scholarly journals Statistical Characteristics of Stationary Flow of Substance in a Network Channel Containing Arbitrary Number of Arms

Entropy ◽  
2020 ◽  
Vol 22 (5) ◽  
pp. 553 ◽  
Author(s):  
Roumen Borisov ◽  
Zlatinka I. Dimitrova ◽  
Nikolay K. Vitanov
Keyword(s):  
Finite Number ◽  
Infinite Number ◽  
Arbitrary Number ◽  
Probability Distributions ◽  
Stationary Flow ◽  
Stationary Regime ◽  
Information Measure ◽  
Statistical Characteristics ◽  
Waring Distribution ◽  
Network Channel

We study flow of substance in a channel of network which consists of nodes of network and edges which connect these nodes and form ways for motion of substance. The channel can have arbitrary number of arms and each arm can contain arbitrary number of nodes. The flow of substance is modeled by a system of ordinary differential equations. We discuss first a model for a channel which arms contain infinite number of nodes each. For stationary regime of motion of substance in such a channel we obtain probability distributions connected to distribution of substance in any of channel’s arms and in entire channel. Obtained distributions are not discussed by other authors and can be connected to Waring distribution. Next, we discuss a model for flow of substance in a channel which arms contain finite number of nodes each. We obtain probability distributions connected to distribution of substance in the nodes of the channel for stationary regime of flow of substance. These distributions are also new and we calculate corresponding information measure and Shannon information measure for studied kind of flow of substance.

Application of Mathematical Modeling during Monitoring and Optimization of Non-Stationary Regime of Oil Well

2016 ◽  
Vol 11 (1) ◽  
pp. 53-59
Author(s):  
A.S. Topolnikov
Keyword(s):  
Mathematical Modeling ◽  
Model Problem ◽  
Cylindrical Tube ◽  
Field Measurements ◽  
Stationary Flow ◽  
Stationary Regime ◽  
Oil Well ◽  
Time Duration ◽  
Typical Time ◽  
Radial Model

The paper presents results of modeling of periodical regime of oil well for the purpose of monitoring and optimization of its operation. To describe non-stationary flow in the reservoir a planar-radial model of filtration is employed. The flow of multiphase flux in the well elements (casing, tubing, annulus) is described by 1D Navier-Stoks equations. The pump work is modelled by specification of its rate-head curve. To estimate the typical time duration of the processes in the well and in the reservoir a solution of a model problem for cylindrical tube is given. Through the examples a solution of a problem of optimization of periodical regime of oil wells is demonstrated. The comparison with field measurements is presented.

The inverse problem of recovering the coefficients of a differential equations on a graph

2020 ◽  
Vol 28 (5) ◽  
pp. 727-738
Author(s):  
Victor Sadovnichii ◽  
Yaudat Talgatovich Sultanaev ◽  
Azamat Akhtyamov
Keyword(s):  
Inverse Problem ◽  
Inverse Problems ◽  
Differential Equations ◽  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Finite Number ◽  
Characteristic Equation ◽  
Arbitrary Number ◽  
New Class ◽  
Finite Set

AbstractWe consider a new class of inverse problems on the recovery of the coefficients of differential equations from a finite set of eigenvalues of a boundary value problem with unseparated boundary conditions. A finite number of eigenvalues is possible only for problems in which the roots of the characteristic equation are multiple. The article describes solutions to such a problem for equations of the second, third, and fourth orders on a graph with three, four, and five edges. The inverse problem with an arbitrary number of edges is solved similarly.

scholarly journals Higher spins from exotic dualisations

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Nicolas Boulanger ◽  
Victor Lekeu
Keyword(s):  
Infinite Number ◽  
Arbitrary Number ◽  
Degrees Of Freedom ◽  
Young Tableaux ◽  
Spacetime Dimension ◽  
Massless Field ◽  
Free Level ◽  
Higher Spins

Abstract At the free level, a given massless field can be described by an infinite number of different potentials related to each other by dualities. In terms of Young tableaux, dualities replace any number of columns of height hi by columns of height D − 2 − hi, where D is the spacetime dimension: in particular, applying this operation to empty columns gives rise to potentials containing an arbitrary number of groups of D − 2 extra antisymmetric indices. Using the method of parent actions, action principles including these potentials, but also extra fields, can be derived from the usual ones. In this paper, we revisit this off-shell duality and clarify the counting of degrees of freedom and the role of the extra fields. Among others, we consider the examples of the double dual graviton in D = 5 and two cases, one topological and one dynamical, of exotic dualities leading to spin three fields in D = 3.

An Infinite Number of Laminagrams from a Finite Number of Radiographs

Radiology ◽  
1971 ◽  
Vol 98 (2) ◽  
pp. 249-255 ◽  
Author(s):  
Earl R. Miller ◽  
Edward M. MoCurry ◽  
Bernard Hruska
Keyword(s):  
Finite Number ◽  
Infinite Number

Some comments on positron–atom scattering at intermediate energy

1982 ◽  
Vol 60 (4) ◽  
pp. 558-564 ◽  
Author(s):  
F. W. Byron Jr.
Keyword(s):  
Finite Number ◽  
Cross Sections ◽  
Infinite Number ◽  
Intermediate Energy ◽  
Total Cross Sections ◽  
Type Approximation ◽  
Atom Scattering ◽  
Target States

A brief survey of available theoretical techniques is given for positron–atom scattering. The distinction between methods involving a finite number of target states and those with an infinite number of target states is emphasized. The situation regarding total cross sections is summarized, and a new, non-perturbative, eikonal-type approximation, based on the work of Wallace, is introduced.

scholarly journals Research of Register Pressure Aware Loop Unrolling Optimizations for Compiler

2018 ◽  
Vol 228 ◽  
pp. 03008
Author(s):  
Xuehua Liu ◽  
Liping Ding ◽  
Yanfeng Li ◽  
Guangxuan Chen ◽  
Jin Du
Keyword(s):  
Finite Number ◽  
Infinite Number ◽  
Performance Degradation ◽  
Transformation Process ◽  
Fine Grained ◽  
Loop Unrolling ◽  
Average Improvement ◽  
Register Pressure ◽  
Linpack Benchmark ◽  
Loop Optimizations

Register pressure problem has been a known problem for compiler because of the mismatch between the infinite number of pseudo registers and the finite number of hard registers. Too heavy register pressure may results in register spilling and then leads to performance degradation. There are a lot of optimizations, especially loop optimizations suffer from register spilling in compiler. In order to fight register pressure and therefore improve the effectiveness of compiler, this research takes the register pressure into account to improve loop unrolling optimization during the transformation process. In addition, a register pressure aware transformation is able to reduce the performance overhead of some fine-grained randomization transformations which can be used to defend against ROP attacks. Experiments showed a peak improvement of about 3.6% and an average improvement of about 1% for SPEC CPU 2006 benchmarks and a peak improvement of about 3% and an average improvement of about 1% for the LINPACK benchmark.

Numerical simulation of soliton gas within the Korteweg-de Vries type equations

2019 ◽  
pp. 52-66
Author(s):  
Екатерина Геннадьевна Диденкулова ◽  
Анна Витальевна Кокорина ◽  
Алексей Викторович Слюняев
Keyword(s):  
Numerical Scheme ◽  
Initial Conditions ◽  
Probability Distributions ◽  
Scattering Problem ◽  
Spectral Composition ◽  
Computation Time ◽  
Qualitative Description ◽  
Statistical Characteristics ◽  
De Vries ◽  
Pseudo Spectral Method

Приведены детали численной схемы и способа задания начальных условий для моделирования нерегулярной динамики ансамблей солитонов в рамках уравнений типа Кортевега-де Вриза на примере модифицированного уравнения Кортевега-де Вриза с фокусирующим типом нелинейности. Дано качественное описание эволюции статистических характеристик для ансамблей солитонов одной и разных полярностей. Обсуждаются результаты тестовых экспериментов по столкновению большого числа солитонов. The details of the numerical scheme and the method of specifying the initial conditions for the simulation of the irregular dynamics of soliton ensembles within the framework of equations of the Korteweg - de Vries type are given using the example of the modified Korteweg - de Vries equation with a focusing type of nonlinearity. The numerical algorithm is based on a pseudo-spectral method with implicit integration over time and uses the Crank-Nicholson scheme for improving the stability property. The aims of the research are to determine the relationship between the spectral composition of the waves (the Fourier spectrum or the spectrum of the associated scattering problem) and their probabilistic properties, to describe transient processes and the equilibrium states. The paper gives a qualitative description of the evolution of statistical characteristics for ensembles of solitons of the same and different polarities, obtained as a result of numerical simulations; the probability distributions for wave amplitudes are also provided. The results of test experiments on the collision of a large number of solitons are discussed: the choice of optimal conditions and the manifestation of numerical artifacts caused by insufficient accuracy of the discretization. The numerical scheme used turned out to be extremely suitable for the class of the problems studied, since it ensures good accuracy in describing collisions of solitons with a short computation time.

Statistical characteristics for the defect occurrence of raw silk

2019 ◽  
Vol 90 (3-4) ◽  
pp. 302-312
Author(s):  
Jian-mei Xu ◽  
Ying Zhou ◽  
Jiantao Niu ◽  
Dongping Wu ◽  
Lun Bai
Keyword(s):  
Goodness Of Fit ◽  
Probability Distributions ◽  
Capacitive Sensor ◽  
Test Method ◽  
International Organization ◽  
Statistical Characteristics ◽  
Goodness Of Fit Test ◽  
Polya Distribution ◽  
Silk Filament ◽  
Better Than

In order to consider different defects that occur during the computer simulation of raw silk size series, it is necessary to find out the statistical characteristics for the defect occurrence of raw silk. Under the newest International Organization for Standardization standard for electronic testing of raw silk, the defects are classified into small slubs, big slubs, thick places, thin places, and small imperfection elements. By analyzing some probability distributions that happen during the silk reeling process and the formation of the defects, the study proposed that Pólya distribution may fit better than Poisson distribution in describing the number of defects formed in a certain length of silk filament. To verify this theoretical deduction experimentally, the defects for 15 lots of raw silk were tested every 1000 meters using an electronic tester for raw silk; each time 12 skeins were tested together and each test was repeated from 13 to 17 times. A goodness-of-fit test method for Poisson and Pólya distributions was deduced, which was used to analyze the statistical characteristics for the defects except for small imperfection elements. The results showed that when using the capacitive sensor, the defects of big slubs, small slubs, and thick places had a Pólya distribution with a weak spreading characteristic; the thin places were a combination of independent Pólya distributions, and each subclass of thin places took Pólya distribution; when using the optical sensor, all the defects had a Pólya distribution, which was in line with the theoretical deduction.

A definition of existence in terms of abstraction and disjunction

1957 ◽  
Vol 22 (4) ◽  
pp. 343-344
Author(s):  
Frederic B. Fitch
Keyword(s):  
Finite Number ◽  
Infinite Number ◽  
Recursive Relation ◽  
Basic Logic ◽  
Class A ◽  
Definition Of ◽  
Image Position

Greater economy can be effected in the primitive rules for the system K of basic logic by defining the existence operator ‘E’ in terms of two-place abstraction and the disjunction operator ‘V’. This amounts to defining ‘E’ in terms of ‘ε’, ‘έ’, ‘o, ‘ό’, ‘W’ and ‘V’, since the first five of these six operators are used for defining two-place abstraction.We assume that the class Y of atomic U-expressions has only a single member ‘σ’. Similar methods can be used if Y had some other finite number of members, or even an infinite number of members provided that they are ordered into a sequence by a recursive relation represented in K. In order to define ‘E’ we begin by defining an operator ‘D’ such thatHere ‘a’ may be thought of as an existence operator that provides existence quantification over some finite class of entities denoted by a class A of U-expressions. In other words, suppose that ‘a’ is such that ‘ab’ is in K if and only if, for some ‘e’ in A, ‘be’ is in K. Then ‘Dab’ is in K if and only if, for some ‘e and ‘f’ in A, ‘be’ or ‘b(ef)’ is in K; and ‘a’, ‘Da’, ‘D(Da)’, and so on, can be regarded as existence operators that provide for existence quantification over successively wider and wider finite classes. In particular, if ‘a’ is ‘εσ’, then A would be the class Y having ‘σ’ as its only member, and we can define the unrestricted existence operator ‘E’ in such a way that ‘Eb’ is in K if and only if some one of ‘εσb’, ‘D(εσ)b’, ‘D(D(εσ))b’, and so on, is in K.

Resonance Analysis of Train–Track–Bridge Interaction Systems with Correlated Uncertainties

2019 ◽  
Vol 20 (01) ◽  
pp. 2050008 ◽  
Author(s):  
Lifeng Xin ◽  
Xiaozhen Li ◽  
Jiaxin Zhang ◽  
Yan Zhu ◽  
Lin Xiao
Keyword(s):  
Probability Distributions ◽  
Three Dimensional ◽  
Estimation Method ◽  
Interaction Model ◽  
Point Estimation ◽  
Statistical Characteristics ◽  
Resonance Analysis ◽  
Track Bridge ◽  
Point Estimation Method ◽  
Nataf Transformation

Over the last decades, the resonance-related dynamics for bridge systems subjected to a moving train has been researched and discussed from mechanics, physics and mathematics. In the current work, new perspectives of train-induced resonance analysis are investigated through introducing random propagation process into the train–bridge dynamic interactions. Besides, the Nataf-transformation-based point estimation method is applied to generate pseudorandom variables following arbitrarily correlated probability distributions. A three-dimensional (3D) nonlinear train-ballasted track–bridge interaction model founded on fundamental physical and mechanical principles is employed to convey and depict train–bridge interactions with random properties considered. After that, extensive applications are illustrated in detail for revealing the statistical characteristics of the so-called “random resonance”. Numerical results show that the critical train speeds associated with resonance and cancelation are random in essence owing to the variability of system parameters; the correlation between parameters exerts obvious influences on system dynamic behaviors; the last vehicle of a train will be in more violent vibrations compared to the front vehicles; the influences of track irregularities on the wheel–rail interactions are significantly greater than those of resonance.

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