated. The dispersion relation is derived by using the low-frequency magnetized dusty dielectric function and the surface wave dispersion integral for the slab geometry. We find that the self-gravitating effect suppresses the frequency of surface dust ion-acoustic wave for the symmetric mode in the long wavelength regime, whereas it hardly changes the frequency for the anti-symmetric mode. As the slab thickness and the wave number increase, the surface wave frequency slowly decreases for the symmetric mode but increases significantly for the anti-symmetric mode. The influence of external magnetic field is also investigated in the case of symmetric mode. We find that the strength of the magnetic field enhances the frequency of the symmetric-mode of the surface plasma wave. The increase of magnetic field reduces the self-gravitational effect and thus the self-gravitating collapse may be suppressed and the stability of dusty objects in space is enhanced.

Electromagnetic plasma waves in the nonextensive statistics

This paper presents theoretical findings of new electromagnetic plasma waves in nonextensive and Maxwellian plasma below and above plasma frequency. The new waves are observed among the solutions of general and exact nonextensive dispersion relations for electromagnetic waves in unmagnetized collisionless plasma. The solutions for all values of nonextensive q parameter are also containing a light mode. The exact dispersion relations are obtained via calculation of kinetic dispersion integral using nonextensive distributions and hypergeometric function properties. Finally the effects of q parameter on the oscillation modes and damps are discussed.

Formula omitted] results from BaBar and their impact on the muon [formula omitted] prediction

The BaBar collaboration has nearly completed a program of precise measurements of the cross sections for the dominant channels of e+e−→hadrons from threshold to 3 GeV using the initial-state radiation (ISR) method, i.e. the measurement of the cross sections e+e−→γhadrons with the energetic γ detected at large angle to the beams. These data are used as input to vacuum polarization dispersion integrals, in particular the hadronic contribution to the muon g−2 anomaly. In addition to the recently measured π+π− and K+K− cross sections, giving the dominant contribution, multihadronic channels have been investigated, with some recent examples presented here for the π+π−π+π−, K+K−ππ, KSKL, KSKLπ+π−, KSKSπ+π− channels. The BaBar results have the best precision and cover for the first time almost all significant hadronic contributions below 2 GeV entering the muon g−2 prediction.

Forward sum rule for the2γ-exchange correction to the charge-radius extraction from elastic electron scattering

Two-photon exchange (TPE) contributions to elastic electron-proton scattering in the forward regime and in leading log $\sim t\ln|t|$ approximation in the momentum transfer $|t|$ are considered. The imaginary part of TPE amplitude in these kinematics is related to the total photo absorption cross section. The real part of the TPE amplitude is obtained from the imaginary part by means of a fixed-$t$ dispersion relation. The dispersion integrals for the relevant elastic $ep$-scattering amplitude converge and do not need subtraction. This allows us to make clean a prediction for the real part of the TPE amplitude at forward angles with the leading term $\sim t\ln|t|$. Numerical estimates are comparable to the experimental precision in extracting the charge radius from experimental data.

Enel Distribuzione projects for renewable energy sources integration in distribution grid

The integration of the dispersed generation, based on constantly increasing renewable energy sources, is one of the biggest challenges of the modern distribution system operator.Enel Distribuzione, that operate the 85% of the Italian distribution grid with 33 million customers, connected more than 25GW of dispersed generations, mainly based on renewable energy sources, in Italy up to 2013; these numbers are most impressive taking into account that the consumption peak for medium voltage and low voltage distribution networks was 40GW during the 2007 (the period before the economical crisis and with very small dispersed generation connected).The original design of Enel Distribuzione networks is radial and does not consider interconnection of any generation with significant size. In a radial feeder, the power flows unidirectionally from a single source to the loads. The penetration of dispersed generation into the feeder can cause a flow reversal. This flow reversal violates the concept of “radial design” and has a significant impact on the operation of the feeder and, in particular, on the protection systems and on the voltage regulation.In this scenery, Enel Distribuzione implemented and is implementing several large area demonstrations to test innovative smart grid technologies, in particular for dispersed generation integration. In this paper, two of these projects are presented focusing on the innovative solutions for voltage regulation and dispersed generation dispatching.

Precision measurements of the [formula omitted] cross section with the KLOE detector

The muon anomalous magnetic moment is one of the most precisely measured quantities in particle physics and a persistent discrepancy of about 3 σ between standard model (SM) prediction and the experimental measurement has been observed. The leading order contribution aμhlo is actually the main source of uncertainty in the theoretical evaluation of the muon anomaly. It is obtained by a dispersion integral using the precision measurement of hadronic cross section. The KLOE experiment at the DAΦNE ϕ−factory in Frascati was the first to exploit Initial State Radiation (ISR) processes to obtain the e+e−→π+π−(γ) cross section below 1 GeV, that accounts for most (70%) of the leading order contribution to the muon anomaly. In year 2005 and 2008 the KLOE-collaboration has published two measurements of the π+π− cross section with the photon in the initial state emitted at small angle, and an independent measurement with the photon emitted at large angle was finalized in year 2011. These measurements were normalized using luminosity from Bhabha. In the last years, a new analysis of KLOE data has been performed for obtaining the pion form factor directly from the bin-by-bin π+π−γ to μ+μ−γ ratio. We present the results of this new measurement, showing the comparison with our previous measurements, and its impact on the hadronic contribution to the muon anomaly.

Status of Leading-Order Hadronic Vacuum Polarization Dispersion Calculation

The leading-order hadronic contribution to the muon magnetic anomaly aμ≡(gμ−2)/2, calculated using a dispersion integral of e+e− annihilation data and τ decay data, is briefly reviewed. This contribution has the largest uncertainty to the predicted value of aμ, which differs from the experimental value by ∼ 3.6 (2.4) standard deviations for the e+e− (τ) based analysis. New results since the last workshop and main open issues on the subject are discussed.

Formula omitted] results from BABAR and implications for the muon g-2

The BaBar collaboration has nearly completed a program of precise measurements of the cross sections for the dominant channels of e+e−→hadrons from threshold to an energy of 3–5 GeV using the initial-state radiation (ISR) method, i.e. the measurement of the cross sections e+e−→γhadrons with the energetic γ detected at large angle to the beams. These data are used as input to vacuum polarization dispersion integrals, in particular the hadronic contribution to the muon g−2 anomaly. In addition to the recently measured π+π− cross section, giving the dominant contibution, many multihadronic channels have been investigated, with some recent examples presented here. We give preliminary results for the process e+e−→K+K−(γ) using 232fb−1 of data collected with the BaBar detector at e+e− center-of-mass energies near 10.6 GeV. The lowest-order contribution to the hadronic vacuum polarization term in the muon magnetic anomaly is obtained for this channel: aμKK,LO=(22.95±0.14(stat)±0.22(syst))×10−10, which is about a factor of three more precise than the previous world average value.

New sum rule determination of the nucleon mass and strangeness content

A new QCD calculation of the mass of the nucleon is presented. It makes use of a polynomial kernel in the dispersion integrals tailored to practically eliminate the contribution of the unknown $1/{2}^{+}$ and $1/{2}^{\ensuremath{-}}$ continuum. This approach avoids the arbitrariness and instability attached to the Borel kernel used in previous sum rules calculations. Our method yields stable results for the nucleon mass and coupling for standard values of the condensates. The prediction of the nucleon mass in the chiral limit is ${m}_{N}=(830\ifmmode\pm\else\textpm\fi{}50)$ MeV. When the nucleon sigma terms are added this gives ${M}_{N}=990\ifmmode\pm\else\textpm\fi{}50$ MeV, which leaves little room for a large strangeness content of the nucleon.