Topological defects in crystals: A density-wave theory

A new approach for describing dislocations and other topological defects in crystals, based on the density wave theory of Ramakrishnan and Yussouff is presented. Quantitative calculations are discussed in brief for the order parameter profiles, the atomic configuration and the free energy of a screw dislocation with Burgers vector b = (a/2, a/2,a/2 ) in a bcc solid. Our results for the free energy of the dislocation in a crystal of sizeR, when expressed as (λb 2/4π) ln (αR/|b|) whereλ is the shear elastic constant, yield, for example, the valueα ⋍ 1·85 for sodium at its freezing temperature (371°K). The density distribution in the presence of the dislocation shows that the dislocation core has a columnar character. To our knowledge, this study represents the first calculation of dislocation structure, including the core, within the framework of an order parameter theory incorporating thermal effects.

Understorey vegetation as an indicator of forest site potential in Southern Finland.

The relationship between site characteristics and understorey vegetation composition was analysed with quantitative methods, especially from the viewpoint of site quality estimation. Theoretical models were applied to an empirical data set collected from the upland forests of southern Finland comprising 104 sites dominated by Scots pine (Pinus sylvestris L.), and 165 sites dominated by Norway spruce (Picea abies (L.) Karsten). Site index H100 was used as an independent measure of site quality. A new model for the estimation of site quality at sites with a known understorey vegetation composition was introduced. It is based on the application of Bayes' theorem to the density function of site quality within the study area combined with the species-specific presence-absence response curves. The resulting posterior probability density function may be used for calculating an estimate for the site variable. Using this method, a jackknife estimate of site index H100 was calculated separately for pine- and spruce-dominated sites. The results indicated that the cross-validation root mean squared error (RMSEcv) of the estimates improved from 2.98 m down to 2.34 m relative to the "null" model (standard deviation of the sample distribution) in pine-dominated forests. In spruce-dominated forests RMSEcv decreased from 3.94 m down to 3.16 m. In order to assess these results, four other estimation methods based on understorey vegetation composition were applied to the same data set. The results showed that none of the methods was clearly superior to the others. In pine-dominated forests, RMSEcv varied between 2.34 and 2.47 m, and the corresponding range for spruce-dominated forests was from 3.13 to 3.57 m.

Estimation of cutting volume with three inventory methods for harvest planning in Canadian boreal forests.

Two methods of pre-harvest inventory were designed and tested on three cutting sites containing a total of 197 500 m3 of wood. These sites were located on flat-ground boreal forests located in northwestern Quebec. Both methods studied involved scaling of trees harvested to clear the road path one year (or more) prior to harvest of adjacent cut-blocks. The first method (ROAD) considers the total road right-of-way volume divided by the total road area cleared. The resulting volume per hectare is then multiplied by the total cut-block area scheduled for harvest during the following year to obtain the total estimated cutting volume. The second method (STRATIFIED) also involves scaling of trees cleared from the road. However, in STRATIFIED, log scaling data are stratified by forest stand location. A volume per hectare is calculated for each stretch of road that crosses a single forest stand. This volume per hectare is then multiplied by the remaining area of the same forest stand scheduled for harvest one year later. The sum of all resulting estimated volumes per stand gives the total estimated cutting-volume for all cut-blocks adjacent to the studied road. A third method (MNR) was also used to estimate cut-volumes of the sites studied. This method represents the actual existing technique for estimating cutting volume in the province of Quebec. It involves summing the cut volume for all forest stands. The cut volume is estimated by multiplying the area of each stand by its estimated volume per hectare obtained from standard stock tables provided by the governement. The resulting total estimated volume per cut-block for all three methods was then compared with the actual measured cut-block volume (MEASURED). This analysis revealed a significant difference between MEASURED and MNR methods with the MNR volume estimate being 30 % higher than MEASURED. However, no significant difference from MEASURED was observed for volume estimates for the ROAD and STRATIFIED methods which respectively had estimated cutting volumes 19 % and 5 % lower than MEASURED. Thus the ROAD and STRATIFIED methods are good ways to estimate cut-block volumes after road right-of-way harvest for conditions similar to those examined in this study.

Estimation of variables at ungaged locations by empirical orthogonal functions

A technique based on empirical orthogonal functions is used to estimate hydrologic time-series variables at ungaged locations. The technique is applied to estimate daily and monthly rainfall, temperature and runoff values. The accuracy of the method is tested by application to locations where data are available. The second-order characteristics of the estimated data are compared with those of the observed data. The results indicate that the method is quick and accurate.

Structure and representation of correlation functions and the density matrix for a statistical wave field in optics

A systematic structure analysis of the correlation functions of statistical quantum optics is carried out. From a suitably defined auxiliary two‐point function we are able to identify the excited modes in the wave field. The relative simplicity of the higher order correlation functions emerge as a byproduct and the conditions under which these are made pure are derived. These results depend in a crucial manner on the notion of coherence indices and of unimodular coherence indices. A new class of approximate expressions for the density operator of a statistical wave field is worked out based on discrete characteristic sets. These are even more economical than the diagonal coherent state representations. An appreciation of the subtleties of quantum theory obtains. Certain implications for the physics of light beams are cited.

MPD arcjet cathode surface current density

The radial current density distribution on the cathode longitudinal surface of magnetoplasmadynamic arcjets for axisymmetric geometries has been obtained by simultaneous solution of the electromagnetic equations for a given uniform gas dynamic field. The problem formulation permits a parametric study of the effects of the Hall parameter and the magnetic Reynolds number. The solution for the current density distribution displays current concentrations at two locations, that is, at the upstream and downstream ends of the cathode. This result is in conformity with known experimental data. The parameters responsible for these current concentrations are identified. It is shown that the effect of the magnetic Reynolds number on the current density distribution is different depending on whether or not the Hall effect is included. This result is also found to be consistent with experimental data.

Numerical estimation of hotspot temperatures in electrodes subjected to pulsed electron beam heating in vacuum

A numerical solution for the transient temperature distribution in a cylindrical disc heated on its top surface by a circular source is presented. A finite difference form of the governing equations is solved by the Alternating Direction Implicit (ADI) time marching scheme. This solution has direct applications in analyzing transient electron beam heating of target materials as encountered in the prebreakdown current enhancement and consequent breakdown in high voltage vacuum gaps stressed by alternating and pulsed voltages. The solution provides an estimate of the temperature for pulsed electron beam heating and the size of thermally activated microparticles originating from anode hot spots. The calculated results for a typical 45kV (a.c.) electron beam of radius 2.5 micron indicate that the temperature of such spots can reach melting point and could give rise to microparticles which could initiate breakdown.

The Single Langmuir Probe under Orbital-Limited Conditions in a Low-Density Collisional Plasma

The cylindrical Langmuir probe under orbital-limited conditions was used to determine the charge density in a low-density collisional plasma. The Langmuir's theory was applied to both electron and ion saturation currents in their respective accelerating regions. Present study indicates that the length of the probe significantly affects the probe characteristics. A probe of suitable length under orbital-limited conditions may be useful under the experimental conditions where the radius of the probe is much smaller than the Debye lengt.

Estimation of soil hydraulic properties and their uncertainty: comparison between laboratory and field experiment

Often the soil hydraulic parameters are obtained by the inversion of measured data (e.g. soil moisture, pressure head, and cumulative infiltration, etc.). However, the inverse problem in unsaturated zone is ill-posed due to various reasons, and hence the parameters become non-unique. The presence of multiple soil layers brings the additional complexities in the inverse modelling. The generalized likelihood uncertainty estimate (GLUE) is a useful approach to estimate the parameters and their uncertainty when dealing with soil moisture dynamics which is a highly non-linear problem. Because the estimated parameters depend on the modelling scale, inverse modelling carried out on laboratory data and field data may provide independent estimates. The objective of this paper is to compare the parameters and their uncertainty estimated through experiments in the laboratory and in the field and to assess which of the soil hydraulic parameters are independent of the experiment. The first two layers in the field site are characterized by Loamy sand and Loamy. The mean soil moisture and pressure head at three depths are measured with an interval of half hour for a period of 1 week using the evaporation method for the laboratory experiment, whereas soil moisture at three different depths (60, 110, and 200 cm) is measured with an interval of 1 h for 2 years for the field experiment. A one-dimensional soil moisture model on the basis of the finite difference method was used. The calibration and validation are approximately for 1 year each. The model performance was found to be good with root mean square error (RMSE) varying from 2 to 4 cm(3) cm(-3). It is found from the two experiments that mean and uncertainty in the saturated soil moisture (theta(s)) and shape parameter (n) of van Genuchten equations are similar for both the soil types. Copyright (C) 2010 John Wiley & Sons, Ltd.

On a Ratio of Functions of Exponential Random Variables and Some Applications

Consider L independent and identically distributed exponential random variables (r.vs) X-1, X-2 ,..., X-L and positive scalars b(1), b(2) ,..., b(L). In this letter, we present the probability density function (pdf), cumulative distribution function and the Laplace transform of the pdf of the composite r.v Z = (Sigma(L)(j=1) X-j)(2) / (Sigma(L)(j=1) b(j)X(j)). We show that the r.v Z appears in various communication systems such as i) maximal ratio combining of signals received over multiple channels with mismatched noise variances, ii)M-ary phase-shift keying with spatial diversity and imperfect channel estimation, and iii) coded multi-carrier code-division multiple access reception affected by an unknown narrow-band interference, and the statistics of the r.v Z derived here enable us to carry out the performance analysis of such systems in closed-form.