scholarly journals Damped oscillations of the probability of random events followed by absolute refractory period

2019 ◽  
Author(s):  
A.V. Paraskevov ◽  
A.S. Minkin
Keyword(s):  
Analytical Calculation ◽  
Analytical Description ◽  
Initial Condition ◽  
Absolute Refractory Period ◽  
Damping Coefficients ◽  
Event Probability ◽  
Damped Oscillations ◽  
Bernoulli Scheme ◽  
Random Events ◽  
Refractory State

AbstractMany events are followed by an absolute refractory state, when for some time after the event a repetition of a similar event is impossible. If uniform events, each of which is followed by the same period of absolute refractoriness, occur randomly, as in the Bernoulli scheme, then the event probability as a function of time can exhibit damped transient oscillations caused by a specific initial condition. Here we give an exact analytical description of the oscillations, with a focus on application within neuroscience. The resulting formulas stand out for their relative simplicity, enabling analytical calculation of the damping coefficients for the second and third peaks of the event probability.

scholarly journals Analytical description of the specific electric conductivity of halogenides KHal melts and its calculation for the KAt melt

2019 ◽  
Vol 58 (6) ◽  
pp. 138-145
Author(s):  
Ivan K. Garkushin ◽  
◽  
Olga V. Lavrenteva ◽  
Yana A. Andreeva ◽  
Karina R. Gilmanova ◽  
...  
Keyword(s):  
Least Squares Method ◽  
Specific Conductivity ◽  
Analytical Calculation ◽  
Analytical Description ◽  
Order Number ◽  
Specific Electric Conductivity ◽  
Alkaline Earth Elements ◽  
Straight Line ◽  
Electronegativity Difference ◽  
Calculation Results

In this paper, the analytical description of the specific conductivity of the potassium halogenides melts KHal (Hal – F, Cl, Br, I) is presented. The analitical description is provided on dependence of the specific conductivity on the halogen order number ӕ = f(Z), the ionic radius of halogen-ion ӕ = f(r), the ionic potential ӕ = f(1/r), the electronegativity difference ӕ = f(∆χ) ((∆χ = χ (Hal) – χ(K)). The interrelation of a reduced property with an order number ӕ/Z = f(Z) is considered. According to the obtained analytical dependencies, the calculation of the value of the potassium astatide specific conductivity is given for temperatures above the melting point on 5, 10, 50, 75, 100, 150 и 200°, in literature Information for KAt absent. The calculation was carried out using comparative methods for calculating M.Kh. Karapetyan in the coordinates of "property-parameter" and "property-property." Least squares method was applied for processing the analytical description results with the choice of optimal dependencies on the maximum correlation coefficient and the minimum standard deviation. The analysis of the interrelation of the calculated numerical values with similar characteristics for NaAt и LiAt is presented. Comparison of the specific conductivity obtained numerical values of the astatide potassium melt showed good consistency with the values ӕ obtained from the straight line dependence ӕТпл+n = a∙ ӕТпл+5 (n = 10°…200°) and also with similar characteristics for lithium astatide and sodium astatide. The analytical calculation results allow to describe the temperature dependence of the potassium halogenides specific conductivity, including KAt. The calculation method can be used to describe the melts specific conductivity in the same type series of compounds of alkaline and alkaline-earth elements that make up electrolytes for chemical current sources.

scholarly journals Analytical Calculation of the Mechanical Properties of Honeycombs Printed Using the FDM Additive Manufacturing Technology

2021 ◽  
Vol 24 (2) ◽  
pp. 16-23
Author(s):  
Kostiantyn V. Avramov ◽  
◽  
Borys V. Uspenskyi ◽  
Ihor I. Derevianko ◽  
◽  
...  
Keyword(s):  
Mechanical Properties ◽  
Shear Modulus ◽  
Analytical Data ◽  
Three Dimensional ◽  
Analytical Calculation ◽  
Analytical Description ◽  
Analytical Prediction ◽  
Plane Shear ◽  
Analytical Formulae ◽  
3D Printed

FDM 3D printed honeycombs are investigated. A honeycomb is composed of regular hexagonal cells. A honeycomb is 3D printed so that the fused filament runs along the walls of its cells. We emphasize that the thickness of these walls is one or two times the thickness of the fused filament. When calculating the mechanical properties of a honeycomb, its walls are considered as a Euler-Bernoulli beam bending in one plane. To describe honeycombs, a homogenization procedure is used, which reduces a honeycomb to a homogeneous orthotropic medium. An adequate analytical calculation of the mechanical properties of this medium is the subject of our research. Analytical formulae for calculating the mechanical properties of honeycombs are presented. To assess the adequacy of the calculation results, the analytical data are compared with the results of simulation in the commercial ANSYS package. For this, the mechanical properties of the honeycombs made of the ULTEM 9085 material are determined numerically. To assess these properties, from a large number of analytical formulae are selected those that predict them adequately. As a result of calculations, an analytical prediction of all mechanical properties is obtained, with the exception of the in-plane shear modulus of a honeycomb. This is due to the fact that to simulate such a shear modulus one has to use a three-dimensional theory that does not have an adequate analytical description. A thin aluminum honeycomb was considered. In the future, three-layer structures with such a honeycomb will be investigated. Analytical results for ULTEM 9085 and aluminum honeycombs are similar.

On the Damping Properties of the Shoulder Complex

1984 ◽  
Vol 106 (4) ◽  
pp. 360-363 ◽  
Author(s):  
A. E. Engin
Keyword(s):  
Nonlinear Behavior ◽  
Damping Properties ◽  
Human Response ◽  
Body Segment ◽  
Damping Coefficients ◽  
Damped Oscillations ◽  
Shoulder Complex ◽  
The Subject ◽  
Human Body Models

Effectiveness of the multi-segmented total-human-body models to predict accurately live human response depends heavily on the task of proper biomechanical description and simulation of the articulating joints. Determination of the damping properties in articulating joints is an important part of this task and constitutes the subject of this paper. A new method which is based on the damped oscillations of a body segment is introduced by considering the shoulder complex as an example. The numerical results for the angular damping coefficients at the shoulder complex are presented for forty different orientations of the arm with respect to torso. The angular damping coefficients exhibit a nonlinear behavior as a function of the arm orientation.

On amendments to the calculation formulas for the required number of receiving and departure tracks in the technical station yards

2021 ◽  
Vol 18 (1) ◽  
pp. 16-24
Author(s):  
V. V. Kostenko ◽  
◽  
D. E. Bogdanovich ◽  
Keyword(s):  
Performance Indicators ◽  
Practical Importance ◽  
Analytical Calculation ◽  
External Factors ◽  
Preliminary Assessment ◽  
Freight Train ◽  
Calculation Technique ◽  
Factors Influencing ◽  
Random Events ◽  
Adjustment Factors

Objective: To discuss the feasibility of modifying the analytical calculation technique for the required number of receiving and departure tracks in the technical station yards. To show the need to introduce new adjustment factors to assess the time spent by a transit freight train at the station, considering the influence of external factors – often random events – on the duration of the receiving and departure track occupation; to determine the possibility of adjustment factors application for a preliminary assessment of the required number of receiving and departure tracks; to substantiate the need for simulation of the station operation for a more accurate assessment of the required number of receiving and departure tracks depending on the time spent by a transit freight train at the station, considering the influence of external factors. Methods: Comparative analysis of the existing techniques for determining the required number of receiving and departure tracks, assessment of analytical dependencies, and substantiation of the need to introduce new adjustment factors based on the analysis of the technical stations’ reported performance indicators are applied. Results: The need to improve the existing analytical calculation technique for the required number of receiving and departure tracks has been indicated. The groups of factors influencing the time spent by a transit freight train at the station, including the required number of tracks, have been determined. New adjustment factors to assess the time spent by a transit freight train at the station have been proposed. The need for additional study of this issue has been revealed. Practical importance: The authors have shown that it is necessary to clarify the existing analytical calculation technique for the required number of receiving and departure tracks by introducing the adjustment factors, which will improve the accuracy of determining the required number of receiving and departure tracks at a technical station.

Quantitative Analysis Of X-Ray Images From Geological Materials

1990 ◽  
Vol 48 (2) ◽  
pp. 244-245
Author(s):  
J. M. Paque ◽  
R. Browning ◽  
P. L. King ◽  
P. Pianetta
Keyword(s):  
Quantitative Analysis ◽  
Bulk Composition ◽  
Principal Component ◽  
Analytical Description ◽  
Bulk Sample ◽  
Geological Samples ◽  
X Ray ◽  
Software And Hardware ◽  
And Storage ◽  
Insight Into

Geological samples typically contain many minerals (phases) with multiple element compositions. A complete analytical description should give the number of phases present, the volume occupied by each phase in the bulk sample, the average and range of composition of each phase, and the bulk composition of the sample. A practical approach to providing such a complete description is from quantitative analysis of multi-elemental x-ray images.With the advances in recent years in the speed and storage capabilities of laboratory computers, large quantities of data can be efficiently manipulated. Commercial software and hardware presently available allow simultaneous collection of multiple x-ray images from a sample (up to 16 for the Kevex Delta system). Thus, high resolution x-ray images of the majority of the detectable elements in a sample can be collected. The use of statistical techniques, including principal component analysis (PCA), can provide insight into mineral phase composition and the distribution of minerals within a sample.

Monte Carlo Modelling of Secondary Electron Yield from Rough Surfaces

1990 ◽  
Vol 48 (1) ◽  
pp. 422-423
Author(s):  
John C. Russ
Keyword(s):  
Monte Carlo ◽  
Energy Loss ◽  
Secondary Electron ◽  
Secondary Electron Emission ◽  
Analytical Calculation ◽  
Mean Free Path ◽  
Single Scattering ◽  
High Energy ◽  
Secondary Electron Yield ◽  
Electron Yield

Monte-Carlo programs are well recognized for their ability to model electron beam interactions with samples, and to incorporate boundary conditions such as compositional or surface variations which are difficult to handle analytically. This success has been especially powerful for modelling X-ray emission and the backscattering of high energy electrons. Secondary electron emission has proven to be somewhat more difficult, since the diffusion of the generated secondaries to the surface is strongly geometry dependent, and requires analytical calculations as well as material parameters. Modelling of secondary electron yield within a Monte-Carlo framework has been done using multiple scattering programs, but is not readily adapted to the moderately complex geometries associated with samples such as microelectronic devices, etc.This paper reports results using a different approach in which simplifying assumptions are made to permit direct and easy estimation of the secondary electron signal from samples of arbitrary complexity. The single-scattering program which performs the basic Monte-Carlo simulation (and is also used for backscattered electron and EBIC simulation) allows multiple regions to be defined within the sample, each with boundaries formed by a polygon of any number of sides. Each region may be given any elemental composition in atomic percent. In addition to the regions comprising the primary structure of the sample, a series of thin regions are defined along the surface(s) in which the total energy loss of the primary electrons is summed. This energy loss is assumed to be proportional to the generated secondary electron signal which would be emitted from the sample. The only adjustable variable is the thickness of the region, which plays the same role as the mean free path of the secondary electrons in an analytical calculation. This is treated as an empirical factor, similar in many respects to the λ and ε parameters in the Joy model.

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