cross term
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2022 ◽  
Vol 934 ◽  
Author(s):  
E. Guilbert ◽  
B. Metzger ◽  
E. Villermaux

The interplay between chemical reaction and substrate deformation is discussed by adapting Ranz's formulation for scalar mixing to the case of a reactive mixture between segregated reactants, initially separated by an interface whose thickness may not be vanishingly small. Experiments in a simple shear flow demonstrate the existence of three regimes depending on the Damköhler number $Da=t_s/t_c$ where $t_s$ is the mixing time of the interface width and $t_c$ is the chemical time. Instead of treating explicitly the chemical cross-term, we rationalize these different regimes by globalizing it as a production term involving a flux which depends on the rate at which the reaction zone is fed by the reactants, a formulation valid for $Da>1$ . For $Da<1$ , the reactants interpenetrate before they react, giving rise to a ‘diffusio-chemical’ regime where chemical production occurs within a substrate whose width is controlled by molecular diffusion.


Entropy ◽  
2021 ◽  
Vol 23 (12) ◽  
pp. 1675
Author(s):  
Salvador Miret-Artés ◽  
Randall S. Dumont ◽  
Tom Rivlin ◽  
Eli Pollak

In this work, our purpose is to show how the symmetry of identical particles can influence the time evolution of free particles in the nonrelativistic and relativistic domains as well as in the scattering by a potential δ-barrier. For this goal, we consider a system of either two distinguishable or indistinguishable (bosons and fermions) particles. Two sets of initial conditions have been studied: different initial locations with the same momenta, and the same locations with different momenta. The flight time distribution of particles arriving at a `screen’ is calculated in each case from the density and flux. Fermions display broader distributions as compared with either distinguishable particles or bosons, leading to earlier and later arrivals for all the cases analyzed here. The symmetry of the wave function seems to speed up or slow down the propagation of particles. Due to the cross terms, certain initial conditions lead to bimodality in the fermionic case. Within the nonrelativistic domain, and when the short-time survival probability is analyzed, if the cross term becomes important, one finds that the decay of the overlap of fermions is faster than for distinguishable particles which in turn is faster than for bosons. These results are of interest in the short time limit since they imply that the well-known quantum Zeno effect would be stronger for bosons than for fermions. Fermions also arrive earlier and later than bosons when they are scattered by a δ-barrier. Although the particle symmetry does affect the mean tunneling flight time, in the limit of narrow in momentum initial Gaussian wave functions, the mean times are not affected by symmetry but tend to the phase time for distinguishable particles.


2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Bo Yang ◽  
Jun Tang ◽  
Chen Yang ◽  
Xiaofeng Dong ◽  
Kun Huang ◽  
...  

Aiming at the operation and maintenance requirements of the fault location of high-temperature superconducting cables, a fault location method of high-temperature superconducting cables based on the improved time-frequency domain reflection method and EEMD noise reduction is proposed. Considering the cross-term interference problem in the traditional time-frequency domain reflection method, this paper introduces the affine transformation to project the time-frequency distribution of the self-term and the cross term and further highlights the characteristic differences between the two through coordinate transformation, and the particle swarm algorithm is employed to solve the optimal stagger angle of the affine transformation. The unscented particle filter is adopted to separate the cross term, and EEMD noise reduction is introduced to solve the signal noise problem. Finally, two software programs, PSCAD and MATLAB, are employed for joint simulation to build a model of high-temperature superconducting cable. The simulation example shows that the proposed method in this paper can eliminate the cross-term interference of the traditional time-frequency domain reflection method, effectively locate the fault of the high-temperature superconducting cable, and improve the positioning accuracy.


2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Karolina Dorozynska ◽  
Simon Ek ◽  
Vassily Kornienko ◽  
David Andersson ◽  
Alexandra Andersson ◽  
...  

AbstractFluorescence-based multispectral imaging of rapidly moving or dynamic samples requires both fast two-dimensional data acquisition as well as sufficient spectral sensitivity for species separation. As the number of fluorophores in the experiment increases, meeting both these requirements becomes technically challenging. Although several solutions for fast imaging of multiple fluorophores exist, they all have one main restriction; they rely solely on spectrally resolving either the excitation- or the emission characteristics of the fluorophores. This inability directly limits how many fluorophores existing methods can simultaneously distinguish. Here we present a snapshot multispectral imaging approach that not only senses the excitation and emission characteristics of the probed fluorophores but also all cross term combinations of excitation and emission. To the best of the authors’ knowledge, this is the only snapshot multispectral imaging method that has this ability, allowing us to even sense and differentiate between light of equal wavelengths emitted from the same fluorescing species but where the signal components stem from different excitation sources. The current implementation of the technique allows us to simultaneously gather 24 different spectral images on a single detector, from which we demonstrate the ability to visualize and distinguish up to nine fluorophores within the visible wavelength range.


Author(s):  
Hong-Cai Xin ◽  
Bing-Zhao Li

AbstractLinear canonical transform as a general integration transform has been considered into Wigner-Ville distribution (WVD) to show more powerful ability for non-stationary signal processing. In this paper, a new WVD associated with linear canonical transform (WVDL) and integration form of WVDL (IWVDL) are presented. First, the definition of WVDL is derived based on new autocorrelation function and some properties are investigated in details. It removes the coupling between time and time delay and lays the foundation for signal analysis and processing. Then, based on the characteristics of WVDL over time-frequency plane, a new parameter estimation method, IWVDL, is proposed for linear modulation frequency (LFM) signal. Two phase parameters of LFM signal are estimated simultaneously and the cross term can be suppressed well by integration operator. Finally, compared with classical WVD, the simulation experiments are carried out to verify its better estimation and suppression of cross term ability. Error analysis and computational cost are discussed to show superior performance compared with other WVD in linear canonical transform domain. The further application in radar imaging field will be studied in the future work.


Geophysics ◽  
2021 ◽  
pp. 1-30
Author(s):  
Haifa Alsalmi ◽  
Yanghua Wang

The Wigner-Ville distribution (WVD) is a high-resolution time-frequency spectral analysis method for non-stationary signals, and yet it suffers from cross-term interference among signal components. We proposed applying a masking filter directly to the WVD time-frequency spectrum to suppress the cross-term interference. Conventional methods for suppressing the interference include the smoothed-pseudo WVD (SP-WVD) method, which incorporates smooth filtering in both time and frequency directions. We exploited the SP-WVD spectrum as a reference to design the masking filter, and thus the mask filtered WVD (MF-WVD) procedure is data adaptive. The MF-WVD method preserves the high-resolution energy concentration in the spectrum portrayed by the standard WVD, while suppressing the cross-term interference cleanly like in the SP-WVD method. Applying the MF-WVD method to field 3D seismic data generates high-resolution spectral cubes for various frequencies, and these spectral cubes may be used intuitively for detecting reservoir-related characteristics.


Mathematics ◽  
2021 ◽  
Vol 9 (14) ◽  
pp. 1695
Author(s):  
Tzitlali Gasca-Ortiz ◽  
Francisco J. Domínguez-Mota ◽  
Diego A. Pantoja

In this study, optimal diffusion coefficients for Lake Zirahuén, Mexico, were found under particular conditions based on images taken with a drone of a dye release experiment. First, the dye patch concentration was discretized using image processing tools, and it was then approximated by an ellipse, finding the optimal major and minor axes. The inverse problem was implemented by comparing these observational data with the concentration obtained numerically from the 2D advection–diffusion equation, varying the diffusion tensor. When the tensor was isotropic, values of K11=K22≈0.003 m2/s were found; when nonequal coefficients were considered, it was found that K11≈0.005 m2/s and K22≈0.002 m2/s, and the cross-term K12 influenced the results of the orientation of the ellipse. It is important to mention that, with this simple technique, the parameter estimation had consequences of great importance as the value for the diffusion coefficient was bounded significantly under particular conditions for this site of study.


Linearly efficient RF power amplifiers have a tremendous role in wireless communication and radar systems as they lie at the front end of most RF systems. In today’s world of wireless communication, it is not an easy task to design a RF power amplifier that is linearly efficient. There are two main key challenges that one face for making RF power amplifier’s behavior linearly efficient. First is to characterize RF power amplifier’s coefficients smartly. Second is to propose an approach that works on input signal and make its behavior inverse to that of the designed amplifier behavior so that overall response of the system becomes linear. For countering first challenge, most advanced universally accepted algorithms like Memory Polynomial, Generalized Hammerstein, Cross-term Memory Polynomial and Cross-term Hammerstein are implemented to design RF power amplifier models. For countering second challenge, latest DPD algorithms are implemented which make net response of a system linear. The memory models for modelling RF power amplifier are categorized for narrowband and wideband applications. The narrowband power amplifier models include Memory Polynomial and Cross-term Memory Polynomial models whereas wideband power amplifier models include Generalized Hammerstein and Cross-term Hammerstein models. In this paper, various performance indicators like Standard Deviation (SD), Third Order Intercept (TOI), Intermodulation Distortion Products (IMD3), Modulation Error Ratio (MER), Spurious Free Dynamic Range (SFDR) and Error Vector Magnitude (EVM) are used to characterize RF power amplifier for both narrow and wide band applications. The simulation results show that under narrowband applications, Cross-term Memory Polynomial model works best as it has least standard deviation and is also satisfying other performance parameters up to appreciable level with and without DPD algorithm implementation. While for wideband applications, Cross-term Hammerstein model satisfies the performance measuring parameters excellently.


Sensors ◽  
2021 ◽  
Vol 21 (13) ◽  
pp. 4306
Author(s):  
Kewen Sun ◽  
Baoguo Yu ◽  
Mireille Elhajj ◽  
Washington Yotto Ochieng ◽  
Tengteng Zhang ◽  
...  

This paper develops novel Global Navigation Satellite System (GNSS) interference detection methods based on the Hough transform. These methods are realized by incorporating the Hough transform into three Time-Frequency distributions: Wigner–Ville distribution, pseudo -Wigner–Ville distribution and smoothed pseudo-Wigner–Ville distribution. This process results in the corresponding Wigner–Hough transform, pseudo-Wigner–Hough transform and smoothed pseudo-Wigner–Hough transform, which are used in GNSS interference detection to search for local Hough-transformed energy peak in a small limited area within the parameter space. The developed GNSS interference detection methods incorporate a novel concept of zero Hough-transformed energy distribution percentage to analyze the properties of energy concentration and cross-term suppression. The methods are tested with real GPS L1-C/A data collected in the presence of sweep interference. The test results show that the developed methods can deal with the cross-term problem with improved interference detection performance. In particular, the GNSS interference detection performance obtained with the smoothed pseudo-Wigner–Hough transform method is at least double that of the Wigner–Hough transform-based approach; the smoothed pseudo-Wigner–Hough transform-based GNSS interference detection method is improved at least 20% over the pseudo-Wigner–Hough transform-based technique in terms of the zero Hough-transformed energy percentage criteria. Therefore, the proposed smoothed pseudo-Wigner–Hough transform-based method is recommended in the interference detection for GNSS receivers, particularly in challenging electromagnetic environments.


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