Density Dependence Research Articles

Theoretical Substantiation of the Dependence of Spring Deformation of an Improved Opener

The article presents factors influencing the germination and development of plants after seeding with disk seeders. Schemes of improved two-disk seeders are proposed, forces acting on the improved seeder during operation, determination of the maximum distance between the seeder disks at the field surface level, and calculation schemes for determining the draft resistance of the serial and improved seeders, the area of the flat disk segment of the seeder, determination of the deformer, and tailstock area of the pressing plate. During the theoretical study of the seeding process, the following parameters and observations were obtained: analytical dependencies of soil density created by the pressing plate; geometric parameters of the pressing plate with a curvature radius r = 52…57 mm, plate section thickness of 2.5 mm; installation of the pressing plate insignificantly increases the draft resistance of the seeder; and the depth of the seeder’s travel has the greatest influence on spring deformation. Experimental studies reveal that the stiffness of the pressing plate is 7500…7600 N/m, ensuring an optimal furrow bottom density of 1.1–1.3 g/cm3; in the range of seed embedding depth of 0.05…0.07 m, 89% of the total number of seeds are placed compared to 76% of seeds embedded by the serial seeder.

Investigation of the properties of alumophosphate solutions and products crystallized from them

The physicochemical properties of freshly prepared alumophosphate solutions obtained in the Al(OH)3 – H3PO4 – H2O system with the molar ratio n(Al2O3) : n(P2O5) = 1.0 : 2.75 have been investigated. The density and temperature dependence of the dynamic viscosity of the studied solutions with a concentration of P2O5 300–485 g/l were studied. The values of the apparent activation energy of the viscous flow (Eη) of alumophosphate solutions are calculated and the concentration range (390–420 g/l P2O5) is established, in which Eη is practically constant and is 15.0 kJ/mol. It is suggested that the change in the activation energy of the viscous flow of alumophosphate solutions is due to their structure determined by the composition of aluminum phosphate complexes. The influence of the viscosity properties of alumophosphate solutions and their concentration on the crystallization process of hydrated alumophosphate, in particular, the duration of the induction period and the rate of phase formation, is shown.

Photo-Physical Characteristics of Janus Green B in Different Solvents and its Interaction Mechanism with Silver Nanoparticles.

This work explores the effects of solvent polarity on Janus Green B (JGB) photophysical properties. The Lippert-Mataga, Billot, and Ravi equations were utilized to calculate the singlet-state excited dipole moments (µe) and ground state dipole moments (µg) using absorption and fluorescence spectra analyses. The results showed an increase in the former, which is suggestive of electronic structural alterations upon excitation. Analysis of fluorescence quantum yield values revealed that JGB's environment had an impact on its emission characteristics; it was particularly sensitive to silver nanoparticles, suggesting possible interactions. While simulations of electron density, electrostatic potential, and energy gap (Eg) helped to understand the electronic structure of JGB, theoretical absorption spectra produced by Time Dependent Density Function Theory (TD-DFT) calculations offered insights into electronic transitions during absorption. To sum up, the present study contributes to our comprehension of the molecular behavior of JGB in various solvents by elucidating the intricate relationship among solvent polarity, molecular environment, and interactions with silver nanoparticles. Additionally, theoretical computations support the interpretation of experimental results.

MATHEMATICAL MODELLING ELECTRICALLY DRIVEN FREE SHEAR FLOWS IN A DUCT UNDER UNIFORM MAGNETIC FIELD

We consider a mathematical model of two-dimensional electrically driven laminar free shear flows in a straight duct under action of an applied uniform homogeneous magnetic field. The mathematical approach is based on studies by J.C.R. Hunt and W.E. Williams [10], Yu. Kolesnikov and H. Kalis [22,23]. We solve the system of stationary partial differential equations (PDEs) with two unknown functions of velocity U and induced magnetic field H. The flows are generated as a result of the interaction of injected electric current in liquid and the applied field using one or two couples of linear electrodes located on duct walls: three cases are considered. In dependence on direction of current injection and uniform magnetic field, the flows between the end walls are realized. Distributions of velocities and induced magnetic fields, electric current density in dependence on the Hartmann number Ha are studied. The solution of this problem is obtained analytically and numerically, using the Fourier series method and Matlab.

Density‐dependent influence of ribbed mussels on salt marsh nitrogen pools and processes

Abstract Bivalves are becoming an increasingly popular tool to counteract eutrophication, particularly in vegetated coastal ecosystems where synergistic interactions between bivalves and plants can govern important N sequestration pathways. In turn, new calls to evaluate how bivalve densities modify N pools and processes across multiple scales have surfaced. Ribbed mussels, Geukensia demissa, and their relationship with smooth cordgrass present a classic demonstration of positive bivalve‐plant interactions and offer a useful model for assessing density dependence. We measure porewater ammonium concentrations, N stable isotope signatures in cordgrass tissue, and sediment N fluxes in mussel aggregations and in cordgrass‐only plots across a southeastern U.S. salt marsh. In addition to measuring the effect of mussel presence, we evaluate mussel density dependence through a multiscale approach. At the patch scale, we quantify mussel density effects within their aggregations (individuals m−2) while at a larger landscape scale, we quantify mussel density effects on the cordgrass‐only areas they neighbour (individuals ~30 m−2). Porewater ammonium concentrations were halved in mussel biodeposits relative to sediments in cordgrass‐only areas and negatively related to mussel density within aggregations. Leaf clip ẟ15N signatures were nearly 2‰ higher in cordgrass growing among mussel aggregations and increased with increasing patch mussel density. Microcosm incubations showed that mussels enhanced N2 flux (i.e., nitrogen removal) and DIN flux (i.e., N regeneration) into the water column, where only nitrogen removal increased with increasing patch‐scale mussel density. Across the marsh landscape, mussel coverage drove ammonium accumulation and N2 flux in sediments. Synthesis. Our results suggest that, at the patch scale, mussels stimulate the microbial metabolism of N, the assimilation of this bioavailable N by cordgrass, and nitrogen removal in a positive, density‐dependent manner. Tidal currents redistribute mussel biodeposits from mussel aggregations to surrounding areas, influencing biogeochemical transformations at scales beyond their physical footprint. We emphasize that the N regeneration potential of bivalve populations is a significant metric contributing to their mitigation potential and that bivalve density effects may be non‐linear, vary across patch to ecosystem scales, and have differing implications for the plants with which they interact.

Nuclear Matter Equation of State in the Brueckner–Hartree–Fock Approach and Standard Skyrme Energy Density Functionals

The equation of state of asymmetric nuclear matter as well as the neutron and proton effective masses and their partial-wave and spin–isospin decomposition are analyzed within the Brueckner–Hartree–Fock approach. Theoretical uncertainties for all these quantities are estimated by using several phase-shift-equivalent nucleon–nucleon forces together with two types of three-nucleon forces, phenomenological and microscopic. It is shown that the choice of the three-nucleon force plays an important role above saturation density, leading to different density dependencies of the energy per particle. These results are compared to the standard form of the Skyrme energy density functional, and we find that it is not possible to reproduce the BHF predictions in the (S,T) channels in symmetric and neutron matter above saturation density, already at the level of the two-body interaction, and even more including the three-body interaction.

Towards the understanding of convective dissolution in confined porous media: thin bead pack experiments, two-dimensional direct numerical simulations and physical models

We consider the process of convective dissolution in a homogeneous and isotropic porous medium. The flow is unstable due to the presence of a solute that induces a density difference responsible for driving the flow. The mixing dynamics is thus driven by a Rayleigh–Taylor instability at the pore scale. We investigate the flow at the scale of the pores using Hele-Shaw type experiment with bead packs, two-dimensional direct numerical simulations and physical models. Experiments and simulations have been specifically designed to mimic the same flow conditions, namely matching porosities, high Schmidt numbers and linear dependency of fluid density with solute concentration. In addition, the solid obstacles of the medium are impermeable to fluid and solute. We characterise the evolution of the flow via the mixing length, which quantifies the extension of the mixing region and grows linearly in time. The flow structure, analysed via the centreline mean wavelength, is observed to grow in agreement with theoretical predictions. Finally, we analyse the dissolution dynamics of the system, quantified through the mean scalar dissipation, and three mixing regimes are observed. Initially, the evolution is controlled by diffusion, which produces solute mixing across the initial horizontal interface. Then, when the interfacial diffusive layer is sufficiently thick, it becomes unstable, forming finger-like structures and driving the system into a convection-dominated phase. Finally, when the fingers have grown sufficiently to touch the horizontal boundaries of the domain, the mixing reduces dramatically due to the absence of fresh unmixed fluid. With the aid of simple physical models, we explain the physics of the results obtained numerically and experimentally. The solute evolution presents a self-similar behaviour, and it is controlled by different length scales in each stage of the mixing process, namely the length scale of diffusion, the pore size and the domain height.

Effect of polymer concentration and cross-linking density on the microstructure and properties of polyimide aerogels

Polyimide aerogels display excellent mechanical strength, high thermal stability, low thermal conductivity, and outstanding dielectric properties. Typically, the synthesis of polyimide aerogels involves the polycondensation of dianhydride and diamine into poly(amic acid) (PAA) oligomers, which are then cross-linked and chemically imidized into polyimide. The stoichiometry of dianhydride and diamine determines the number of repeat units and length of the PAA oligomers, which in turn determines the cross-linking density. Despite the critical role of polymer concentration and number of repeating units in determining the microstructure and properties of polyimide aerogels, few detailed studies exist on these two parameters. Here, we synthesized and characterized 16 polyimide aerogel formulations from the common monomers biphenyl-3,3′,4,4′-tetracarboxylic dianhydride (BPDA) and 4,4′-oxydianiline (ODA), with different repeat units (n = 5, 15, 30, 45) and total polymer concentrations (4, 7, 10, 13 wt%). An increased polymer concentration accelerated gelation and enhanced the mechanical performance of aerogels, but surprisingly, it also led to higher volumetric shrinkage during aging, solvent exchange, and supercritical drying (SCD). Specific surface areas (SSAs) reached a maximum at intermediate polymer concentrations. A shorter oligomer chain length, i.e., a higher cross-linking density, led to moderately higher SSAs (between 320 and 400 m2/g) and reduced shrinkage, resulting in lower densities for a given polymer concentration. The density dependence of the thermal conductivity exhibits a pronounced U-shaped curve with a minimum in thermal conductivity of 21–23 mW/(m·K) between 0.080 and 0.120 g/cm3, with somewhat lower values for more highly cross-linked aerogels. This systematic study of polyimide aerogels forms the basis for designing polyimide aerogels with tailored properties for targeted applications.Graphical

Inclusive quasielastic neutrino-nucleus scattering with energy density functional nuclear models* *Supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (2018R1A5A1025563, 2023R1A2C1003177, IBS-R031-D1)

In this study, we calculated the inclusive charged-current neutrino-nucleus scattering from 40Ar in the quasielastic region. To explore the effect of uncertainties stemming from the nuclear structure, we used the KIDS (Korea-IBS-Daegu-SKKU) nuclear energy density functional and Skyrme force models, namely SLy4, SkI3, and MSk7. These models were selected to have distinct behavior in terms of the density dependence of the symmetry energy and the effective mass of the nucleon. In the charged-current neutrino scattering, the single- and double-differential cross sections were calculated for various kinematics. Total cross sections are reported as a function of the incident neutrino energy. The theoretical cross sections were compared with experimental data, and the roles of the effective mass and symmetry energy were investigated in terms of charged-current neutrino-nucleus scattering.

Controlled Self-Assembly of Nanoscale Superstructures in Phase-Change Ge-Sb-Te Nanowires.

Controlled growth of semiconductor nanowires with atomic precision offers the potential to tune the material properties for integration into scalable functional devices. Despite significant progress in understanding the nanowire growth mechanism, definitive control over atomic positions of its constituents, structure, and morphology via self-assembly remains challenging. Here, we demonstrate an exquisite control over synthesis of cation-ordered nanoscale superstructures in Ge-Sb-Te nanowires with the ability to deterministically vary the nanowire growth direction, crystal facets, and periodicity of cation ordering by tuning the relative precursor flux during synthesis. Furthermore, the role of anisotropy on material properties in cation-ordered nanowire superstructures is illustrated by fabricating phase-change memory (PCM) devices, which show significantly different growth direction dependent amorphization current density. This level of control in synthesizing chemically ordered nanoscale superstructures holds potential to precisely modulate fundamental material properties such as the electronic and thermal transport, which may have implications for PCM, thermoelectrics, and other nanoelectronic devices.

Fluid statics of a self-gravitating isothermal sphere of van der Waals' gas

We subject to scrutiny the physical consistency of adopting the perfect-gas thermodynamic model within self-gravitation circumstances by studying the fluid statics of a self-gravitating isothermal sphere with the van der Waals' thermodynamic model, whose equation of state features well-known terms that account for molecular attraction and size. The governing equations are formulated for any thermodynamic model with two intensive degrees of freedom, applied with the van der Waals' model and solved numerically in nondimensional form by finite-difference algorithms. After a brief summary of thermodynamic characteristics possessed by the van der Waals' model, and relevant to the present study, we proceed to the description of the results in terms of comparative graphs illustrating radial profiles of density, pressure, and gravitational field. We complement them with graphs that compare the dependence of central and wall densities on gravitational number for both perfect-gas and van der Waals' models and that attest dramatically and unequivocally how the presence of molecular-attraction and -size terms removes questionable fluid-statics results systematically found accompanying the perfect-gas model in standard treatments. We also describe, within a very brief and preliminary digression, how the sanitizing action of the mentioned terms affects the thermodynamics of the isothermal sphere by providing evidence of how the gravitational correction to entropy corresponding to the van der Waals' model makes sure that there is no risk of gravothermal catastrophes, negative specific heats, and thermal instabilities. Furthermore, we investigate the phenomenology related to self-gravitationally induced both liquid-gas phase equilibria and metastable-gas states and we describe how they arise naturally and self-consistently from the governing equations. We conclude with a summary of the main results and with a challenging proposal of future work meant to attempt a revalorization the perfect-gas model.

Plasma propagation velocity dependence on driving and restricting forces

According to the time-averaged expression for an alternating electric field, the normalized electromagnetic pressure is proportional to the square of the voltage intensity and inversely proportional to the square of the voltage repetition frequency. Moreover, the plasma propagation velocity is either directly proportional, inversely proportional, or nonproportional to the normalized electromagnetic pressure at all neutral gas flow rates. Because the plasma current is only directly proportional to the normalized electromagnetic pressure at all neutral gas flow rates, the dependence of the plasma density on the electromagnetic pressure changes to obtain a balance of dependence. In the momentum transfer equation, plasma density does not originally depend on electromagnetic pressure, but the dynamic pressure associated with the neutral gas flow also exerts a force on the plasma through collisions. Therefore, when the ionization generation of plasma by collisions between the plasma and neutral particles is dominant over recombination by collisions, the plasma density is square proportional or directly proportional to the electromagnetic pressure.

A unified theory of the self-similar supersonic Marshak wave problem

We present a systematic study of the similarity solutions for the Marshak wave problem in the local thermodynamic equilibrium (LTE) diffusion approximation and in the supersonic regime. Self-similar solutions exist for a temporal power law surface temperature drive and a material model with power law temperature dependent opacity and energy density. The properties of the solutions in both linear and nonlinear conduction regimes are studied as a function of the temporal drive, opacity, and energy density exponents. We show that there exists a range of the temporal exponent for which the total energy in the system decreases, and the solution has a local maxima. For nonlinear conduction, we specify the conditions on the opacity and energy density exponents under which the heat front is linear or even flat and does possess its common sharp characteristic; this characteristic is independent of the drive exponent. We specify the values of the temporal exponents for which analytical solutions exist and employ the Hammer–Rosen perturbation theory to obtain highly accurate approximate solutions, which are parameterized using only two numerically fitted quantities. The solutions are used to construct a set of benchmarks for supersonic LTE radiative heat transfer, including some with unusual and interesting properties such as local maxima and non-sharp fronts. The solutions are compared in detail to implicit Monte Carlo and discrete-ordinate transport simulations as well gray diffusion simulations, showing a good agreement, which highlights their usefulness as a verification test problem for radiative transfer simulations.

Demography, Structure, and Composition of a Low-Disturbance Forest in Luzon, Philippines

Tropical forests continue to face deforestation in countries such as the Philippines. To look at the long-term behavior of forests in response to intrinsic and extrinsic factors, continual monitoring of forest dynamics is needed. To do this, we established a 2-ha permanent tropical forest plot in a low-disturbance area in Maluyon, Philippines. We addressed three main questions: 1) How does the plot change through time? 2) How do different species in the plot change through time? 3) Would the responses differ by tree size? We measured, mapped, and identified all trees >1 cm in diameter in 2011. In 2015, we re-measured surviving trees and measured, mapped, and identified recruits. A total of 177 tree species were found in the plot. The forest exhibited a mean growth rate of 0.054 cm/year, mortality rate of 0.011%/year, and recruitment rate of 0.019%/year. Overall growth and mortality rates were lower in Maluyon than in other plots, possibly due to the forest’s high tree density and low disturbance. Species-specific rates revealed the presence of both the growth-survival and the stature-recruitment trade-offs. Size class analysis showed higher growth rates in large-sized than in small-sized trees. In contrast, small-sized trees exhibited a higher mortality rate compared to large-sized trees, likely due to density dependence. Key findings of the study may be utilized to increase the success rate of restoration efforts in this watershed. Using a mix of fast-growing, generalist species with high survival rates (e.g., Allophyllus cobbe and Anisoptera thurifera) is highly recommended.

Disparities in tree mortality among plant functional types (PFTs) in a temperate forest: Insights into size-dependent and PFT-specific patterns

Tree mortality significantly influences forest structure and function, yet our understanding of its dynamic patterns among a range of tree sizes and among different plant functional types (PFTs) remains incomplete. This study analysed size-dependent tree mortality in a temperate forest, encompassing 46 tree species and 32,565 individuals across different PFTs (i.e., evergreen conifer vs. deciduous broadleaf species, shade-tolerant vs. shade-intolerant species). By employing all-subset regression procedures and logistic generalized linear mixed-effects models, we identified distinct mortality patterns influenced by biotic and abiotic factors. Our results showed a stable mortality pattern in evergreen conifer species, contrasted by a declining pattern in deciduous broadleaf and shade-tolerant, as well as shade-intolerant species, across size classes. The contribution to tree mortality of evergreen conifer species shifted from abiotic to biotic factors with increasing size, while the mortality of deciduous broadleaf species was mainly influenced by biotic factors, such as initial diameter at breast height (DBH) and conspecific negative density. For shade-tolerant species, the mortality of small individuals was mainly determined by initial DBH and conspecific negative density dependence, whereas the mortality of large individuals was subjected to the combined effect of biotic (competition from neighbours) and abiotic factors (i.e., convexity and pH). As for shade-intolerant species, competition from neighbours was found to be the main driver of tree mortality throughout their growth stages. Thus, these insights enhance our understanding of forest dynamics by revealing the size-dependent and PFT-specific tree mortality patterns, which may inform strategies for maintaining forest diversity and resilience in temperate forest ecosystems.

Versatile aggregation induced emissive molecular probes incorporating different donor/acceptor groups for tunable multiple color fluorescence

Excited state intramolecular proton transfer (ESIPT) and aggregation induced emission active multicolour fluorescent probes for bioimaging applications has grown popularly in recent years. Herein, we report a series of different donor/acceptor units (Cl, NO2 and O–CH3) bearing anthracene-salicylaldehyde based fluorescent probes and their antibacterial activity and fluorescence imaging of E. Coli bacteria and zebrafish embryos. All the compounds (ASA1, ASA2, ASA3 and ASA4) synthesized via facile one pot condensation reaction of anthracene hydrazide with Salicylaldehyde, 5-Chlorosalicylaldehyde, 5-Nitrosalicylaldehyde, 5-methoxysalicylaldehyde and characterized using all the possible spectroscopic techniques. The noteworthy tuneable emission wavelength shifts from 471 nm to 625 nm and ESIPT characteristics of the compounds were demonstrated through photophysical experiments and single crystal X-ray diffraction analysis. All the experimental results were completely analyzed theoretically on the ground as well as the excited state using density functional theory (DFT) and time dependent density functional theory (TD-DFT) calculations. Compounds ASA1-ASA4 showed fascinating different colour fluorescent (Green, Yellow and Orange) aggregation induced emission features in the THF-H2O mixture. AIE characteristics of ASA1, ASA2, ASA3 and ASA4 were recognized using absorption, emission, fluorescence quantum yield (Φ), DLS and SEM analysis. ASA1, ASA2, ASA3 and ASA4 showed excellent antibacterial activity and ROS generation against E. Coli bacteria. Further, owing to their multicolour fluorescent property all the compounds successfully applied for fluorescent imaging in E. Coli bacteria and live zebrafish embryos.

What drives wild boar density and population growth in Mediterranean environments?

Accurate prediction of fluctuations of wildlife local number of individuals is crucial for effective population management to minimise human-wildlife conflicts. Climate, habitat, food availability, and density dependence are among the main factors influencing mammalian population dynamics. In southern Europe, precipitation and temperature, particularly during summer have been suggested as key factors affecting wild boar (Sus scrofa L.). However, there is uncertainty regarding the role of these factors and the mechanisms driving population fluctuations. This study utilized long-term data of wild boar populations from 14 study sites collected for 23 years in Catalonia, Spain, to analyse the factors that drive population density and growth rate. Generalized Additive Mixed Models (GAMM) explained respectively, 94 % and 65 % of the density and growth rate variability. Spring precipitation in both current and previous year, female weight, and forest cover (particularly above 60 %) were directly associated with higher wild boar densities and population growth rates. The interaction between crop cover and total annual precipitation also played a significant role in determining population density. Higher densities were linked to lower population growth in the following year, likely due to a density-dependent process. These results suggest that the expected decrease in rainfall linked with global warming may limit the availability of natural resources and potentially slow wild boar population growth. Nevertheless, wild boar can exploit alternative anthropogenic food sources, potentially leading to an increase of human-wildlife conflicts. Therefore, incorporating management policies aimed at restricting wild boar access to human food sources is key for controlling their reproductive output. Additionally, landscape management strategies targeted at diminishing refuge and resource availability in regions experiencing high wild boar impact are essential for contributing to sustainable coexistence between wild boars and human populations.

Quark star matter in the color-flavor-locked state with a density-dependent quark mass model

The properties of strange quark matter (SQM) and color-flavor-locked (CFL) quark matter are investigated in quark stars (QSs) at zero temperature case within confined-isospin-density-dependent-mass (CIDDM) model. The mass–radius relation of QSs are also studied by considering newly proposed mass–radius constraints in CFL phase. Our results indicate that we can obtain more stable and stiffer equation of state (EOS) by considering CFL phase within CIDDM model at zero temperature. While the GW190814's secondary component with a mass around 2.6 M ⊙ cannot be QSs within CIDDM model in SQM case, it can be well described as QSs by considering CFL phase within CIDDM model in this work. In particular, we further construct a density-dependent pairing energy gap to connect the EOS of SQM and CFL quark matter with constant pairing energy gap Δ, and the results indicate that by extending the paring energy gap to include density dependence, the mass–radius lines within CIDDM model can satisfy most of the mass–radius region constraints in recent pulsar observations.

Effects of the Charge Density of Nanopapers Based on Carboxymethylated Cellulose Nanofibrils Investigated by Complementary Techniques.

Cellulose nanofibrils (CNFs) with different charge densities were prepared and investigated by a combination of different complementary techniques sensitive to the structure and molecular dynamics of the system. The morphology of the materials was investigated by scanning electron microscopy (SEM) and X-ray scattering (SAXS/WAXS). The latter measurements were quantitatively analyzed yielding to molecular parameters in dependence of the charge density like the diameter of the fibrils, the distance between the fibrils, and the dimension of bundles of nanofibrils, including pores. The influence of water on the properties and the charge density is studied by thermogravimetric analysis (TGA), differential scanning calorimetry (DSC) and broadband dielectric spectroscopy. The TGA measurements reveal two mass loss processes. The one at lower temperatures was related to the loss of water, and the second process at higher temperatures was related to the chemical decomposition. The resulting char yield could be correlated to the distance between the microfibrils. The DSC investigation for hydrated CNFs revealed three glass transitions due to the cellulose segments surrounded by water molecules in different states. In the second heating scan, only one broad glass transition is observed. The dielectric spectra reveal two relaxation processes. At low temperatures or higher frequencies, the β-relaxation is observed, which is assigned to localized fluctuation of the glycosidic linkage. At higher temperatures and lower frequencies, the α-relaxation takes places. This relaxation is due to cooperative fluctuations in the cellulose segments. Both processes were quantitatively analyzed. The obtained parameters such as the relaxation rates were related to both the morphological data, the charge density, and the content of water for the first time.

Spin-orbit torques due to topological insulator surface states: an in-plane magnetization as a probe of extrinsic spin-orbit scattering.

Topological insulator (TI) surface states exert strong spin-orbit torques. When the magnetization is in the plane its interaction with the TI conduction electrons is non-trivial, and is influenced by extrinsic spin-orbit scattering. This is expected to be strong in TIs but is difficult to calculate and to measure unambiguously. Here we show that extrinsic spin-orbit scattering sizably renormalizes the surface state spin-orbit torque resulting in a strong density dependence. The magnitude of the renormalization of the spin torque and the effect of spin-orbit scattering on the relative sizes of the in-plane and out-of-plane field-like torques have strong implications for experiment: We propose two separate experimental signatures for the measurement of its presence.