Multifractal scaling of the kinetic energy flux in solar wind turbulence

The geometrical and scaling properties of the energy flux of the turbulent kinetic energy in the solar wind have been studied. Using present experimental technology in solar wind measurements we cannot directly measure the real volumetric dissipation rate, <varepsilon>(t), but are constrained to represent it by its surrogate the energy flux near the dissipation range at the proton gyro scale. There is evidence for the multifractal nature of the so defined dissipation field <varepsilon>(t), a result derived from the scaling exponents of its statistical moments. The generalized dimension D _q has been determined and reveals that the dissipation field has a multifractal structure, which is not compatible with a scale-invariant cascade. The related multifractal spectrum f(<alpha>) has been estimated for the first time for MHD turbulence in the solar wind. Its features resemble those obtained for turbulent fluids and other nonlinear multifractal systems. The generalized dimension D _q can for turbulence in high-speed streams be fitted well by the functional dependence of the p-model with a comparatively large parameter p ₁=0.87, indicating a strongly intermittent multifractal energy cascade. The experimental value for D _p/3 used in the scaling exponent s(p) of the velocity structure function gives an exponent that can describe some of the observations. The scaling exponent <mu> of the autocorrelation function of <varepsilon>(t) has also been directly evaluated, being 0.37. Finally, the mean dissipation rate was determined, which could be used in solar wind heating models.     

Polar thermospheric response to solar magneticcloud/coronal mass ejection interactions with themagnetosphere

The Solar Magnetic Cloud (SMC)/Coronal Mass Ejection (CME) event of January1997 triggered auroral displays in all sectors of the auroral oval as well as in the polar cap region.Near infrared emissions from these auroras were recorded simultaneously in the night sector overSondrestromfjord (Sonde), Greenland, in the day sector over Longyearbyen, Svalbard and in thepolar cap region over Eureka, Canada. The spectral distributions of these emissions indicateprecipitation of electrons with average energy (E_AV) of (500±100) eV,dissipating most of their energy around (180±20) km height (h_max) in thethermosphere. These findings are consistent with the concurrent auroral ionization profilesrecorded by the Incoherent Scatter Radar soundings at Sonde. In contrast, most of the nighttimeauroras, not related to SMC/CME events, are excited by electrons with E_AV > a few keV and peak in the lower thermosphere with h_max around 110 km.Similarly, normal dayside cusp auroras and polar cap drizzle excited emissions emanate from theupper thermosphere above 200 km altitude. SMC/CME related auroras were also observed inOctober 1995 at Sonde, and in May 1996 as well as in May 1997 at the South Pole Station inAntarctica. Spectral characteristics, and hence E_AV and h_max, of all these other SMC/CME related auroras, are similar to those of the January 1997event. These observations suggest that during a significant part of the period when SMC/CMEplasmas and fields interact with the magnetosphere, relatively low energy electrons precipitate inthe thermosphere. Such SMC/CME triggered auroras interact with the middle thermosphereconstituents in the 160–200 km height region. The latter region is inaccessible for remote sensingits composition and thermodynamics in normal auroras, which generally peak at lower heights; theSMC/CME events provide the opportunity for such investigations.     

Response of the radiation belt electron flux to the solar wind velocity: Parameterization by radial distance and energy

The solar wind velocity is the primary driver of the electron flux variability in Earth's radiation belts. The response of the logarithmic flux (“log-flux”) to this driver has been determined at the geosynchronous orbit and at a fixed energy [Baker, D.N., McPherron, R.L., Cayton, T.E., Klebesadel, R.W., 1990. Linear prediction filter analysis of relativistic electron properties at 6.6 RE. Journal of Geophysical Research 95(A9), 15,133–15,140) and as a function of L shell and fixed energy [Vassiliadis, D., Klimas, A.J., Kanekal, S.G., Baker, D.N., Weigel, R.S., 2002. Long-term average, solar-cycle, and seasonal response of magnetospheric energetic electrons to the solar wind speed. Journal of Geophysical Research 107, doi:10.1029/2001JA000506). In this paper we generalize the response model as a function of particle energy (0.8–6.4 MeV) using POLAR HIST measurements. All three response peaks identified earlier figure prominently in the high-altitude POLAR measurements. The positive response around the geosynchronous orbit is peak P₁ (τ=2±1 d; L=5.8±0.5; E=0.8–6.4 MeV), associated with high-speed, low-density streams and the ULF wave activity they produce. Deeper in the magnetosphere, the response is dominated by a positive peak P₀ (0±1 d; 2.9±0.5R_E; 0.8–1.1 MeV), of a shorter duration and producing lower-energy electrons. The P₀ response occurs during the passage of geoeffective structures containing high IMF and high-density parts, such as ICMEs and other mass ejecta. Finally, the negative peak V₁ (0±0.5 d; 5.7±0.5R_E; 0.8–6.4 MeV) is associated with the “D_st effect” or the quasiadiabatic transport produced by ring-current intensifications. As energies increase, the P₁ and V₁ peaks appear at lower L, while the D_st effect becomes more pronounced in the region L<3. The P₀ effectively disappears for E>1.6 MeV because of low statistics, although it is evident in individual events. The continuity of the response across radial and energy scales supports the earlier hypothesis that each of the three modes corresponds to a qualitatively different type of large-scale electron acceleration and transport.     

Variations in the amplitude of the chandler wobble

It is shown that within the framework of the Kolmogorov model the “energy” of the pole E(t) = x ₁² + x ₂² can be interpreted as a Markovian process. The exact analytical expression has been obtained for the density of the conditional probability of the quantity E(t) and the problem of the first passage time of the process E(t) has been analyzed. It was shown that the available data on the swing of the function E(t) are not at variance with the Kolmogorov model and a short-period drop of the amplitude of the Chandler wobble in the early 20th century fits this model at Q = 50–200 too; values of Q > 350 are less reasonable.     

Hydrogen and calcium lines in solar prominence spectra

The solar prominence radiation spectrum has been simulated in close H and K lines of ionized calcium and hydrogen line H? convenient for processing in CCD observations. Equations of radiation transfer and statistical equilibrium in absence of LTE are solved for a model of homogeneous plane layer, taking into account the partial frequency redistribution for a 20-level continuum model of hydrogen atoms and a 5-level continuum model of calcium ions. The ratio of the integral intensities s = E(H Ca II)/E(H?) and t = E(K)/E(H) Ca II is calculated for a model grid (pressure 0.001 < P < 1.0 dyn/cm², temperature 4000 < T < 20000 K). The s(T, P) and t(T, P) constructed diagnostic charts for solar prominences are obtained for the first time with allowance for the influence of the Ly?? line on the ionization of Ca II ions.     

Exploring the nature of non-Fickian transport in laboratory experiments

Observations of non-Fickian transport in sandbox experiments [Levy M, Berkowitz B. Measurement and analysis of non-Fickian dispersion in heterogeneous porous media. J Contam Hydrol 2003;64:203–26] were analyzed previously using a power law tail ψ(t) ∼ t^−1−β with 0 < β < 2 for the spectrum of transition times comprising a tracer plume migration. For each sandbox medium a choice of β resulted in an excellent fit to the breakthrough curve (BTC) data, and the value of β decreased slowly with increasing flow velocity. Here, the data are reanalyzed with the full spectrum of ψ(t) gleaned from analytical calculations [Cortis A, Chen Y, Scher H, Berkowitz B. Quantitative characterization of pore-scale disorder effects on transport in “homogeneous” granular media. Phys Rev E 2004;10(70):041108. doi: 10.1103/PhysRevE.70.041108], numerical simulations [Bijeljic B, Blunt MJ. Pore-scale modeling and continuous time random walk analysis of dispersion in porous media. Water Resour Res 2006;42:W01202. doi: 10.1029/2005WR004578] and permeability fields [Di Donato G, Obi E-O, Blunt MJ. Anomalous transport in heterogeneous media demonstrated by streamline-based simulation. Geophys Res Lett 2003;30:1608–12s. doi: 10.1029/2003GL017196]. We represent the main features of the full spectrum of transition times with a truncated power law (TPL), ψ(t) ∼ (t₁ + t)^−1−βexp(−t/t₂), where t₁ and t₂ are the limits of the power law spectrum. An excellent fit to the entire BTC data set, including the changes in flow velocity, for each sandbox medium is obtained with a single set of values of t₁, β, t₂. The influence of the cutoff time t₂ is apparent even in the regime t < t₂. Significantly, we demonstrate that the previous apparent velocity dependence of β is a result of choosing a pure power law tail for ψ(t). The key is the change in the log–log slope of the TPL form of ψ(t) with a shifting observational time window caused by the change in the mean velocity. Hence, the use of the full spectrum of ψ(t) is not only necessary for the transition to Fickian behavior, but also to account for the dynamics of these laboratory observations of non-Fickian transport.     

The erosion rates of cohesive sediments in Venice lagoon,Italy

The stability of cohesive sediments from Venice lagoon has been measured in situ using the benthic flume Sea Carousel. Twenty four stations were occupied during summertime, and a sub-set of 13 stations was re-occupied during the following winter. Erosion thresholds and first-order erosion rates were estimated and showed a distinct difference between inter-tidal and sub-tidal stations. The higher values for inter-tidal stations are the result of exposure that influences consolidation, density, and organic adhesion. The thresholds for each state of sediment motion are well established. However, the rate of erosion once the erosion threshold has been exceeded has been poorly treated. This is because normally a time-series of sediment concentration (C) and bed shear stress (τ₀(t)) is used to define threshold stress or cohesion (τ_crit,z) and erosion rate (E). Whilst solution of the onset of erosion, τ_crit,0, is often reported, the evaluation of the erosion threshold variation through the process of erosion (eroded depth) is usually omitted or not estimated. This usually leads to assumptions on the strength profile of the bed which invariably has no credibility within the topmost mm of the bed where most erosion takes place. It is possible to extract this information from a time-series through the addition of a step in data processing. This paper describes how this is done, and the impact of this on the accuracy of estimates of the excess stress (τ₀(t)–τ_crit,z) on E.     

A two-dimensional model of thermospheric nitric oxide sources and their contributions to the middle atmospheric chemical balance

The NASA/Goddard Space Flight Center two-dimensional (GSFC 2D) photochemical transport model has been used to study the influence of thermospheric NO on the chemical balance of the middle atmosphere. Lower thermospheric NO sources are included in the GSFC 2D model in addition to the sources that are relevant to the stratosphere. A time series of hemispheric auroral electron power has been used to modulate the auroral NO production in the auroral zone. A time series of the Ottawa 10.7-cm solar flux index has been used as a proxy to modulate NO production at middle and low latitudes by solar EUV and soft X-rays. An interhemispheric asymmetry is calculated for the amounts of odd nitrogen in the polar stratosphere. We compute a <∼3% enhancement in the odd nitrogen (NO_y=N, NO, NO₂, NO₃, N₂O₅, BrONO₂, ClONO₂, HO₂NO₂, and HNO₃) budget in the north polar stratosphere (latitude > 50°) due to thermospheric sources, whereas we compute a <∼8% enhancement in the NO_y budget in the south polar stratosphere (latitude > 50°).     

Acoustic, Electromagnetic, and Photon Emission from Dynamically Fracturing Granite

Laboratory samples of Westerly granite were impacted by a falling striker, and the time series of acoustic and electromagnetic emission (AE and EME) from fracturing rock were recorded with the time resolution of 10?ns. In order to determine precisely the actual instants of beginning and termination of fracturing, the fractoluminescence (FL) signal related to chemical bond ruptures on the sample surface was recorded in parallel to both AE and EME signals. Energy distributions in all three series were characterized by the function N(E?>?E′), where N is the number of emitted signals characterized with the energy release E exceeding a threshold value E′. The fracture dynamics was studied using both the scaling analysis and the non-extensive Tsallis statistics. The energy distributions were approximated with both the empirical Gutenberg–Richter-type relation N(E?>?E′) ∝ E′^?b , and the analytical function N _q (E?>?E′) that includes the Tsallis’ parameter of non-extensivity, q, and the released energy density. A comparative consideration of information taken from the data of EME, AE and FL emission techniques was carried out in the context of the physical sense of the parameters b and q. The AE time series reflected adequately the cracking process both at microscopic and laboratory scale levels, while the photon emission did not show a direct response on the split-off formation. Time resolution of the EME method was found to be insufficient for studying the dynamic fracture of the given kind.     

Compressional behavior of MgCr2O4 spinel from first-principles simulation

The compressional behavior of the MgCr_2O_4 spinel has been investigated with the CASTEP code using density functional theory and planewave pseudopotential technique. We treated the exchange-correlation interaction by both the local density approximation(LDA) and generalized gradient approximation(GGA) with the Perdew-Burker-Ernzerhof functional. Our simulation was conducted for the pressure range of 0–19 GPa. We obtained the isothermal bulk modulus(K_T) of the MgCr_2O_4 spinel as 181.46(48) GPa(GGA; low boundary) or 216.1(11) GPa(LDA; high boundary), with its first derivative(K'_T) as 4.41(6) or 4.5(1), respectively. The oxygen parameter u is not constant but negatively correlated with P, and decreases by about 0.5–0.6% for the investigated P range. The component polyhedra have different compressibilities, increasing in the order of(O_4)_1CrO_6(O_4)_2O_6MgO_4. The Mg-O bond in the MgO_4 tetrahedron is much more compressible than the Cr-O bond in the CrO_6 octahedron.     

Plasmas in the near-Earth magnetotail lobes: Properties and sources

The magnetotail lobes are two vast regions between the plasma sheet (PS) and the magnetotail boundary layers at the magnetopause, where the plasma has very low temperature and densities. The open magnetic field lines of the lobes directly couple the ionospheric polar caps with the solar wind (SW) through the magnetosheath. The survey of 576 h INTERBALL-1 measurements in the near (X_GSM>−27R_E) lobes in October–November 1997 shows that they are populated with plasmas of various origin and properties. Presented and discussed in details are four cases of lobe measurements under different geomagnetic conditions. Discrete plasma structures encountered in the lobes could originate from the PS, from the magnetosheath or the mantle. A ubiquitous picture in the lobes is the registration of ‘clouds’ of anisotropic electrons with energies up to 300–500 eV, with no accompanying ions. The electron distributions are highly variable and complex, with different degree of anisotropy. The earthward flowing electrons originate in the SW, the anisotropy of the electron fluxes reflects the anisotropy of the SW electrons. In some cases the tailward electrons are not only mirrored earthward fluxes but an additional source earthward of the observations is present. The positive spacecraft potential plays a substantial role in modifying the observed electron distributions.     

Hydroclimatology of the Volta River Basin in West Africa: Trends and variability from 1901 to 2002

Long-term historical records of rainfall (P), runoff (Q) and other climatic factors were used to investigate hydrological variability and trends in the Volta River Basin over the period 1901-2002. Potential (E_p) and actual evaporation (E), rainfall variability index (δ), Budyko’s aridity index (I_A), evaporation ratio (C_E) and runoff ratio (C_Q) were estimated from the available hydroclimatological records. Mann-Kendall trend analysis and non-parametric Sen’s slope estimates were performed on the respective time series variables to detect monotonic trend direction and magnitude of change over time.Rainfall variability index showed that 1968 was the wettest year (δ = +1.75) while 1983 was the driest (δ = −3.03), with the last three decades being drier than any other comparable period in the hydrological history of the Volta. An increase of 0.2 mm/yr² (P < 0.05) was observed in E_p for the 1901-1969 sub-series while an increased of 1.8 mm/yr² (P < 0.01) was recorded since 1970. Rainfall increased at the rate of 0.7 mm/yr² or 49 mm/yr between 1901 and 1969, whereas a decrease of 0.2 mm/yr² (6 mm/yr) was estimated for 1970-2002 sub-series. Runoff increased significantly at the rate of 0.8 mm/yr (23 mm/yr) since 1970. Runoff before dam construction was higher (87.5 mm/yr) and more varied (CV = 41.5%) than the post-dam period with value of 73.5 mm/yr (CV = 23.9%). A 10% relative decrease in P resulted in a 16% decrease in Q between 1936 and 1998. Since 1970, all the months showed increasing runoff trends with significant slopes (P < 0.05) in 9 out of the 12 months. Possible causes, such as climate change and land cover change, on the detected changes in hydroclimatology are briefly discussed.     

Numerical simulations of transport of non-ergodic solute plumes in heterogeneous aquifers

Transport of non-ergodic solute plumes by steady-state groundwater flow with a uniform mean velocity, μ, were simulated with Monte Carlo approach in a two-dimensional heterogeneous and statistically isotropic aquifer whose transmissivity, T, is log-normally distributed with an exponential covariance. The ensemble averages of the second spatial moments of the plume about its center of mass, <S _{i i} (t)>, and the plume centroid covariance, R _{i i} (t) (i=1,2), were simulated for the variance of Y=log T, σ _Y ²=0.1, 0.5 and 1.0 and line sources normal or parallel to μ of three dimensionless lengths, 1, 5, and 10. For σ _Y ²=0.1, all simulated <S _{i i} (t)>−S _{i i} (0) and R _{i i} (t) agree well with the first-order theoretical values, where S _{i i} (0) are the initial values of S _{i i} (t). For σ _Y ²=0.5 and 1.0 and the line sources normal to μ, the simulated longitudinal moments, <S ₁₁(t)>−S ₁₁(0) and R ₁₁(t), agree well with the first-order theoretical results but the simulated transverse moments <S ₂₂(t)>−S ₂₂(0) and R ₂₂(t) are significantly larger than the first-order values. For the same two larger values of σ _Y ² but the line sources parallel to μ, the simulated <S ₁₁(t)>−S ₁₁(0) are larger than but the simulated R ₁₁ are smaller than the first-order values, and both simulated <S ₂₂(t)>−S ₂₂(0) and R ₂₂(t) stay larger than the first-order values. For a fixed value of σ _Y ², the summations of <S _{i i} (t)>−S _{i i} (0) and R _{i i} , i.e., X _{i i} (i=1,2), remain almost the same no matter what kind of source simulated. The simulated X ₁₁ are in good agreement with the first-order theory but the simulated X ₂₂ are significantly larger than the first-order values. The simulated X ₂₂, however, are in excellent agreement with a previous modeling result and both of them are very close to the values derived using Corrsin's conjecture. It is found that the transverse moments may be significantly underestimated if less accurate hydraulic head solutions are used and that the decreasing of <S ₂₂(t)>−S ₂₂(0) with time or a negative effective dispersivity, defined as , may happen in the case of a line source parallel to μ where σ _Y ² is small.     

Numerical simulations of transport of non-ergodic solute plumes in heterogeneous aquifers

Transport of non-ergodic solute plumes by steady-state groundwater flow with a uniform mean velocity, μ, were simulated with Monte Carlo approach in a two-dimensional heterogeneous and statistically isotropic aquifer whose transmissivity, T, is log-normally distributed with an exponential covariance. The ensemble averages of the second spatial moments of the plume about its center of mass, <S _{i i} (t)>, and the plume centroid covariance, R _{i i} (t) (i=1,2), were simulated for the variance of Y=log T, σ _Y ²=0.1, 0.5 and 1.0 and line sources normal or parallel to μ of three dimensionless lengths, 1, 5, and 10. For σ _Y ²=0.1, all simulated <S _{i i} (t)>−S _{i i} (0) and R _{i i} (t) agree well with the first-order theoretical values, where S _{i i} (0) are the initial values of S _{i i} (t). For σ _Y ²=0.5 and 1.0 and the line sources normal to μ, the simulated longitudinal moments, <S ₁₁(t)>−S ₁₁(0) and R ₁₁(t), agree well with the first-order theoretical results but the simulated transverse moments <S ₂₂(t)>−S ₂₂(0) and R ₂₂(t) are significantly larger than the first-order values. For the same two larger values of σ _Y ² but the line sources parallel to μ, the simulated <S ₁₁(t)>−S ₁₁(0) are larger than but the simulated R ₁₁ are smaller than the first-order values, and both simulated <S ₂₂(t)>−S ₂₂(0) and R ₂₂(t) stay larger than the first-order values. For a fixed value of σ _Y ², the summations of <S _{i i} (t)>−S _{i i} (0) and R _{i i} , i.e., X _{i i} (i=1,2), remain almost the same no matter what kind of source simulated. The simulated X ₁₁ are in good agreement with the first-order theory but the simulated X ₂₂ are significantly larger than the first-order values. The simulated X ₂₂, however, are in excellent agreement with a previous modeling result and both of them are very close to the values derived using Corrsin's conjecture. It is found that the transverse moments may be significantly underestimated if less accurate hydraulic head solutions are used and that the decreasing of <S ₂₂(t)>−S ₂₂(0) with time or a negative effective dispersivity, defined as , may happen in the case of a line source parallel to μ where σ _Y ² is small.     

Fe-Mg interdiffusion in magnesiowüstite up to 35 GPa

Fe-Mg interdiffusivities in (Fe,Mg)O magnesiowüstite have been measured in experiments conducted at pressures of 7-35 GPa and temperatures of 1573-1973 K using a Kawai-type high-pressure apparatus. The diffusion profiles were measured across the interface between MgO and (Fe_0.5,Mg_0.5)O samples by electron microprobe analysis, and the Fe-Mg interdiffusivities were determined as D_Fe-Mg=D₀exp{−E*(1+PV*_Mg/E*_Mg)/RT}, where D₀=4.1(^+16.1_−3.3)×10⁻⁷ m²/s, E*=(1−C_Mg)E*_Fe+C_MgE*_Mg (activation energy for the concentration of Mg, where E*_Fe=113(±74) kJ/mol and E*_Mg=226(±32) kJ/mol), the activation volume V*_Mg=1.8(±1.2)×10⁻⁶ m³/mol. By extrapolating these results to the P-T conditions of the core-mantle boundary, we conclude that the interdiffusivity of Fe-Mg in magnesiowüstite at the bottom of the lower mantle is at least one order of magnitude larger than that at the top of the lower mantle.     

A new approach to geospeedometry based on the `compensation law'

Lasaga's model [Lasaga, A.C., 1983. Geospeedometry: an extension of geothermometry. In: Saxena, S.K. (Ed.), Kinetics and Equilibrium in Mineral Reactions. Spring, New York, pp. 82–114.] to estimate cooling rate (s=dT/dt), as other analytical formulations available in the literature for instance the work of Dodson, M.H., 1976 [Dodson, M.H., 1976. Kinetic processes and thermal history of slowly cooling solids. Nature, 259, 551–553; Dodson, M.H., 1986. Closure profiles in cooling systems. Mat. Sci. Forum 7, 145–154.] can be difficult to apply to natural rocks for two reasons: (i) heavy numerical computations; (ii) the choice of the appropriate set of diffusion data. We propose a new formulation of Lasaga's equation which is simpler to use and less tight in the choice of a particular experimental data set. It is based on `frozen in' diffusion profiles in mineral pairs which are chemically isolated from the rest of the host rock. In this model, ions are exchanged by solid-state diffusion through the common surface of coexisting minerals. Our method approximates the shape of the elemental concentration profiles after cooling to an error function (with an effective diffusion coefficient D<sub>eff</sub>), as most of the variation of C(x) from rim (x=0) to core (x=d) occurs over a distance 0<x<a (a is the `characteristic diffusion length' of the profile: a≈3√(D_efft)). Our analytical formula to calculate s is straightforward to use. It allows excellent estimates of s as long as 2a<d when the grain size is large compared to diffusion distances. For small grain sizes, we give another analytical formula that evaluates s at the value s_trial. We show by how much s_trial underestimates s. Expressing cooling rates s requires diffusion parameters D_o and E (the pre-exponential factor and activation energy of diffusion). Available experimental data of (D_o,E) are scattered due to different experimental conditions (T, fO₂, mineral compositions). Therefore geospeedometric results range widely. It had been long noticed that the (D_o,E) pairs are linearly correlated. This correlation can be expressed as the `compensation law' [Hart, S.R., 1981. Diffusion compensation in natural silicates. Geochim. Cosmochim. Acta 45, 200–215.]. We give the compensation law for Fe/Mg interdiffusion in two minerals used in geospeedometry, olivines and garnets. We show that implementing the `compensation law' into the analytical expression of cooling rate gives final s value consistent with all the (D_o,E) experimental data sets and consequently greatly reduces the uncertainty on cooling rate (s or s_trial).     

Electric and dielectric properties of forsterite between 400 and 900°C

The electrical impedance of a sintered forsterite sample containing 1 mol percent SiO₂ in excess has been studied as a function of frequency (1–10⁵ Hz) and temperature (400–900°C). The electrical properties are strongly frequency-dependent, requiring both conduction and displacement current for their interpretation. The electrical conductivity is thermally activated with a mean activation energy of 1.15 eV. It is interpreted as being ionic and caused by migration of magnesium ions via a vacancy mechanism. Dielectric data deduced from impedance measurements vary as ω^n?1 (0 < n < 1) at constant temperature. The value of n is different below and above a critical frequency ω_c, which is thermally activated and interpreted as the jump frequency of the migrating species.     

On I(5577 Å) and I (7620 Å) auroral emissions and atomic oxygen densities

A model of auroral electron deposition processes has been developed using Monte Carlo techniques to simulate electron transport and energy loss. The computed differential electron flux and pitch angle were compared with in situ auroral observations to provide a check on the accuracy of the model. As part of the energy loss process, a tally was kept of electronic excitation and ionization of the important atomic and molecular states. The optical emission rates from these excited states were computed and compared with auroral observations of (3914 Å), (5577 Å), (7620 Å) and (N₂VK). In particular, the roles played by energy transfer from N₂(A³⁺_u) and by other processes in the excitation of O(¹S) and O₂(b¹⁺_g) were investigated in detail. It is concluded that the N₂(A³⁺_u) mechanism is dominant for the production of OI(5577 Å) in the peak emission region of normal aurora, although the production efficiency is much smaller than the measured laboratory value; above 150 km electron impact on atomic oxygen is dominant. Atomic oxygen densities in the range of 0.75±0.25 MSIS-86 [O] were derived from the optical comparisons for auroral latitudes in mid-winter for various levels of solar and magnetic activity.     

Application of possibility-probability distribution in assessing water resource risk in Yiwu city

The possibility-probability risk calculated using the interior-outer set model is referred to as fuzzy risk. A fuzzy expected value of the possibility-probability distribution is a set with E _α(x) and [`(E)]<sub>a</sub>\bar E_\alpha (x) as its boundaries. The fuzzy expected values E <sub>α</sub>(x) and [`(E)]_a\bar E_\alpha (x) of a possibility-probability distribution represent the fuzzy risk values being calculated. Under such an α level, three risk values can be calculated: conservative risk value, venture risk value and maximum probability risk value. As α adopts all values throughout the set [0, 1], it is possible to obtain a series of risk values. Therefore, the fuzzy risk can be a multi-valued risk or set-valued risk. Calculation of the fuzzy expected value of Yiwu city’s water resource risk has been performed based on the interior-outer set model. We can get a conservative risk value (R _C ) of 800 mm for Yiwu city’s water resource risk, a venture risk value (R _V ) of 1020 mm, and a maximum probability risk value (R _M ) of 988 mm for the α = 0.1 level cut set.     

Conditions when anisotropy is negligible for solute transfer in sediment beds of lakes or streams

To reduce the complexity and save computation time, an isotropic and a scalar dispersion model are explored and compared to the anisotropic advection/dispersion model to study the interstitial flow in a stream and lake sediment induced by a periodic pressure wave. In these systems, the solute transport is controlled by the ratio (R = a/(LS)) of the pressure wave steepness (a/L) to the stream slope (S), and the dispersivity ratio (λ = α_L/L) that measures the longitudinal dispersivity (α_L) relative to the pressure wave length (L). Through a series of numerical experiments, the conclusion is reached that a scalar dispersion model can be applied with satisfactory results for advection-dominated transport, i.e. when R ?  0.1 and λ ? 0.01, or λ ? 0.0001, i.e. Peclet number (Pe) ? 10000; an isotropic dispersion model can be applied when R ? 10 or λ ? 0.001, and the full anisotropic advection/dispersion model has to be applied when R > 10 and λ > 0.001.