scholarly journals Wavelet field decomposition and UV ‘opaqueness’

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
E. T. Tomboulis
Keyword(s):  
Field Theory ◽  
String Field Theory ◽  
Wavelet Decomposition ◽  
Large Body ◽  
Length Scale ◽  
General Version ◽  
Planck Length ◽  
Multi Resolution Analysis ◽  
Feynman Rules ◽  
Resolution Analysis

Abstract A large body of work over several decades indicates that, in the presence of gravitational interactions, there is loss of localization resolution within a fundamental (∼ Planck) length scale ℓ. We develop a general formalism based on wavelet decomposition of fields that takes this UV ‘opaqueness’ into account in a natural and mathematically well-defined manner. This is done by requiring fields in a local Lagrangian to be expandable in only the scaling parts of a (complete or, in a more general version, partial) wavelet Multi-Resolution Analysis. This delocalizes the interactions, now mediated through the opaque regions, inside which they are rapidly decaying. The opaque regions themselves are capable of discrete excitations of ∼ 1/ℓ spacing. The resulting effective Feynman rules, which give UV regulated and (perturbatively) unitary physical amplitudes, resemble those of string field theory.

Visualization of Three-Dimensional Turbulent Structure Based on Orthogonal Wavelet Decomposition

2003 ◽  
Author(s):  
Hui Li ◽  
Hui Hu ◽  
Toshio Kobayashi ◽  
Tetsuo Saga ◽  
Nobuyuki Taniguchi
Keyword(s):  
Digital Imaging ◽  
Wavelet Decomposition ◽  
Three Dimensional ◽  
Time Varying ◽  
Orthogonal Wavelet ◽  
Turbulent Structures ◽  
Vortical Structures ◽  
Multi Scale ◽  
Multi Resolution Analysis ◽  
Resolution Analysis

The orthogonal multi-resolution analysis was applied to the digital imaging photographs of lobed mixing jets for revealing the time varying turbulent structures of various scales. The image components of five different broad scales are obtained, and each image components can provide information on the multi-scale turbulent structures. The complex vortical structures of various scales were clearly extracted and visualized at different instances.

scholarly journals Towards Feynman rules for conformal blocks

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Sarah Hoback ◽  
Sarthak Parikh
Keyword(s):  
Field Theory ◽  
Effective Field Theory ◽  
Hypergeometric Functions ◽  
Power Series Expansion ◽  
Effective Field ◽  
Conformal Block ◽  
Tree Level ◽  
Conformal Blocks ◽  
Simple Set ◽  
Feynman Rules

Abstract We conjecture a simple set of “Feynman rules” for constructing n-point global conformal blocks in any channel in d spacetime dimensions, for external and exchanged scalar operators for arbitrary n and d. The vertex factors are given in terms of Lauricella hypergeometric functions of one, two or three variables, and the Feynman rules furnish an explicit power-series expansion in powers of cross-ratios. These rules are conjectured based on previously known results in the literature, which include four-, five- and six-point examples as well as the n-point comb channel blocks. We prove these rules for all previously known cases, as well as two new ones: the seven-point block in a new topology, and all even-point blocks in the “OPE channel.” The proof relies on holographic methods, notably the Feynman rules for Mellin amplitudes of tree-level AdS diagrams in a scalar effective field theory, and is easily applicable to any particular choice of a conformal block beyond those considered in this paper.

scholarly journals On Recovery Guarantees for One-Bit Compressed Sensing on Manifolds

2021 ◽  
Vol 65 (4) ◽  
pp. 953-998
Author(s):  
Mark A. Iwen ◽  
Felix Krahmer ◽  
Sara Krause-Solberg ◽  
Johannes Maly
Keyword(s):  
Compressed Sensing ◽  
Numerical Experiments ◽  
Optimal Scaling ◽  
Intrinsic Dimension ◽  
Recovery Method ◽  
Multi Resolution Analysis ◽  
Resolution Analysis

AbstractThis paper studies the problem of recovering a signal from one-bit compressed sensing measurements under a manifold model; that is, assuming that the signal lies on or near a manifold of low intrinsic dimension. We provide a convex recovery method based on the Geometric Multi-Resolution Analysis and prove recovery guarantees with a near-optimal scaling in the intrinsic manifold dimension. Our method is the first tractable algorithm with such guarantees for this setting. The results are complemented by numerical experiments confirming the validity of our approach.

scholarly journals Classical black hole scattering from a worldline quantum field theory

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
Gustav Mogull ◽  
Jan Plefka ◽  
Jan Steinhoff
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Black Hole ◽  
Quantum Field ◽  
Expectation Values ◽  
Path Integral Representation ◽  
S Matrix ◽  
Feynman Rules ◽  
Definition Of ◽  
Three Body

Abstract A precise link is derived between scalar-graviton S-matrix elements and expectation values of operators in a worldline quantum field theory (WQFT), both used to describe classical scattering of black holes. The link is formally provided by a worldline path integral representation of the graviton-dressed scalar propagator, which may be inserted into a traditional definition of the S-matrix in terms of time-ordered correlators. To calculate expectation values in the WQFT a new set of Feynman rules is introduced which treats the gravitational field hμν(x) and position $$ {x}_i^{\mu}\left({\tau}_i\right) $$ x i μ τ i of each black hole on equal footing. Using these both the 3PM three-body gravitational radiation 〈hμv(k)〉 and 2PM two-body deflection $$ \Delta {p}_i^{\mu } $$ Δ p i μ from classical black hole scattering events are obtained. The latter can also be obtained from the eikonal phase of a 2 → 2 scalar S-matrix, which we show corresponds to the free energy of the WQFT.

scholarly journals Simulation of response spectrum-compatible ground motions using wavelet-based multi-resolution analysis

2021 ◽  
pp. 002029402110130
Author(s):  
Guan Chen ◽  
Zhiren Zhu ◽  
Jun Hu
Keyword(s):  
Ground Motion ◽  
Response Spectrum ◽  
Ground Motions ◽  
Power Spectra ◽  
Simulation Method ◽  
Eurocode 8 ◽  
Effective Response ◽  
Multi Resolution Analysis ◽  
Resolution Analysis ◽  
Simulated Ground Motions

This study proposed a simple and effective response spectrum-compatible ground motions simulation method to mitigate the scarcity of ground motions on seismic hazard analysis base on wavelet-based multi-resolution analysis. The feasibility of the proposed method is illustrated with two recorded ground motions in El Mayor-Cucapah earthquake. The results show that the proposed method enriches the ground motions exponentially. The simulated ground motions agree well with the attenuation characteristics of seismic ground motion without modulating process. Moreover, the pseudo-acceleration response spectrum error between the recorded ground motion and the average of the simulated ground motions is 5.2%, which fulfills the requirement prescribed in Eurocode 8 for artificially simulated ground motions. Besides, the cumulative power spectra between the simulated and recorded ground motions agree well on both high- and low-frequency regions. Therefore, the proposed method offers a feasible alternative in enriching response spectrum-compatible ground motions, especially on the regions with insufficient ground motions.

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