Divergent Parts Research Articles

Non-relativistic limits of bosonic and heterotic Double Field Theory

The known stringy non-relativistic (NR) limit of the universal NS-NS sector of supergravity has a finite Lagrangian due to non-trivial cancellations of divergent parts coming from the metric and the B-field. We demonstrate that in Double Field Theory (DFT) and generalised geometry these cancellations already happen at the level of the generalised metric, which is convergent in the limit c → ∞, implying that the NR limit can be imposed before solving the strong constraint. We present the c-expansion of the generalised metric, which reproduces the Non-Riemannian formulation of DFT at the (finite) leading order, and the c-expansion of the generalised frame, which contains divergences. We also extend this approach to the non-Abelian gauge field of Heterotic DFT assuming a convergent expansion for the O(D, D + n) generalised metric. From this proposal, we derive a novel c-expansion for the bosonic part of the heterotic supergravity which is, by construction, compatible with O(D, D)-symmetry.

Decomposition of the Horizontal Wind Divergence Associated With the Rossby, Mixed Rossby‐Gravity, Inertia‐Gravity, and Kelvin Waves on the Sphere

AbstractThe paper presents a new method for the decomposition of the horizontal wind divergence among linear waves on the sphere: inertia‐gravity (IG), mixed Rossby‐gravity (MRG), Kelvin and Rossby waves. The work is motivated by the need to quantify the vertical velocity and momentum fluxes in the tropics where the distinction between the Rossby and gravity regime, present in the extratropics, becomes obliterated. The method leads to divergence power spectra as a function of latitude and pressure. The spectra follow the same power laws as the vertical kinetic energy spectra for different wave types. The key novel aspect of the work is the coexistence of wave types at the same zonal wavenumbers. Applied to ERA5 data in August 2018, the new method reveals that the zonally‐integrated Kelvin wave divergence makes up about 19% of the upper‐troposphere divergence within 10°S–10°N. The MRG wave divergence has four times smaller magnitude. The relative roles of the two waves vary with scale. Overall small roles of the Kelvin and MRG waves in the tropical divergence is explained by decomposing their kinetic energies into rotational and divergent parts. The beta effects produces less then 5% of the tropospheric divergence associated with Rossby waves. The majority of divergence belongs to IG modes and is nearly equipartitioned between the eastward‐ and westward‐propagating IG modes in the upper troposphere, whereas stratospheric partitioning depends on the background flow.

Hot Jupiter diversity and the onset of TiO/VO revealed by a large grid of non-grey global circulation models

ABSTRACT The population of hot Jupiters is extremely diverse, with large variations in their irradiation, period, gravity, and chemical composition. To understand the intrinsic planet diversity through the observed population level trends, we explore the a priori scatter in the population created by the different responses of atmospheric circulation to planetary parameters. We use the SPARC/MITgcm three-dimensional global circulation model to simulate 345 planets spanning a wide range of instellation, metallicity, gravity, and rotation periods typical for hot Jupiters, while differentiating between models with and without titanium oxide (TiO)/vanadium oxide (VO) in their atmosphere. We show that the combined effect of the planetary parameters leads to a large diversity in the ability of atmospheres to transport heat from day-side to night-side at a given equilibrium temperature. We further show that the hotspot offset is a non-monotonic function of planetary rotation period and explain our findings by a competition between the rotational and divergent parts of the circulation. As a consequence, hotspot offset and phase curve amplitude are not necessarily correlated. Finally, we compare the observables from our grid to the population of Spitzer and Hubble observations of hot Jupiters. We find that the sudden jump in brightness temperature observed in the Spitzer secondary eclipse measurements can be naturally explained by the cold-trapping of TiO/VO at approximately 1800 K. Spectra, phase curves and thermal structures from the model grid used in this study are available to the community, for more details see the data availability section.

CGDD: Multiview Graph Clustering via Cross-Graph Diversity Detection.

Multiview graph clustering has emerged as an important yet challenging technique due to the difficulty of exploiting the similarity relationships among multiple views. Typically, the similarity graph for each view learned by these methods is easily corrupted because of the unavoidable noise or diversity among views. To recover a clean graph, existing methods mainly focus on the diverse part within each graph yet overlook the diversity across multiple graphs. In this article, instead of merely considering the sparsity of diversity within a graph as previous methods do, we incline to a more suitable consideration that the diversity should be sparse across graphs. It is intuitive that the divergent parts are supposed to be inconsistent with each other, otherwise it would contradict the definition of diversity. By simultaneously and explicitly detecting the multiview consistency and cross-graph diversity, a pure graph for each view can be expected. The multiple pure graphs are further fused to the structured consensus graph with exactly r connected components where r is the number of clusters. Once the consensus graph is obtained, the cluster label to each instance can be directly allocated as each connected component precisely corresponds to an individual cluster. An alternating iterative algorithm is designed to optimize the subtasks of learning the similarity graphs adaptively, detecting the consistency as well as cross-graph diversity, fusing the multiple pure graphs, and assigning cluster label to each instance in a mutual reinforcement manner. Extensive experimental results on several benchmark multiview datasets demonstrate the effectiveness of our model, in comparison to several state-of-the-art algorithms.

The Role of Stratified Turbulence in the Cold Summer Mesopause Region

AbstractThe summer mesopause at middle and high latitudes is the coldest place on Earth, and atmospheric gravity waves are responsible for the emergence of this extreme thermal phenomenon. Although the main physical mechanism behind the latter is understood, a deeper insight into it can be gained from the investigation of the mesoscale energy spectrum. In this work, we decompose the frequency spectra into divergent and rotational parts and find that their energy contributions are equipartitioned at high frequencies. This mesoscale energy equipartition is a feature of stratified turbulence and illustrates the complexity of the mesoscale dynamics in the summer mesopause region. We also analyze the power spectra of observed and simulated mesoscale zonal and meridional winds at middle latitudes in the Southern Hemisphere and show that stratified turbulence plays a role in the mesopause region during summer.

Field-theoretic analysis of directed percolation: Three-loop approximation.

The directed bond percolation is a paradigmatic model in nonequilibrium statistical physics. It captures essential physical information on the nature of continuous phase transition between active and absorbing states. In this paper, we study this model by means of the field-theoretic formulation with a subsequent renormalization group analysis. We calculate all critical exponents needed for the quantitative description of the corresponding universality class to the third order in perturbation theory. Using dimensional regularization with minimal subtraction scheme, we carry out perturbative calculations in a formally small parameter ɛ, where ɛ=4-d is a deviation from the upper critical dimension d_{c}=4. We use a nontrivial combination of analytical and numerical tools in order to determine ultraviolet divergent parts of Feynman diagrams.

Systematic Part Transfer by Extending a Modular Toolkit to Diverse Bacteria.

It is impractical to develop a new parts collection for every potential host organism. It is well-established that gene expression parts, like genes, are qualitatively transferable, but there is little quantitative information defining transferability. Here, we systematically quantified the behavior of a parts set across multiple hosts. To do this, we developed a broad host range (BHR) plasmid system compatible with the large, modular CIDAR parts collection for E.coli, which we named openCIDAR. This enabled testing of a library of DNA constructs across the Pseudomonadota─Escherichia coli, Pseudomonas putida, Cupriavidus necator, and Komagataeibacter nataicola. Part performance was evaluated with a standardized characterization procedure that quantified expression in terms of molecules of equivalent fluorescein (MEFL), an objective unit of measure. The results showed that the CIDAR parts enable graded gene expression across all organisms─meaning that the same parts can be used to program E.coli, P.putida, C.necator, and K.nataicola. Most parts had a similar expression trend across hosts, although each organism had a different average gene expression level. The variability is enough that to achieve the same MEFL in a different organism, a lookup table is required to translate a design from one host to another. To identify truly divergent parts, we applied linear regression to a combinatorial set of promoters and ribosome binding sites, finding that the promoter J23100 behaves very differently in K.nataicola than in the other hosts. Thus, it is now possible to evaluate any CIDAR compatible part in three other hosts of interest, and the diversity of these hosts implies that the collection will also be compatible with many other Proteobacteria (Pseudomonadota). Furthermore, this work defines an approach to generalize modular synthetic biology parts sets beyond a single host, implying that only a few parts sets may be needed to span the tree of life. This will accelerate current efforts to engineer diverse species for environmental, biotechnological, and health applications.

Single inclusive hadron production in DIS at small x: next to leading order corrections

We calculate the one-loop corrections to single inclusive hadron production in Deep Inelastic Scattering (DIS) at small x in the forward rapidity region using the Color Glass Condensate formalism. We show that the divergent parts of the next to leading order (NLO) corrections either cancel among each other or lead to x (rapidity) evolution of the leading order (LO) dipole cross section according to the JIMWLK evolution equation and DGLAP evolution of the parton-hadron fragmentation function. The remaining finite parts constitute the NLO (αs) corrections to the LO single inclusive hadron production cross section in DIS at small x.

Scalar and vector one-loop massive tadpole light-front gauge Feynman integrals

Light-front gauge is the most popular one to work with fundamental interactions, due to its characteristic maximum kinematical Poincare operators that it allows. However, it is also known to be one of the trickiest gauges one can work with for gauge theories, due to its singular nature. So, in terms of perturbative calculations in the light-front, there are only a few published and tabulated results for the pertinent Feynman integrals, mostly involving massless integrals. And the majority of the results given are only for the divergent parts of them and the complete closed form (or with the finite parts) of these are not known. In this paper, we use the technique of negative dimensional integration for the simplest of the one-loop massive integrals as a working bench for massive Feynman integrals in the light front and show that novel results for the finite parts not known before are obtained.

Advances towards the systematization of calculations with Implicit Regularization

There is currently a high demand for theoretical predictions for processes at next-to-next-to-leading order (NNLO) and beyond, mainly due to the large amount of data which has already been collected at LHC. This requires practical methods that meet the physical requirements of the models under study. We develop a new procedure for applying Constrained Implicit Regularization which simplifies the calculation of amplitudes, including finite parts. The algebraic identities to separate the divergent parts free from the external momenta are used after the Feynman parametrization. These algebraic identities establish a set of scale relations which are always the same and do not need to be calculated in each situation. This procedure unifies the calculations in massive and non-massive models in an unique procedure. We establish a systematization of the calculation of one-loop amplitudes and extend the procedure for higher-loop orders.

One-loop calculations in CPT-even Lorentz-breaking scalar QED

In this paper, we study a CPT-even Lorentz-breaking extension of the scalar QED. For this theory, we calculate the one-loop lower-order contributions in the Lorentz-violating parameters to the two-point functions of scalar and gauge fields. We found that the two background tensors, coming from the two sectors (scalar and gauge) are mixed in the one-loop corrections both in finite and divergent parts. This shows that these two Lorentz-breaking terms cannot be studied in an isolated form. Besides, the results in the gauge sector are confirmed to be transversal.

Scalar one-loop four-point integral with one massless vertex in loop regularization

The scalar one-loop four-point function with one massless vertex is evaluated analytically by employing the loop regularization method. According to the method, a characteristic scale μ s is introduced to regularize the divergent integrals. The infrared divergent parts, which take the form of and as μ s → 0 where λ is a constant and expressed in terms of masses and Mandelstam variables, and the infrared stable parts are well separated. The result is shown explicitly via 44 dilogarithms in the kinematic sector in which our evaluation is valid.

Finite and divergent parts of the self-force of a point charge from its spherically averaged self-field

The electromagnetic self-force of a point charge moving arbitrarily on a rectilinear trajectory is calculated by averaging its retarded electric self-field over a sphere of infinitesimal radius centred on the charge's present position. The finite part of the self-force obtained is the well-established relativistic radiation reaction, while its divergent part implies the pre-relativistic longitudinal electromagnetic mass of Abraham.

Modern methods of calculations of bremsstrahlung in the interaction of elementary particles

. The problem of real bremsstrahlung calculation is considered using the modern methods of regularization of divergencies. In particular, we calculate soft photon bremsstrahlung in the most general form using the method of dimensional regularization of infrared divergences. The general calculation algorithm of hard photon bremsstrahlung is described. It is shown that the contribution of hard bremsstrahlung can be separated into the finite and divergent parts. The divergent part can be factorized with the contribution of the initial process in the Born approximation. It is shown that a good choice of kinematic variables makes an analytic covariant calculation of the divergent part of the hard bremsstrahlung possible. In a particular case, an algorithm for determining the kinematic constraints on the invariants is described. A numerical analysis of the radiative corrections for gauge bosons production processes in the case of electron-photon collisions is performed. It is discovered that the contribution of the finite part of bremsstrahlung at high collision energies reaches 20 per cent and must be taken into account in calculations of radiative corrections. The results obtained can be used in various calculations, including covariant ones, performed in the context of confirmation of the Standard Model theoretical predictions or searching for manifestations of alternative gauge models.

An overview on isotopic divergences – causes for instability of tree-ring isotopes and climate correlations

Abstract. Climatic reconstructions based on tree-ring isotopic series convey substantial information about past conditions prevailing in forested regions of the globe. However, in some cases, the relations between isotopic and climatic records appear unstable over time, generating the “isotopic divergences”. Former reviews have thoroughly discussed the divergence concept for tree-ring physical properties but not for isotopes. Here we want to take stock of the isotopic divergence problem, express concerns and stimulate collaborative work for improving paleoclimatic reconstructions. There are five main causes for divergent parts in isotopic and climatic series: (1) artefacts due to sampling and data treatment, relevant for dealing with long series using sub-fossil stems; (2) stand dynamics, including juvenile effects mostly occurring in the early part of tree-ring series; (3) rise in atmospheric pCO2, which can directly influence the foliar behaviour; (4) change in climate, which may modify the isotope–climate causal links; and finally (5) atmospheric pollution, which may alter leaf and root functions. Future paleoclimate research would benefit from interdisciplinary efforts designed to develop further process-based models integrating multi-proxy inputs so as to help identify causes of isotopic divergences and circumvent some of them in inverse applications.

Non-compact duality, super-Weyl invariance and effective actions

In both mathcal{N} = 1 and mathcal{N} = 2 supersymmetry, it is known that Sp(2n, ℝ) is the maximal duality group of n vector multiplets coupled to chiral scalar multiplets τ(x, θ) that parametrise the Hermitian symmetric space Sp(2n, ℝ)/U(n). If the coupling to τ is introduced for n superconformal gauge multiplets in a supergravity background, the action is also invariant under super-Weyl transformations. Computing the path integral over the gauge prepotentials in curved superspace leads to an effective action Γ[τ, overline{tau} ] with the following properties: (i) its logarithmically divergent part is invariant under super-Weyl and rigid Sp(2n, ℝ) transformations; (ii) the super-Weyl transformations are anomalous upon renormalisation. In this paper we describe the mathcal{N} = 1 and mathcal{N} = 2 locally supersymmetric “induced actions” which determine the logarithmically divergent parts of the corresponding effective actions. In the mathcal{N} = 1 case, superfield heat kernel techniques are used to compute the induced action of a single vector multiplet (n = 1) coupled to a chiral dilaton-axion multiplet. We also describe the general structure of mathcal{N} = 1 super-Weyl anomalies that contain weight-zero chiral scalar multiplets ΦI taking values in a Kähler manifold. Explicit anomaly calculations are carried out in the n = 1 case.

Schwinger production of scalar particles during and after inflation from the first principles

By using the first-principles approach, we derive a system of three quantum kinetic equations governing the production and evolution of charged scalar particles by an electric field in an expanding universe. Analyzing the ultraviolet asymptotic behavior of the kinetic functions, we found the divergent parts of the electric current and the energy-momentum tensor of the produced particles and determined the corresponding counterterms. The renormalized system of equations is used to study the generation of electromagnetic fields during and after inflation in the kinetic coupling model $\mathcal{L}_{\rm EM}=-(1/4)f^{2}(\phi)F_{\mu\nu}F^{\mu\nu}$ with the Ratra coupling function $f=\exp(\beta\phi/M_{p})$. It is found that the electric current of created particles is retarded with respect to the electric field. This leads to an oscillatory behavior of both quantities in agreement with the results obtained previously in phenomenological kinetic and hydrodynamical approaches.

FeynCalc 9.3: New features and improvements

We present FeynCalc 9.3, a new stable version of a powerful and versatile Mathematica package for symbolic quantum field theory (QFT) calculations. Some interesting new features such as highly improved interoperability with other packages, automatic extraction of the ultraviolet divergent parts of 1-loop integrals, support for amplitudes with Majorana fermions and γ-matrices with explicit Dirac indices are explained in detail. Furthermore, we discuss some common problems and misunderstandings that may arise in the daily usage of the package, providing explanations and workarounds. Program summaryProgram Title: FeynCalcCPC Library link to program files:http://dx.doi.org/10.17632/cmpjr5ktmp.2Licensing provisions: GNU GPLv3Programming language: Wolfram Mathematica 8 and higherExternal routines/libraries: FeynArts [1]Journal reference of previous version: Comput. Phys. Commun., 207, 432–444, (2016).Does the new version supersede the previous version?: YesNature of problem: Symbolic calculation of Feynman diagrams in particle physics and suitable standalone expressions in Quantum Field Theory.Solution method: The required algorithms and algebraic identities are implemented in Wolfram Mathematica.Reasons for the new version: Highly improved interoperability with other packages, new routines for Dirac algebra and loop integral evaluation.Summary of revisions:FeynCalc can be loaded with arbitrary packages into the same Mathematica kernel without causing shadowing issues. Algebraic manipulations of Dirac matrices and spinors with explicit Dirac indices are now available. Amplitudes involving Majorana fermions (both written by hand or obtained with FeynArts [1] can be evaluated out-of-the box. The same goes for FeynArts-generated diagrams with 4-fermion operators. The algorithm of [2] is added to extract UV-poles from scalar 1-loop integrals (Passarino–Veltman functions) with an arbitrary number of external legs.Restrictions: In the case of multi-particle (beyond 1→3 and 2→3) or multiloop processes, it is not advisable to perform all algebraic evaluations only with FeynCalc and Mathematica.

Design and optimization of plasma jet nozzles based on computational fluid dynamics

This study aims at identifying an optimal solution for the design of convergent-divergent nozzles discharging high-temperature plasma jets. Optimized profile parameters (e.g. throat size, depths of convergent and divergent parts) were developed to enhance the processing capability of the inductively coupled plasma torch. The temperature and velocity of the plasma jet are studied both along the axis of the nozzle and onto the impinged substrate surface. Computational fluid dynamics analysis of 55 models with different cross-sectional profiles highlights cases that can be used to enhance plasma figuring processes. The enhanced nozzles are compared with the benchmark nozzle in all selection criteria. This optimization approach is proven to provide an efficient design method of plasma nozzles for future processing activities. The rapid design and optimization of the nozzle are expected to adjust the material removal footprint of plasma process in metre-scale optical fabrication. Experimental results prove that the enhanced nozzle has 5% higher efficiency against the original one.

Effective resolution in high resolution global atmospheric models for climate studies

AbstractWe estimate the extent of spatial scales that atmospheric models in a new generation of global climate models, used in the Coupled Model Intercomparison Project 6, are able to resolve on the basis of kinetic energy spectra, commonly referred to as the effective resolution. We examine the spectra derived from the rotational and divergent parts of the wind for six state‐of‐the‐art global climate models that have been run with at least two horizontal resolutions. For each of the high resolution configurations, the effective resolution enhancement is less than proportional to the increase of the nominal resolution. The highest effective resolution obtained by the models in this study is roughly 200 km. This shows that the newest generation of high resolution climate models starts to resolve synoptic scales relevant for the dynamics of weather events.