EXPANSION ABOUT THE GAUSSIAN (OR SPHERICAL) MODEL

1990 ◽  
pp. 192-203
Author(s):  
George A. Baker
Keyword(s):  
Spherical Model

scholarly journals Practical application of synthetic head models in real ballistic cases

2021 ◽  
Author(s):  
F. Riva ◽  
T. Fracasso ◽  
A. Guerra ◽  
P. Genet
Keyword(s):  
Soft Tissues ◽  
Spherical Model ◽  
Brain Parenchyma ◽  
Human Bone ◽  
Shape Model ◽  
The Difference ◽  
Open Shape ◽  
The Brain ◽  
Synthetic Models ◽  
Representative Material

AbstractIn shooting crimes, ballistics tests are often recommended in order to reproduce the wound characteristics of the involved persons. For this purpose, several “simulants” can be used. However, despite the efforts in the research of “surrogates” in the field of forensic ballistic, the development of synthetic models needs still to be improved through a validation process based on specific real caseworks. This study has been triggered by the findings observed during the autopsy performed on two victims killed in the same shooting incident, with similar wounding characteristics; namely two retained head shots with ricochet against the interior wall of the skull; both projectiles have been recovered during the autopsies after migration in the brain parenchyma. The thickness of the different tissues and structures along the bullets trajectories as well as the incident angles between the bullets paths and the skull walls have been measured and reproduced during the assemblage of the synthetic head models. Two different types of models (“open shape” and “spherical”) have been assembled using leather, polyurethane and gelatine to simulate respectively skin, bone and soft tissues. Six shots have been performed in total. The results of the models have been compared to the findings of post-mortem computed tomography (PMCT) and the autopsy findings.Out of the six shots, two perforated the models and four were retained. When the projectile was retained, the use of both models allowed reproducing the wounds characteristics observed on both victims in terms of penetration and ricochet behaviour. However, the projectiles recovered from the models showed less deformation than the bullets collected during the autopsies. The “open shape” model allowed a better controlling on the shooting parameters than the “spherical” model. Finally, the difference in bullet deformation could be caused by the choice of the bone simulant, which might under-represent either the strength or the density of the human bone. In our opinion, it would be worth to develop a new, more representative material for ballistic which simulates the human bone.

Mathematical Modeling of Betanin Extraction from Red Beet (Beta vulgaris L.) by Solid–Liquid Method

2015 ◽  
Vol 11 (1) ◽  
pp. 17-22 ◽  
Author(s):  
Honggao Xu ◽  
Qiang Peng ◽  
Fang Yuan ◽  
Yanxiang Gao
Keyword(s):  
Mathematical Modeling ◽  
Effective Diffusion ◽  
Spherical Model ◽  
Extraction Process ◽  
Extraction Temperature ◽  
Optimal Parameters ◽  
Practical Application ◽  
Sulfurous Acid ◽  
Red Beet ◽  
Solid Liquid

Abstract Effective diffusion coefficient (D-value) is an important parameter for the extraction process. In this study, a cylindrical model to estimate the D-value of betanin extraction from red beet roots was developed. The influence of extraction temperature, pH, cylindrical thickness and type of acids on the D-value was also investigated. The optimal parameters of betanin extraction were 30°C, pH 4.0 adjusted with sulfurous acid or acetic acid. D-values under the above conditions were 18.95×10−11 m2/s and 17.87×10−11 m2/s, respectively. The result showed that D-value elevated with the increase of cylindrical thickness, which was consistent with earlier conclusion from spherical model. The modeling may be useful for the investigation into extraction process and practical application.

scholarly journals Vortex–Vortex Interactions for the Maintenance of Blocking. Part II: Numerical Experiments

2013 ◽  
Vol 70 (3) ◽  
pp. 743-766 ◽  
Author(s):  
Akira Yamazaki ◽  
Hisanori Itoh
Keyword(s):  
Numerical Experiments ◽  
Channel Model ◽  
Spherical Model ◽  
Zonal Flow ◽  
Selective Absorption ◽  
Absorption Mechanism ◽  
Vortex Interactions ◽  
Maintenance Mechanism ◽  
Uniform Background

Abstract The selective absorption mechanism (SAM), newly proposed in Part I of this study on the maintenance mechanism of blocking, is verified through numerical experiments. The experiments were based on the nonlinear equivalent-barotropic potential vorticity equation, with varying conditions with respect to the shape and amplitude of blocking, and characteristics of storm tracks (displacement and strength) and background zonal flow. The experiments indicate that the SAM effectively maintains blocking, irrespective of the above conditions. At first, by applying a channel model on a β plane, numerical experiments were conducted using a uniform background westerly with and without a jet. The results show that the presence of a jet promotes the effectiveness of the SAM. Then, two types of spherical model experiments were also performed. In idealized experiments, the SAM was as effective as the β-plane model in explaining the maintenance of blocking. Moreover, experiments performed under realistic meteorological conditions showed that the SAM maintained a real block, demonstrating that the SAM is effective. These results, and the case study in Part I, verify that the SAM is the effective general maintenance mechanism for blocking.

scholarly journals Out-of-equilibrium properties of the semi-infinite kinetic spherical model

2006 ◽  
Vol 39 (9) ◽  
pp. 1981-1999 ◽  
Author(s):  
Florian Baumann ◽  
Michel Pleimling
Keyword(s):  
Spherical Model

scholarly journals USE OF SCALED SEMIVARIOGRAMS IN THE PLANNING SAMPLE OF SOIL CHEMICAL PROPERTIES IN SOUTHERN AMAZONAS, BRAZIL

2015 ◽  
Vol 39 (1) ◽  
pp. 31-39 ◽  
Author(s):  
Ivanildo Amorim de Oliveira ◽  
Milton César Costa Campos ◽  
José Marques Junior ◽  
Renato Eleotério de Aquino ◽  
Daniel de Bortoli Teixeira ◽  
...  
Keyword(s):  
Chemical Properties ◽  
Spherical Model ◽  
Exponential Model ◽  
Soil Samples ◽  
Soil Chemical Properties ◽  
Sampling Density ◽  
Sugarcane Crop ◽  
Lack Of Information ◽  
Set Up ◽  
Almost All

The lack of information concerning the variability of soil properties has been a major concern of researchers in the Amazon region. Thus, the aim of this study was to evaluate the spatial variability of soil chemical properties and determine minimal sampling density to characterize the variability of these properties in five environments located in the south of the State of Amazonas, Brazil. The five environments were archaeological dark earth (ADE), forest, pasture land, agroforestry operation, and sugarcane crop. Regular 70 × 70 m mesh grids were set up in these areas, with 64 sample points spaced at 10 m distance. Soil samples were collected at the 0.0-0.1 m depth. The chemical properties of pH in water, OM, P, K, Ca, Mg, H+Al, SB, CEC, and V were determined at these points. Data were analyzed by descriptive and geostatistical analyses. A large part of the data analyzed showed spatial dependence. Chemical properties were best fitted to the spherical model in almost all the environments evaluated, except for the sugarcane field with a better fit to the exponential model. ADE and sugarcane areas had greater heterogeneity of soil chemical properties, showing a greater range and higher sampling density; however, forest and agroforestry areas had less variability of chemical properties.

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