Nonquasineutral current equilibria as elementary structures of plasma dynamics

A study is made of the fundamental features of current filaments with a nonzero electron vorticity Ω _e ≡ B − (c/e) ▿ × p _ee ≠ 0 and the corresponding Lagrangian invariant I _e . Such current structures can exist on spatial scales of up to ω _pi ⁻¹. It is shown that the dissipative stage of the plasma evolution and the violation of Thomson’s theorem on vorticity conservation in an electron fluid are of fundamental importance for the onset of electron current structures. A key role of the screening of electric and magnetic fields at distances on the order of the magnetic Debye radius r _B = B/(4πen _e )—the main property of such current structures in a Hall medium with σB/(en _e c) ≫ 1—is stressed. Since the minimum size of a vortex structure is the London length c/ω _pe , the structures under consideration correspond to the condition r _B > c/ω _pe or B ² > 4πn _e m _e c ², which leads to strong charge separation in the filament and relativistic electron drift. It is demonstrated that the specific energy content in current structures is high at a filament current of 10–15 kA: from 100 J/cm³ at a plasma density of 10¹⁴ cm⁻³ (the parameters of a lightning leader) to 10⁷ J/cm³ for a fully ionized atmospheric-pressure air. Estimates are presented showing that the Earth’s ionosphere, circumsolar space, and interstellar space are all Hall media in which current vortex structures can occur. A localized cylindrical equilibrium with a magnetic field reversal is constructed—an equilibrium that correlates with the magnetic structures observed in intergalactic space. It is shown that a magnetized plasma can be studied by using evolutionary equations for the electron and ion Lagrangian invariants I _e and I _i . An investigation is carried out of the evolution of a current-carrying plasma in a cylinder with a strong external magnetic field and with a longitudinal electron current turned on in the initial stage—an object that can serve as the simplest electrodynamic model of a tokamak. In this case, it is assumed that the plasma conductivity is low in the initial stage and then increases substantially with time. Based on the conservation of the integral momentum of the charged particles and electromagnetic field in a plasma cylinder within a perfectly conducting wall impenetrable by particles, arguments are presented in support of the generation of a radial electric field in a plasma cylinder and the production of drift ion fluxes along the cylinder axis. A hypothesis is proposed that the ionized intergalactic gas expands under the action of electromagnetic forces.     

Study of the oxygen transfer in a disposable flexible bioreactor with surface aeration in vibrated medium

The oxygen mass transfer is a critical design parameter for most bioreactors. It can be described and analyzed by means of the volumetric mass transfer coefficient K _L a. This coefficient is affected by many factors such as geometrical and operational characteristics of the vessels, type, media composition, rheology and microorganism’s morphology and concentration. In this study, we aim to develop and characterize a new culture system based on the surface aeration of a flexible, single-used bioreactor fixed on a vibrating table. In this context, the K _L a was evaluated using a large domain of operating variables such as vibration frequency of the table, overpressure inside the pouch and viscosity of the liquid. A novel method for K _L a determination based on the equilibrium state between oxygen uptake rate and oxygen transfer rate of the system at given conditions was also developed using resting cells of baker’s fresh yeast with a measured oxygen uptake rate of 21 mg g⁻¹ h⁻¹ (at 30°C). The effect of the vibration frequency on the oxygen transfer performance was studied for frequencies ranging from 15 to 30 Hz, and a maximal K _L a of 80 h⁻¹ was recorded at 30 Hz. A rheological study of the medium added with carboxymethylcellulose at different concentrations and the effect of the liquid viscosity on K _L a were determined. Finally, the mixing time of the system was also measured using the pH method.     

Compressive and rarefactive DIA solitons beyond the KdV limit

The modified Gardner equation (MGE), showing the existence of compressive and rarefactive dust-ion-acoustic (DIA) solitons in a nonplanar dusty plasma (containing inertial ions, Boltzmann electrons, and negatively charged stationary dust) beyond the KdV Korteweg-de Vries (KdV) limit, is derived and numerically solved. The basic features of the compressive and rarefactive cylindrical and spherical DIA solitons, which are found to exist beyond the KdV limit, i.e., exist for μ ∼ 2/3 (where μ = Z _n n _d0/n _i0, z _d is the number of electrons residing onto the dust grain surface, n _d0(n _i0) is the dust (ion) number density at equilibrium, and μ ∼ 2/3 means that μ is not equal to 2/3, but it is around 2/3) are identified. These solitons (which can be referred to as DIA Gardner solitons (DIA-GSs)) are completely different from the KdV solitons because μ = 2/3 corresponds to the vanishing of the nonlinear coefficient of the KdV equation, and μ ∼ 2/3 corresponds to extremely large amplitude KdV solitons for which the validity of the reductive perturbation method breaks down. It is also shown that the properties of the nonplanar (cylindrical and spherical) DIA-GSs are significantly different from those of the one dimensional planar ones.     

Characteristic features of temperature evolution in ultracold plasmas

The theoretical interpretation of recent experiments on the time evolution of the temperature in freely expanding, ultracold plasma clouds released from a magneto-optical trap is discussed. The most interesting result of those experiments was the asymptotic behavior T _e ∝ t ^{−(1,2±0.1)}, instead of the behavior proportional to t ⁻², which was expected for a rarefied monatomic gas in the inertial expansion stage. It is shown that such a substantially slower temperature fall can be well explained by the specific properties of the equation of state of ultracold plasma with a large Coulomb coupling parameter; whereas the heat release in inelastic processes (in particular, three-body recombination) turns out to be relatively unimportant in the first approximation. This conclusion is confirmed by approximate analytic estimates from the model of virializing the energies of charged particles and also by the results of ab initio computer simulations; moreover, the computations demonstrate that the law of decrease in the electron temperature is established very rapidly, when the virialization criterion begins to be satisfied only to within a factor of order unity.     

Plasma dynamics and generation of hard radiations in experiments with cylindrical Z-pinches

A survey of experimental studies on the generation of hard ionizing radiations from dynamic cylindrical Z-pinches is presented. Comprehensive experimental data do not confirm the hypothesis that charged particles responsible for the generation of hard radiations (neutrons and X-rays) are accelerated in short-scale Z-pinch necks (m = 0). Analysis of the experimental data indicates that, in discharges in pure hydrogen and deuterium, these particles are most probably accelerated in the axial direction along H _φ ≈ 0 lines by the induction electric field generated during the initiation of the secondary near-wall breakdown, which disconnects the pinch from the power supply. In discharges excited in heavy gases and at high initial current growth rates (İ ₀ ≥ 10¹² A/s) in experiments with hydrogen and deuterium contaminated with admixtures arriving from the chamber wall, there is an additional acceleration mechanism related to the growth of the resistance of a radiatively cooled Z-pinch.     

The stability of the molybdenum-azotochelin complex and its effect on siderophore production in Azotobacter vinelandii

 Azotobacter vinelandii produces five siderophores with different metal binding properties, depending on the concentrations of Fe(III) and molybdate in the growth medium. The three lower protonation constants of the unusual bis(catecholamide) siderophore azotochelin (L) were determined by a simultaneous spectrophotometric and potentiometric titration as log K ₅=3.65(5), log K ₄=7.41(3) and log K ₃=8.54(4). The metal-ligand equilibrium constant for [MoO₂(L)]^3– was obtained from analysis of the absorbance concentration data: at 20  °C and pH 6.6, log K _eq=4(1). Based on an average log K _a value of 12.1 for the two basic phenolic oxygens of azotochelin, the equilibrium formation constant was converted into the conventional formation constant K _f(MoL) = [MoO₂L^{3 –}]/[MoO₂ ²⁺][L^{5 –}] = 10³⁵ M^–1. To assess the influence of molybdenum-siderophore interactions on metal uptake in A. vinelandii, the dose-response effect of molybdate in the growth medium on siderophore biosynthesis was followed by UV-vis spectroscopy and HPLC. It could be shown that the formation of molybdenum siderophore complexes clearly reduces the concentration of free siderophores available for iron solubilization. Furthermore, in media with initial molybdate concentrations up to 100 μM, the molybdenum azotochelin complex is the predominant molybdenum species, suggesting that azotochelin might also possess sequestering activity towards molybdenum. Even higher molybdate levels result in a complete repression of the synthesis of the tetradentate siderophore azotochelin, while they initiate the alternative release of the more efficient iron chelator, the hexadentate siderophore protochelin. Received: 20 April 1998 / Accepted: 29 June 1998     

Application of Polyelectrolyte Theory to the Study of the B-Z Transition in DNA (1)

Abstract

We have used the polyelectrolyte theory to study the ionic strength dependence of the B-Z equilibrium in DNA. A DNA molecule is molded as an infinitely long continuously charged cylinder of radius a with reduced linear charge density q. The parameters a and q for the B and Z forms were taken from X-ray data: a _B = 1nm, q _B = 4.2, a _z = 0.9 nm and q _z = 3.9. A simple theory shows that at low ionic strengths (when Debye screening length r _D>>a) the electrostatic free energy difference F ^el _Bz = F ^el _Z - F ^el _B increases with increasing ionic strength since q _B>q_z. At high ionic strengths (when r _D<<a) the F ^el _BZ would go on growing with increasing ionic strength if the inequality q _B/^a _B<q_z/a _z were valid. In the converse case when q _z/q _B<a_z/a _B the F ^el _BZ value decreases with increasing salt concentration at high ionic strength. Since X-ray data correspond to the latter case, theory predicts that the F ^el _BZ value reaches a maximum at an intermediate ionic strength of about 0.1 M (where r _D～a). We also performed rigorous calculations based on the Poisson-Boltzmann equation. These calculations have confirmed the above criterion of nonmonotonous behaviour of the F ^el _BZ value as a function of ionic strength. Different theoretical predictions for the B-Z transition in linear and superhelical molecules are discussed. Theory predicts specifically that at a very low ionic strength the Z form may prove to be more stable than the B form. Thus, one can observe the Z-B-Z transition with increasing ionic strength. In the light of our theoretical findings we discuss numerous experimental data on the B-Z transition in linear and superhelical DNA.     

Gallium uptake by transferrin and interaction with receptor 1

The kinetics and thermodynamics of Ga(III) exchange between gallium mononitrilotriacetate and human serum transferrin as well as those of the interaction between gallium-loaded transferrin and the transferrin receptor 1 were investigated in neutral media. Gallium is exchanged between the chelate and the C-site of human serum apotransferrin in interaction with bicarbonate in about 50 s to yield an intermediate complex with an equilibrium constant K ₁ = (3.9 ± 1.2) × 10⁻², a direct second-order rate constant k ₁ = 425 ± 50 M⁻¹ s⁻¹ and a reverse second-order rate constant k ₋₁ = (1.1 ± 3) × 10⁴ M⁻¹ s⁻¹. The intermediate complex loses a single proton with proton dissociation constant K _1a = 80 ± 40 nM to yield a first kinetic product. This product then undergoes a modification in its conformation which lasts about 500 s to produce a second kinetic intermediate, which in turn undergoes a final extremely slow (several hours) modification in its conformation to yield the gallium-saturated transferrin in its final state. The mechanism of gallium uptake differs from that of iron and does not involve the same transitions in conformation reported during iron uptake. The interaction of gallium-loaded transferrin with the transferrin receptor occurs in a single very fast kinetic step with a dissociation constant K _d = 1.10 ± 0.12 μM and a second-order rate constant k _d = (1.15 ± 0.3) × 10¹⁰ M⁻¹ s⁻¹. This mechanism is different from that observed with the ferric holotransferrin and suggests that the interaction between the receptor and gallium-loaded transferrin probably takes place on the helical domain of the receptor which is specific for the C-site of transferrin and HFE. The relevance of gallium incorporation by the transferrin receptor-mediated iron-acquisition pathway is discussed.     

Accuracy of Optimized Chemical-exchange Parameters Derived by Fitting CPMG R 2 Dispersion Profiles when R 2 0a ≠ R 2 0b

The transverse relaxation rate, R₂, measured as a function of the effective field (R₂ dispersion) using a Carr-Purcell-Meiboom-Gill (CPMG) pulse train, is well suited to detect conformational exchange in proteins. The dispersion data are commonly fitted by a two-site (sites a and b) exchange model with four parameters: the relative population, p_a, the difference in chemical shifts of the two sites, δω, the correlation time for exchange, τ_ex, and the intrinsic relaxation rate (i.e., transverse relaxation rate in the absence of chemical exchange), R₂⁰. Although the intrinsic relaxation rates of the two sites, R₂^0a and R₂^0b, can differ, they are normally assumed to be the same (i.e., R₂^0a = R₂^0b = R₂⁰) when fitting dispersion data. The purpose of this investigation is to determine the magnitudes of the errors in the optimized exchange parameters that are introduced by the assumption that R₂^0a = R₂^0b. In order to accomplish this goal, we first generated synthetic constant-time CPMG R₂ dispersion data assuming two-site exchange with R₂^0a ≠ R₂^0b, and then fitted the synthetic data assuming two-site exchange with R₂⁰ = R₂^0a = R₂^0b. Although all the synthetic data generated assuming R₂^0a ≠ R₂^0b were well fitted (assuming R₂^0a = R₂^0b), the optimized values of p_a and τ _ex differed from their true values, whereas the optimized values of δω values did not. A theoretical analysis using the Carver–Richards equation explains these results, and yields simple, general equations for estimating the magnitudes of the errors in the optimized parameters, as a function of ( R₂^0a − R₂^0b).     

Filling the vacuum chamber of a technological system with homogeneous plasma using a stationary glow discharge

Experimental study of a glow discharge with electrostatic confinement of electrons is carried out in the vacuum chamber volume V ≈ 0.12 m³ of a technological system “Bulat-6” in argon pressure range 0.005–5 Pa. The chamber is used as a hollow cathode of the discharge with the inner surface area S ≈ 1.5 m². It is equipped with two feedthroughs, which make it possible to immerse in the discharge plasma interchangeable anodes with surface area S _a ranging from ∼0.001 to ∼0.1 m², as well as floating electrodes isolated from both the chamber and the anode. Dependences of the cathode fall U _c = 0.4−3 kV on the pressure p at a constant discharge current in the range I = 0.2−2 A proved that aperture of the electron escape out of the electrostatic trap is equal to the sum S _o = S _a + S _f of the anode surface S _a and the floating electrode surface S _f . The sum S _o defines the lower limit p _o of the pressure range, in which U _c is independent of p. At p < p _o the cathode fall U _c grows up dramatically, when the pressure decreases, and the pressure p tends to the limit p ^ex, which is in fact the discharge extinction pressure. At p ≈ p ^ex electrons emitted by the cathode and the first generation of fast electrons produced in the cathode sheath spend almost all their energy up to 3 keV on heating the anode and the floating electrode up to 600–800°C and higher. In this case the gas in the chamber is being ionized by the next generations of electrons produced in the cathode sheath, their energy being one order of magnitude lower. When S _a < (2m/M)^1/2 S, where m is the electron mass and M is the ion mass, the anode may be additionally heated by plasma electrons accelerated by the anode fall of potential U _a up to 0.5 kV.     

Interaction of albumins and hemin with aromatic antioxidants: A spectrophotometric and fluorometric study

Difference spectrophotometry and fluorescence quenching of human and bovine serum albumins were used to determine their association constants(K _a) with hemin in buffered physiological saline (pH 7.4) supplemented with 2% dimethylsulfoxide or in 40% aqueous dimethylformamide (pH 7.4).K _a values depended on the medium, the extent of albumin delipidation, and on the method of determination. The formation of hemin complexes witho-phenylenediamine, tetramethylbenzidine, gallic acid, its polydisulfide, and two substituted di-tert-butyl pyrocatechols was studied by difference spectrophotometry in the same media;K _a values for the complexes were calculated and compared to each other. The formation of complexes of these aromatic ligands with albumins was studied fluorometrically;K _a values were of order of ∼10⁵ M⁻¹ and decreased with the ligand hydrophobicity.     

A study of absorption characteristics of chromophoric dissolved organic matter and particles in Lake Taihu,China

Absorptions by non-phytoplankton particles and phytoplankton, and chromophoric dissolved organic matter (CDOM) were measured at 50 sites in large, shallow, Lake Taihu in winter and summer 2006 to study their seasonal and spatial variations, and their relative contributions to total absorption. The CDOM absorption was significantly higher in winter than in summer, due to degradation and release of fixed carbon in phytoplankton and submerged aquatic vegetation (SAV). The hyperbolic model was used to model the spectral absorption of CDOM, and the mean spectral slope of 6.38 nm⁻¹ was obtained. At most sites, the spectral absorption of non-phytoplankton particles was similar to that of the total particles, demonstrating that the absorption of the total particles is dominated by the absorption of non-phytoplankton particles. In summer, phytoplankton absorption increased markedly, due to frequent algal blooms especially in Meiliang Bay. In winter, the significant increase in non-phytoplankton particle absorption resulted from the increase of inorganic particulate matter caused by sediment resuspension. Strong linear relationships were found between a _d(440) and total suspended matter (TSM), organic suspended matter (OSM), and inorganic suspended matter (ISM). Strong linear relationships were also found between a _ph(440), a _ph(675) and chlorophyll a (Chl-a) concentration. The total relative contributions of non-phytoplankton particles over the range of photosynthetically active radiation (PAR) (400–700 nm) were 48.4 and 79.9% in summer and winter respectively. Non-phytoplankton particle absorption dominated the total absorption, especially in winter, in Lake Taihu, due to frequent sediment resuspension in the large shallow lake as a result of strong windy conditions. The results indicate that strong absorption by CDOM and non-phytoplankton particles at the blue wavelength has an impact on the spectral availability, and acts as a selection factor for the composition of the phytoplankton community, with cyanobacteria being the dominate species in Lake Taihu. Handling editor: L. Naselli-Flores     

Adaptation of the photosynthetic apparatus of Nitellopsis obtusa to changing light intensity at the molecular level: different pathways of a singlet excitation quenching

The effect of prolonged illumination (60 min) with photosynthetically active monochromatic radiation of low intensity (3 μmol m⁻² s⁻¹) and high intensity (60 μmol m⁻² s⁻¹), corresponding to the physiological conditions and light stress conditions, respectively, was studied in the algae Nitellopsis obtusa. Illumination of Nitellopsis obtusa cells with strong light was associated with activation of the xanthophyll cycle, manifested by the deepoxidation of violaxanthin and accumulation of antheraxanthin and zeaxanthin. At the same time, the efficient singlet excitation quenching in the photosynthetic apparatus was activated, as demonstrated by the decrease in the intensity of the chlorophyll a fluorescence emission by ca 50 %. The difference of the fluorescence excitation spectra recorded before and after the light treatment match the difference absorption spectrum of the xanthophyll cycle pigments. The illumination with low light intensity resulted also in the chlorophyll a fluorescence quenching but the effect was very small (less than 10 %). The fluorescence quenching is interpreted in terms of the energy transfer between the Q_y energy level of chlorophyll a and the 2¹ A_g ⁻ energy level of zeaxanthin. The singlet energy levels of carotenoids, corresponding to the green spectral region, are also taken into consideration in the interpretation of the excitation energy exchange between the carotenoids and chlorophylls. Possible molecular mechanisms involved in the activation of the strong and the weak excitation quenching, including violaxanthin isomerization, and possible physiological functions of such pathways of energy transfer are discussed.     

Impact of environmental pollution on cyanobacterial proline content

This study describes the toxic effects of different prominent aquatic pollutants—heavy metals (Cd & Pb), pesticides (alphamethrin and deltamethrin) and salt (NaCl)—on the intracellular proline content in the cyanobacterium, Westiellopsis prolifica–Janet strain–NCCU331. Despite a reduction in growth (measured as chlorophyll a content), the intracellular proline content increased in the presence of heavy metals, pesticides and high salt concentration. The intracellular cyanobacterial proline accumulation was more pronounced under salt stress than in the presence of pesticides and heavy metals. We have also compared whether or not anionic components influence heavy metal toxicity. It was found that the chlorides of Cd and Pb were more toxic than the NO₃ and the order of toxicity was CdCl₂ > PbCl₂ > Cd (NO₃)₂ > Pb (NO₃)₂. Among pyrethroids, deltamethrin was more toxic than alphamethrin. Presented at the 6th Meeting of the Asian Pacific Society of Applied Phycology, Manila, Philippines.     

The Relative Rates of Thiol–Thioester Exchange and Hydrolysis for Alkyl and Aryl Thioalkanoates in Water

This article reports rate constants for thiol–thioester exchange (k _ex), and for acid-mediated (k _a), base-mediated (k _b), and pH-independent (k _w) hydrolysis of S-methyl thioacetate and S-phenyl 5-dimethylamino-5-oxo-thiopentanoate—model alkyl and aryl thioalkanoates, respectively—in water. Reactions such as thiol–thioester exchange or aminolysis could have generated molecular complexity on early Earth, but for thioesters to have played important roles in the origin of life, constructive reactions would have needed to compete effectively with hydrolysis under prebiotic conditions. Knowledge of the kinetics of competition between exchange and hydrolysis is also useful in the optimization of systems where exchange is used in applications such as self-assembly or reversible binding. For the alkyl thioester S-methyl thioacetate, which has been synthesized in simulated prebiotic hydrothermal vents, k _a = 1.5 × 10⁻⁵ M⁻¹ s⁻¹, k _b = 1.6 × 10⁻¹ M⁻¹ s⁻¹, and k _w = 3.6 × 10⁻⁸ s⁻¹. At pH 7 and 23°C, the half-life for hydrolysis is 155 days. The second-order rate constant for thiol–thioester exchange between S-methyl thioacetate and 2-sulfonatoethanethiolate is k _ex = 1.7 M⁻¹ s⁻¹. At pH 7 and 23°C, with [R″S(H)] = 1 mM, the half-life of the exchange reaction is 38 h. These results confirm that conditions (pH, temperature, pK _a of the thiol) exist where prebiotically relevant thioesters can survive hydrolysis in water for long periods of time and rates of thiol–thioester exchange exceed those of hydrolysis by several orders of magnitude.     

Efficient method of gas laser pumping by an electron beam in the SIGE-1 experimental setup

Lasers, sources of coherent UV and vacuum UV radiation, plasmachemical reactors, reactors for cleaning fouled gases, etc., can be classified as devices the working medium of which is plasma formed as a result of the interaction of a high-current relativistic electronic beam with gas. Efficiency of such devices which are united under the common name “systems of injection gas electronics” (SIGE) depends mainly on the efficiency of energy transfer from a beam to gas (ηg = W _g /W _b ) and that of the transform of the energy transferred to gas into the energy of the ultimate product W _in (η_in = W _in/W _g ). As a special case of SIGE, an experimental bench laser is considered. The new efficient method of pumping is supposed to be implemented on this laser to optimize the energy contribution η _g and useful output η_in.     

Charging of submicron structures during silicon dioxide etching in one- and two-frequency gas discharges

A model that combines the Monte Carlo method for calculating electron and ion trajectories in three-dimensional geometry and an analytic approach developed for calculating an electric field in two-dimensional geometry is used to simulate the charging of the surface of periodic submicron SiO₂ structures by electron and ion fluxes in the plasma of a one- and a two-frequency capacitive RF discharge. The energy distribution function of the electrons and ions that come to the bottom of a submicron structure in an argon and an argon-containing plasma is calculated for structures with a width of 11–45 nm and an aspect ratio of d/w = 1–10 (where d and w are the depth and width of the structure). It is shown that secondary electronelectron emission plays an important role in the redistribution of the electric charge and, accordingly, of the electric potential in a submicron structure. It is demonstrated that, when the secondary electron-electron emission mechanism is taken into account, the ion energy spectrum at the bottom of a submicron structure is shifted toward lower energies and becomes broader in comparison with the spectrum of an ion flux from an RF discharge plasma. Moreover, the shift and broadening depend only on the secondary electron-electron emission coefficient, the energy of the charged particles, and the aspect ratio.     

Effect of gamma radiation on mutant induction of <Emphasis Type="Italic">Fagopyrum dibotrys</Emphasis> Hara

Agronomic traits, photosynthetic pigments, gas exchange, and chlorophyll (Chl) fluorescence parameters of red stem buckwheat (Fagopyrum dibotrys Hara) mutants induced by γ-radiation were compared with green control at seedling stage. Plant height, number of first-class branches, and rhizome biomass were inhibited significantly (p<0.01). Chl a, Chl b, and Chl a+b contents decreased with elevated dose of γ-rays, while increasing carotenoid content indicated that buckwheat was capable of adjusting to the radiation damage. Decrease in net photosynthetic rate was the result of both stomatal and non-stomatal limitations. Fluorescence parameters, such as F₀, F_m, F_v/F_m, F_v/F₀, Φ_PS2, electron transport rate, and photochemical quenching declined significantly (p<0.01) as compared with control due to photoinhibition, while non-photochemical quenching increased to enhance thermal dissipation. Lower parameters implied that leaf tissue was damaged significantly by high dose of γ-radiation and therefore leaf senescence was accelerated.     

The root–soil system of Norway spruce subjected to turning moment: resistance as a function of rotation

The reactions of trees to wind, rockfall, and snow and debris flow depend largely on how strong and deformable their anchorage in the soil is. Here, the resistive turning moment M of the root–soil system as a function of the rotation ϕ at the stem base plays the major role. M(ϕ) describes the behavior of the root–soil system when subject to rotational moment, with the maximum M(ϕ) indicating the anchorage strength M _a of the tree. We assessed M(ϕ) of 66 Norway spruce (Picea abies L. Karst) by pulling them over with a winch. These 45- to 170-year-old trees grew at sites of low and high elevation, with a diameter at breast height DBH = 14–69 cm and a height H = 9–42 m. M(ϕ) displayed a strong nonlinear behavior. M _a was reached at a lower ϕ for large trees than for small trees. Thus overhanging tree weight contributed less to M _a for the large trees. Overturning also occurred at a lower ϕ for the large trees. These observations show that the rotational ductility of the root–soil system is higher for small trees. M _a could be described by four monovariate linear regression equations of tree weight, stem weight, stem volume and DBH ² ·H (0.80 < R ² < 0.95), and ϕ at M _a, ϕ _a, by a power law of DBH²·H (R ² = 0.85). We found significantly higher M _a for the low-elevation spruces than for the high-elevation spruces, which were more shallowly anchored, but no significant difference in ϕ _a. The 66 curves of M(ϕ), normalized (_n) by M _a in M-direction and by ϕ _a in ϕ-direction, yielded one characteristic average curve: . Using and the predictions of M _a and ϕ _a, it is shown that M(ϕ) and the curves associated with M(ϕ) can be predicted with a relative standard error ≤25%. The parameterization of M(ϕ) by tree size and weight is novel and provides useful information for predicting with finite-element computer models how trees will react to natural hazards.