Dipole Description Research Articles

Investigation of proton structure function F2p at HERA in light of an analytical solution to the Balitsky–Kovchegov equation

In this paper, the proton structure function F2p(x,Q2) at small-x is investigated using an analytical solution to the Balitsky–Kovchegov (BK) equation. In the context of the color dipole description of deep inelastic scattering (DIS), the structure function F2p(x,Q2) is computed by applying the analytical expression for the scattering amplitude N(k, Y) derived from the BK solution. At transverse momentum k and total rapidity Y, the scattering amplitude N(k, Y) represents the propagation of the quark-antiquark dipole in the color dipole description of DIS. Using the BK solution we extracted the integrated gluon density xg(x, Q 2) and then compared our theoretical estimation with the LHAPDF global data fits, NNPDF3.1sx and CT18. Finally, we have investigated the behavior of F2p(x,Q2) in the kinematic region of 10−5 ≤ x ≤ 10−2 and 2.5 GeV2 ≤ Q 2 ≤ 60 GeV2. Our predicted results for F2p(x,Q2) within the specified kinematic region are in good agreement with the recent high-precision data for F2p(x,Q2) from HERA (H1 Collaboration) and the LHAPDF global parametrization group NNPDF3.1sx.

Spatiospectral Description of Current Dipole as a Source of the Magnetic Field of the Heart

Spatiospectral Description of Current Dipole as a Source of the Magnetic Field of the Heart

Active Electric Dipole Energy Sources: Transduction via Electric Scalar and Vector Potentials.

The creation of electromagnetic energy may be realised by engineering a device with a method of transduction, which allows an external energy source, such as mechanical, chemical, nuclear, etc., to be impressed into the electromagnetic system through a mechanism that enables the separation of opposite polarity charges. For example, a voltage generator, such as a triboelectric nanogenerator, enables the separation of charges through the transduction of mechanical energy, creating an active physical dipole in the static case, or an active Hertzian dipole in the time-dependent case. The net result is the creation of a static or time-dependent permanent polarisation, respectively, without an applied electric field and with a non-zero vector curl. This system is the dual of a magnetic solenoid or permanent magnet excited by a circulating electrical current or fictitious bound current, respectively, which supplies a magnetomotive force described by a magnetic vector potential and a magnetic geometric phase proportional to the enclosed magnetic flux. Thus, the active electric dipole voltage generator has been described macroscopically by a circulating fictitious magnetic current boundary source and exhibits an electric vector potential with an electric geometric phase proportional to the enclosed electric flux density. This macroscopic description of an active dipole is a semi-classical average description of some underlying microscopic physics, which exhibits emergent nonconservative behaviour not found in classical closed-system laws of electrodynamics. We show that the electromotive force produced by an active dipole in general has both electric scalar and vector potential components to account for the magnitude of the electromotive force it produces. Independent of the electromagnetic gauge, we show that Faraday’s and Ampere’s law may be derived from the time rate of change of the magnetic and dual electric geometric phases. Finally, we analyse an active cylindrical dipole in terms of scalar and vector potential and confirm that the electromotive force produced, and hence potential difference across the terminals is a combination of vector and scalar potential difference depending on the aspect ratio (AR) of the dipole. For long thin active dipoles (AR approaches 0), the electric field is suppressed inside, and the voltage is determined mainly by the electric vector potential. For large flat active dipoles (AR approaches infinity), the electric flux density is suppressed inside, and the voltage is mainly determined by the scalar potential.

Nuclear magnetic transitions in the relativistic energy density functional approach

Recently a novel theory framework has been established for description of magnetic dipole (M1) transitions in finite nuclei, based on relativistic nuclear energy density functional with point coupling interactions. The properties of M1 transitions have been studied, including the sum rules, spin, orbital, isoscalar and isovector M1 transition strengths in magic and open shell nuclei. It is shown that pairing correlations and spinorbit interaction plays an important role in the description of M1 transition strength distributions. The analysis of the evolution of M1 transition properties in the isotope chain100-140Sn shows the interplay between single and double-peak structures, determined by the evolution of single-particle states, their occupations governed by the pairing correlations, and two-quasiparticle transitions involved. Comparison of the calculated B(M1) transition strength with recent data from inelastic proton scattering on112-124Sn, shows that quenching of thegfactorsgeff/gfree=0.80-0.93 is required to reproduce the experimental data. Further experimental investigations are needed to determine accurately the quenching factor.

Consequences of Treating the Solar Magnetic Field as a Dipole on the Global Structure of the Heliosphere and Heliosheath

We investigate the effect of including the heliospheric current sheet on global modeling of the heliosphere. Due to inherent numerical dissipation in the current handling of the heliospheric current sheet, models have chosen to remove it to avoid numerical problems. We compare a model where the polarity of the Parker spiral is the same in both hemispheres (unipolar) to a dipole description of the solar magnetic field, with the magnetic and rotational axes aligned forming a flat heliospheric current sheet. The flat current sheet is pulled into the northern hemisphere, which reduces the magnetic field strength at the Voyager 1 trajectory over the last 22% of the heliosheath. The decrease in magnetic field intensity is transferred into the thermal energy of the plasma causing the dipole model to predict an entirely thermally dominated heliosheath; this is a stark contrast to the magnetically dominated region ahead of the heliopause in the unipole model. We find that the two-lobe structure of the solar wind magnetic field persists within the dipole model, with the flat current sheet not able to fully erode the magnetic tension force. However, there is a large amount of magnetic dissipation in the tail between the lobes, which affects the structure of the plasma in the region. Furthermore, the draped interstellar magnetic field in the dipole model is strongly affected by reconnection at the nose of the heliosphere, yielding a distinctly different draping pattern than that observed at Voyager 1.

Polarizability extraction of complementary metamaterial elements in waveguides for aperture modeling

We consider the design and modeling of metasurfaces that couple energy from guided waves to propagating wavefronts. This is a first step towards a comprehensive, multiscale modeling platform for metasurface antennas-large arrays of metamaterial elements embedded in a waveguide structure that radiates into free-space--in which the detailed electromagnetic responses of metamaterial elements are replaced by polarizable dipoles. We present two methods to extract the effective polarizability of a metamaterial element embedded in a one- or two-dimensional waveguide. The first method invokes surface equivalence principles, averaging over the effective surface currents and charges within an element to obtain the effective dipole moments; the second method is based on computing the coefficients of the scattered waves within the waveguide, from which the effective polarizability can be inferred. We demonstrate these methods on several variants of waveguide-fed metasurface elements, finding excellent agreement between the two, as well as with analytical expressions derived for irises with simpler geometries. Extending the polarizability extraction technique to higher order multipoles, we confirm the validity of the dipole approximation for common metamaterial elements. With the effective polarizabilities of the metamaterial elements accurately determined, the radiated fields generated by a metasurface antenna (inside and outside the antenna) can be found self-consistently by including the interactions between polarizable dipoles. The dipole description provides an alternative language and computational framework for engineering metasurface antennas, holograms, lenses, beam-forming arrays, and other electrically large, waveguide-fed metasurface structures.

Suppression versus enhancement of heavy quarkonia in pA collisions

We describe production of heavy quarkonia in pA collisions within the dipole approach, assuming dominance of the perturbative color-singlet mechanism (CSM) in the $p_T$-integrated cross section. Although accounting for a nonzero heavy $Q$-$\bar Q$ separation is a higher twist correction, usually neglected, we found it to be the dominant source of nuclear effects, significantly exceeding the effects of leading twist gluon shadowing and energy loss. Moreover, this contribution turns out to be the most reliably predicted, relying on the precise measurements of the dipole cross section at HERA. The nuclear suppression of quarkonia has been anticipated to become stronger with energy, because the dipole cross section steeply rises. However, the measured nuclear effects remain essentially unchanged within the energy range from RHIC to the LHC. A novel production mechanism is proposed, which enhances the charmonium yield. Nuclear effects for the production of $J/\psi$, $\psi(2S)$, $\Upsilon(1S)$ and $\Upsilon(2S)$ are calculated, in agreement with data from RHIC and LHC. The dipole description offers a unique explanation for the observed significant nuclear suppression of $\psi(2S)$ to $J/\psi$ ratio, related to the nontrivial features of the $\psi(2S)$ wave function.

Gribov inelastic shadowing in the dipole representation

The dipole phenomenology, which has been quite successfully applied to various hard reactions, especially on nuclear targets, is applied for calculation of Gribov inelastic shadowing. This approach does not include ad hoc procedures, which are unavoidable in calculations done in hadronic representation. Several examples of Gribov corrections evaluated within the dipole description are presented.

Quantum electrodynamical corrections to a magnetic dipole in general relativity

Magnetized neutron stars are privileged places where strong electromagnetic fields as high as $\BQ=4.4\times10^9$~T exist, giving rise to non-linear corrections to Maxwell equations described by quantum electrodynamics (QED). These corrections need to be included to the general relativistic (GR) description of a magnetic dipole supposed to be anchored in the neutron star. In this paper, these QED and GR perturbations to the standard flat space-time dipole are calculated to the lowest order in the fine structure constant~$\alpha_{\rm sf}$ and to any order in the ratio $\Rs/R$ where $R$ is the neutron star radius and $\Rs$ its Schwarzschild radius. Following our new 3+1~formalism developed in a previous work, we compute the multipolar non-linear corrections to this dipole and demonstrate the presence of a small dipolar~$\ell=1$ and hexapolar~$\ell=3$ component.

High-energy behavior of photon, neutrino, and proton cross sections

By combining the color dipole model of the nucleon with the assumption that cross sections behave asymptotically as $\ln^2(s)$, we are able to describe the data for photon, neutrino and hadron interactions with protons at all energies, $s$ is the center-of-mass energy of the interacting particles. Specifically, we extrapolate the perturbative QCD calculations into the regime of small fractional parton momenta $x$ using a color dipole description of the proton target that guarantees an asymptotic $\ln^2(s)$ behavior of all cross sections. The ambiguity of introducing a parametrization associated with the dipole approximation is mitigated by the requirement that the saturation of the small-$x$ structure functions produces $\ln^2(s)$-behaved asymptotic cross sections, in agreement with the data. The same formalism allows us to calculate the cross section for the hadronic pair production of charm particles. The results, in particular those for the high-energy neutrino and charm cross sections, are relevant for evaluating the sensitivity as well as the background in neutrino telescopes.

Effect of curvature and confinement on the Casimir-Polder interaction

Modifications of Casimir-Polder interactions due to confinement inside a cylindrical cavity and due to curvature in- and outside the cavity are studied. We consider a perfectly conducting cylindrical shell with a single particle (atom or macroscopic sphere) located next to its interior or exterior surface, or two atoms placed inside the shell. By employing the scattering approach, we obtain the particle-cavity interaction and the modification of the two-particle interaction due to the cavity. We consider both retardation and thermal effects. While for the atoms a dipole description is sufficient, for the macroscopic sphere we sum (numerically) over many multipole fluctuations to compute the interaction at short separations. In the latter limit we compare to the proximity approximation and a gradient expansion and find agreement. Our results indicate an confinement induced suppression of the force between atoms. General criteria for suppression and enhancement of Casimir interactions due to confinement are discussed.

Prospects for Vibrational-Mode EELS with High Spatial Resolution

Taking advantage of previous measurements by Geiger and co-workers, we discuss the possibilities and problems of measuring vibrational modes of energy loss in a transmission electron microscope fitted with a monochromator and a high-resolution energy-loss spectrometer. The tail of the zero-loss peak is seen to be a major limitation, rather than its full-width at half-maximum. Because of the low oscillator strengths and small cross-sections involved, radiation damage will limit the spatial resolution if this technique is applied to organic specimens. Delocalization of the inelastic scattering may also be a limitation, if a dipole description of the scattering process is valid.

A study on the versatility of metallacycles in host-guest chemistry: interactions in halide-centered hexanuclear copper(II) pyrazolate complexes.

Hexanuclear copper(II) pyrazolate complexes have shown the ability to encapsulate different halide ions, leading to [trans-Cu6{μ-3,5-(CF3)2pz}6(μ-OH)6X](-) (X = F, Cl, Br, I). They offer an interesting case study for variation in local properties at host binding sites, due to the presence of a six membered ring involving Cu(II) centers considered as the borderline Lewis acid according to the Pearson Hard and Soft Acids and Bases (HSAB) principle. Here, we describe the host-guest interactions via relativistic density functional calculations, involving the graphical description of local dipole and quadrupole moments, energy decomposition analysis, non-covalent indices, and magnetic behavior. The observed variation in the copper local dipole and quadrupole moments suggests that a metallacycle host offers great advantages in comparison to their organic counterparts, prompted by the versatility of the metallic centers to modulate the surrounding electron density accordingly. According to our results, the contribution of ion-dipole forces in the halide-centered series decreases from 95.0% to 77.0% from the fluoride to the iodide complex, whereas the contribution of higher order interactions such as quadrupole-dipole and quadrupole-quadrupole, goes from 5.0% to 23.0% towards a softer guest. In addition, the through-the-space magnetic response of trans-Cu6{μ-3,5-(CF3)2pz}6(μ-OH)6, reveals a noteworthy aromatic structure, which is driven by the superexchange through the ligands leading to a singlet ground state.

Comparing the group theoretical approaches to the description of dipole and quadrupole collectivity in nuclei

The comparison of the two types of collectivity in nuclear dynamics is based on the equal realizations of their basic symmetries, represented by the algebra-chain u(3) ⊃ su(3) ⊃ so(3). We illustrate this on the example of two phenomenological algebraic models: the semimicroscopic algebraic cluster model (SACM) with one of the clusters considered as a scalar and the interacting two vector boson model (IVBM). In both of them the root group structure that leads to the above chain is based on the coupling of two different U(3) representations, with different physical interpretations. These similarities allow for the use of the same mathematical tools in building the theory, but there are important differences that come from the different higher symmetries in which this equal substructures are embedded.

Low‐degree structure in Mercury's planetary magnetic field

The structure of Mercury's internal magnetic field has been determined from analysis of orbital Magnetometer measurements by the MESSENGER spacecraft. We identified the magnetic equator on 531 low‐altitude and 120 high‐altitude equator crossings from the zero in the radial cylindrical magnetic field component,Bρ. The low‐altitude crossings are offset 479 ± 6 km northward, indicating an offset of the planetary dipole. The tilt of the magnetic pole relative to the planetary spin axis is less than 0.8°. The high‐altitude crossings yield a northward offset of the magnetic equator of 486 ± 74 km. A field with only nonzero dipole and octupole coefficients also matches the low‐altitude observations but cannot yield off‐equatorialBρ= 0 at radial distances greater than 3520 km. We compared offset dipole and other descriptions of the field with vector field observations below 600 km for 13 longitudinally distributed, magnetically quiet orbits. An offset dipole with southward directed moment of 190 nT‐RM3yields root‐mean‐square (RMS) residuals below 14 nT, whereas a field with only dipole and octupole terms tuned to match the polar field and the low‐altitude magnetic equator crossings yields RMS residuals up to 68 nT. Attributing the residuals from the offset‐dipole field to axial degree 3 and 4 contributions we estimate that the Gauss coefficient magnitudes for the additional terms are less than 4% and 7%, respectively, relative to the dipole. The axial alignment and prominent quadrupole are consistent with a non‐convecting layer above a deep dynamo in Mercury's fluid outer core.

Germanium core-level shifts at Ge/GeO2interfaces through hybrid functionals

The Ge core-level shift across the Ge/GeO${}_{2}$ interface is determined within semilocal and hybrid density functional schemes. We first assess the accuracy achieved within these theoretical frameworks by comparing calculated and measured core-level shifts for a set of Ge-based molecules. The comparison with experimental data results in rms deviations of 0.19 and 0.09 eV for core-level shifts calculated with semilocal and hybrid density functionals, respectively. We also compare calculated core-level shifts at the Ge(001)-$c(4\ifmmode\times\else\texttimes\fi{}2)$ surface with high-resolution x-ray photoemission spectra finding similar agreement. We then turn to the Ge/GeO${}_{2}$ interface, which we describe with atomistic superlattice models showing alternating layers of Ge and GeO${}_{2}$. The adopted models include a substoichiometric transition region in which all Ge atoms are fourfold coordinated and all O atoms are twofold coordinated, as inferred for Si/SiO${}_{2}$ interfaces. Since the calculation of core-level shifts involves charged systems subject to finite-size effects, we use two different methods to ascertain the core-level shift $\ensuremath{\Delta}{E}_{\mathrm{XPS}}$ between the oxidation state Ge${}^{0}$ and Ge${}^{+4}$ across the interface. In the first method, core-hole relaxations are first evaluated in bulk models of the interface components and then complemented by the initial-state shift calculated across the interface, while the second method consists of direct interface calculations corrected through classical electrostatics. Using the more accurate hybrid functional scheme, we obtain a shift $\ensuremath{\Delta}{E}_{\mathrm{XPS}}$ of $2.7\ifmmode\pm\else\textpm\fi{}0.1$ eV. This value is significantly lower than experimental data, which typically fall around 3.3 eV or higher, but the underestimation is consistent with that found for the valence band offset of the same model. This leads to the conclusion that the adopted model structures yield an incorrect description of the interface dipole and emphasizes that Ge/GeO${}_{2}$ interfaces possess different structural properties than their silicon counterparts.

Neutrino production of single pions: Dipole description

The light-cone distribution amplitudes for the axial current are derived within the instanton vacuum model (IVM), which incorporates nonperturbative effects including spontaneous chiral symmetry breaking. This allows to extend applicability of the dipole approach, usually used in the perturbative domain, down to $Q^{2}\to0$, where partially conserved axial current (PCAC) imposes a relation between the neutrino-production cross section and the one induced by pions. A dramatic breakdown of the Adler relation (AR) for diffractive neutrino-production of pions, caused by absorptive corrections, was revealed recently in arXiv:1105.1711. Indeed, comparing with the cross section predicted by the dipole phenomenology at $Q^{2}\to0$ on a proton target we confirmed the sizable deviation from the value given by the AR, as was estimated in arXiv:1105.1711 within a simplified two-channel model. The dipole approach also confirms that in the black-disc limit, where the absorptive corrections maximize, the diffractive cross section ceases, on the contrary to the expectation based on PCAC.

Nuclear suppression of : From RHIC to the LHC

A parameter-free calculation for J/Psi suppression in pA collisions, based on the dipole description, is confronted with the new data from the PHENIX experiment. Achieving good agreement, we employed this model predicting the contribution of initial state interactions (ISI) to J/Psi suppression in AA collisions. Such a transition from pA to AA is not straightforward, since involves specific effects of double color filtering and boosting of the saturation scale. Relying on this refined ISI contribution, we updated the previous analysis of RHIC data on J/Psi production in Cu-Cu and Au-Au collisions at \sqrt{s}=200 GeV, and determined the transport coefficient of the created dense medium at q_0=0.6 GeV^2/fm. Nuclear effects for J/Psi production at the LHC are predicted using the transport coefficient q_0=0.8 GeV^2/fm, extracted from data on suppression of high-p_T hadrons in central lead-lead collisions at \sqrt{s}=2.76 TeV. Our analysis covers only direct J/Psi production, while data may also include the feed-down from decay of heavier states and B-mesons.

Line stress of step edges at crystal surfaces

Step edges at crystal surfaces interact elastically with the underlying bulk solid. The resulting attraction or repulsion between neighboring steps is well described by an established dipole model. Here, we focus on the average stress which a step edge generates in the bulk. This quantity represents an excess of surface stress due to the presence of the step. Within the standard dipole description of the stress field of steps, that excess is zero. Yet, atomistic simulation testifies to a significant variation in the apparent surface stress of vicinal surfaces with the number density of steps. We show how a line stress can be defined as an excess in surface stress per line length. The definition is analogous to that of line tension as an excess of surface tension. Even though the step edge may be viewed as a one-dimensional object, we show that the line stress cannot be represented by a vector along the line; it is also not adequately represented by dipole forces. The line stresses give rise to cusps, typically upward, in polar plots of the principal values of the surface stress tensor in the surface orientation domain. We present a continuum model that links the directionality and magnitude of the line stress to the surface stress at the inclined step face.

Electrostatic interactions in ionic liquids: the dangers of dipole and dielectric descriptions

Ionic liquids have attracted a great deal of attention as media for chemical processes, but many fundamental questions about their behavior remain unanswered. Their electrostatic character remains particularly mysterious, and a number of theoretical studies have attempted to address it using various models. These models often make use of a dipolar description of the charge distribution of an ion, or the dielectric continuum model for the medium. In this work, we review these approaches and show that their application to ionic liquids is questionable on fundamental physical grounds. While not formally incorrect, the descriptions are prone to certain conceptual or numerical errors when applied to molecular ionic systems. We highlight these problems, and discuss some alternative approaches currently in the literature.