A Semi-Empirical Approach to Gas Flow Velocity Measurement by Means of the Thermal Time-of-Flight Method

This paper presents a method of measuring gas flow velocity based on the thermal time-of-flight method. The essence of the solution is an analysis of the time shift and the shape of voltage signals at the transmitter and at a temperature wave detector. The measurements used a probe composed of a wave transmitter and a detector, both in the form of thin tungsten wires. A rectangular signal was used at the wave transmitter. The time-of-flight of the wave was determined on the basis of the time shift of two selected characteristic points of the voltage waveform at the transmitter and the wave detector. To obtain the correct velocity indication, a correction in the form of a simple power function was applied. From the measurements performed, the relative uncertainty of the method was obtained, from approx. 4% of the measured value at an inflow velocity of 6.5 cm/s to 1% for an inflow velocity of 50 cm/s and higher.

A geometrical model for the evolution of spherical planetary nebulae based on thin-shell formalism

A spherical planetary nebula is described as a geometric model. The nebula itself is considered as a thin-shell, which is visualized as a boundary of two spacetimes. The inner and outer curvature tensors of the thin-shell are found in order to get an expression of the energy-momentum tensor on the thin-shell. The energy density and pressure expressions are derived using the energy-momentum tensor. The time evolution of the radius of the thin-shell is obtained in terms of the energy density. The model is tested by using a simple power function for decreasing energy density and the evolution pattern of the planetary nebula is attained.

Multiplicity dependencies of midrapidity transverse momentum spectra of identified charged particles in p+p collisions at (s)1/2 = 13 TeV at LHC

Multiplicity dependencies of midrapidity [Formula: see text] spectra of identified charged particles in inelastic [Formula: see text] collisions at [Formula: see text] TeV at the Large Hadron Collider (LHC), measured by ALICE Collaboration, have been analyzed. The combined minimum [Formula: see text] fits with thermodynamically consistent Tsallis function as well as Hagedorn function with the embedded transverse flow describe quite satisfactorily the [Formula: see text] spectra of particles in the studied 10 different classes of charged-particle multiplicity in inelastic [Formula: see text] collisions at [Formula: see text] TeV. The obtained effective temperatures [Formula: see text] of thermodynamically consistent Tsallis function demonstrate a consistent growth with an increase in multiplicity of charged particles in inelastic [Formula: see text] collisions at [Formula: see text] TeV, and the corresponding [Formula: see text] versus the average charged-particle (pseudorapidity) multiplicity density [Formula: see text] dependence is described very well by the simple power function with exponent parameter [Formula: see text] (1/3) in the whole analyzed range [Formula: see text]. It is found that the transverse (radial) flow becomes significant at higher multiplicity events in [Formula: see text] collisions at [Formula: see text] TeV, reaching the maximum value [Formula: see text] at the largest studied multiplicity density [Formula: see text]. It is estimated from analysis of [Formula: see text] and [Formula: see text] versus [Formula: see text] dependencies, obtained using Hagedorn function with the embedded transverse flow, that the probable onset of deconfinement phase transition in inelastic [Formula: see text] collisions at [Formula: see text] TeV occurs at [Formula: see text].

Refinement of the relationship between effective radii and ionization energies of alkali metal atoms

One of the key explanations for the peculiarities of the change in the first ionization energies (IE Ei1) of the elements of the periodic table is based on the postulation of an unambiguous relationship between Ei1 and atomic radii (rat). Due to the certain conventionality of the rat parameters, they do not belong to the category of attributive atomic characteristics. Usually they are found either by implementing various kinds of theoretical or semi-empirical calculation schemes, or by using experimental data on Ei1 for the corresponding approximations. As follows from the literature data, the known values of rat, even in the case of "quasi-hydrogen-like" alkali metals (AM), –relatively simple manyelectron systems – are characterized, as a rule, by a significant scatter. In addition, the canonical analytical formulas describing rаt within the framework of a hydrogen-like model with two effective interaction parameters (according to Slater) do not ultimately lead to adequate results in this set of elements. In this work, to correct the relationship rat = f (Еi1) related to the properties of the aggregate of alkaline elements, the publication of the effective Slater radii (reff) and Weber-Cromer orbital radii (rorb), and some results of later data are used. The effective principal quantum numbers n* for each of the AM (except for Li, for which it is assumed that n*=n=2) are estimated on the basis of the values of Ei1. A further step, by introducing n*, made it possible to use the criterion for optimizing the value of the effective radius r* and to correct the formula that determines its relationship with Ei1 in the form of a simple power function. At the same time, the radii Li, Na, and Fr have been refined towards some underestimation, compared with rorb. Arguments are presented in favor of the reliability of the proposed approach. It is shown that the obtained estimates of r* correlate better with the amplitudes of the solution of the wave equation covering all AMs than the known corresponding values of rorb and reff.

Role of Reynolds and Archimedes numbers in particle-fluid flows

Any scientific behavior is best represented by nondimensional numbers. However, in many cases, for pneumatic conveying systems, dimensional equations are developed and used. In some cases, many of the nondimensional equations include Reynolds (Re) and Froude (Fr) numbers; they are usually defined for a limited range of materials and operating conditions. This study demonstrates that most of the relevant flow types, whether in horizontal or vertical pipes, can be better described by Re and Archimedes (Ar) numbers. Ar can also be used in hydraulic conveying systems. This paper presents many threshold velocities that are accurately defined by Re as a simple power function of Ar. Many particulate materials are considered by Ar, thereby linking them to a common behavior. Using various threshold velocities, a flow regime chart for horizontal conveying is presented in this paper.

A dimensionless approach for the runoff peak assessment: effects of the rainfall event structure

The present paper proposes a dimensionless analytical framework to predict the hydrologic response of a given catchment thus assessing the impact of the rainfall event structure on the runoff peak. The dimensionless form of the rainfall depth is described as a simple power function of the dimensionless duration. Soil abstractions are modelled using the Soil Conservation Service method and the Instantaneous Unit Hydrograph theory is undertaken to determine the dimensionless form of the hydrograph; the two-parameter gamma-distribution is selected to test the proposed methodology. A set of analytical expressions are derived in case of constant-intensity hyetograph to assess the highest runoff peak with respect to a given rainfall event structure irrespective of the specific catchment. Looking at the results, the curve of the highest values of the runoff peak reveals a local minimum point in the neighbourhood of d* and n values equal to 1 and 0.3, respectively. As an example, the proposed approach has been applied to analyse the hydrologic response of a small Mediterranean catchment to three observed rainfall events characterized by different rainfall internal structures.

Ecoregion-Based Local Volume Equations for Appalachian Hardwoods

Local merchantable board foot, cubic foot, and weight equations are developed for six economically important hardwood species in central Appalachia. Equations were based on a simple power function and were fit to volumes from the US Forest Service Forest Inventory Analysis data for West Virginia and parts of Ohio, Pennsylvania, Maryland, Virginia, and Kentucky. Five ecoregions were identified and the volume equations were tested to determine whether differences by ecoregion were statistically significant. Results varied by species, volume type, and ecoregion. Average bias between a single-species region-wide model and specific ecoregion forms ranged from −9.1 to 8.5% for gross board foot volume (International ¼ in.), −3.5 to 9.2% for gross merchantable cubic foot volume, and −9.5 to 16.7% for merchantable drybole weight (pounds).

Estimation of Geometric Attributes and Masses of Individual Cucumber Organs Using Three-dimensional Digitizing and Allometric Relationships

The objective of this study was to estimate geometric attributes and masses of individual cucumber (Cucumis sativus L.) organs in situ. Using three-dimensional (3D) digitizing techniques, geometric data were obtained that were used to establish allometric relationships between geometric organ attribute and organ mass. Moreover, the authors were looking for the effects of ontogeny and the influence of environmental factors on the allometric relationships in cucumber. If such an allometric relationship did not exist, they alternatively tested the relationship between organ dry weight and organ number counted from the top of the plant downward. Lastly, they included allometric relationships based on biomechanical approaches focused on lamina mass and petiole attributes. The digitizing method provided accurate data for the calculation of geometric plant part attributes, such as length, area, and volume. Based on these data it was possible to describe the relationships between plant part dry weight and plant part geometry by allometric functions except for internode length. Apart from this exception, two different kinds of allometric equations were used: a simple power function with two parameters and a linear function without intercept. Information about more than one dimension of the considered plant part (e.g., area or volume) led to a simple linear relationship, whereas knowledge of just one dimension, like plant part length, resulted in more complex nonlinear relationships. Ontogeny led, in general, to a reduction in the scaling exponent or in the scaling factor, whereas changes of the environment distributed these values. Considering these effects makes it possible to determine dry matter partitioning on organ scale nondestructively and investigate long-term processes on intact plants.

Red Snapper: Ecology and Fisheries in the U.S. Gulf of Mexico

<em>Abstract.</em>—The red snapper <em>Lutjanus campechanus </em>exhibits rapid growth early in life, yet is a relatively long-lived species with an indeterminate spawning pattern. Batch fecundity (<EM>BF</EM>), a principal determinant of the reproductive potential of indeterminate spawners, appears to increase geometrically with length and asymptotically with age based upon combined data from National Marine Fisheries Service (NMFS) and Marine Fisheries Initiative (MARFIN) reproductive sampling programs. As the life history pattern sets up a potential disconnection between size and age, we modeled their interaction as explanatory variables of <EM>BF</EM>. Visual analysis suggests a dome-shaped relationship between <EM>BF </EM>and age within a given size-class. To test this, a general log-linear model and a new “standardized-age” model (where the effect of age depends explicitly on the size of the fish) were fitted to data. These analyses suggest that the effect of age, while statistically significant, was relatively small (the models with age and length terms explaining only slightly more of the variation in <EM>BF </EM>than a simple power function of length). The age effect seems to be most pronounced for fish that are exceptionally small or exceptionally large given their age, which constitute a small fraction of the sample and presumably also a small fraction of the population at large. Hence, it seems unlikely that including this interaction would have any important ramifications for stock assessments of red snapper. Nevertheless, the effect of age on <EM>BF </EM>remains open to the degree that old fish (i.e., greater than age 13) were rare in the combined data set and tended to exhibit lower <EM>BF </EM>values than predicted. Age effects of other reproductive determinants remain to be evaluated but we found hydrated females to be of greater size-at-age than nonhydrated red snapper suggesting an age-length interaction on batch frequency.

Characterization of processing pores and their relevance to the strength in alumina ceramics

Characterization of bulk defects was successfully accomplished in alumina with a transmission optical microscope. The characterization technique used is based on the fact that many ceramics are essentially transparent. Most defects in this particular ceramic were found to be pore. Their size distribution was found to follow a simple power function. With these characteristics of defects, the strength distribution of the ceramics was calculated with Baratta's model and compared to the measured strength of the ceramics. A good agreement was found between them when the pore was assumed to be accompanied with cracks 4 times the length of the grain size.