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Journal articles on the topic 'Perturbative computations'

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Published: 9 March 2023

Last updated: 10 March 2023

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1

Shindler, Andrea. "Gradient Flow: Perturbative and Non-Perturbative Renormalization." EPJ Web of Conferences 274 (2022): 01005. http://dx.doi.org/10.1051/epjconf/202227401005.

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We review the gradient flow for gauge and fermion fields and its applications to lattice gauge theory computations. Using specific examples, we discuss the interplay between perturbative and non-perturbative calculations in the context of renormalization with the gradient flow.

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2

Debbio, Luigi Del, Francesco Di Renzo, and Gianluca Filaci. "High-order perturbative expansions in massless gauge theories with NSPT." EPJ Web of Conferences 175 (2018): 11023. http://dx.doi.org/10.1051/epjconf/201817511023.

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We investigate the possibility of using numerical stochastic perturbation theory (NSPT) to probe high orders in the perturbative expansion of lattice gauge theories with massless Wilson fermions. Twisted boundary conditions are used to regularise the gauge zero-mode; the extension of these boundary conditions to include fermions in the fundamental representation requires to introduce a smell degree of freedom. Moreover, the mass of Wilson fermions is affected by an additive renormalisation: we study how to determine the mass counterterms consistently in finite volume. The knowledge of the critical masses will enable high-order perturbative computations in massless QCD, e.g. (as a first application) for the plaquette.

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3

Lüscher, M., and P. Weisz. "Efficient numerical techniques for perturbative lattice gauge theory computations." Nuclear Physics B 266, no. 2 (March 1986): 309–56. http://dx.doi.org/10.1016/0550-3213(86)90094-5.

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4

Bern, Z. "Perturbative gravity from gauge theory." Modern Physics Letters A 29, no. 32 (October 20, 2014): 1430036. http://dx.doi.org/10.1142/s0217732314300365.

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Here, we describe a recently conjectured duality between color and kinematics for gauge-theory amplitudes. Whenever this duality is manifest, the integrands of loop-level gravity scattering amplitudes can be obtained from corresponding gauge-theory amplitudes via a double-copy relation. This duality has been used to enormously simplify a number of explicit multiloop supergravity calculations. The results of these computations is that supergravity theories have a surprisingly tame ultraviolet behavior, and in some cases may even be finite. As an example, we summarize a recent calculation showing that half-maximal [Formula: see text] supergravity in four spacetime dimensions is ultraviolet finite at three loops, contrary to previous expectations.

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5

DEMETERFI, KRESIMIR, ANTAL JEVICKI, and JOĀO P. RODRIGUES. "PERTURBATIVE RESULTS OF COLLECTIVE STRING FIELD THEORY." Modern Physics Letters A 06, no. 35 (November 20, 1991): 3199–212. http://dx.doi.org/10.1142/s0217732391003699.

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We present a summary of perturbative results obtained in the framework of collective string field theory. We discuss computations of tree-level scattering amplitudes, loop corrections to tachyon self-energy, ground state energy and finite temperature free energy. A comparison with results obtained in different approaches is given. We also discuss the physical implications of our results.

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6

Reyes, Edilson, and Raffaele Fazio. "High-Precision Calculations of the Higgs Boson Mass." Particles 5, no. 1 (February 17, 2022): 53–73. http://dx.doi.org/10.3390/particles5010006.

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In this paper, we review the status of the computations of the perturbative quantum corrections to the Higgs boson mass in the Standard Model and in its supersymmetric extensions. In particular, supersymmetric theories require a very accurate computation of the Higgs boson mass, which includes corrections even up to the three-loop level, since their predictions are limited by theoretical uncertainties. A discussion about these uncertainties in the context of the Minimal and Next To Minimal Supersymmetric Standard Model is included.

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7

MANIN, YURI I. "Renormalisation and computation II: time cut-off and the Halting Problem." Mathematical Structures in Computer Science 22, no. 5 (September 6, 2012): 729–51. http://dx.doi.org/10.1017/s0960129511000508.

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This is the second instalment in the project initiated in Manin (2012). In the first Part, we argued that both the philosophy and technique of perturbative renormalisation in quantum field theory could be meaningfully transplanted to the theory of computation, and sketched several contexts supporting this view.In this second part, we address some of the issues raised in Manin (2012) and develop them further in three contexts: a categorification of the algorithmic computations; time cut-off and anytime algorithms; and, finally, a Hopf algebra renormalisation of the Halting Problem.

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8

SURGULADZE, LEVAN R. "COMPUTER PROGRAMS FOR ANALYTICAL PERTURBATIVE CALCULATIONS IN HIGH ENERGY PHYSICS." International Journal of Modern Physics C 05, no. 06 (December 1994): 1089–101. http://dx.doi.org/10.1142/s0129183194001161.

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A short review of the present status of computer packages for the high order analytical perturbative calculations is presented. The mathematical algorithm and the quantum field theory methods used are briefly discussed. The most recent computer package HEPLoops for analytical computations in high energy physics up to four-loops is also discussed.

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9

Karanikas, A. I., and C. N. Ktorides. "Polyakov's spin factor and new algorithms for efficient perturbative computations in QCD." Physics Letters B 500, no. 1-2 (February 2001): 75–86. http://dx.doi.org/10.1016/s0370-2693(01)00062-4.

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10

Creedon, Ryan, Bernard Deconinck, and Olga Trichtchenko. "High-Frequency Instabilities of a Boussinesq–Whitham System: A Perturbative Approach." Fluids 6, no. 4 (April 1, 2021): 136. http://dx.doi.org/10.3390/fluids6040136.

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We analyze the spectral stability of small-amplitude, periodic, traveling-wave solutions of a Boussinesq–Whitham system. These solutions are shown numerically to exhibit high-frequency instabilities when subject to bounded perturbations on the real line. We use a formal perturbation method to estimate the asymptotic behavior of these instabilities in the small-amplitude regime. We compare these asymptotic results with direct numerical computations.

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11

Krmar, Marija, and Miljenko Peric. "Interplay between vibronic and spin-orbit couplings in 3П states of triatomic molecules using as an example the A3Пu electronic state of NCN." Journal of the Serbian Chemical Society 66, no. 9 (2001): 613–30. http://dx.doi.org/10.2298/jsc0109613k.

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A systematic study of various effects on the structure of the spectra of linear triatomic molecules in the 3P electronic states has been carried out. Paricular attention was paid to the interplay between the vibronic and spin-orbit couplings. Variational and perturbative computations at various levels of sophistication were performed for the A3Pu state of the NCN radical.

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12

Lin, Ying-Tsong. "Higher-order perturbative parabolic-equation solutions for reduced-order sound propagation modeling." Journal of the Acoustical Society of America 152, no. 4 (October 2022): A156. http://dx.doi.org/10.1121/10.0015871.

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The parabolic-equation (PE) approximation to the Helmholtz equation has been shown to be one of the most effective and efficient numerical methods for sound propagation modeling. In this talk, a recursive and iterative algorithm will be introduced to compute the PE solutions due to perturbations in the medium wavenumber, which is a function of frequency and sound speed. This algorithm is developed based on perturbation theory with higher-order nonlinear terms, and it can efficiently compute higher-order derivatives of the sound pressure field with respect to changes in the local wavenumber. This higher-order perturbative PE (HOPPE) method can eventually lead to model order reduction for sound propagation simulations. An example of broadband computations with nonlinear interpolations between sampled frequencies will be presented to demonstrate the application of reduced-order modeling. A sensitivity kernel with higher-order nonlinear terms will also be introduced. Applications to data assimilation modeling and sensitivity tracking will be discussed. [Work supported by the Office of Naval Research.]

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13

Jeszenszki, Péter, Dávid Ferenc, and Edit Mátyus. "Variational Dirac–Coulomb explicitly correlated computations for atoms and molecules." Journal of Chemical Physics 156, no. 8 (February 28, 2022): 084111. http://dx.doi.org/10.1063/5.0075096.

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The Dirac–Coulomb equation with positive-energy projection is solved using explicitly correlated Gaussian functions. The algorithm and computational procedure aims for a parts-per-billion convergence of the energy to provide a starting point for further comparison and further developments in relation with high-resolution atomic and molecular spectroscopy. Besides a detailed discussion of the implementation of the fundamental spinor structure, permutation, and point-group symmetries, various options for the positive-energy projection procedure are presented. The no-pair Dirac–Coulomb energy converged to a parts-per-billion precision is compared with perturbative results for atomic and molecular systems with small nuclear charge numbers. Paper II [D. Ferenc, P. Jeszenszki, and E. Mátyus, J. Chem. Phys. 156, 084110 (2022).] describes the implementation of the Breit interaction in this framework.

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14

Parisi, Giorgio. "Scientific and personal recollections of Roberto Petronzio." EPJ Web of Conferences 175 (2018): 01001. http://dx.doi.org/10.1051/epjconf/201817501001.

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This paper aims to recall some of the main contributions of Roberto Petronzio to physics, with a particular regard to the period we have been working together. His seminal contributions cover an extremely wide range of topics: the foundation of the perturbative approach to QCD, various aspects of weak interaction theory, from basic questions (e.g. the mass of the Higgs) to lattice weak interaction, lattice QCD from the beginning to most recent computations.

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15

BJERRUM-BOHR, N. E. J., and PIERRE VANHOVE. "SURPRISING SIMPLICITY OF $\mathcal{N}=8$ SUPERGRAVITY." International Journal of Modern Physics D 18, no. 14 (December 31, 2009): 2295–301. http://dx.doi.org/10.1142/s0218271809015874.

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Gravity amplitudes are, via the Kawai–Lewellen–Tye relations intimately linked to products of Yang–Mills amplitudes. Explicitly, this shows up in computations of [Formula: see text] supergravity where the perturbative expansion and ultraviolet behavior of this theory is akin to [Formula: see text] super-Yang–Mills at least through three loops. Full persistence to all loop orders would be truly remarkable and imply finiteness of [Formula: see text] supergravity in four dimensions.

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16

Gracey, J. A. "Large Nf quantum field theory." International Journal of Modern Physics A 33, no. 35 (December 20, 2018): 1830032. http://dx.doi.org/10.1142/s0217751x18300326.

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We review the development of the large [Formula: see text] method, where [Formula: see text] indicates the number of flavours, used to study perturbative and nonperturbative properties of quantum field theories. The relevant historical background is summarized as a prelude to the introduction of the large [Formula: see text] critical point formalism. This is used to compute large [Formula: see text] corrections to [Formula: see text]-dimensional critical exponents of the universal quantum field theory present at the Wilson–Fisher fixed point. While pedagogical in part the application to gauge theories is also covered and the use of the large [Formula: see text] method to complement explicit high order perturbative computations in gauge theories is also highlighted. The usefulness of the technique in relation to other methods currently used to study quantum field theories in [Formula: see text]-dimensions is also summarized.

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17

MAMEDOVA, YEGANA V. "INFRARED RENORMALON EFFECTS ON LIGHT MESONS ELECTROMAGNETIC TRANSITION FORM FACTOR FMγ*(Q2, ω)." International Journal of Modern Physics A 18, no. 07 (March 20, 2003): 1023–50. http://dx.doi.org/10.1142/s0217751x03013806.

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The light pseudoscalar π0, η and η′ mesons electromagnetic transition γ* + γ* → M form factors FMγ*(Q2,ω) are calculated, applying the perturbative QCD factorization formula and the frozen coupling constant approximation. In the computations the O(αS) order expression for FMγ*(Q2,ω) and the mesons' infrared renormalon corrected distribution amplitudes are used. In the case of the η and η′ mesons, the SUf(3) ordinary octet-singlet mixing scheme is utilized. Comparisons are made with the results obtained, employing the mesons' ordinary distribution amplitudes and with γ + γ* → M transition form factors.

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18

Arsie, Alessandro, Paolo Lorenzoni, and Antonio Moro. "On integrable conservation laws." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 471, no. 2173 (January 2015): 20140124. http://dx.doi.org/10.1098/rspa.2014.0124.

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We study normal forms of scalar integrable dispersive (not necessarily Hamiltonian) conservation laws, via the Dubrovin–Zhang perturbative scheme. Our computations support the conjecture that such normal forms are parametrized by infinitely many arbitrary functions that can be identified with the coefficients of the quasi-linear part of the equation. Moreover, in general, we conjecture that two scalar integrable evolutionary partial differential equations having the same quasi-linear part are Miura equivalent. This conjecture is also consistent with the tensorial behaviour of these coefficients under general Miura transformations.

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19

Heitger, Jochen, Fabian Joswig, Anastassios Vladikas, and Christian Wittemeier. "Non-perturbative determination of cV, ZV and ZS/ZP in Nf = 3 lattice QCD." EPJ Web of Conferences 175 (2018): 10004. http://dx.doi.org/10.1051/epjconf/201817510004.

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We report on non-perturbative computations of the improvement coefficient cV and the renormalization factor ZV of the vector current in three-flavour O(a) improved lattice QCD with Wilson quarks and tree-level Symanzik improved gauge action. To reduce finite quark mass effects, our improvement and normalization conditions exploit massive chiral Ward identities formulated in the Schrödinger functional setup, which also allow deriving a new method to extract the ratio ZS/ZP of scalar to pseudoscalar renormalization constants. We present preliminary results of a numerical evaluation of ZV and cV along a line of constant physics with gauge couplings corresponding to lattice spacings of about 0:09 fm and below, relevant for phenomenological applications.

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20

Grats, Yuri V., and Pavel Spirin. "Vacuum Polarization in a Zero-Width Potential: Self-Adjoint Extension." Universe 7, no. 5 (May 2, 2021): 127. http://dx.doi.org/10.3390/universe7050127.

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The effects of vacuum polarization associated with a massless scalar field near pointlike source with a zero-range potential in three spatial dimensions are analyzed. The “physical” approach consists in the usage of direct delta-potential as a model of pointlike interaction. We use the Perturbation theory in the Fourier space with dimensional regularization of the momentum integrals. In the weak-field approximation, we compute the effects of interest. The “mathematical” approach implies the self-adjoint extension technique. In the Quantum-Field-Theory framework we consider the massless scalar field in a 3-dimensional Euclidean space with an extracted point. With appropriate boundary conditions it is considered an adequate mathematical model for the description of a pointlike source. We compute the renormalized vacuum expectation value ⟨ϕ2(x)⟩ren of the field square and the renormalized vacuum averaged of the scalar-field’s energy-momentum tensor ⟨Tμν(x)⟩ren. For the physical interpretation of the extension parameter we compare these results with those of perturbative computations. In addition, we present some general formulae for vacuum polarization effects at large distances in the presence of an abstract weak potential with finite-sized compact support.

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21

Fraidenraich, A., P. M. Jacovkis, and F. R. de A. Lima. "Sensitivity computations using first and second orders perturbative methods for the advection-diffusion-reaction model of pollutant transport." Journal of the Brazilian Society of Mechanical Sciences and Engineering 25, no. 1 (March 2003): 23–29. http://dx.doi.org/10.1590/s1678-58782003000100004.

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22

Kurtadikar, M. L., and S. C. Mehrotra. "Collision-Induced Rotational Excitations of Interstellar Molecules due to He and H2." Symposium - International Astronomical Union 120 (1987): 47–48. http://dx.doi.org/10.1017/s007418090015377x.

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An Effective Straight-line Trajectory (EST) approach by introducing a parameter RX has been proposed for computations of collision-induced rotational line widths (HWHM) and excitation rates in case of atom-molecule systems under the frame work of Smith, Giraud and Cooper (1976) and molecule-molecule systems under the frame work of normalized semi-classical perturbative approach. An optimised parameter RX, which is a measure of significance of the curved trajectories of the colliding molecules, can be determined from the temperature dependence of collision-induced line widths. the EST approach has been tested for HCl-Ar system and further applied to X-He and X-H2 systems of interstellar interest, where X represents interstellar molecules CO, OCS and HCN. The results are given in Table I and II.

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23

BERAKDAR, J. "SCATTERING PATH FORMALISM FOR THE PROPAGATION OF INTERACTING COMPOUNDS IN ORDERED AND DISORDERED MATERIALS." Surface Review and Letters 07, no. 03 (June 2000): 205–10. http://dx.doi.org/10.1142/s0218625x00000257.

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This study presents a theoretical framework for the propagation of a compound consisting of N interacting particles in a multicenter potential. A novel Green operator approach is proposed that disentangles the geometrical and dynamical properties of the scatterers from the internal evolution of the projectile compound. Furthermore, the transition operator for the scattering from the multicenter potential is expanded in terms of many-body scattering path operators, which in turn are expressed in terms of single site transition operators that are amenable to computations. To deduce the correlated many-body Green operator of the scattering compound, a cumulative method is designed that reduces the problem to the evaluation of Green operators of systems with a reduced number of interacting particles. This is particularly useful for efficient calculations and encompasses the usual perturbative approaches.

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24

Lahoche, Vincent, Dine Ousmane Samary, and Mohamed Tamaazousti. "Generalized scale behavior and renormalization group for data analysis." Journal of Statistical Mechanics: Theory and Experiment 2022, no. 3 (March 1, 2022): 033101. http://dx.doi.org/10.1088/1742-5468/ac52a6.

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Abstract Some recent results showed that the renormalization group (RG) can be considered as a promising framework to address open issues in data analysis. In this work, we focus on one of these aspects, closely related to principal component analysis (PCA) for the case of large dimensional data sets with covariance having a nearly continuous spectrum. In this case, the distinction between ‘noise-like’ and ‘non-noise’ modes becomes arbitrary and an open challenge for standard methods. Observing that both RG and PCA search for simplification for systems involving many degrees of freedom, we aim to use the RG argument to clarify the turning point between noise and information modes. The analogy between coarse-graining renormalization and PCA has been investigated in Bradde and Bialek (2017 J. Stat. Phys. 167 462–75), from a perturbative framework, and the implementation with real sets of data by the same authors showed that the procedure may reflect more than a simple formal analogy. In particular, the separation of sampling noise modes may be controlled by a non-Gaussian fixed point, reminiscent of the behaviour of critical systems. In our analysis, we go beyond the perturbative framework using nonperturbative techniques to investigate non-Gaussian fixed points and propose a deeper formalism allowing us to go beyond power-law assumptions for explicit computations.

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25

Noriega, Hernán E., Alejandro Aviles, Sebastien Fromenteau, and Mariana Vargas-Magaña. "Fast computation of non-linear power spectrum in cosmologies with massive neutrinos." Journal of Cosmology and Astroparticle Physics 2022, no. 11 (November 1, 2022): 038. http://dx.doi.org/10.1088/1475-7516/2022/11/038.

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Abstract We compute 1-loop corrections to the redshift space galaxy power spectrum in cosmologies containing additional scales, and hence kernels different from Einstein-de Sitter (EdS). Specifically, our method is tailored for cosmologies in the presence of massive neutrinos and some modified gravity models; in this article we concentrate on the former case. The perturbative kernels have contributions that we notice appear either from the logarithmic growth rate f(k,t), which is scale-dependent because of the neutrino free-streaming, or from the failure of the commonly used approximation f 2 = Ω m . The latter contributions make the computation of loop corrections quite slow, precluding full-shape analyses for parameter estimation. However, we identify that the dominant pieces of the kernels come from the growth factor, allowing us to simplify the kernels but retaining the characteristic free-streaming scale introduced by the neutrinos' mass. Moreover, with this simplification one can exploit FFTLog methods to speed up the computations even more. We validate our analytical modeling and numerical method with halo catalogs extracted from the Quijote simulations finding good agreement with the, a priori, known cosmological parameters. We make public our Python code FOLPSν to compute the redshift space power spectrum in a fraction of second. Code available at https://github.com/henoriega/FOLPS-nu.

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Kevrekidis, P. G., R. Carretero-González, and D. J. Frantzeskakis. "Stability of single and multiple matter-wave dark solitons in collisionally inhomogeneous Bose–Einstein condensates." International Journal of Modern Physics B 31, no. 10 (April 20, 2017): 1742013. http://dx.doi.org/10.1142/s0217979217420139.

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We examine the spectral properties of single and multiple matter-wave dark solitons in Bose–Einstein condensates confined in parabolic traps, where the scattering length is periodically modulated. In addition to the large density limit picture previously established for homogeneous nonlinearities, we explore a perturbative analysis in the vicinity of the linear limit, which provides good agreement with the observed spectral modes. Between these two analytically tractable limits, we use numerical computations to fill in the relevant intermediate regime. We find that the scattering length modulation can cause a variety of features absent for homogeneous nonlinearities. Among them, we note the potential oscillatory instability even of the single dark soliton, the potential absence of instabilities in the immediate vicinity of the linear limit for two dark solitons, and the existence of an exponential instability associated with the in-phase motion of three dark solitons.

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27

Gerlach, Marvin. "Three-loop topology analysis of neutral B-meson mixing with tapir." Journal of Physics: Conference Series 2438, no. 1 (February 1, 2023): 012156. http://dx.doi.org/10.1088/1742-6596/2438/1/012156.

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Abstract Modern advances in particle physics depend strongly on the usage of reliable computer programs. In this context two issues become important: The usage of powerful algorithms to handle the amount of evaluated data properly, and a software architecture capable of overcoming the problems of maintainability and extendability. We present our approach to such a computer program, called tapir. This tool assists computations in perturbative quantum field theory in many ways. Such calculations often involve the evaluation of a large amount of Feynman diagrams with multiple loops. tapir helps in reducing the number of diagrams, and the resulting integrals thereof, by identifying and minimizing their topological structure. We will focus on a three-loop calculation which is needed for the next-to-next-to leading order predictions of neutral B-meson systems. We show how tapir can be utilized for this kind of calculation.

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28

Boyd, John P., and Zhengjie Xu. "Numerical and perturbative computations of solitary waves of the Benjamin–Ono equation with higher order nonlinearity using Christov rational basis functions." Journal of Computational Physics 231, no. 4 (February 2012): 1216–29. http://dx.doi.org/10.1016/j.jcp.2011.10.004.

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Bhattacharya, Sourav. "Massless minimal quantum scalar field with an asymmetric self interaction in de Sitter spacetime." Journal of Cosmology and Astroparticle Physics 2022, no. 09 (September 1, 2022): 041. http://dx.doi.org/10.1088/1475-7516/2022/09/041.

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Abstract Massless minimally coupled quantum scalar field with an asymmetric self interaction, V(ϕ) = λϕ 4/4! + βϕ 3/3! (with λ > 0) is considered in the (3+1)-dimensional inflationary de Sitter spacetime. This potential is bounded from below irrespective of the sign of β. Earlier computations mostly considered the quartic part. Our chief motivation behind this study is to assess the vacuum expectation values of V(ϕ) and ϕ, both of which can be negative, and hence may lead to some screening of the inflationary cosmological constant value. First using the in-in formalism, the renormalised quantum correction to the cubic potential appearing in the energy-momentum tensor is computed at two loop, which is the leading order in this case. The quantum correction to the kinetic term at two loop are subleading compared to the above result at late cosmological times. Next, using some of these results we compute the renormalised vacuum expectation value of ϕ, by computing the tadpoles at 𝒪(β) and 𝒪(λβ). Due to the appearance of the de Sitter isometry breaking logarithms, the tadpoles cannot be completely renormalised away in this case, unlike the flat spacetime. All these results, as expected, show secularly growing logarithms at late cosmological times. We next use a recently proposed renormalisation group inspired formalism to resum perturbative secular effects, to compute a non-perturbative 〈ϕ〉 at late cosmological times. 〈ϕ〉 turns out to be approximately one order of magnitude less compared to the position of the classical minima ϕ = -3β/λ of V(ϕ). Estimation on the possible screening of the inflationary cosmological constant due to this 〈ϕ〉 is also presented.

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JOHNSON, CLIFFORD V. "THE ENHANÇON, MULTIMONOPOLES AND FUZZY GEOMETRY." International Journal of Modern Physics A 16, no. 05 (February 20, 2001): 990–1001. http://dx.doi.org/10.1142/s0217751x01004062.

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The presentation at Strings 2000 was intended to be in two main parts, but there was only time for part one. However both parts appeared on the online proceedings, and are also included in this document. The first part concerns an exploration of the connection between the physics of the "enhançon" geometry arising from wrapping N D6–branes on the K3 manifold in Type IIA string theory and that of a charge N BPS multi–monopole. This also relates to the physics of 2+1 dimensional SU(N) gauge theory with eight supercharges. The main results uncovered by this exploration are: a) better insight into the non–perturbative geometry of the enhançon; b) the structure of the moduli space geometry, and its characterisation in terms of a family of Atiyah–Hitchin–like manifolds; c) the use of Nahm data to describe aspects of the geometry, showing that the enhançon locus itself has a description as a fuzzy sphere. Part two discusses the addition of extra D2–branes into the geometry. Two probe computations show the difference between the geometry as seen by D2–branes and that seen by wrapped D6–branes, and the accompanying gauge theory interpretations are discussed.

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Wan, Qingyun, Jun Yang, Wai-Pong To, and Chi-Ming Che. "Strong metal–metal Pauli repulsion leads to repulsive metallophilicity in closed-shell d8 and d10 organometallic complexes." Proceedings of the National Academy of Sciences 118, no. 1 (December 28, 2020): e2019265118. http://dx.doi.org/10.1073/pnas.2019265118.

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Metallophilicity is defined as the interaction among closed-shell metal centers, the origin of which remains controversial, particularly for the roles of spd orbital hybridization (mixing of the spd atomic orbitals of the metal atom in the molecular orbitals of metal complex) and the relativistic effect. Our studies reveal that at close M–M′ distances in the X-ray crystal structures of d8 and d10 organometallic complexes, M–M′ closed-shell interactions are repulsive in nature due to strong M–M′ Pauli repulsion. The relativistic effect facilitates (n + 1)s-nd and (n + 1)p-nd orbital hybridization of the metal atom, where (n + 1)s-nd hybridization induces strong M–M′ Pauli repulsion and repulsive M–M′ orbital interaction, and (n + 1)p-nd hybridization suppresses M–M′ Pauli repulsion. This model is validated by both DFT (density functional theory) and high-level coupled-cluster singles and doubles with perturbative triples computations and is used to account for the fact that the intermolecular or intramolecular Ag–Ag′ distance is shorter than the Au–Au′ distance, where a weaker Ag–Ag′ Pauli repulsion plays an important role. The experimental studies verify the importance of ligands in intermolecular interactions. Although the M–M′ interaction is repulsive in nature, the linear coordination geometry of the d10 metal complex suppresses the L–L′ (ligand–ligand) Pauli repulsion while retaining the strength of the attractive L–L′ dispersion, leading to a close unsupported M–M′ distance that is shorter than the sum of the van der Waals radius (rvdw) of the metal atoms.

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STEPHENS, CHRISTOPHER R., and ADOLFO ZAMORA. "SYSTEMATIC APPROXIMATIONS FOR GENETIC DYNAMICS." Advances in Complex Systems 12, no. 06 (December 2009): 583–618. http://dx.doi.org/10.1142/s0219525909002350.

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Although much progress has been made in recent years in describing the dynamics of genetic systems, both in population genetics and evolutionary computation, there is still a conspicuous lack of tools with which to derive systematic, approximate solutions to their dynamics. In this article, we propose and study perturbation theory and the renormalization group as potential tools to fill this gap. We concentrate mainly on selection–mutation systems, showing different implementations of the perturbative framework, developing, for example, perturbative expansions for the eigenvalues and eigenvectors of the transition matrix. The main focus, however, is on diagrammatic methods, taken from physics, where we show how approximations can be built up using a pictorial representation generated by a simple set of rules, and how the renormalization group can be used to systematically improve the perturbation theory.

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33

ADAM, C. "SCHWINGER MASS IN RENORMAL-ORDERED CHIRAL PERTURBATION THEORY." International Journal of Modern Physics A 14, no. 31 (December 20, 1999): 4943–52. http://dx.doi.org/10.1142/s0217751x99002335.

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The massive Schwinger model may be analyzed by a perturbation expansion in the fermion mass. However, the results of this mass perturbation theory are sensible only for sufficiently small fermion mass. By performing a renormal-ordering, we arrive at a chiral perturbation expansion where the expansion parameter remains small even for large fermion mass. We use this renormal-ordered chiral perturbation theory for a computation of the Schwinger mass and compare our results with lattice computations.

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34

Pauley, Laura L. "Response of Two-Dimensional Separation to Three-Dimensional Disturbances." Journal of Fluids Engineering 116, no. 3 (September 1, 1994): 433–38. http://dx.doi.org/10.1115/1.2910295.

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The present study investigates the development and structure of three-dimensionality due to a three-dimensional velocity perturbation applied to the inlet of an unsteady two-dimensional separation computation. A random noise perturbation and a sine-wave perturbation are considered separately. In both cases, the spanwise variations were amplified in the separation and within the shed vortices. The vortex shedding frequency observed in the two-dimensional computation was not altered by the three dimensionality of the flow field. No observable spanwise structure was produced by the random noise perturbation. The sine-wave perturbation, however, produced longitudinal Go¨rtler vortices within the separation. Using a linear stability analysis, the presence of longitudinal vortices in a separated laminar boundary layer was predicted by Inger (1987). When the velocity field was averaged across the span, it was found that the sine-wave perturbation increased the separation length and reduced the strength of shed vortex. The span-averaged streamlines from the random noise perturbation, however, reproduced the unsteady separation of the two-dimensional computations.

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35

PAPASOTIRIOU, P. J., and V. S. GEROYANNIS. "A SCILAB PROGRAM FOR COMPUTING GENERAL-RELATIVISTIC MODELS OF ROTATING NEUTRON STARS BY IMPLEMENTING HARTLE'S PERTURBATION METHOD." International Journal of Modern Physics C 14, no. 03 (March 2003): 321–50. http://dx.doi.org/10.1142/s0129183103004516.

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We implement Hartle's perturbation method to the computation of relativistic rigidly rotating neutron star models. The program has been written in SCILAB (© INRIA–ENPC), a matrix-oriented high-level programming language. The numerical method is described in very detail and is applied to many models in slow or fast rotation. We show that, although the method is perturbative, it gives accurate results for all practical purposes and it should prove an efficient tool for computing rapidly rotating pulsars.

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36

Ettrich, Norman, and Dirk Gajewski. "Traveltime computation by perturbation with FD-eikonal solvers in isotropic and weakly anisotropic media." GEOPHYSICS 63, no. 3 (May 1998): 1066–78. http://dx.doi.org/10.1190/1.1444385.

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First‐order perturbation theory is used for fast 2-D computation of traveltimes. For highest efficiency we implement the perturbation integrals into Vidale’s finite‐difference (FD) eikonal solver. Traveltimes in the unperturbed reference medium are computed with Vidale’s method, while perturbed traveltimes in a slightly deviating perturbed medium are obtained by adding a correction Δt to the traveltimes of the reference medium. To compute Δt, raypaths between source and receivers in the reference medium must be known. In Vidale’s method traveltimes are computed on a discrete grid assuming local plane wavefronts inside the grid cells. Rays are not determined in this method. Therefore, we suggest approximating rays by ray segments corresponding to the plane wavefronts in each cell. We compute Δt along these segments and obtain initial values for Δt at cell boundaries by linear interpolation between the corner points of the cells. The FD perturbation method can be used for simultaneous computations of traveltime to a number of slightly different models and is, therefore, applicable to prestack velocity estimation techniques. Furthermore, using isotropic reference media the FD perturbation method allows very fast traveltime computations for weakly general anisotropic media. For the computation of traveltimes to a large number of subsurface grid points, the FD perturbation method is about three orders of magnitude faster than classical anisotropic ray‐shooting algorithms. Furthermore, we modify Vidale’s FD-eikonal solver for elliptically anisotropic media. Using reference media with elliptical anisotropy allows a higher accuracy of the FD perturbation method and let us consider perturbed models of stronger anisotropy. The extension of the FD-perturbation method to 3-D is straightforward.

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37

Dijkgraaf, R., M. T. Grisaru, C. S. Lam, C. Vafa, and D. Zanon. "Perturbative computation of glueball superpotentials." Physics Letters B 573 (October 2003): 138–46. http://dx.doi.org/10.1016/j.physletb.2003.08.060.

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38

Arnal, Ana, Fernando Casas, and Cristina Chiralt. "Exponential Perturbative Expansions and Coordinate Transformations." Mathematical and Computational Applications 25, no. 3 (August 13, 2020): 50. http://dx.doi.org/10.3390/mca25030050.

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We propose a unified approach for different exponential perturbation techniques used in the treatment of time-dependent quantum mechanical problems, namely the Magnus expansion, the Floquet–Magnus expansion for periodic systems, the quantum averaging technique, and the Lie–Deprit perturbative algorithms. Even the standard perturbation theory fits in this framework. The approach is based on carrying out an appropriate change of coordinates (or picture) in each case, and it can be formulated for any time-dependent linear system of ordinary differential equations. All of the procedures (except the standard perturbation theory) lead to approximate solutions preserving by construction unitarity when applied to the time-dependent Schrödinger equation.

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39

Ratchagar, Nirmala, and S. Subramanian. "Solution of the SEIR model of epidemics using HAM." World Journal of Engineering 11, no. 3 (June 1, 2014): 297–310. http://dx.doi.org/10.1260/1708-5284.11.3.297.

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In this paper, a new semi analytic technique namely the Homotopy Analysis Method (HAM) is applied for SEIR Epidemic model. HAM is different from already existing perturbation methods, and is most suitable for strongly non linear simultaneous differential equations arising in this model. The advantage of this method is that it provides a direct scheme for solving the problem, i.e. without the need for linearization, perturbation, massive computation and any transformation. MATHEMATICA 8.0 is used to carry out computations. Results were discussed graphically, for four childhood diseases.

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40

TEMELSO, BERHANE, NANCY A. RICHARDSON, LEVENT SARI, YUKIO YAMAGUCHI, and HENRY F. SCHAEFER. "CHARACTERIZATION OF THE $\tilde{X}\,^2 \Pi$ AND Ã2Σ+ ELECTRONIC STATES OF THE PHOSPHAETHYNE CATION (HCP+)." Journal of Theoretical and Computational Chemistry 04, spec01 (January 2005): 707–24. http://dx.doi.org/10.1142/s0219633605001738.

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The electronic ground state [Formula: see text] and first excited state (Ã2Σ+) of phosphaethyne cation (HCP+) have been systematically investigated using ab initio electronic structure theory. The total energies, geometries, rotational constants, dipole moments, harmonic vibrational frequencies, and parameters for Renner–Teller splittings were determined using self-consistent-field (SCF), configuration interaction with single and double excitations (CISD), coupled cluster (CC) with single and double excitations (CCSD), CCSD with perturbative triple excitations [CCSD(T)], CC with single, double, and iterative partial triple excitations (CCSDT-3), and CC with single, double, and full triple excitations (CCSDT) methods and eight different basis sets. Some of the largest full triples coupled cluster computations to date are reported. Degenerate bending frequencies for the Ã2Σ+ state were determined using the equation-of-motion (EOM)-CCSD technique. The two states have been confirmed to have linear equilibrium structures. At the full CCSDT level of theory with the correlation-consistent polarized valence quadruple zeta (cc-pVQZ) basis set, the classical [Formula: see text] splitting ( T e value) is predicted to be 47.7 kcal/mol (2.07 eV, 16,700 cm-1) and the quantum mechanical splitting (T0 value) to be 48.1 kcal/mol (2.08 eV, 16,800 cm-1), which are in excellent agreement with the experimental values of T e = 47.77 kcal/mol (2.072 eV , 16,708 cm -1) and T0 = 47.94 kcal/mol (2.079 eV, 16,766 cm-1). The excitation energies predicted by the CCSDT-3 and CCSD(T) methods differ from the full triples CCSDT result by 0.38 and 0.45 kcal/mol, respectively. With the aug-cc-pVQZ CCSDT-3 method the Renner parameter and the averaged harmonic bending vibrational frequency are determined to be ∊= -0.0390 and [Formula: see text] for the ground state of HCP+, which are reasonably consistent with the experimental values of ∊=-0.0415 and [Formula: see text]. The predicted dipole moments are 1.30 Debye ([Formula: see text] state, polarity-hydrogen atom positive) and 0.06 Debye (Ã2Σ+ state, polarity-phosphorus atom positive).

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Zhang, Mingjie, Jiangang Yang, Wanfu Zhang, and Qianlei Gu. "Orbit Decomposition Method for Rotordynamic Coefficients Identification of Annular Seals." Applied Sciences 11, no. 9 (May 7, 2021): 4237. http://dx.doi.org/10.3390/app11094237.

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The elliptical orbit whirl model is widely used to identify the frequency-dependent rotordynamic coefficients of annular seals. The existing solution technique of an elliptical orbit whirl model is the transient computational fluid dynamics (CFD) method. Its computational time is very long. For rapid computation, this paper proposes the orbit decomposition method. The elliptical whirl orbit is decomposed into the forward and backward circular whirl orbits. Under small perturbation circumstances, the fluid-induced forces of the elliptical orbit model can be obtained by the linear superposition of the fluid-induced forces arising from the two decomposed circular orbit models. Due to that the fluid-induced forces of circular orbit, the model can be calculated with the steady CFD method, and the transient computations can be replaced with steady ones when calculating the elliptical orbit whirl model. The computational time is significantly reduced. To validate the present method, its rotordynamic results are compared with those of the transient CFD method and experimental data. Comparisons show that the present method can accurately calculate the rotordynamic coefficients. Elliptical orbit parameter analysis reveals that the present method is valid when the whirl amplitude is less than 20% of seal clearance. The effect of ellipticity on rotordynamic coefficients can be ignored.

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42

Faiz, Alfian, Subiyanto Subiyanto, and Ulfah Mediaty Arief. "An efficient meta-heuristic algorithm for solving capacitated vehicle routing problem." International Journal of Advances in Intelligent Informatics 4, no. 3 (November 11, 2018): 212. http://dx.doi.org/10.26555/ijain.v4i3.244.

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This work aims to develop an enhanced Perturbation based Variable Neighborhood Search with Adaptive Selection Mechanism (PVNS ASM) to solve the capacitated vehicle routing problem (CVRP). This approach combined Perturbation based Variable Neighborhood Search (PVNS) with Adaptive Selection Mechanism (ASM) to control perturbation scheme. Instead of stochastic approach, selection of perturbation scheme used in the algorithm employed an empirical selection based on success rate of each perturbation scheme along the search. The ASM helped algorithm to get more diversification degree and jumping from local optimum condition using most successful perturbation scheme empirically in the search process. A comparative analysis with existing heuristics in the literature has been performed on 21 CVRP benchmarks. The computational results proof that the developed method is competitive and very efficient in achieving high quality solution within reasonable computation time.

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43

Eberhardt, Lorenz. "A perturbative CFT dual for pure NS–NS AdS₃ strings." Journal of Physics A: Mathematical and Theoretical 55, no. 6 (January 19, 2022): 064001. http://dx.doi.org/10.1088/1751-8121/ac47b2.

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Abstract We construct a conformal field theory dual to string theory on AdS3 with pure NS–NS flux. It is given by a symmetric orbifold of a linear dilaton theory deformed by a marginal operator from the twist-2 sector. We compute two- and three-point functions on the CFT side to 4th order in conformal perturbation theory at large N. They agree with the string computation at genus 0, thus providing ample evidence for a duality. We also show that the full spectra of both short and long strings on the CFT and the string side match. The duality should be understood as perturbative in N −1.

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44

Nitish, R., Rohit K. Gupta, and Supriya Kar. "Perspectives of perihelion precession in torsion modified gravity." International Journal of Modern Physics D 29, no. 10 (July 2020): 2050074. http://dx.doi.org/10.1142/s0218271820500741.

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Killing symmetries are revisited in [Formula: see text] bulk geometric torsion (GT) perturbation theory to investigate the perihelion precession. Computation reveals a nonperturbative (NP) modification to the precession known in General Relativity (GR). Remarkably the analysis reassures our proposed holographic correspondence between a perturbative GT in bulk and a boundary GR coupled to [Formula: see text]. In fact, the topological correction is sourced by a non-Newtonian potential in GR and we identify it with an “electro-gravito” (EG) dipole. Interestingly, the dipole correction is shown to possess its origin in a [Formula: see text]-form underlying a propagating GT and leads to a NP gravity in [Formula: see text].

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45

Duhr, Claude. "Function Theory for Multiloop Feynman Integrals." Annual Review of Nuclear and Particle Science 69, no. 1 (October 19, 2019): 15–39. http://dx.doi.org/10.1146/annurev-nucl-101918-023551.

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Precise predictions for collider observables require the computation of higher orders in perturbation theory. This task usually involves the evaluation of complicated multiloop integrals, which typically give rise to complicated special functions. This article discusses recent progress in understanding the mathematics underlying multiloop Feynman integrals and discusses a class of functions that generalizes the logarithm and that often appears in multiloop computations. The same class of functions is an active area of research in modern mathematics, which has led to the development of new powerful tools to compute Feynman integrals. These tools are at the heart of some of the most complicated computations ever performed for a hadron collider.

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46

Oliveira, R., and B. M. Terhal. "The complexity of quantum spin systems on a two-dimensional square lattice." Quantum Information and Computation 8, no. 10 (November 2008): 900–924. http://dx.doi.org/10.26421/qic8.10-2.

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The problem 2-LOCAL HAMILTONIAN has been shown to be complete for the quantum computational class QMA. In this paper we show that this important problem remains QMA-complete when the interactions of the 2-local Hamiltonian are between qubits on a two-dimensional (2-D) square lattice. Our results are partially derived with novel perturbation gadgets that employ mediator qubits which allow us to manipulate k-local interactions. As a side result, we obtain that quantum adiabatic computation using 2-local interactions restricted to a 2-D square lattice is equivalent to the circuit model of quantum computation. Our perturbation method also shows how any stabilizer space associated with a k-local stabilizer (for constant k) can be generated as an approximate ground-space of a 2-local Hamiltonian.

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47

Bandrauk, André D. "Molecular multiphoton transitions. Computational spectroscopy for perturbative and non-perturbative regimens." International Reviews in Physical Chemistry 13, no. 1 (March 1994): 123–61. http://dx.doi.org/10.1080/01442359409353292.

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48

Blouin, Vincent Y., and Michael M. Bernitsas. "Cognate Space Identification for Forced Response Structural Redesign." Journal of Offshore Mechanics and Arctic Engineering 127, no. 3 (January 26, 2003): 227–33. http://dx.doi.org/10.1115/1.1979512.

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Large admissible perturbations (LEAP) is a general methodology, which solves redesign problems of complex structures with, among others, forced response amplitude constraints. In previous work, two LEAP algorithms, namely the incremental method (IM) and the direct method (DM), were developed. A powerful feature of LEAP is the general perturbation equations derived in terms of normal modes, the selection of which is a determinant factor for a successful redesign. The normal modes of a structure may be categorized as stretching, bending, torsional, and mixed modes and grouped into cognate spaces. In the context of redesign by LEAP, the physical interpretation of a mode-to-response cognate space lies in the fact that a mode from one space barely affects change in a mode from another space. Perturbation equations require computation of many perturbation terms corresponding to individual modes. Identifying modes with negligible contribution to the change in forced response amplitude eliminates a priori computation of numerous perturbation terms. Two methods of determining mode-to-response cognate spaces, one for IM and one for DM, are presented and compared. Trade-off between computational time and accuracy is assessed in order to provide practical guidelines to the designer. The developed LEAP redesign algorithms are applied to the redesign of a simple cantilever beam and a complex offshore tower.

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Cornille, B. S., M. T. Beidler, S. Munaretto, B. E. Chapman, D. Del-Castillo-Negrete, N. C. Hurst, J. S. Sarff, and C. R. Sovinec. "Computational study of runaway electrons in MST tokamak discharges with applied resonant magnetic perturbation." Physics of Plasmas 29, no. 5 (May 2022): 052510. http://dx.doi.org/10.1063/5.0087314.

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A numerical study of magnetohydrodynamics (MHD) and tracer-particle evolution investigates the effects of resonant magnetic perturbations (RMPs) on the confinement of runaway electrons (REs) in tokamak discharges conducted in the Madison Symmetric Torus. In computational results of applying RMPs having a broad toroidal spectrum but a single poloidal harmonic, m = 1 RMP does not suppress REs, whereas m = 3 RMP achieves significant deconfinement but not the complete suppression obtained in the experiment [Munaretto et al., Nuclear Fusion 60, 046024 (2020)]. MHD simulations with the NIMROD code produce sawtooth oscillations, and the associated magnetic reconnection can affect the trajectory of REs starting in the core region. Simulations with m = 3 RMP produce chaotic magnetic topology over the outer region, but the m = 1 RMP produces negligible changes in field topology, relative to applying no RMP. Using snapshots of the MHD simulation fields, full-orbit relativistic electron test particle computations with KORC show [Formula: see text] loss from the m = 3 RMP compared to the [Formula: see text] loss from the m = 1 RMP. Test particle computations of the m = 3 RMP in the time-evolving MHD simulation fields show correlation between MHD activity and late-time particle losses, but total electron confinement is similar to computations using magnetic-field snapshots.

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50

Bezerra, V. B., E. M. F. Curado, and M. A. Rego-Monteiro. "Perturbative Computation in a Deformed Quantum Field Theory." International Journal of Modern Physics A 18, no. 12 (May 10, 2003): 2025–31. http://dx.doi.org/10.1142/s0217751x03015441.

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We present the result concerning the perturbative computation of the scattering process 1 + 2 → 1′ + 2′ up to second order in the coupling constant. This was obtained in the context of a deformed quantum field theory which is interpreted as a phenomenological theory describing the scattering of spin-0 composite particles.

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