BazTech - Yadda

1

On the one-dimensional mean-field games with congestion

Sedjro Marc

Mathematica Applicanda

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2022

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Vol. 50, no. 1

139--151

EN

In this work, we consider a one dimensional forward-forward model of Mean-field Games with congestion. We establish a connection between such models and conservation laws. Next, we show the existence of a non trivial convex entropies. Finally, we investigate the existence of solutions in the parabolic case and derived some estimates thanks to the existence of such convex entropies.

PL

Praca poświęcona jest jednowymiarowym modelom gier z uśrednionym oddziaływaniem w zarządzaniu. Takie badania mają na celu analizę podejmowania strategicznych decyzji przez czynniki mało oddziaływające w bardzo dużych populacjach. Ustalany jest związek między takimi modelami a prawami zachowania. W wyniku tych badań pokazano istnienie nietrywialnych entropii wypukłych. W końcowej części badane jest istnienie rozwiązań w przypadku parabolicznym i wyprowadzane są pewne oszacowania z istnienia takich wypukłych entropii.

2

Energy Harvesting From Bistable Systems Under Random Excitation

Lentz L., Nguyen H. T., von Wagner U.

Machine Dynamics Research

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2017

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Vol. 41, No. 1

5--16

EN

The transformation of otherwise unused vibrational energy into electric energy through the use of piezoelectric energy harvesting devices has been the subject of numerous investigations. The mechanical part of such a device is often constructed as a cantilever beam with applied piezo patches. If the harvester is designed as a linear resonator the power output relies strongly on the matching of the natural frequency of the beam and the frequency of the harvested vibration which restricts the applicability since most vibrations which are found in built environments are broad-banded or even totally random. A possible approach to overcome this restriction is the use of permanent magnets to impose a nonlinear restoring force on the beam that leads to a broader operating range due to large amplitude motions over a large range of excitation frequencies. In this paper such a system is considered introducing a refined modeling with multiple spacial ansatz functions and a refined modeling of the magnet beam interaction. The corresponding probability density function in case of random excitation is calculated by the solution of the corresponding Fokker-Planck equation and compared with results from Monte Carlo simulations. Finally some measurements of ambient excitations are discussed.

3

The application process of the Ornstein-Ulenbek to the formation of cavitation bubbles

Kapranova A., Lebedev A., Solopov S., Meltser A.

Czasopismo Techniczne. Mechanika

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2016

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Y. 113, iss. 2-M

139--144

EN

In this paper we propose the process of formation of cavitation bubbles in the pilot valve, considered as the steady and homogeneous Markov process.

PL

W pracy przedstawiono proces powstawania pęcherzy kawitacyjnych w zaworze sterującym jako stabilny i homogeniczny proces Markowa.

4

Probabilistic model of the chain-like structures' translocation through the pore in membrane

Bartłomiejczyk K.

Journal of Applied Mathematics and Computational Mechanics

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2015

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Vol. 14, nr 4

5--10

EN

The paper is devoted to the analysis of the translocation of the chain-like structures (CLS) through the pore in membrane. It focuses on the so-called passage time and the principal aim is to propose a proper probabilistic model for its distribution. The article starts with some preliminary results concerning stochastic processes. Next, an approximate analytic solution of the considered problem that was received in literature is presented. It is known that the resulting probability distribution of the passage time manifests some important shortcomings. Thus it is important to find a reasonable alternative. It is argued here that the beta Moyal probability distribution can be a good candidate for approximation of the theoretical distribution in various interesting situations. In this paper, two different problems connected with CLS translocation are considered. For both problems the theoretical distributions are known from literature and in both situations the beta Moyal approximations turn out to be very satisfactory.

5

Approximation algorithm supported on minimizing the Kullback-Leibler information divergence in some class of dynamical systems

Owedyk J., Mathia Z., Zarzycki H.

Biuletyn Naukowy Wrocławskiej Wyższej Szkoły Informatyki Stosowanej. Informatyka

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2015

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vol. 5

12--18

EN

In this work an algorithm is presented for creating approximate solutions in some class of dynamical systems describing the time evolution probability densities. The approximate solutions are obtained by minimizing Kullback- Leibler divergence under some constrains. It is shown that the derivatives of the Kullback-Leibler divergence for exact solutions and for approximate solutions are described by the same formula. In consequence if in a dynamical system the Kullback-Leibler divergence decreases in time for exact solutions, it also decreases for approximate solutions.

PL

W pracy przedstawiono algorytm, który umożliwia skonstruowanie przybliżonych rozwiązań dla pewnej klasy systemów dynamiczych opisujących ewolucję w czasie gęstości prawdopodobieństwa. Przybliżone rozwiązania otrzymujemy minimalizując informację Kullbacka-Leiblera przy dodatkowych warunkach. Wykazano, że pochodna informacji Kullbacka-Leiblera dla dokładnych i przybliżonych rozwiązań jest opisana przez tą samą formułę. W konsekwencji gdy w dynamicznym systemie maleje informacja Kullbacka-Leiblera dla dokładnych rozwiązań to także maleje dla przybliżonych rozwiązań.

6

Kolmogorov equation solution: multiple scattering expansion and photon statistics evolution modeling

Guirao M., Leble S.

TASK Quarterly : scientific bulletin of Academic Computer Centre in Gdansk

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2014

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Vol. 18, No 2

187--203

EN

We consider a formulation of the Cauchy problem for the Kolmogorov equation which corresponds to a localized source of particles to be scattered by a medium with a given scattering amplitude density. The multiple scattering ampl itudes are introduced and the corresponding series solution of the equation is constructed. We investigate the integral representation for the first series terms, its estimations and values of the photon number of finite and point receivers. Application to the LIDAR problem and X-ray beam scattering for orthogonal and inclined to a layer is considered.

7

Analytical solution of the time fractional Fokker-Planck equation

Sutradhar T., Datta B. K., Bera R. K.

International Journal of Applied Mechanics and Engineering

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2014

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Vol. 19, no. 2

435--440

EN

A nonperturbative approximate analytic solution is derived for the time fractional Fokker-Planck (F-P) equation by using Adomian’s Decomposition Method (ADM). The solution is expressed in terms of Mittag-Leffler function. The present method performs extremely well in terms of accuracy, efficiency and simplicity.

8

On reconstruction of the Ito-like equation from persistent time series

Czechowski Z.

Acta Geophysica

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2013

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Vol. 61, no. 6

1504--1521

EN

The Langevin equation with finite-range persistence was introduced as a macroscopic model of various geophysical phenomena. The modified histogram procedure (MHP) of reconstruction of the equation from time series was proposed. An efficiency of MHP was tested on artificial persistent time series (with short and long-tail distributions) generated by different Ito-like equations. For an exemplary geophysical time series, the appropriate Ito-like equation was reconstructed.

9

Metoda oceny bezpieczeństwa lotów z wykorzystaniem danych z procesu eksploatacji

Zieja M., Zieja M.

Problemy Eksploatacji

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2011

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nr 1

221-230

PL

W związku z wdrożeniem do eksploatacji w lotnictwie Sił Zbrojnych RP systemu informatycznego TURAWA obecnie niezwykle ważnym problemem jest konieczność kompleksowego wykorzystania gromadzonych danych. W artykule przedstawiono metodę oceny bezpieczeństwa lotów z wykorzystaniem danych z procesu eksploatacji wojskowych statków powietrznych, gromadzonych przez system TURAWA. Opracowana metoda pozwala: - ocenić poziom bezpieczeństwa systemu lotniczego, - wyznaczyć intensywność powstawania zawodności systemu lotniczego, - prognozować stan bezpieczeństwa systemu lotniczego w procesie eksploatacji statków powietrznych, - wyznaczyć bezpośrednie przyczyny obniżenia poziomu bezpieczeństwa systemu lotniczego, - ocenić skuteczność wdrożonych przedsięwzięć profilaktycznych, - ocenić stan bezpieczeństwa systemu lotniczego w czasie rzeczywistym.

EN

The paper has been written in connection with the TURAWA system implementation in the aviation of Armed Forces of the Polish Republic. At present, the necessity of complex analyses of gathered data is the most important problem. In the paper, a method of flight safety assessment using operational data gathered in the TURAWA system has been presented. The developed method allows to: - assess a flight safety level, - determine reasons for flight safety decrease, - forecast a flight safety level in aircraft operation, and - assess effectiveness of preventive measures.

10

A method of determining fatigue life of a structural component using the probability density function of time of exceeding the boundary condition - an outline

Tomaszek H., Klimaszewski S., Zieja M.

Prace Naukowe Instytutu Technicznego Wojsk Lotniczych

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2009

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nr 25

143-156

EN

The article is development of the paper [5] presented on 35th International Scientific Con-gress on Powertrain and Transport Means - European KONES 2009. An attempt has been made to present a probabilistic method to determine fatigue life of an aeronautical struc-ture's component by means of a density function of time a growing crack needs to reach the boundary condition. It has been assumed that in a component of a structure given consideration there is a small crack that grows due to fatigue load affecting it. After having reached the boundary value the component in question loses its usability. Time of the crack growth up to the boundary value is termed a fatigue life of the component. From the aspect of physics, the propagation of a crack within the component, if approached in a deterministic way, is described with the Paris's relationship for m = 2. In papers [2, 3] was found density function of the crack length and has been applied to find density function of time of reaching the boundary condition. This function has been used in the present paper to determine the randomly approached fatigue life of a component of a structure.

11

Zarys probabilistycznego opisu wzrostu pęknięcia zmęczeniowego elementu konstrukcji statku powietrznego.

Klimaszewski S., Tomaszek H.

Zagadnienia Eksploatacji Maszyn

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2004

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Vol. 39, nr 4

69-82

PL

W artykule przedstawiono probabilistyczną metodę określania funkcji gęstości rozkładu długości pęknięcia zmęczeniowego elementu konstrukcji statku powietrznego w procesie eksploatacji. Opracowany model probabilistyczny opisu wzrostu pęknięcia zmęczeniowego umożliwia ocenę rozkładu długości pęknięcia w funkcji liczby lotów statku powietrznego lub w funkcji czasu kalendarzowego. Otrzymane wyniki pozwalają na ocenę niezawodności i trwałości elementu konstrukcji.

EN

The probabilistic method of determining density function of distribution of the fatigue crack length of aircraft's structure element during operation/maintenance has been presented in this paper. The worked out probabilistic model of the fatigue crack growth description allows to estimate the distribution of the fatigue crack length in the function of the aircraft's numbers of flights or in the function of calendar time. The received results permit to estimate the reliability and durability of the structure element.

12

Derivation of the SCS-CN parameter S from linearized Fokker-Planck equation

Mishra S., Singh V.

Acta Geophysica Polonica

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2003

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Vol. 51, nr 2

179-202

EN

The potential maximum retention, S, of the Soil Conservation Service Curve Number (SCS-CN) method (SCS, 1956) was derived for a large set of published infiltration data ranging from Plainfield sand to Yololight clay using the relations between psi (negative pressure) and theta (moisture content) and between K (hydraulic conductivity) and theta. The physical significance of S is explained using the diffusion term of the linearized, Fokker-Planck equation for infiltration, which relates S to the storage and transmission properties of the soil. The s-values exhibit a strong looped relationship with the initial moisture content, analogous to that for curve numbers for three antecedent moisture conditions. The variations of S in vertical infiltration is also explained and discussed.

13

A kinetic theory of crystal growth from aqueous solutions

Jakubczyk M.

Prace Naukowe. Chemia / Wyższa Szkoła Pedagogiczna w Częstochowie

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2001

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Vol. 5

15--19

EN

The process of the crystal growth kinetics was investigated using the Fokker-Planck equation. The use of the diffusion Fick equation to relate the surface concentration and diffusion requires the use of the modified surface diffusion coefficient which is D = Ds( 1+o(β) where: Ds - is a diffusion coefficient witch the absence of adsorption and desorption, β =1/ξTD is a ratio of relation time characterizing the diffusion surface (1/β)and desorption TD.