scholarly journals Sector Decomposition Scheme for N\(^3\)LO Beam Function

2021 ◽  
Vol 52 (8) ◽  
pp. 947
Author(s):  
T. Goda ◽  
P. Müllender
Keyword(s):  
Decomposition Scheme ◽  
Beam Function

scholarly journals DECOMPOSITION OF UNITARY MATRICES AND QUANTUM GATES

2013 ◽  
Vol 11 (01) ◽  
pp. 1350015 ◽  
Author(s):  
CHI-KWONG LI ◽  
REBECCA ROBERTS ◽  
XIAOYAN YIN
Keyword(s):  
General Scheme ◽  
Quantum Gate ◽  
Quantum Gates ◽  
Unitary Matrix ◽  
Additional Structure ◽  
Unitary Matrices ◽  
Decomposition Scheme ◽  
Single Qubit ◽  
Matlab Program

A general scheme is presented to decompose a d-by-d unitary matrix as the product of two-level unitary matrices with additional structure and prescribed determinants. In particular, the decomposition can be done by using two-level matrices in d - 1 classes, where each class is isomorphic to the group of 2 × 2 unitary matrices. The proposed scheme is easy to apply, and useful in treating problems with the additional structural restrictions. A Matlab program is written to implement the scheme, and the result is used to deduce the fact that every quantum gate acting on n-qubit registers can be expressed as no more than 2n-1(2n-1) fully controlled single-qubit gates chosen from 2n-1 classes, where the quantum gates in each class share the same n - 1 control qubits. Moreover, it is shown that one can easily adjust the proposed decomposition scheme to take advantage of additional structure evolving in the process.

scholarly journals Collinear expansion for color singlet cross sections

2020 ◽  
Vol 2020 (9) ◽  
Author(s):  
Markus A. Ebert ◽  
Bernhard Mistlberger ◽  
Gherardo Vita
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Production Cross ◽  
Gluon Fusion ◽  
Building Blocks ◽  
Color Singlet ◽  
Final State ◽  
Beam Function ◽  
Kinematic Limit ◽  
State Radiation

Abstract We demonstrate how to efficiently expand cross sections for color-singlet production at hadron colliders around the kinematic limit of all final state radiation being collinear to one of the incoming hadrons. This expansion is systematically improvable and applicable to a large class of physical observables. We demonstrate the viability of this technique by obtaining the first two terms in the collinear expansion of the rapidity distribution of the gluon fusion Higgs boson production cross section at next-to-next-to leading order (NNLO) in QCD perturbation theory. Furthermore, we illustrate how this technique is used to extract universal building blocks of scattering cross section like the N-jettiness and transverse momentum beam function at NNLO.

scholarly journals Gaussons: optical solitons with log-law nonlinearity by Laplace–Adomian decomposition method

Open Physics ◽  
2020 ◽  
Vol 18 (1) ◽  
pp. 182-188
Author(s):  
O. González-Gaxiola ◽  
Anjan Biswas ◽  
Abdullah Kamis Alzahrani
Keyword(s):  
Numerical Simulations ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Optical Solitons ◽  
Decomposition Scheme ◽  
Error Analyses ◽  
Adomian Decomposition ◽  
Log Law

AbstractThis paper presents optical Gaussons by the aid of the Laplace–Adomian decomposition scheme. The numerical simulations are presented both in the presence and in the absence of the detuning term. The error analyses of the scheme are also displayed.

BENDING OF ORTHOTROPIC RECTANGULAR CANTILEVER PLATE

2021 ◽  
pp. 2-9
Author(s):  
M.V. Sukhoterin ◽  
◽  
A.M. Maslennikov ◽  
T.P. Knysh ◽  
I.V. Voytko ◽  
...  
Keyword(s):  
Iterative Method ◽  
Boundary Conditions ◽  
Trigonometric Series ◽  
Bending Moment ◽  
Partial Solution ◽  
Numerical Results ◽  
Cantilever Plate ◽  
Degree Polynomial ◽  
Fourth Degree ◽  
Beam Function

Abstract. An iterative method of superposition of correcting functions is proposed. The partial solution of the main differential bending equation is represented by a fourth-degree polynomial (the beam function), which gives a residual only with respect to the bending moment on parallel free faces. This discrepancy and the subsequent ones are mutually compensated by two types of correcting functions-hyperbolic-trigonometric series with indeterminate coefficients. Each function satisfies only a part of the boundary conditions. The solution of the problem is achieved by an infinite superposition of correcting functions. For the process to converge, all residuals must tend to zero. When the specified accuracy is reached, the process stops. Numerical results of the calculation of a square ribbed plate are presented.

Experimental Investigation of Vortex-Induced Vibrations on Yawed and Inclined Flexible Cylinders

2021 ◽  
pp. 1-16
Author(s):  
Daniel P. Vieira ◽  
Guilherme R. Franzini ◽  
Fredi Cenci ◽  
Andre Fujarra
Keyword(s):  
A Priori ◽  
Flexible Structures ◽  
Resonance Region ◽  
Offshore Structures ◽  
Natural Mode ◽  
Flexible Cylinder ◽  
Decomposition Scheme ◽  
Independence Principle ◽  
Modal Amplitude ◽  
Time Histories

Abstract An experimental setup was built to investigate the Vortex-Induced Vibration (VIV) phenomenon on yawed and inclined flexible cylinders, in which five yaw angles θ = 0°, 10°, 20°, 30° and 45° and five azimuth angles ß = 0°, 45°, 90°, 135°, and 180° were combined. The experiments were carried out in a towing tank facility at Reynolds numbers from 1800 to 18000, comprising vibrations up to the eighth natural mode. Time histories of displacements were recorded using a submerged optical system that tracks 17 reflective targets. A modal decomposition scheme based on Galerkin's method was applied, aiming multimodal behavior investigations. Such an approach allowed the analysis of the modal amplitude throughout time, revealing interesting results for such a class of VIV tests. The flexible cylinder total response is generally a combination of two or more modes. Only for azimuths 0°, 90°, and 180°, a unimodal response was observed for the two first lock-in regimes. The frequency response showed that, when the response was multimodal, non-dominant modes can follow the vibration frequency of the dominant one. Assuming a priori the Independence Principle (IP) valid to define the reduced velocities (Vr), it was observed that the resonance region was restricted to 3 <= Vr <= 8 for the tested cases, indicating that the IP can be at least partially applied for flexible structures. As the literature scarcely explores the simultaneous yawed and inclined configurations, the present work may contribute to further code validation and improvements regarding the design of slender offshore structures.

Three-component analysis of regional seismograms

1990 ◽  
Vol 80 (6B) ◽  
pp. 2032-2052 ◽  
Author(s):  
D. C. Jepsen ◽  
B. L. N. Kennett
Keyword(s):  
Free Surface ◽  
Time Window ◽  
Seismic Station ◽  
P Wave ◽  
Sh Waves ◽  
Near Surface ◽  
Source Discrimination ◽  
Decomposition Scheme ◽  
Phased Array Techniques ◽  
The Stability

Abstract Both phased array techniques for single-component sensors and vectorial analysis of three-component recordings can provide estimates of the azimuth and slowness of seismic phases. However, a combination of these approaches provides a more powerful tool to estimate the propagation characteristics of different seismic phases at regional distances. Conventional approaches to the analysis of three-component seismic records endeavor to exploit the apparent angles of propagation in horizontal and vertical planes as well as the polarization of the waves. The basic assumption is that for a given time window there is a dominant wavetype (e.g., a P wave) traveling in a particular direction arriving at the seismic station. By testing a range of characteristics of the three-component records, a set of rules can be established for classifying much of the seismogram in terms of wavetype and direction. It is, however, difficult to recognize SH waves in the presence of other wavetypes. Problems also arise when more than one signal (in either wavetype or direction) arrive in the same window. The stability and robustness of the classification scheme is much improved when records from an array of three-component sensors are combined. For a set of three-component instruments forming part of a larger array, it is possible to estimate the slowness and azimuth of arrivals from the main array and then extract the relative proportions of the current P-, SV-, and SH-wave contributions to the seismogram. This form of wavetype decomposition depends on a model of near-surface propagation. A convenient choice for hard-rock sites is to include just the effect of the free surface, which generates a frequency-independent operation on the three-component seismograms and which is not very sensitive to surface velocities. This approach generates good estimates of the character of the S wavefield, because the phase distortion of SV induced by the free surface can be removed. The method has been successfully applied to regional seismograms recorded at the medium aperture Warramunga array in northern Australia, and the two small arrays NORESS and ARCESS in Norway, which were designed for studies of regional phases. The new wavefield decomposition scheme provides results in which the relative proportions of P, SV, and SH waves as a function of time can be compared without the distortion imposed by free surface amplification. Such information can provide a useful adjunct to existing measures of signal character used in source discrimination.

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