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At least 1,585 records · Page 88

A subleading power operator basis for the scalar quark current

Factorization theorems play a crucial role in our understanding of the strong interaction. For collider processes they are typically formulated at leading power and much less is known about power corrections in the λ << 1 expansion. Here we present a complete basis of power suppressed operators for a scalar quark current at O(λ 2 ) in the amplitude level power expansion in the Soft Collinear Effective Theory, demonstrating that helicity selection rules significantly simplify the construction. This basis applies for the production of any color singlet scalar in qq¯¯ annihilation (such as bb¯¯→H ). We also classify all operators which contribute to the cross section at O(λ 2 ) and perform matching calculations to determine their tree level Wilson coefficients. Furthermore, these results can be exploited to study power corrections in both resummed and fixed order perturbation theory, and for analyzing the factorization properties of gauge theory amplitudes and cross sections at subleading power.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Wave kinetic equation for inhomogeneous drift-wave turbulence beyond the quasilinear approximation

Here, the formation of zonal flows from inhomogeneous drift-wave (DW) turbulence is often described using statistical theories derived within the quasilinear approximation. However, this approximation neglects wave–wave collisions. Hence, some important effects such as the Batchelor–Kraichnan inverse-energy cascade are not captured within this approach. Here we derive a wave kinetic equation that includes a DW collision operator in the presence of zonal flows. Our derivation makes use of the Weyl calculus, the quasinormal statistical closure and the geometrical-optics approximation. The obtained model conserves both the total enstrophy and energy of the system. The derived DW collision operator breaks down at the Rayleigh–Kuo threshold. This threshold is missed by homogeneous-turbulence theory but expected from a full-wave quasilinear analysis. In the future, this theory might help better understand the interactions between drift waves and zonal flows, including the validity domain of the quasilinear approximation that is commonly used in the literature.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

The gravity duals of modular Hamiltonians

In this study, we investigate modular Hamiltonians defined with respect to arbitrary spatial regions in quantum field theory states which have semi-classical gravity duals. We find prescriptions in the gravity dual for calculating the action of the modular Hamiltonian on its defining state, including its dual metric, and also on small excitations around the state. Curiously, use of the covariant holographic entanglement entropy formula leads us to the conclusion that the modular Hamiltonian, which in the quantum field theory acts only in the causal completion of the region, does not commute with bulk operators whose entire gauge-invariant description is space-like to the causal completion of the region.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

On the feasibility of real-time prediction of aircraft carrier motion at sea

Landing aircraft on board carriers is a most delicate phase of flight operations at sea. The ability to predict the aircraft carrier's motion over an interval of several seconds within reasonable error bounds may allow an improvement in touchdown dispersion and reduce the value of the ramp clearance due to a smoother aircraft trajectory. Also, improved information to the landing signal officer should decrease the number of waveoffs substantially. This paper indicates and shows quantitatively that, based upon the power density spectrum data for pitch and heave measured for various ships and sea conditions, the motion can be predicted well, for up to 15 s. Moreover, the zero crossover times for both pitch and heave motions can be predicted with impressive accuracy. The predictor was designed on the basis of Kalman's optimum filtering theory (the discrete time case), being compatible with real-time digital computer operation.

Sidar, M. M.↗

Dark matter at colliders

We show that colliders can impose strong constraints on dark matter. We take an effective field theory approach where dark matter couples to quarks and gluons through high dimensional operators. We discuss limits on interactions of dark matter and hadronic matter from the ATLAS experiment at the Large Hadron Collider (LHC). For spin-independent scattering, the LHC limits are stronger than those from direct detection experiments for light WIMPs. For spin-dependent scattering, the LHC sets better limits over much of parameter space.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Tools for Designing, Evaluating, and Certifying NextGen Technologies and Procedures: Automation Roles and Responsibilities

Barbara Kanki from NASA Ames Research Center will discuss research that focuses on the collaborations between pilots, air traffic controllers and dispatchers that will change in NextGen systems as automation increases and roles and responsibilities change. The approach taken by this NASA Ames team is to build a collaborative systems assessment template (CSAT) based on detailed task descriptions within each system to establish a baseline of the current operations. The collaborative content and context are delineated through the review of regulatory and advisory materials, policies, procedures and documented practices as augmented by field observations and interviews. The CSAT is developed to aid the assessment of key human factors and performance tradeoffs that result from considering different collaborative arrangements under NextGen system changes. In theory, the CSAT product may be applied to any NextGen application (such as Trajectory Based Operations) with specified ground and aircraft capabilities.

Kanki, Barbara G.↗

Electron density measurement using a partially covered hairpin resonator in an inductively coupled plasma

Hairpin probes are used to determine electron densities via measuring the shift of the resonant frequency of the probe structure when immersed in a plasma. This manuscript presents new developments in hairpin probe hardware and theory that have enabled measurements in a high electron density plasma, up to approximately 10 12 cm -3 , corresponding to a plasma frequency of about 9 GHz. Hardware developments include the use of both quarter-wavelength and three-quarter-wavelength partially covered hairpin probes in a transmission mode together with an easily reproducible implementation of the associated microwave electronics using commercial off-the-shelf components. The three-quarter-wavelength structure is operated at its second harmonic with the purpose of measuring higher electron densities. New theory developments for interpreting the probe measurements include the use of a transmission line model to find an accurate relationship between the resonant frequency of the probe and the electron density, including effects of partially covering the probes with epoxy. Measurements are taken in an inductively coupled plasma sustained in argon at pressures below 50 mTorr. Results are compared with Langmuir probe and interferometry measurements.

47 OTHER INSTRUMENTATION↗

Helicopter theory

A comprehensive presentation is made of the engineering analysis methods used in the design, development and evaluation of helicopters. After an introduction covering the fundamentals of helicopter rotors, configuration and operation, rotary wing history, and the analytical notation used in the text, the following topics are discussed: (1) vertical flight, including momentum, blade element and vortex theories, induced power, vertical drag and ground effect; (2) forward flight, including in addition to momentum and vortex theory for this mode such phenomena as rotor flapping and its higher harmonics, tip loss and root cutout, compressibility and pitch-flap coupling; (3) hover and forward flight performance assessment; (4) helicopter rotor design; (5) rotary wing aerodynamics; (6) rotary wing structural dynamics, including flutter, flap-lag dynamics ground resonance and vibration and loads; (7) helicopter aeroelasticity; (8) stability and control (flying qualities); (9) stall; and (10) noise.

Johnson, W.↗

Spectral Analysis of Linear Models of Viscoelasticity

In this paper, we examine Volterra integrodifferential equations with unbounded operator coefficients in Hilbert spaces. Equations considered are abstract hyperbolic equations perturbed by terms containing Volterra integral operators. These equations can be realized as partial integrodifferential equations that appear in the theory of viscoelasticity (see [2, 5]), as Gurtin–Pipkin integrodifferential equations (see [1, 7]) that describe finite-speed heat transfer in materials with memory. They also appear in averaging problems for multiphase media (Darcy’s law.

97 MATHEMATICS AND COMPUTING↗

Local chiral interactions and magnetic structure of few-nucleon systems

The magnetic form factors of 2 H, 3 H, and 3 He, deuteron photodisintegration cross sections at low energies, and deuteron threshold electrodisintegration cross sections at backward angles in a wide range of momentum transfers are calculated with the chiral two-nucleon (and three-nucleon) interactions including Δ intermediate states that have recently been constructed in configuration space. The A=3 wave functions are obtained from hyperspherical-harmonics solutions of the Schrödinger equation. The electromagnetic current includes one- and two-body terms, the latter induced by one- and two-pion exchange (OPE and TPE, respectively) mechanisms and contact interactions. The contributions associated with Δ intermediate states are only retained at the OPE level and are neglected in TPE loop (tree-level) corrections to two-body (three-body) current operators. Expressions for these currents are derived and regularized in configuration space for consistency with the interactions. The low-energy constants that enter the contact currents are determined by reproducing the magnetic moments of these few-nucleon systems. The predicted form factors and deuteron electrodisintegration cross section are in excellent agreement with experiment for momentum transfers up to 2–3fm –1 . However, the experimental values for the deuteron photodisintegration cross section are consistently underestimated by theory, unless use is made of the Siegert form of the electric dipole transition operator. In conclusion, a complete analysis of the results is provided, including the clarification of the origin of the aforementioned discrepancy.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Automatic derivation of many-body theories based on general Fermi vacua

This paper describes Wick&D, an implementation of the algebra of second-quantized operators normal ordered with respect to general correlated references and the corresponding Wick theorem [D. Mukherjee, Chem. Phys. Lett. 274, 561 (1997) and W. Kutzelnigg and D. Mukherjee, J. Chem. Phys. 107, 432 (1997)]. Wick&D employs a compact representation of operators and a backtracking algorithm to efficiently evaluate Wick contractions. Since Wick&D can handle both fully and partially contracted terms, it can be applied to both projective and Fock-space many-body formalisms. To demonstrate the usefulness of Wick&D, here we use it to evaluate the single-reference coupled cluster equations up to octuple excitations and report an automated derivation and implementation of the second-order driven similarity renormalization group multireference perturbation theory.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Comparison of theory with experiment in the phenomenon of wing flutter

Direct measurements were undertaken at the Aeronautics Laboratory in Turin of the aerodynamic actions on an oscillating wing. The tests conducted had as their essential object the examination of the operation of apparatus designed for this measurement. The values experimentally obtained for the aerodynamic coefficients are in good agreement with the theory of oscillatory motion of the wing of finite span and show clear deviation from the values obtained by theory of plane motion.

Cicala, P↗

Self-organization of network dynamics into local quantized states

Self-organization and pattern formation in network-organized systems emerges from the collective activation and interaction of many interconnected units. A striking feature of these non-equilibrium structures is that they are often localized and robust: only a small subset of the nodes, or cell assembly, is activated. Understanding the role of cell assemblies as basic functional units in neural networks and socio-technical systems emerges as a fundamental challenge in network theory. A key open question is how these elementary building blocks emerge, and how they operate, linking structure and function in complex networks. Here we show that a network analogue of the Swift-Hohenberg continuum model—a minimal-ingredients model of nodal activation and interaction within a complex network—is able to produce a complex suite of localized patterns. Thus, the spontaneous formation of robust operational cell assemblies in complex networks can be explained as the result of self-organization, even in the absence of synaptic reinforcements.

59 BASIC BIOLOGICAL SCIENCES↗

Theory of tokamak disruptions

Theoretical guidance is needed on two disruption questions: (1) When is a tokamak operating in a metastable state in which loss of control is credible (avoidance question)? (2) What is the worst credible level of destructive effects when plasma control lost and how can these effects be mitigated (effects question)? The success of ITER and the future of tokamaks as fusion systems depend on the precision with which these questions can be answered. Existing capabilities are far from those desired. Nevertheless, one can give physical constraints on the answers and scientific issues that must be addressed to provide reliable guidance. A theoretical program of moderate scale interacting with ongoing experiments could greatly advance the state of development of appropriate tools for simulating, avoiding, and mitigating disruptions.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Actuator disk theory for incompressible highly rotating flows.

A solution has been obtained for a stator-rotor pair operating in an annulus with constant hub and tip radii. The stator and rotor are represented as actuator discs, and perfect fluid flow is assumed. The solutions are exact within these limitations, no linearization being required. The forms of blade loadings considered allow the introduction of large vorticity by either the rotor or stator. As a result, the rotor may be a ?nonconstant-work' row. The solutions obtained are of summational form, but many of the summations are obtained in closed form, the resultant formulas allowing rapid calculation of desired examples. An example numerical result is included.

Oates, G. C.↗

Classification and equivalence in estimation theory

A method is proposed for classifying estimation problems based on the Lie algebra generated by the operators which appear in the conditional density equation. A natural class of automorphisms of this algebra is examined and a systematic method of generating equivalent problems is developed. Finally, a new class of nonlinear filtering problems with essentially nonlinear filtering equations are presented.

Brockett, R. W.↗

A mathematical theory of learning control for linear discrete multivariable systems

When tracking control systems are used in repetitive operations such as robots in various manufacturing processes, the controller will make the same errors repeatedly. Here consideration is given to learning controllers that look at the tracking errors in each repetition of the process and adjust the control to decrease these errors in the next repetition. A general formalism is developed for learning control of discrete-time (time-varying or time-invariant) linear multivariable systems. Methods of specifying a desired trajectory (such that the trajectory can actually be performed by the discrete system) are discussed, and learning controllers are developed. Stability criteria are obtained which are relatively easy to use to insure convergence of the learning process, and proper gain settings are discussed in light of measurement noise and system uncertainties.

Phan, Minh↗

Theory of the optimally coupled Q-switched laser

The general equations describing Q-switched laser operation are transcendental in nature and require numerical solutions, which greatly complicates the optimization of real devices. Here, it is shown that, using the mathematical technique of Lagrange multipliers, one can derive simple analytic expressions for all of the key parameters of the optimally coupled laser, i.e., one which uses an optimum reflector to obtain maximum laser efficiency for a given pump level. These parameters can all be expressed as functions of a single dimensionless variable z, defined as the ratio of the unsaturated small-signal gain to the dissipative (nonuseful) optical loss, multiplied by a few simple constants. Laser design tradeoff studies and performance projections can be accomplished quickly with the help of several graphs and a simple hand calculator. Sample calculations for a high-gain Nd:YAG and a low-gain alexandrite laser are presented as illustrations of the technique.

Degnan, John J.↗