scholarly journals Appendix D: General Expression for Intercept Point Derivation

2021 ◽  
pp. 217-218
2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
Martin Fluder ◽  
Christoph F. Uhlemann

Abstract Renormalization group flows are studied between 5d SCFTs engineered by (p, q) 5-brane webs with large numbers of external 5-branes. A general expression for the free energy on S5 in terms of single-valued trilogarithm functions is derived from their supergravity duals, which are characterized by the 5-brane charges and additional geometric parameters. The additional geometric parameters are fixed by regularity conditions, and we show that the solutions to the regularity conditions extremize a trial free energy. These results are used to survey a large sample of $$ \mathcal{O} $$ O (105) renormalization group flows between different 5d SCFTs, including Higgs branch flows and flows that preserve the SU(2) R- symmetry. In all cases the free energy changes monotonically towards the infrared, in line with a 5d F -theorem.


Author(s):  
Jun-Yong Lee ◽  
Hyeong-Guen Kim ◽  
H Jin Kim

This article proposes an impact-time-control guidance law that can keep a non-maneuvering moving target in the seeker’s field of view (FOV). For a moving target, the missile calculates a predicted intercept point (PIP), designates the PIP as a new virtual stationary target, and flies to the PIP at the desired impact time. The main contribution of the article is that the guidance law is designed to always lock onto the moving target by adjusting the guidance gain. The guidance law for the purpose is based on the backstepping control technique and designed to regulate the defined impact time error. In this procedure, the desired look angle, which is a virtual control, is designed not to violate the FOV limit, and the actual look angle of the missile is kept within the FOV by tracking the desired look angle. To validate the performance of the guidance law, numerical simulation is conducted with different impact times. The result shows that the proposed guidance law intercepts the moving target at the desired impact time maintaining the target lock-on condition.


The paper is a continuation of the last paper communicated to these 'Proceedings.' In that paper, which we shall refer to as the first paper, a more general expression for space curvature was obtained than that which occurs in Riemannian geometry, by a modification of the Riemannian covariant derivative and by the use of a fifth co-ordinate. By means of a particular substitution (∆ μσ σ = 1/ψ ∂ψ/∂x μ ) it was shown that this curvature takes the form of the second order equation of quantum mechanics. It is not a matrix equation, however but one which has the character of the wave equation as it occurred in the earlier form of the quantum theory. But it contains additional terms, all of which can be readily accounted for in physics, expect on which suggested an identification with energy of the spin.


2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Selomit Ramírez-Uribe ◽  
Roger J. Hernández-Pinto ◽  
Germán Rodrigo ◽  
German F. R. Sborlini ◽  
William J. Torres Bobadilla

Abstract The perturbative approach to quantum field theories has made it possible to obtain incredibly accurate theoretical predictions in high-energy physics. Although various techniques have been developed to boost the efficiency of these calculations, some ingredients remain specially challenging. This is the case of multiloop scattering amplitudes that constitute a hard bottleneck to solve. In this paper, we delve into the application of a disruptive technique based on the loop-tree duality theorem, which is aimed at an efficient computation of such objects by opening the loops to nondisjoint trees. We study the multiloop topologies that first appear at four loops and assemble them in a clever and general expression, the N4MLT universal topology. This general expression enables to open any scattering amplitude of up to four loops, and also describes a subset of higher order configurations to all orders. These results confirm the conjecture of a factorized opening in terms of simpler known subtopologies, which also determines how the causal structure of the entire loop amplitude is characterized by the causal structure of its subtopologies. In addition, we confirm that the loop-tree duality representation of the N4MLT universal topology is manifestly free of noncausal thresholds, thus pointing towards a remarkably more stable numerical implementation of multiloop scattering amplitudes.


2002 ◽  
Vol 80 (8) ◽  
pp. 847-854 ◽  
Author(s):  
C D Palmer ◽  
M E Carrington

The calculation of the symmetry factor corresponding to a given Feynman diagram is well known to be a tedious problem. We have derived a simple formula for these symmetry factors. Our formula works for any diagram in scalar theory (ϕ3 and ϕ4 interactions), spinor QED, scalar QED, or QCD. PACS Nos.: 11.10-z, 11.15-q, 11.15Bt


1987 ◽  
Vol 38 (2) ◽  
pp. 209-222 ◽  
Author(s):  
Hussain M. Rizk

The relation between various surface quantities required in hydrodynamic calculations, and the relation between the parallel and perpendicular currents in an arbitrary magnetic toroidal plasma configuration with scalar pressure, are generalized to the case of anisotropic pressure. Magnetic co-ordinates for hydrodynamic equilibria in this configuration are defined. A general expression for the mean velocity of diffusion through a magnetic surface, on the basis of the one-fluid magnetohydrodynamic equation with anisotropic pressure, is derived.


1966 ◽  
Vol 10 (01) ◽  
pp. 18-24
Author(s):  
Pung Nien Hu ◽  
King Eng

A general expression for the drifting moment about the vertical axis of an oscillating ship in regular oblique waves is derived from the potential theory, following a similar procedure developed by Maruo for drifting force. Explicit analytical solutions for the drifting side force and yaw moment on thin ships in long waves are obtained in terms of simple elementary functions. The effect of the wave frequency, the draft of the ship, the displacement, and the phase angle of the ship oscillation are discussed.


2010 ◽  
Vol 107 (2) ◽  
pp. 026101 ◽  
Author(s):  
Kejia Chen ◽  
Ramakrishnan Vaidyanathan ◽  
Edmund G. Seebauer ◽  
Richard D. Braatz

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