Heavy inertial particles in rotating turbulence : distribution of particles in flow and evolution of Lagrangian trajectories

We revisited the problem of heavy particles suspended in homogeneous box turbulence flow subjected to rotation along the vertical axis, which introduces anisotropy along the vertical and horizontal planes. We investigate the effect of the emergent structures due to rotation, on the spatial distribution and temporal statistics of the particles. The spatial distributions were studied using the joint probability distribution function (JPDFs) of the two invariants, $Q$ and $R$, of the velocity gradient tensor. At high rotation rates, the JPDFs of Lagrangian $Q-R$ plots show remarkable deviations from the well known \textit{teardrop} shape. The cumulative probability distribution functions (CDFs) for times during which a particle remains in vortical or straining regions, show exponentially decaying tails except for the deviations at the highest rotation rate. The average residence times of the particles in vortical and straining regions are also affected considerably due to the addition of rotation. In addition, we compute the temporal velocity autocorrelation and connect it to the Lagrangian anisotropy in presence of rotation. The spatial and temporal statistics of the particles are determined by a complex competition between the rotation rate and the heaviness of the particles.Comment: 9 pages, 8 figure

Collective variables between large-scale states in turbulent convection

The dynamics in a confined turbulent convection flow is dominated by multiple long-lived macroscopic circulation states, which are visited subsequently by the system in a Markov-type hopping process. In the present work, we analyze the short transition paths between these subsequent macroscopic system states by a data-driven learning algorithm that extracts the low-dimensional transition manifold and the related new coordinates, which we term collective variables, in the state space of the complex turbulent flow. We therefore transfer and extend concepts for conformation transitions in stochastic microscopic systems, such as in the dynamics of macromolecules, to a deterministic macroscopic flow. Our analysis is based on long-term direct numerical simulation trajectories of turbulent convection in a closed cubic cell at a Prandtl number $Pr = 0.7$ and Rayleigh numbers $Ra = 10^6$ and $10^7$ for a time lag of $10^5$ convective free-fall time units. The simulations resolve vortices and plumes of all physically relevant scales resulting in a state space spanned by more than 3.5 million degrees of freedom. The transition dynamics between the large-scale circulation states can be captured by the transition manifold analysis with only two collective variables which implies a reduction of the data dimension by a factor of more than a million. Our method demonstrates that cessations and subsequent reversals of the large-scale flow are unlikely in the present setup and thus paves the way to the development of efficient reduced-order models of the macroscopic complex nonlinear dynamical system.Comment: 24 pages, 12 Figures, 1 tabl

Collective variables between large-scale states in turbulent convection

The dynamics in a confined turbulent convection flow is dominated by multiple long-lived macroscopic circulation states that are visited subsequently by the system in a Markov-type hopping process. In the present work, we analyze the short transition paths between these subsequent macroscopic system states by a data-driven learning algorithm that extracts the low-dimensional transition manifold and the related new coordinates, which we term collective variables, in the state space of the complex turbulent flow. We therefore transfer and extend concepts for conformation transitions in stochastic microscopic systems, such as in the dynamics of macromolecules, to a deterministic macroscopic flow. Our analysis is based on long-term direct numerical simulation trajectories of turbulent convection in a closed cubic cell at a Prandtl number Pr=0.7 and Rayleigh numbers Ra=106 and 107 for a time lag of 105 convective free-fall time units. The simulations resolve vortices and plumes of all physically relevant scales, resulting in a state space spanned by more than 3.5 million degrees of freedom. The transition dynamics between the large-scale circulation states can be captured by the transition manifold analysis with only two collective variables, which implies a reduction of the data dimension by a factor of more than a million. Our method demonstrates that cessations and subsequent reversals of the large-scale flow are unlikely in the present setup, and thus it paves the way for the development of efficient reduced-order models of the macroscopic complex nonlinear dynamical system

Large-scale flow in a cubic Rayleigh-B ́enard cell: Long-term turbulence statistics and Markovianity of macrostate transitions

We investigate the large-scale circulation (LSC) in a turbulent Rayleigh-B ́enard convection flow in a cubic closed convection cell by means of direct numerical simulations at a Rayleigh number Ra = 106. The numerical studies are conducted for a single flow trajectory up to 105 convective free-fall times to obtain a sufficient sampling of the four discrete LSC states and the two crossover configurations which are taken in between for short periods. It is found that the statistics and time history depends strongly on the Prandtl number Pr of the working fluid which takes values of 0.1, 0.7, and 10. It changes from very rapid switches for the lowest Prandtl number to the spontaneous lock in one of the four states for the whole period for the largest one. Alternatively, we run ensembles of up to 1800 short-term simulations to study the transition probabilities between the discrete LSC states. This second approach is also used to probe the Markov property of the dynamics. The ensemble analysis revealed that the sample size might still be too small to conclude firmly the Markovianity of the transition process from one LSC state to another even though it is indicated. PACS numbers: 47.20.Bp, 47.27-i., 02.50.G

Robust Linear Hybrid Beamforming Designs Relying on Imperfect CSI in mmWave MIMO IoT Networks

Linear hybrid beamformer designs are conceived for the decentralized estimation of a vector parameter in a millimeter wave (mmWave) multiple-input multiple-output (MIMO) Internet of Things network (IoTNe). The proposed designs incorporate both total IoTNe and individual IoTNo power constraints, while also eliminating the need for a baseband receiver combiner at the fusion center (FC). To circumvent the non-convexity of the hybrid beamformer design problem, the proposed approach initially determines the minimum mean square error (MMSE) digital transmit precoder (TPC) weights followed by a simultaneous orthogonal matching pursuit (SOMP)-based framework for obtaining the analog RF and digital baseband TPCs. Robust hybrid beamformers are also derived for the realistic imperfect channel state information (CSI) scenario, utilizing both the stochastic and norm-ball CSI uncertainty frameworks. The centralized MMSE bound derived in this work serves as a lower bound for the estimation performance of the proposed hybrid TPC designs. Finally, our simulation results quantify the benefits of the various designs developed.Comment: 15 pages, 7 figure

Weed dynamics, wheat (Triticum aestivum) yield and irrigation water-use efficiency under conservation agriculture

A field experiment was conducted to evaluate the impacts of a 12-year old conservation agriculture (CA)- based pigeon pea-wheat system on weeds, wheat crop, and resource use during winter (rabi) 2021–22. Results indicated that surface retention of residue irrespective of ZT permanent bed and N dose led to significant reduction in weed interference at 60 DAS. CA-based systems reduced weed density and dry weight considerably than CT. CA- based systems led to significantly higher wheat grain yield (by 11.6–14.9%) and net B:C (by 24.0 –28.0%) than CT, and PFBR100N and PBBR100N were slightly superior to others. PBBR100N and PBBR75N had lower irrigation water use and significantly higher irrigation water productivity than CT. Contrast analysis showed that wheat yield and water productivity were comparable between 75% N and 100% N in CA, indicating a saving of 25% N under CA

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