Mathematical modeling of the correlation function and the energy spectra of the noise modulation function

2021 ◽  
pp. 77-92
Author(s):  
В.И. Воловач
Keyword(s):  
Mathematical Modeling ◽  
Correlation Function ◽  
Energy Spectrum ◽  
Correlation Functions ◽  
Narrow Band ◽  
Energy Spectra ◽  
Discrete Component ◽  
Modulation Function ◽  
Interference Modulation ◽  
Multiplicative Interference

Рассмотрены и проанализированы вопросы, связанные с математическим моделированием корреляционных функций и энергетических спектров функции помеховой модуляции. Показано, что при воздействии на сигнал узкополосной мультипликативной помехи в энергетическом спектре функции помеховой модуляции присутствует дискретная составляющая, мощность которой зависит от глубины фазовых искажений. При импульсно-флуктуационной модулирующей помехе с детерминированным тактовым интервалом энергетический спектр функции помеховой модуляции представляет собой сумму непрерывной и дискретной частей. The issues related to mathematical modeling of correlation functions and energy spectra of the noise modulation function are considered and analyzed. It is shown that when a signal is affected by a narrow-band multiplicative interference, a discrete component is present in the energy spectrum of the interference modulation function, the power of which depends on the depth of the phase distortion. In the case of pulse-fluctuating modulating interference with a deterministic clock interval, the energy spectrum of the interference modulation function is the sum of the continuous and discrete parts.

scholarly journals From correlation functions to event shapes in QCD

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
D. Chicherin ◽  
J. M. Henn ◽  
E. Sokatchev ◽  
K. Yan
Keyword(s):  
Correlation Function ◽  
Correlation Functions ◽  
Event Shape ◽  
Proof Of Concept ◽  
Yang Mills ◽  
Point Correlation ◽  
Point Correlation Function ◽  
Event Shapes ◽  
A Charge ◽  
Conserved Currents

Abstract We present a method for calculating event shapes in QCD based on correlation functions of conserved currents. The method has been previously applied to the maximally supersymmetric Yang-Mills theory, but we demonstrate that supersymmetry is not essential. As a proof of concept, we consider the simplest example of a charge-charge correlation at one loop (leading order). We compute the correlation function of four electromagnetic currents and explain in detail the steps needed to extract the event shape from it. The result is compared to the standard amplitude calculation. The explicit four-point correlation function may also be of interest for the CFT community.

scholarly journals On the three-dimensional spatial correlations of curved dislocation systems

2021 ◽  
Vol 5 (1) ◽  
Author(s):  
Joseph Pierre Anderson ◽  
Anter El-Azab
Keyword(s):  
Correlation Function ◽  
Slip System ◽  
Correlation Functions ◽  
Mean Field ◽  
Coarse Graining ◽  
Dislocation Dynamics ◽  
Coarse Grained ◽  
Spatial Correlation Function ◽  
Line System ◽  
Dislocation Densities

AbstractCoarse-grained descriptions of dislocation motion in crystalline metals inherently represent a loss of information regarding dislocation-dislocation interactions. In the present work, we consider a coarse-graining framework capable of re-capturing these interactions by means of the dislocation-dislocation correlation functions. The framework depends on a convolution length to define slip-system-specific dislocation densities. Following a statistical definition of this coarse-graining process, we define a spatial correlation function which will allow the arrangement of the discrete line system at two points—and thus the strength of their interactions at short range—to be recaptured into a mean field description of dislocation dynamics. Through a statistical homogeneity argument, we present a method of evaluating this correlation function from discrete dislocation dynamics simulations. Finally, results of this evaluation are shown in the form of the correlation of dislocation densities on the same slip-system. These correlation functions are seen to depend weakly on plastic strain, and in turn, the dislocation density, but are seen to depend strongly on the convolution length. Implications of these correlation functions in regard to continuum dislocation dynamics as well as future directions of investigation are also discussed.

A Side-Peak Cancellation Scheme for Unambiguous BOC Signal Tracking

2015 ◽  
Vol 764-765 ◽  
pp. 462-465
Author(s):  
Keun Hong Chae ◽  
Hua Ping Liu ◽  
Seok Ho Yoon
Keyword(s):  
Correlation Function ◽  
Correlation Functions ◽  
Numerical Results ◽  
Tracking Performance ◽  
Side Peak ◽  
Signal Tracking ◽  
Partial Correlations

In this paper, we propose a side-peak cancellation scheme for unambiguous BOC signal tracking. We obtain partial correlations using a pulse model of a BOC signal, and then, we finally obtain an unambiguous correlation function based on the partial correlations. The proposed correlation function is confirmed from numerical results to provide an improved tracking performance over the conventional correlation functions.

QUANTUM MAGNETIC VORTICES AT FINITE TEMPERATURE IN (3 + 1)-D

2000 ◽  
Vol 15 (11n12) ◽  
pp. 731-735
Author(s):  
E. C. MARINO ◽  
D. G. G. SASAKI
Keyword(s):  
Correlation Function ◽  
Correlation Functions ◽  
Large Distance ◽  
Finite Temperature ◽  
Higgs Model ◽  
Magnetic Vortex ◽  
Zero Temperature ◽  
Magnetic Vortices ◽  
Vortex Lines ◽  
Distance Behavior

We study the effect of a finite temperature on the correlation function of quantum magnetic vortex lines in the framework of the (3 + 1)-dimensional Abelian Higgs model. The vortex energy is inferred from the large distance behavior of these correlation functions. For large straight vortices of length L, we obtain that the energy is proportional to TL2 differently from the zero temperature result which is proportional to L. The case of closed strings is also analyzed. For T = 0, we evaluate the correlation function and energy of a large ring. Finite closed vortices do not exist as genuine excitations for any temperature.

System analysis of the assessment of the influence of multiplicative interference on the Conditions signal resolutions based on statistical criteria using mathematical modeling

2020 ◽  
pp. 82-95
Author(s):  
В.И. Воловач
Keyword(s):  
Mathematical Modeling ◽  
Frequency Shift ◽  
Delay Time ◽  
System Analysis ◽  
Statistical Characteristics ◽  
Statistical Criterion ◽  
Multiplicative Interference ◽  
Statistical Criteria

Проведен системный анализ влияния мультипликативных помех на условия разрешения сигналов на основе статистического критерия с помощью математического моделирования. Показано, что интервалы разрешения по времени запаздывания и частотному сдвигу при известных статистических характеристиках сигналов, аддитивных и мультипликативных помех однозначно определяются вероятностями правильного и ложного разрешения. A system analysis of the influence of multiplicative interference on the signal resolution conditions based on a statistical criterion using mathematical modeling is performed. It is shown that the resolution intervals for delay time and frequency shift with known statistical characteristics of signals, additive and multiplicative interference are uniquely determined by the probabilities of correct and false resolution.

scholarly journals Random boundary geometry and gravity dual of $$ T\overline{T} $$ deformation

2020 ◽  
Vol 2020 (11) ◽  
Author(s):  
Shinji Hirano ◽  
Masaki Shigemori
Keyword(s):  
Field Theory ◽  
Free Energy ◽  
Energy Spectrum ◽  
Correlation Functions ◽  
Degrees Of Freedom ◽  
Dual Language ◽  
Renormalization Group Flow ◽  
Conformal Field ◽  
Logarithmic Corrections ◽  
Group Flow

Abstract We study the random geometry approach to the $$ T\overline{T} $$ T T ¯ deformation of 2d conformal field theory developed by Cardy and discuss its realization in a gravity dual. In this representation, the gravity dual of the $$ T\overline{T} $$ T T ¯ deformation becomes a straightforward translation of the field theory language. Namely, the dual geometry is an ensemble of AdS3 spaces or BTZ black holes, without a finite cutoff, but instead with randomly fluctuating boundary diffeomorphisms. This reflects an increase in degrees of freedom in the renormalization group flow to the UV by the irrelevant $$ T\overline{T} $$ T T ¯ operator. We streamline the method of computation and calculate the energy spectrum and the thermal free energy in a manner that can be directly translated into the gravity dual language. We further generalize this approach to correlation functions and reproduce the all-order result with universal logarithmic corrections computed by Cardy in a different method. In contrast to earlier proposals, this version of the gravity dual of the $$ T\overline{T} $$ T T ¯ deformation works not only for the energy spectrum and the thermal free energy but also for correlation functions.

Diffraction properties of a strongly bent diamond crystal used as a dispersive spectrometer for XFEL pulses

2019 ◽  
Vol 26 (4) ◽  
pp. 1069-1072 ◽  
Author(s):  
Liubov Samoylova ◽  
Ulrike Boesenberg ◽  
Aleksandr Chumakov ◽  
Vladimir Kaganer ◽  
Ilia Petrov ◽  
...  
Keyword(s):  
Experimental Data ◽  
Energy Spectrum ◽  
Strain Gradient ◽  
Free Electron ◽  
Diamond Crystal ◽  
Energy Spectra ◽  
Theoretical Modelling ◽  
Free Electron Lasers ◽  
X Ray ◽  
Stochastic Nature

Self-amplified spontaneous emission (SASE) enables X-ray free-electron lasers (XFELs) to generate hard X-ray pulses of sub-100 fs duration. However, due to the stochastic nature of SASE, the energy spectrum fluctuates from pulse to pulse. Many experiments that employ XFEL radiation require the resolution of the spectrum of each pulse. The work presented here investigates the capacity of a thin strongly bent diamond crystal to resolve the energy spectra of hard X-ray SASE pulses by studying its diffraction properties. Rocking curves of the symmetric C*(440) reflection have been measured for different bending radii. The experimental data match the theoretical modelling based on the Takagi–Taupin equations of dynamical diffraction. A uniform strain gradient has proven to be a valid model of strain deformations in the crystal.

scholarly journals Energy spectra of muonic atoms in quantum electrodynamics

2019 ◽  
Vol 204 ◽  
pp. 05007 ◽  
Author(s):  
A. E. Dorokhov ◽  
A. A. Krutov ◽  
A. P. Martynenko ◽  
F. A. Martynenko ◽  
O. S. Sukhorukova
Keyword(s):  
Experimental Data ◽  
Perturbation Theory ◽  
Energy Spectrum ◽  
Hyperfine Structure ◽  
Nuclear Structure ◽  
Quantum Electrodynamics ◽  
Vacuum Polarization ◽  
Energy Spectra ◽  
Hyperfine Splittings ◽  
S States

Vacuum polarization, nuclear structure and recoil, radiative corrections to the hyperfine structure of S-states in muonic ions of lithium, beryllium and boron are calculated on the basis of quasipotential method in quantum electrodynamics. We consider contributions in first and second orders of perturbation theory which have the order α5 and α6 in the energy spectrum. Total values of hyperfine splittings are obtained which can be used for a comparison with future experimental data.

scholarly journals Measurement of ambient neutrons in an underground laboratory at the Kamioka Observatory

2018 ◽  
Vol 2018 (12) ◽  
Author(s):  
Keita Mizukoshi ◽  
Ryosuke Taishaku ◽  
Keishi Hosokawa ◽  
Kazuyoshi Kobayashi ◽  
Kentaro Miuchi ◽  
...  
Keyword(s):  
Monte Carlo ◽  
Energy Spectrum ◽  
Neutron Flux ◽  
Thermal Neutron Flux ◽  
Spectral Shape ◽  
Underground Laboratory ◽  
Energy Spectra ◽  
Detector Response ◽  
Total Neutron ◽  
Important Input

Abstract Ambient neutrons are one of the most serious backgrounds for underground experiments searching for rare events. The ambient neutron flux in an underground laboratory at the Kamioka Observatory was measured using a $\mathrm{^3He}$ proportional counter with various moderator setups. Since the detector response largely depends on the spectral shape, the energy spectra of the neutrons transported from the rock to the laboratory were estimated by Monte Carlo simulations. The ratio of the thermal neutron flux to the total neutron flux was found to depend on the thermalizing efficiency of the rock. Therefore, the ratio of the count rate without a moderator to that with a moderator was used to determine this parameter. Consequently, the most likely neutron spectrum predicted by the simulations for the parameters determined by the experimental results was obtained. The result suggests an interesting spectral shape, which has not been indicated in previous studies. The total ambient neutron flux is $(23.5 \pm 0.7 \ \mathrm{_{stat.}} ^{+1.9}_{-2.1} \ \mathrm{_{sys.}}) \times 10^{-6}$ cm$^{-2}$ s$^{-1}$. This result, especially the energy spectrum information, could be a new and important input for estimating the background in current and future experiments in the underground laboratory at the Kamioka Observatory.

From Brownian Motion to Bending Beams

2021 ◽  
pp. 84-98
Author(s):  
Robert W. Batterman
Keyword(s):  
Brownian Motion ◽  
Correlation Function ◽  
Correlation Functions ◽  
Materials Science ◽  
Prima Facie ◽  
Representative Volume ◽  
Representative Volume Elements ◽  
Hydrodynamic Correlation

This chapter argues that the hydrodynamic, correlation function methodology discussed in “fluid” contexts is really the same methodology employed in materials science to determine effective values for quantities like conductivity, elasticity, stiffness. Thus, Einstein’s arguments discussed in the previous chapter have a bearing on what prima facie appear to be completely different problems. The mesoscale approach using representative volume elements and correlation functions to describe the important features of those representative volume elements is presented in some detail.

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