Linear-model-based estimation in wall turbulence: Improved stochastic forcing and eddy viscosity terms

We use Navier–Stokes-based linear models for wall-bounded turbulent flows to estimate large-scale fluctuations at different wall-normal locations from their measurements at a single wall-normal location. In these models, we replace the nonlinear term by a combination of a stochastic forcing term and an eddy dissipation term. The stochastic forcing term plays a role in energy production by the large scales, and the eddy dissipation term plays a role in energy dissipation by the small scales. Based on the results in channel flow, we find that the models can estimate large-scale fluctuations with reasonable accuracy only when the stochastic forcing and eddy dissipation terms vary with wall distance and with the length scale of the fluctuations to be estimated. The dependence on the wall distance ensures that energy production and energy dissipation are not concentrated close to the wall but are evenly distributed across the near-wall and logarithmic regions. The dependence on the length scale of the fluctuations ensures that lower wavelength fluctuations are not excessively damped by the eddy dissipation term and hence that the dominant scales shift towards lower wavelengths towards the wall. This highlights that, on the one hand, energy extraction in wall turbulence is predominantly linear and thus physics-based linear models give reasonably accurate results. On the other hand, the absence of linearly unstable modes in wall turbulence means that the nonlinear term still plays an essential role in energy extraction and thus the modelled terms should include the observed wall distance and length scale dependencies of the nonlinear term.This work was supported by the National Natural Science Foundation of China (grant nos. 91752201, 12002147 and 12050410247), the Shenzhen Science and Technology Innovation Committee (KQTD20180411143441009), the Department of Science and Technology of Guangdong Province (grant nos. 2019B21203001 and 2020B1212030001) and the Key Special Project for Introduced Talents Team of Southern Marine Science and Engineering Guangdong Laboratory, Guangzhou (GML2019ZD0103). We acknowledge support from the Centers for Mechanical Engineering Research and Education at MIT and SUSTech, as well as from the Center for Computational Science and Engineering at SUSTech. AM and SJI are grateful for the financial support of the Australian Research Council

Bifurcation analysis of phytoplankton-fish model through parametric control by fish mortality rate and food transfer efficiency

An Algae-zooplankton fish model is studied in this article. First the proposed model is evaluated for positive invariance and boundedness. Then,the Routh-Hurwitz parameters and the Lyapunov function are used to determine the presence of a positive interior steady state and the criteria for plankton model stability (both local and global). Taylor’s sequence is also used to discuss Hopf bifurcation and the stability of bifurcated periodic solutions. The model’s bifurcation analysis reveals that Hopf-bifurcation can occur when mortality rate and food transfer efficiency are used as bifurcation parameters. Finally, we use numerical simulation to validate the analytical results

Impact of Harvesting in Three Species Food Web Model With Two Distinct Functional Responses

Abstract: The intuition with two-species models may be applied to community food web questions. The critical behavior to community function may arise only through the interaction of three or more species. In this paper we investigate the dynamical behavior of the system consisting of two preys with distinct functional responses and a predator. We also study the effect of harvesting on prey species. Harvesting is strong impact on the dynamics evaluation of population. To a certain extent it can control the long term stationary density of population efficiently. Finally the local and global stability analyses were carried out

Fuzzy Analysis of Artificial Drug Transmission Model with Optimal Control

This article presents an artificial drug abusers system consolidating the impact of treatment with psychological and physiological addicts under fuzzy parameters. In the fuzzy model, all of the parameters are considered to be triangular fuzzy numbers to represent the uncertainty that pervaded the dynamics. To handle the arrangements while avoiding problems, the fuzzy model is turned into a defuzzified model using the utility function method. The fuzzy model’s positivity and boundedness are carefully explored, and an equilibrium analysis is also completed. Both the drug-addict equilibrium and the drug-free equilibrium have established stability analyses. This article explains fuzzy optimum control using Pontryagin’s maximum principle. Finally, it is shown that the treatment alongside counselling and conducting awareness programs is more fruitful and drug-related controlling is more viable in the fuzzy nature. Likewise, we plot the 3D associations with fuzzy parameters which show the inventiveness and appropriateness of the results.2022-2

Constraints on the χ_(c1) versus χ_(c2) polarizations in proton-proton collisions at √s = 8 TeV

The polarizations of promptly produced χ_(c1) and χ_(c2) mesons are studied using data collected by the CMS experiment at the LHC, in proton-proton collisions at √s=8  TeV. The χ_c states are reconstructed via their radiative decays χ_c → J/ψγ, with the photons being measured through conversions to e⁺e⁻, which allows the two states to be well resolved. The polarizations are measured in the helicity frame, through the analysis of the χ_(c2) to χ_(c1) yield ratio as a function of the polar or azimuthal angle of the positive muon emitted in the J/ψ → μ⁺μ⁻ decay, in three bins of J/ψ transverse momentum. While no differences are seen between the two states in terms of azimuthal decay angle distributions, they are observed to have significantly different polar anisotropies. The measurement favors a scenario where at least one of the two states is strongly polarized along the helicity quantization axis, in agreement with nonrelativistic quantum chromodynamics predictions. This is the first measurement of significantly polarized quarkonia produced at high transverse momentum