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1

The influence of temperature on the percolation threshold in two-dimensional polymer systems

Sikorski A.

Computational Methods in Science and Technology

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2020

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Vol. 26, No. 4

143--149

EN

The structure of a two-dimensional film formed by strongly adsorbed polymer chains was studied by means of Monte Carlo simulations. We investigated the percolation in systems consisting of flexible polymer chains. A coarse-grained polymer chains representation was assumed and polymer chains were represented by linear sequences of lattice beads. The positions of these beads were restricted to vertices of a two-dimensional square lattice. Properties of the model system were determined by means of Monte Carlo simulations with a refined Verdier-Stockmayer sampling algorithm. Percolation thresholds macromolecules were determined. The methodology concerning the determination of the percolation thresholds for an infinite chain system was discussed. The influence of the chain length and the temperature on the percolation was discussed. It was shown that the introduction of long-range interactions changes the behavior of the percolation threshold dramatically. The percolation threshold initially decreases with the chain length while for longer ones it is stable.

2

Percolation Transitions and Fluid State Boundaries

Woodcock L. W.

Computational Methods in Science and Technology

|

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.

3

Two lilypond systems of finite line-segments

Daley D. J., Ebert S., Last G.

Probability and Mathematical Statistics

|

2016

|

Vol. 36, Fasc. 2

221--246

EN

The paper discusses two models for non-overlapping finite line-segments constructed via the lilypond protocol, operating here on a given array of points P = {Pi} in R2 with which are associated directions {θi}. At time zero, for each and every i, a line-segment Li starts growing at unit rate around the point Pi in the direction θi, the point Pi remaining at the centre of Li; each line-segment, under Model 1, ceases growth when one of its ends hits another line, while under Model 2, its growth ceases either when one of its ends hits another line or when it is hit by the growing end of some other line. The paper shows that these procedures are well defined and gives constructive algorithms to compute the half-lengths Ri of all Li. Moreover, it specifies assumptions under which stochastic versions, i.e. models based on point processes, exist. Afterwards, it deals with the question as to whether there is percolation in Model 1. The paper concludes with a section containing several conjectures and final remarks.

4

Using MathCad environment to calculate leakage currents and power basis on percolation models

Frączak P.

Computer Applications in Electrical Engineering

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2015

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Vol. 13

255--267

EN

This work presents the design and analysis of percolation models for branches and nodes in networks created using electric circuits. Electric circuits were built using square networks consisting of appropriate resistance and impedance elements, as well as of power supply sources. The created percolation models were described mathematically, according to the Maxwell matrix method of cyclic current in the classical form and in the complex number form. Analytical descriptions of electric circuits include random methods of "short-circuiting" branches and creation of “filled” nodes, respectively, in the networks using appropriate calculation procedures in Mathcad. Simulation calculations of surface leakage current for a polymer sample were made using a model of its surface (percolation for a branch in the network) and a numerical program developed on the basis of calculation procedures contained in Mathcad. On the other hand, simulation calculations of power emitted on the surface of a cylindrical insulator performed using its surface model (percolation for nodes in the network) and a numerical program written in the Mathcad environment.

5

The Lennard-Jones Fluid in the Liquid-Vapour Critical Region

Heyes D. M.

Computational Methods in Science and Technology

|

2015

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Vol. 21, No. 4

169--179

EN

The equation of state of the Lennard-Jones (LJ) fluid in the liquid-vapour (LV) critical region is investigated by Molecular Dynamics simulation (MD). The calculated pressure (P) and chemical potential (μ) are, within the simulation statistics, flat at the critical temperature between LJ reduced densities of ca. 0:26 to 0:34. The critical temperature, Tc, determined for an isotherm where (∂P/∂)T = 0 and (∂μ/∂ρ)T = 0, is shown to decrease with increasing system size and pure LJ potential interaction range, rc, using a tapering function going to zero beyond rc. The value of Tc obtained by extrapolating the system size and rc to ∞ is 1:316 ± 0:001, which is statistically within the uncertainties of previous literature values. The percolation threshold separation, rp, along the critical isotherm decreases monotonically with increasing density, ρ, and is for intermediate densities lower than that of the nearest equivalent hard-sphere system. The lines of constant percolation distance on the density-temperature projection of the phase diagram reveal a difference in qualitative behaviour, indicative of underlying structural differences on either side of the critical envelope. The mean square force in the critical region near to Tc is linear in ρ. Probability distributions of the nearest neighbour distance, absolute particle force and potential energy per molecule are presented.

6

The necessity of hydrogeological survey in infiltration systems design

Zeleňáková M., Hudáková G.

Czasopismo Inżynierii Lądowej, Środowiska i Architektury / Journal of Civil Engineering, Environment and Architecture

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2014

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z. 61, nr 3/I

401--409

EN

With the development of construction in large cities and their surroundings there is still more to tackle with congestion of sewer network. There are many alternatives that can reduce the risk of flooding, regulate the quantity and quality of groundwater. Most of these alternatives are proposed as a theoretical conversion according to standards. Infiltration practices represent one of the best methods of rainwater management which may effectively reduce load of interflow network. Rainwater management should be considered to be the sustainable strategy for reconstruction of rural and urban settlement from the aspect of environment, management and social criteria. Our aim in the paper is to compare the theoretical calculations with practice. We would like to stress that the hydrogeological survey is inevitable condition before design of any infiltration systems.

7

Power in model of two - dimensional percolation on hexagonal electric lattice

Czajkowski A. A., Frączak P. S.

Problemy Nauk Stosowanych

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2013

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T. 1

77--86

EN

Introduction and aims: This paper presents a power in some model of two-dimensional percolation on hexagonal lattice for various frequencies of force voltage in matrix notation. Main aim is some determination of current characteristics for created model of percolation in dependence of shorted bounds in accordance with a right algorithm. Material and methods: Taking into account the current characteristics and other parameters some phase characteristics of percolation model have been determined for various frequencies. Analytical and numerical methods in MathCAD program were shown in the paper. Results: Percolation current increases together with some increase of number of shorted-bounds. The characteristics of percolation current for frequency from 50Hz to 5000Hz have the similar form and increasing trend. The value of active power of percolation model increases during some increase of the number of shorted-bounds and has zero value in percolation threshold. The characteristics of active and reactive power for frequency from 50 Hz to 5000 Hz have the similar form. For frequency 10 Hz the graphs of reactive power are symmetrically placed in relation to x-axis. Conclusion: Presented percolation model on hexagonal lattice has been verified taking using numerical values of percolation threshold.

PL

Wstęp i cele: W artykule przedstawiono w zapisie macierzowym moc w modelu dwuwymiarowej perkolacji określonej na sześciokątnej sieci dla różnych częstotliwości napięcia. Głównym celem jest wyznaczenie charakterystyk prądu dla utworzonego modelu perkolacji w zależności od zwierania wiązań sieci zgodnie z przyjętym algorytmem. Materiał i metody: Biorąc pod uwagę charakterystyki prądowe i wartości parametrów niektóre cechy fazowe modelu perkolacji wyznaczone zostały dla różnych częstotliwości prądu. Zastosowano metodę analityczno i numeryczną programie MathCAD. Wyniki: Prąd perkolacji wzrasta równocześnie ze wzrostem liczby zrywanych wiązań. Charakterystyki prądu perkolacji dla częstotliwości od 50Hz do 5000Hz mają podobne grafy i trend wzrastający. Wartość mocy czynnej w modelu perkolacji wzrasta równocześnie ze wzrostem liczby zrywanych wiązań oraz ma wartość zero w progu perkolacji. Charakterystyki mocy czynnej i biernej dla częstotliwości od 50 Hz do 5000 Hz mają podobne grafy. Natomiast dla częstotliwości 10 Hz charakterystyka mocy biernej jest położona symetrycznie względem osi OX. Wniosek: Pokazany model perkolacji na heksagonalnej sieci został zweryfikowany z uwzględnieniem wartości liczbowych progu perkolacji.

8

Ocena środowiskowa stosowania gruzu betonowego w aplikacjach inżynierskich

Król A., Wzorek M.

Instal

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2013

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nr 6

72--75

PL

W artykule przeanalizowano dostępne metody wykonywania wyciągów wodnych z gruzu betonowego używanego w różnych aplikacjach inżynierskich. Wykonano także badania związane z oceną poziomu uwalniania metali ciężkich zarówno z gruzu betonowego jak i materiałów wykonanych z jego udziałem. Wyciągi wodne wykonywano metodą dynamiczną oraz przy zastosowaniu testu perkolacyjnego.

EN

This paper presents the available methods for preparing water extracts of concrete debris used in various engineering applications. Also carried out research related to the assessment of the level of heavy metal release from both the concrete debris and materials made with his participation. Water extracts were performed by using a dynamic and percolation test.

9

Percolation in Systems Containing Ordered Elongated Objects

Romiszowski P., Sikorski A.

Computational Methods in Science and Technology

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2013

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Vol. 19, No. 2

115--121

EN

We studied the percolation and jamming of elongated objects using the Random Sequential Adsorption (RSA) technique. The objects were represented by linear sequences of beads forming needles. The positions of the beads were restricted to vertices of two-dimensional square lattice. The external field that imposed ordering of the objects was introduced into the model. The percolation and the jamming thresholds were determined for all systems under consideration. The influence of the chain length and the ordering on both thresholds was calculated and discussed. It was shown that for a strongly ordered system containing needles the ratio of percolation and jamming thresholds cp=cj is almost independent on the needle length d.

10

DC conductivity mechanisms in granular nanocomposite films Cux(SiO2)1-x, deposited in Ar gas atmosphere

Fedotov A., Swito I., Patryn A., Kalinin Y., Sitnikov A.

Zeszyty Naukowe Wydziału Elektroniki i Informatyki Politechniki Koszalińskiej

|

2012

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Nr 4

29--42

EN

In the article are presented the results of the study of structure of Cux(SiO2)1-x nanocomposites with a wide range of metallic fraction content and their DC conductivity measured in the temperature range between 3 and 300 K. The Cux(SiO2)1-x thin film samples with 0.36 < x < 0 and thicknesses 3 to 5 μm were fabricated by ion-beam sputtering of the compound Cu/SiO2 target with argon onto the glass ceramic substrate. The as-deposited films displayed their evolution from practically homogeneous (at x < 0.50) to granular (in the range of 0.50 < x < 0.58) structure with x increase where the granules dimensions approached approximately 100 - 200 nm. The study of conductivity have shown that the studied nanocomposite films with x < 0.68 are on dielectric side of metal-insulator transition and possess thermally activated tunneling of electrons between Cu nanoparticles whereas the samples with x > 0.68 indicate the metallic-like character of conductance along the percolating net of Cu nanoparticles inside of silica matrix. In dielectric regime (for nanocomposites with x < 0.68) DC carrier transport is realized by VRH mechanism described by Shklowski-Efros law, by jumps of electrons between Cu nanoparticles.

PL

W artykule przedstawiono rezultaty badań struktury nanokompozytów Cux(SiO2)1-x w szerokim zakresie zawarcia fazy metalicznej and ich DC przewodnictwo zmierzone w zakresie temperatur od 3 do 300K. Cienkie warstwy Cux(SiO2)1-x z 0.36 < x < 0 i grubością 3 I 5 μm były przygotowane poprzez rozpylanie wiązką argonową jonową kompaunda Cu/SiO2 tarczy na podłoże ze szklanej ceramiki. Wszystkie warstwy po napylaniu wykazywały transformację struktury od praktycznie jednorodnej (dla x < 0.50) do granulowanej (0.50 < x < 0.58) gdzie, ze wzrostem x liniowe rozmiary granul osiągają 100-200 nm. Badania przewodnictwa wykazało że nanokompozytowe filmy z x < 0.68 są po dielektrynej stronie przejścia metal-izolator i wykazują termiczne aktywowane tunelowanie elektronów pomiędzy Cu nanocząstkami, w tym czasie jak przy x > 0.68 zauważono przewodność podobną do metalicznej wzdłuż perkolacyjnej sieci nanocząstek Cu wewnątrz matrycy silicydu. W trybie dielektrycznym (dla nanocząstek z x<0.68) transport nośników jest realizowany wg VRH mechanizmu zgodnie z prawem Shklowskiego-Efrosa, poprzez skoki elektronów pomiędzy Cu nanocząstkami.

11

Percolation with thick symmetric barrier in finite systems

Pasternak K.

Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej

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2011

|

Vol. 10, nr 2

199-204

EN

In this article site percolation is studied on an LxL square lattice with a thick, symmetric barrier. Long-range connectivity is the result of the occupancy probability defined on the site. The influence of the thin and thick barrier on the percolation is analysed and the algorithm of control of the effectiveness of the scalability is proposed.

12

Badanie procesu przesiąkania roztworów olejów roślinnych i substancji ropopochodnych przez ośrodek porowaty

Sęk J., Dziubiński M., Błaszczyk M., Padyk A.

Inżynieria Ekologiczna

|

2011

|

Nr 26

48-58

PL

Ropa naftowa i jej pochodne stanowią jedno z ważniejszych źródeł zanieczyszczeń gruntów i wód gruntowych. Postępująca industrializacja oraz rozwój motoryzacji są przyczyną większego zapotrzebowania na produkty naftowe. Wzrost wydobycia, przetwórstwa i zużycia ropy naftowej nieuchronnie pociąga za sobą zwiększenie przypadków zanieczyszczenia środowiska związkami ropopochodnymi. W pracy tej przedstawione zostały badania przesiąkania cieczy o różnych właściwościach fizykochemicznych przez warstwy ziarniste w warunkach nieustalonych. Podjęta została próba opisu zjawiska przesiąkania płynów modelowych za pomocą równań matematycznych uwzględniających wpływ lepkości cieczy na przebieg tego procesu. Podjęto także próbę oszacowania łatwości wymywania związków ropopochodnych z warstwy ziarnistej za pomocą wody.

EN

Crude oil and its derivatives are one of the major sources of pollution of land and groundwater. Increasing industrialization and development of automotive industry are causing a greater demand for oil products. The increase in mining, processing and consumption of oil will inevitably entail an increase in cases of environmental pollution with these compounds. In this work were presented penetration research liquids with different physical and chemical properties of granular layer in transients term. Attempt is made to describe the phenomenon of percolation fluid models using mathematical equations taking into account the effect of viscosity on this process. An attempt to estimate the ease of leaching of petroleum compounds from the granular layer by water. The aim of this study was to determine the efficiency of migration processes of high-viscosity substance in the soil.

13

Geoinżynierska ocena ochrony przeciwpowodziowej szpitala w Słubicach

Kołodziejczyk U.

Górnictwo i Geoinżynieria

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2011

|

R. 35, z. 2

359-366

PL

Ekstremalne stany wody w rzekach powodują intensywne przesiąki na tereny zalewowe, zwykle chronione wałami przeciwpowodziowymi. Przykładem jest miasto Słubice (województwo lubuskie), położone w dwumetrowej depresji w stosunku do alarmowego wezbrania wód w Odrze. Artykuł dotyczy geoinżynierskiej oceny stanu wałów przeciwpowodziowych w mieście Słubice, a głównie - intensywności filtracji wody z koryta Odry na teren zawala, gdzie zlokalizowany jest szpital. Modernizacja wałów przeprowadzona tutaj w 1999 r. zredukowała, ale - nie wyeliminowała filtracji wody przez wał; ze względu na niedobór środków nie objęła właściwego dogęszczenia podłoża i korpusu wałów, gdzie - jak wykazały aktualne badania geotechniczne - ciągle znajdują się fragmenty gruntów średnio zagęszczonych i luźnych, a także pakiety gruntów bogatych w substancję organiczną. Nowe rozwiązania przeciwpowodziowe w Słubicach są nieodzowne i dopóki nie zostaną zrealizowane, miasto będzie nieustannie walczyło z nadmiarem wody przesączającej się z koryta Odry.

EN

The extreme river water stages cause intensive seepage on flooded area, normally protected by levees. The example of this is town Slubice (Lubuski District), situated in 2 m lower than alarm water level. The paper describes the geoengineering opinion relating the quality of embankments in Slubice focused on the intensivity of water percolation from Odra bed to the terrains outside levees, where the hospital is situated. The modernization in 1999 limited, but not eliminated, the water percolation through the banks and, due to financial deficiency, did not included the proper condensation of subsoil and the body of banks, where, as it was proved by geotechnical analysis, still remain parts of soil of loose or average structure and parts of soil rich in organic matter. New flood protection solutions in Slubice are necessary and as long as they are not become realized, the town would fight against the excess of water percolating from Odra river bed.

14

Percolation with a barier in finite systems

Drzewiński A., Klimek M., Kośmider M., Pasternak K., Szota K.

Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej

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2010

|

Vol. 9, nr 2

37-41

EN

The site percolation, where the long-range connectivity is the result of the occupancy probability defined on a site, is studied on the L×L square lattice. Method of determining of the location of the percolation pseudo-threshold pc(L) is proposed and the influence of a barrier on the percolation pseudo-threshold is analysed.

15

Badanie procesu przesiąkania wody przez warstwy ziarniste w warunkach nieustalonych

Sęk J., Stopczyk A., Browarski T.

Inżynieria i Aparatura Chemiczna

|

2010

|

Nr 2

111-112

PL

Przeprowadzono badania procesu przesiąkania wody w warunkach nieustalonych przez warstwy ziarniste o różnej granulacji i różnej zawartości początkowej wilgoci. Wykazano, że proces ten może być podzielony na dwa etapy. W czasie pierwszego z nich zachodzi saturacja warstwy porowatej, a przebieg tego zjawiska ma charakter liniowy. Zaproponowany opis matematyczny pozwalający wyznaczyć prędkość wsiąkania w warstwę nieza-wierającą wilgoci. Przebieg drugiego etapu opisano za pomocą zależności potęgowej wprowadzając pojęcie współczynnika oporów przepływu, korzystając przy tym z zasad opisujących przebieg zjawisk grawitacyjnego wypływu cieczy ze zbiornika

EN

Investigations concerning the non-steady water percolation into granular beds were performed. Two process stages were distinguished. In the first one rising saturation of the bed occurred and it can be described using linear equations. The applied procedure aHowed one to determine the percolation velocity in beds during a dry state. The second process stage was described using the approach typical for gravitational flow from a tank. A concept of flow resistance coefficient was introduced.

16

Magnetic measurements of percolation in coated conductors as an analogue of deteriorating living neural networks

Łękawa A., Głowacki B., Woźniak M., Hopkins S., Kozlowski G., Stryczewska H., Janowski T.

Przegląd Elektrotechniczny

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2009

|

R. 85, nr 5

194-197

EN

The possible analogy between the concept of the giant component that occurs in 2D living neural networks, and induced superconducting currents in granular coated conductors, was investigated. Studies of YBCO coated conductors were conducted using transport and Hall probe magnetometry. Encouraging results suggest that the design of superconducting polycrystalline coatings can benefit from knowledge of degrading neural networks.

PL

Badano możliwość istnienia analogii pomiędzy pojęciem gigantycznego komponentu pojawiającego się w dwuwymiarowych żywych sieciach neuronowych oraz indukowanych prądach nadprzewodnikowych w ziarnistych cienkowarstwowych taśmach nadprzewodnikowych. Badania przewodów YBCO były prowadzone za pomocą czujników Halla. Wyniki przeprowadzonych eksperymentów dowodzą, że wiedza na temat rozpadających się sieci neuronowych może być korzystna dla projektowania polikrystalicznych powłok.

17

Percolation Driven Flooding for Energy Efficient Routing in Dense Sensor Networks

Vakulya G., Simon G.

Journal of Telecommunications and Information Technology

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2009

|

nr 2

5-12

EN

Simple flooding algorithms are widely used in ad hoc sensor networks either for information dissemination or as building blocks of more sophisticated routing protocols. In this paper a percolation driven probabilistic flooding algorithm is proposed, which provides large message delivery ratio with small number of sent messages, compared to traditional flooding. To control the number of sent messages the proposed algorithm uses locally available information only, thus induces negligible overhead on network traffic. The performance of the algorithm is analyzed and the theoretical results are verified through simulation examples.

18

Measurement of complex conductivity in carbon nanotube polymer composites under mechanical shear

Obrzut J., Douglas J. F.

Metrology and Measurement Systems

|

2008

|

Vol. 15, nr 4

399-407

EN

We measured the complex conductivity of carbon nanotube-polypropylene composites under mechanical shear conditions. In order to determine how flow alters the properties of these complex fluids we constructed a rheo-dielectric test fixture, which allows for the simultaneous in situ measurement of both the frequency dependent complex electrical conductivity and basic rheological properties, such as shearing rate, viscosity, normal stresses. We analyzed the results using Generalized Effective Medium theory. The scaled conductivity of percolated networks compares well with the universal trend showing a power law scaling with frequency. We find that the conductivity percolation concentration (φc) increases with increasing shear rate. For sufficiently high shear rates, the nanocomposite undergoes a transition from a conducting to an insulating state. The shear rate dependence of φc, which gives rise to this transition, conforms well to a model that we introduced to describe this effect.

19

Fractal variations of the Transcarpathians, West Ukraine, seismicity and their potential relation to changing phases of local seismic cycles

Gnyp A.

Acta Geophysica

|

2007

|

Vol. 55, no. 3

288-301

EN

The evolution of spatial arrangement of the Transcarpathian earthquakes is studied by means of fractal analysis. Spatial correlation dimension is evaluated for a subset of fixed number of catalogue events consecutively shifted in time by one event forward. Distinctive patterns that may be related to different phases of local seismic cycle/cycles have been identified, corresponding to extreme values of the dimension. Their potential relation to evolution of the seismogenic stress field is discussed. The time it takes for the capacity dimension to reach the so-called percolation threshold is estimated for a subset consecutively extended by adding next catalogue events. Temporal and spatial frames of percolation analysis are discussed in relation to parameters of the future earthquake.

20

Modele perkolacji

Fukś H.

Wiadomości Naftowe i Gazownicze

|

2006

|

R. 9, Nr 7 (99)

14-16