On the duality between the problems of stretching and of bending of plates, 16 March - 15 September 1966
Duality of problems of stretching and of bending plates
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Duality in finite element methods.
Duality between basic equations and dependent variables in problems of plate stretching and bending applied to finite element method
Elias, Z. M.↗
Solution of coupled and singular perturbation methods using duality theory.
Dual variational techniques developed by Chan and Leininger (1972) are summarized, and duality theory in the form of the Complementary Variational Principle is employed to provide a suboptimal measure for the singular and epsilon-coupled perturbation methods proposed by Kokotovic and Cruz. The suboptimal measure is independent of any a priori knowledge of the optimal solution, thereby providing an absolute estimate of the performance loss rather than an estimate relative to the unknown optimal solution.
Chan, W. L.↗
Complementary variational principle and duality in mathematical programming.
The relationship between the complementary variational principle and duality in mathematical programming is demonstrated through a geometric approach in a Hilbert space setting. A necessary and sufficient condition for the existence of such a principle is given in the case of a convex functional constrained by linear dynamics. Its relationship to the Kuhn-Tucker saddle point theory is indicated. Applications to various programming and control problems are discussed.
Chan, W. L.↗
N-person differential games. Part 1: Duality-finite element methods
The duality approach, which is motivated by computational needs and is done by introducing N + 1 Language multipliers is addressed. For N-person linear quadratic games, the primal min-max problem is shown to be equivalent to the dual min-max problem.
Chen, G.↗
Inference in infinite-dimensional inverse problems - Discretization and duality
Many techniques for solving inverse problems involve approximating the unknown model, a function, by a finite-dimensional 'discretization' or parametric representation. The uncertainty in the computed solution is sometimes taken to be the uncertainty within the parametrization; this can result in unwarranted confidence. The theory of conjugate duality can overcome the limitations of discretization within the 'strict bounds' formalism, a technique for constructing confidence intervals for functionals of the unknown model incorporating certain types of prior information. The usual computational approach to strict bounds approximates the 'primal' problem in a way that the resulting confidence intervals are at most long enough to have the nominal coverage probability. There is another approach based on 'dual' optimization problems that gives confidence intervals with at least the nominal coverage probability. The pair of intervals derived by the two approaches bracket a correct confidence interval. The theory is illustrated with gravimetric, seismic, geomagnetic, and helioseismic problems and a numerical example in seismology.
Stark, Philip B.↗
A Duality Between Forward and Adjoint MPI Communication Routines
In this article, we explore a natural duality that exist between MPI communication routines in parallel programs, and show the ease of its adjoint implementation via pointers.
adjoint↗
Quark-hadron duality in the free neutron F2 structure function
The Thomas Jefferson National Accelerator Facility (JLab) experiment BONuS used a novel spectator-tagging technique to measure the inclusive electron-free neutron scattering cross section and extract the F2 structure function. This data was used to reconstruct moments of F2 in the three prominent resonance region and the moments integrated over the entire resonance region. Comparisons of the experimental results with moments obtained from global parton distribution function parametrization seem to suggest that the quark-hadron duality hypothesis holds locally for the neutron in the second and third resonance regions down to Q 2 of 1 GeV 2 ; with up to 20% violations observed in the first resonance region.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Model Predictive Control of a Wave Energy Converter Using Duality Techniques
In this paper, a method for implementing model predictive control for vibration energy harvesting systems with the goal of maximizing generated energy is presented. This is generally a nonconvex problem, which can be computationally expensive and converging to a global minimum cannot be guaranteed. We introduce a dual-domain method to relax the nonconvex primal problem into a convex dual optimization problem, which can be performed in real time. Based on previous work, we determine when the duality gap is zero and, by extension, whether the global optimal primal solution is found. We demonstrate the algorithm on a single, buoy-type wave energy converter with energy storage constraints and power take-off force constraints.
16 TIDAL AND WAVE POWER↗
Measurement of H(e,e’) and D(e,e’) Cross-Sections for Bloom-Gilman Quark-Hadron Duality Study
The E12-10-002 experiment which ran in 2018 in Hall C at the Thomas Jefferson National Accelerator Facility measured the inclusive electron scattering cross-sections for hydrogen and deuterium. This was the first experiment conducted with the new Super High-Momentum Spectrometer and accompanying instrumentation. These measurements extend the previous Hall C measurements up to Q2 = 16 GeV2. This dissertation presents the analyses of the new detectors and shows the preliminary results for F2 structure function and the study of quark-hadron duality in the four nucleon-resonance regions.
Sun, Abel↗
Duality and supersymmetry constraints on the weak gravity conjecture
Positivity bounds coming from consistency of UV scattering amplitudes are not always sufficient to prove the weak gravity conjecture for theories beyond Einstein-Maxwell. Additional ingredients about the UV may be necessary to exclude those regions of parameter space which are naïvely in conflict with the predictions of the weak gravity conjecture. In this paper we explore the consequences of imposing additional symmetries inherited from the UV theory on higher-derivative operators for Einstein-Maxwell-dilaton-axion theory. Using black hole thermodynamics, for a preserved SL(2, $\mathbb{R}$) symmetry we find that the weak gravity conjecture then does follow from positivity bounds. For a preserved O(d, d; $\mathbb{R}$) symmetry we find a simple condition on the two Wilson coefficients which ensures the positivity of corrections to the charge-to-mass ratio and that follows from the null energy condition alone. We find that imposing supersymmetry on top of either of these symmetries gives corrections which vanish identically, as expected for BPS states.
79 ASTRONOMY AND ASTROPHYSICS↗
Electromagnetic duality and the electric memory effect
We study large gauge transformations for soft photons in quantum electrodynamics which, together with the helicity operator, form an ISO(2) algebra. We show that the two non-compact generators of the ISO(2) algebra correspond respectively to the residual gauge symmetry and its electromagnetic dual gauge symmetry that emerge at null infinity. The former is helicity universal (electric in nature) while the latter is helicity distinguishing (magnetic in nature). Thus, the conventional large gauge transformation is electric in nature, and is naturally associated with a scalar potential. We suggest that the electric Aharonov-Bohm effect is a direct measure for the electromagnetic memory arising from large gauge transformations.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
How to understand the tunneling in attosecond experiment?: Bohr–Einstein photon box Gedanken experiment, tunneling time and the wave particle duality
The measurement of the tunneling time (T-time) in today’s attosecond and strong field (low-frequency) experiments, despite its controversial discussion, offers a fruitful opportunity to understand time measurement and the time in quantum mechanics. In addition, as we will see in this work, a related controversial issue is the particulate nature of the radiation. The T-time in attosecond experiment and its different aspects and models, is discussed in this work, especially in relation to my model of real T-time (Kullie, 2015), where a good agreement with the experiment and an intriguing similarity to the Bohr–Einstein photon box Gedanken experiment was found. The tunneling process itself is still not well understood, but I am arguing that a scattering mechanism (by the laser wave packet) offers a possibility to understand the tunneling process in the tunneling region. This is related to the question about the corpuscular nature of light which is widely discussed in modern quantum optics experiments.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Conditions for duality between fluxes and concentrations in biochemical networks
Not Available
59 BASIC BIOLOGICAL SCIENCES↗
Duality invariance of s ≥ 3 2 fermions in AdS
Not Available
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Quark–hadron duality constraints on γZ box corrections to parity-violating elastic scattering
Not Available
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Matrix elements and duality for type 2 unitary representations of the Lie superalgebra gl(m|n)
The characteristic identity formalism discussed in our recent articles is further utilized to derive matrix elements of type 2 unitary irreducible gl(m|n) modules. In particular, we give matrix element formulae for all gl(m|n) generators, including the non-elementary generators, together with their phases on finite dimensional type 2 unitary irreducible representations which include the contravariant tensor representations and an additional class of essentially typical representations. Remarkably, we find that the type 2 unitary matrix element equations coincide with the type 1 unitary matrix element equations for non-vanishing matrix elements up to a phase.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Single Electron Self-coherence and Its Wave/Particle Duality in the Electron Microscope
Intensities in high-resolution phase-contrast images from electron microscopes build up discretely in time by detecting single electrons. A wave description of pulse-like coherent-inelastic interaction of an electron with matter implies a time-dependent coexistence of coherent partial waves. Their superposition forms a wave package by phase decoherence of 0.5 - 1 radian with Heisenbergs energy uncertainty ΔE H = $\hbar$/2 Δt -1 matching the energy loss ΔE of a coherent-inelastic interaction and sets the interaction time Δt. In these circumstances, the product of Planck's constant and the speed of light hc is given by the product of the expression for temporal coherence λ 2 /Δλ and the energy loss ΔE. Experimentally, the self-coherence length was measured by detecting the energy-dependent localization of scattered, plane matter waves in surface proximity exploiting the Goos–Hänchen shift. Chromatic-aberration Cc-corrected electron microscopy on boron nitride (BN) proves that the coherent crystal illumination and phase contrast are lost if the self-coherence length shrinks below the size of the crystal unit cell at ΔE > 200 eV. Finally, in perspective, the interaction time of any matter wave compares with the lifetime of a virtual particle of any elemental interaction, suggesting the present concept of coherent-inelastic interactions of matter waves might be generalizable.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗