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1

A global path-planning algorithm based on critical point diffusion binary tree for a planar mobile robot

Yang Zhiyong, Wang Lipeng, Cao Zejun, Zhang Zhi, Xu Zhuang

Bulletin of the Polish Academy of Sciences. Technical Sciences

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2024

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Vol. 72, nr 2

art. no. e148834

EN

A global path-planning algorithm for robots is proposed based on the critical-node diffusion binary tree (CDBT), which solves the problems of large memory consumption, long computing time, and many path inflection points of the traditional methods. First of all, the concept of Quad-connected, Tri-connected, Bi-connected nodes, and critical nodes are defined, and the mathematical models of diverse types of nodes are established. Second, the CDBT algorithm is proposed, in which different planning directions are determined due to the critical node as the diffusion object. Furthermore, the optimization indices of several types of nodes are evaluated in real-time. Third, a path optimization algorithm based on reverse searching is designed, in which the redundant nodes are eliminated, and the constraints of the robot are considered to provide the final optimized path. Finally, on one hand, the proposed algorithm is compared with the A* and RRT methods in the ROS system, in which four types of indicators in the eight maps are analysed. On the other hand, an experiment with an actual robot is conducted based on the proposed algorithm. The simulation and experiment verify that the new method can reduce the number of nodes in the path and the planning time and is suitable for the motion constraints of an actual robot.

2

Existence results for a sublinear second order dirichlet boundary value problem on the half-line

Bouafia Dahmane, Moussaoui Toufik

Opuscula Mathematica

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2020

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Vol. 40, no. 5

537--548

EN

.In this paper we study the existence of nontrivial solutions for a boundary value problem on the half-line, where the nonlinear term is sublinear, by using Ekeland’s variational principle and critical point theory.

3

Percolation Transitions and Fluid State Boundaries

Woodcock L. W.

Computational Methods in Science and Technology

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2017

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Vol. 23, No. 3

281--294

EN

Percolation transitions define gas- and liquid-state limits of existence. For simple model fluids percolation phenomena vary fundamentally with dimensionality (d). In 3d the accessible volume (VA) and excluded volume (VE = V --VA) percolation transitions occur at different densities, whereas in 2d they coincide. The region of overlap for 3d fluids can be identified as the origin of a supercritical mesophase. This difference between 2d and 3d systems vitiates the hypothetical concept of “universality” in the description of critical phenomena. Thermodynamic states at which VA and VE, for a spherical molecule diameter , percolates the whole volume of an ideal gas, together with MD computations of percolation loci for the penetrable cohesive sphere (PCS) model of gas-liquid equilibria, show a connection between the intersection of percolation loci, and the 1st-order phase-separation transition. The results accord with previous findings for square-well and Lennard-Jones model critical and supercritical fluid equilibria. Percolation loci for real liquids, e.g. CO2 and argon, can be determined from literature thermodynamic equation-of-state data, and exhibit similar supercritical gas- and liquid-state bounds. For these real fluids the mesophase bounds extend to low density and pressures and appear to converge onto the Boyle temperature (TB) in the low-density limit.

4

Modelling of transcritical and supercritical nitrogen jets

Antunes E., Silva A., Barata J.

Combustion Engines

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2017

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R. 56, nr 2

125--132

EN

The present paper addresses the modelling of fuel injection at conditions of high pressure and temperature which occur in a variety of internal combustion engines such as liquid fuel rocket engines, gas turbines, and modern diesel engines. For this investigation a cryogenic nitrogen jet ranging from transcritical to supercritical conditions injected into a chamber at supercritical conditions was modelled. Previously a variable density approach, originally conceived for gaseous turbulent isothermal jets, imploying the Favre averaged Navier-Stokes equations together with a “k-ε” turbulence model, and using Amagats law for the determination of density was applied. This approach allows a good agreement with experiments mainly at supercritical injection conditions. However, some departure from experimental data was found at transcritical injection conditions. The present approach adds real fluid thermodynamics to the previous approach, and the effects of heat transfer. The results still show some disagreement at supercritical conditions mainly in the determination of the potential core length but significantly improve the prediction of the jet spreading angle at transcritical injection conditions.

5

Study on P-V Curve and V-Q Curve of an Unbalanced Three- Phase System with Different Static Loads

Ramasamy A. K., Verayiah R., Abidin I. Z., Gunalan S., Perumal P.

Przegląd Elektrotechniczny

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2016

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R. 92, nr 1

159--165

EN

P-V curve and V-Q curve (often term as Q-V curve) are widely used for planning and operation studies. The P-V curve and V-Q curve of an unbalanced three-phase system, unlike the balanced three-phase system, may not have similar loading margin (LM) and reactive power margin (RPM) on each phase. Therefore, DIgSILENT Programming Language (DPL) has been used to study the maximum loading point (MLP), critical point (CP), and also minimum reactive power point (MRPP) on each phase of an unbalanced three-phase system with different static loads. The tracing direction of P-V curve of each phase and the LM and RPM of each phase obtained from the P-V curve and V-Q curve for different static loads are also discussed. On top of that, continuation power flow (CPF) has become a common method to study the MLP. Hence, a simple 2-bus balanced three-phase system is used to validate the result obtained from the DIgSILENT with CPF method.

PL

Krzywe P-V I V-Q w systemie trójfazowym niezrównoważonym mogą nie mieć tego samego marginesu obciążenia LM i marginesu mocy biernej RPM w każdej z faz. Zastosowano język programowania DIgSILENT do określenia maksymalnego punktu obciążenia MLP, punktu krytycznego CP i punktu minimalnej mocy biernej MRPP.

6

Eigenvalue problems for anisotropic equations involving a potential on Orlicz-Sobolev type spaces

Stancut I. L., Stircu I. D.

Opuscula Mathematica

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2016

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Vol. 36, no. 1

81--101

EN

In this paper we consider an eigenvalue problem that involves a nonhomogeneous elliptic operator, variable growth conditions and a potential Von a bounded domain in Rn (N ≥ 3) with a smooth boundary. We establish three main results with various assumptions. The first one asserts that any λ > 0 is an eigenvalue of our problem. The second theorem states the existence of a constant [formula] such that any [formula] is an eigenvalue, while the third theorem claims the existence of a constant λ* > 0 such that every λ ∈ [λ*∞) is an eigenvalue of the problem.

7

Wpływ dnia tygodnia na płynność ruchu w centrum Kielc

Młodzińska D., Szumska E., Jurecki R.

TTS Technika Transportu Szynowego

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2015

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R. 22, nr 12

1494--1502

PL

Wiele osób codzienne przemieszcza się z miejsca zamieszkania do pracy, szkoły, sklepów, itp., często pokonując dość duże odległości. Ceniąc komfort i wygodę niektórzy decydują się na poruszanie własnym autem. Wzrastająca liczba samochodów jest szczególnie widoczna w miastach. W czasie tak zwanych godzin szczytu na ulicach miast pojawia się duża liczba samochodów, wzrasta natężenie ruchu i powstają miejsca, gdzie tworzą się korki. Kierow-ca musi liczyć się wówczas, że spadnie prędkość jazdy i czas przejazdu znacznie się wydłuży. Celem artykułu było zbadanie warunków przejazdu w określonych godzinach dla pięciu dni roboczych głównymi ulicami centrum Kielc. W przeprowadzonym badaniu zidentyfikowano punkty krytyczne, czyli ulice i skrzyżowania, gdzie zanotowano serie spadków i wzrostów prędkości, mające znaczny wpływ na płynność jazdy.

EN

Many people pass through their typical daily trips to work, school, shops, ect., overcoming a large distances. Valuing comfort and convenience, some people decide to move their own car. The increasing number of cars is particularly evident in the city center. Driving through the city during rush hour is really complicated and wasting commuters time. The aim of the paper was to investigate conditions of the travel through the main streets of the city center in Kielce at a specific time for five days. We identified critical points, which have significant impact on traffic flow. In this area vehicle recorded series of decreases and increases in speed.

8

On a new critical point theorem and some applications to discrete equations

Galewski M., Galewska E.

Opuscula Mathematica

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2014

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Vol. 34, no. 4

725--732

EN

Using the Fenchel-Young duality we derive a new critical point theorem. We illustrate our results with solvability for certain discrete BVP. Multiple solutions are also considered.

9

On the existence of three solutions for quasilinear elliptic problem

Goncerz P.

Opuscula Mathematica

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2012

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Vol. 32, no. 3

473-486

EN

We consider a quasilinear elliptic problem of the type - Δpu = λ (ƒ (u)+ μg(u)) in Ω, u/∂Ω = 0, where Ω ⊂ RN is an open and bounded set, ƒ, g are continuous real functions on R and , λ, μ ∈ R. We prove the existence of at least three solutions for this problem using the so called three critical points theorem due to Ricceri.

10

On a class of nonhomogenous quasilinear problems in Orlicz-Sobolev spaces

Souayah A. K.

Opuscula Mathematica

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2012

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Vol. 32, no. 4

731-750

EN

We study the nonlinear boundary value problem [formula], where Ω is a bounded domain in RN with smooth boundary, λ, μ are positive real numbers, q and α are continuous functions and a1,a2 are two mappings such that a1 (/t/)t; a2(/t/)t; are increasing homeomorphisms from R to R. The problem is analysed in the context of Orlicz-Soboev spaces. First we show the existence of infinitely many weak solutions for any λ, μ > 0. Second we prove that for any μ > 0, there exists λ* sufficiently small, and λ* large enough such that for any λ ∈ (0, λ*) ∪ (λ*, ∞), the above nonhomogeneous quasilinear problem has a non-trivial weak solution.

11

Analiza zmęczeniowa miejsca krytycznego struktury małego samolotu

Szot A.

Górnictwo Odkrywkowe

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2010

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R. 51, nr 4

289-292

PL

W artykule przedstawiono metodykę analizy zmęczeniowej konstrukcji w oparciu o miejsce krytyczne. Badania w locie małego samolotu dyspozycyjnego wykazały, że newralgicznym fragmentem struktury było przednie okucie mocowania statecznika poziomego do kadłuba. Wyznaczono obliczeniowo trwałość zmęczeniową dwóch kolejnych modyfikacji tego okucia, zmierzających do podwyższenie okresu jego użytkowania. Umożliwiło to opracowanie wersji końcowej, spełniającej stawiane wymagania.

EN

The paper presents a methodology for the fatigue analysis of the structure, based on it's critical point. The flight test investigations of the small business airplane showed, that sensitive part of the structure was a front tail-plane fitting, attaching it to the fuselage. The fatigue life of two successive modifications of this fitting, leading to increase its useful life, was numerically designated. This enabled the design of the final fitting version, which satisfied the requirements given.

12

Some new generalizations of critical point theorems for locally Lipschitz functions

Chen J.

Journal of Applied Analysis

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2008

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Vol. 14, nr 2

193-208

EN

In the present paper, some generalized critical points theorems for locally Lipschitz functions are given, and some classical important theorems are improved.

13

Punkty krytyczne w projektowaniu central cieplnych współpracujących z odnawialnymi źródłami ciepła i energii

Żarski K.

Zeszyty Naukowe Politechniki Rzeszowskiej. Budownictwo i Inżynieria Środowiska

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2006

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z. 40 [229]

601-608

PL

W referacie opisano 8 zagadnień związanych z projektowaniem central cieplnych współpracujących z odnawialnymi źródłami ciepła i energii. Zagadnienia te, z uwagi na niekonwencjonalne aspekty techniczne, mogą stanowić punkty krytyczne, decydujące o nieprawidłowościach w eksploatacji i prowadzić do niewłaściwej oceny atrakcyjności stosowania odnawialnych źródeł ciepła i energii.

EN

In the paper eith problems concerning designing of central heating stations cooperating with renewable heat or energy sources have been presented. These problems, because of non-conventional technical aspects can be regarded as a critical points, caused troubles inexploitation and pointed to bad decision in application of recoverable heat and energy sources.

14

Numerical Algorithms for Determination of Retrograde Region of Gas Condensate Reservoir

Tarom N., Jalali F., Al-Sayegh A., Moshfeghian M.

Polish Journal of Chemistry

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2006

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Vol. 80, nr 1

51-64

EN

Twomathematical algorithms based on a cubic EOS are developed to determine the retrograde region for reservoir fluids. The first method is based on marching and the second one utilizes regression analysis. In marching method, a series of flash calculations is performed to calculate maximum L/F (moles of liquid/moles of feed). In the regression method, a non-linear regression and an optimizationmethod in addition to a limited number of flash calculations are used to determine the maximum L/F. Based on these mathematical algorithms a computer program to predict a full phase envelope containing the retrograde curve was developed. The computer program consists of three basic parts of bubble point, dew point, and flash calculations. These three basic parts are used to determine the retrograde region. In the course of determination of the retrograde condensation region, the coordinates of critical point and cricondentherm point were also determined and used to speed up the search method. Several cases were studied and it was found that the regression method is faster and more accurate.

15

Punkty krytyczne procesu projektowania form wtryskowych. Cz.1.

Zawistowski H.

Mechanik

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2002

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R. 75, nr 1

28-22

PL

Oczekiwania producentów wyrobów wtryskowych w zakresie jakości, czasu i terminowości wykonania form coraz bardziej rozmijają się z możliwościami krajowych urządzeń. Spełnienie stawianych warunków wymaga zasadniczych przemian w organizacji narzędziowni. Nowoczesna narzędziownia musi być przygotowana do wytwarzania atestowanych form klasy QS, których funkcjonalność jest całkowicie podporządkowana warunkom produkcji kooperacyjnej.

EN

A necessity of making essential changes in the organization of Polish tool-rooms so that they shall be prepared for producing certificated moulds of the QS class the functionality of which is totally submitted to the conditions of cooperative production.

16

Punkty krytyczne procesu projektowania form wtryskowych. Cz.2.

Zawistowski H.

Mechanik

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2002

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R. 75, nr 2

113-116

PL

Oczekiwania producentów wyrobów wtryskowych w zakresie jakości, czasu i terminowości wykonania form coraz bardziej rozmijają się z możliwościami krajowych narzędziowni. Spełnienie stawianych warunków wymaga zasadniczych przemian w organizacji narzędziowni. Nowoczesna narzędziownia musi być przygotowana do wytwarzania atestowanych form klasy QS, których funkcjonalność jest całkowicie podporządkowana warunkom produkcji kooperacyjnej.

EN

A necessity of making essential changes in the organization of Polish tool-rooms so that they shall be prepared for producing certificated moulds of the QS class the functionality of which is totally submitted to the conditions of cooperative production.

17

Critical points for vector-valued functions

Lucchetti R., Revalski J., Thera M.

Control and Cybernetics

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2002

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Vol. 31, no 3

545-555

EN

This paper contains a mountain pass theorem for continuous mappings, defined on a complete metric space and taking values in a real Banach space, ordered by a closed convex cone. We use the concept of critical point introduced by Degiovanni, Lucchetti and Ribarska, and we furnish a variant of their result, allowing for a localization both of the critical point and of the critical value.

18

Existence of periodic solutions for quasilinear ordinary differential eqasilinear ordinary diefferential equations with discontinuities

Matzakos N., Papageorgiou N.

Demonstratio Mathematica

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2000

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Vol. 33, nr 4

753-770

EN

We consider a quasilinear differential equation with discontinuous right hand side and periodic boundary conditions. To obtain an existence theory we pass to a relevant multivalued variant of the original problem, which we solve. Our approach is a mixture of the variational method (for nonsmooth locally Lipschitz functionals) and of the method of upper and Iower solutions. The mixing of these two techniques is made possible by a nonresonance condition below the first nonzero eigenvalue of the one-dimensional p-Laplacian with periodic boundary conditions.

19

The influence of the H/D substitution on the viscosity in acetonitrile-decanol solution near the critical point

Milewska A., Szydłowski J.

Nukleonika

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1999

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Vol. 44, nr 1

31-38

EN

Results of measurements of the temperature and concentration dependence of the kinematic viscosity of the mixture of acetonitrile/decanol, acetonitrile-d [indeks dolny]3 /decanol and acetonitrile/decanol-d using an optoelectronic capillary viscometer are reported. In all cases very weak divergence of the viscosity is observed while approaching the critical point. Concentration dependences also show weak anomalous behavior in the close vicinity of the critical temperature. Large isotope effect on viscosity is found and shortly discussed.

PL

W pracy przedstawiono wyniki pomiarów lepkości w mieszaninach acetonitryl-dekanol, acetonitryl-d [indeks dolny]3 - dekanol i acetonitryl - dekanol-d. Pomiary obejmują szeroki zakres temperatur ze szczególnym uwzględnieniem otoczenia punktu krytycznego. We wszystkich przypadkach obserwuje się słabe anomalie w temperaturowych i stężeniowych zależnościach lepkości kinematycznej. Obserwuje się znaczny wpływ podstawienia deuterem, malejący wraz ze zbliżaniem się do punktu krytycznego.